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NATIONAL ACADEMY OF SCIENCES
NATIONAL ACADEMY OF ENGINEERING
INSTITUTE OF MEDICINE
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PAPERBACK (2012)
Deterrence and the Death Penalty
Daniel S. Nagin and John V. Pepper, editors; Committee on Deterrence
and the Death Penalty; Committee on Law and Justice; Division on
Behavioral and Social Sciences and Education; National Research Council
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
DETERRENCE
AND THE
DEATH PENALT Y
Committee on Deterrence and the Death Penalty
Daniel S. Nagin and John V. Pepper, Editors
Committee on Law and Justice
Division of Behavioral and Social Sciences and Education
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
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Suggested citation: National Research Council. (2012). Deterrence and the Death
Penalty. Committee on Deterrence and the Death Penalty, Daniel S. Nagin and John
V. Pepper, Eds. Committee on Law and Justice, Division of Behavioral and Social
Sciences and Education. Washington, DC: The National Academies Press.
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
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Deterrence and the Death Penalty
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Deterrence and the Death Penalty
v
COMMITTEE ON DETERRENCE AND THE DEATH PENALTY
DANIEL S. NAGIN (Chair), H. John Heinz III College, Carnegie Mellon
University
KERWIN K. CHARLES, Harris School of Public Policy Studies,
University of Chicago
PHILIP J. COOK, Sanford School of Public Policy, Duke University
STEVEN N. DURLAUF, Department of Economics, University of
Wisconsin–Madison
AMELIA M. HAVILAND, H. John Heinz III College, Carnegie Mellon
University
GERARD E. LYNCH, U.S. Court of Appeals for the Second Circuit
CHARLES F. MANSKI, Department of Economics, Northwestern
University
JAMES Q. WILSON, School of Public Policy, Pepperdine University, and
Clough Center for the Study of Constitutional Democracy, Boston
College
JANE L. ROSS, Study Director
JOHN V. PEPPER, Consultant
KEIKO ONO, Senior Program Associate
CAROL HAYES, Christine Mirzayan Fellow
BARBARA BOYD, Administrative Associate
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
vi
COMMITTEE ON LAW AND JUSTICE
2012
JEREMY TRAVIS (Chair), John Jay College of Criminal Justice, City
University of New York
CARL C. BELL, Community Mental Health Council, Inc., Chicago, IL
JOHN J. DONOHUE, III, Stanford Law School, Stanford University
MARK A.R. KLEIMAN, Department of Public Policy, University of
California, Los Angeles
GARY LAFREE, Department of Criminology and Criminal Justice,
University of Maryland
JANET L. LAURITSEN, Department of Criminology and Criminal
Justice, University of Missouri-St. Louis
GLENN C. LOURY, Department of Economics, Brown University
CHARLES F. MANSKI, Department of Economics, Northwestern
University
TERRIE E. MOFFITT, Department of Psychology and Neuroscience,
Duke University
DANIEL S. NAGIN, H. John Heinz III College, Carnegie Mellon
University
RUTH D. PETERSON, Criminal Justice Research Center, Ohio State
University
ANNE MORRISON PIEHL, Department of Economics and Program in
Criminal Justice, Rutgers University
DANIEL B. PRIETO, Public Sector Strategy & Innovation, IBM Global
Business Services, Washington, DC
ROBERT J. SAMPSON, Department of Sociology, Harvard University
DAVID WEISBURD, Department of Criminology, Law and Society,
George Mason University
CATHY SPATZ WIDOM, Psychology Department, John Jay College of
Criminal Justice, City University of New York
PAUL K. WORMELI, Integrated Justice Information Systems,
Ashburn, VA
JANE L. ROSS, Director
BARBARA BOYD, Administrative Associate
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
vii
IN MEMORIAM
James Q. Wilson
1931-2012
“I’ve tried to follow the facts wherever they land.”
This report is dedicated to James Q. Wilson for
his long service to the National Research Council,
his influential career of scholarship and public
service, and his unblinking commitment to the
principle that science requires us to interpret
the evidence as it is, not as we want it to be.
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
ix
Preface
M
ore than three decades ago, in Deterrence and Incapacitation:
Estimating the Effects of Criminal Sanctions on Crime Rates,
the National Research Council (NRC) (1978, p. 9) concluded
that “available studies provide no useful evidence on the deterrent effect
of capital punishment.” That report was issued 2 years after the Supreme
Court decision in Gregg v. Georgia ended a 4-year moratorium on execu-
tion in the United States. In the 35 years since the publication of that report,
especially in recent years, a considerable number of post-Gregg studies have
attempted to estimate the effect of the legal status or the actual implemen-
tation of the death penalty on homicide rates. Those studies have reached
widely varying conclusions.
Against this background, the NRC formed the Committee on Deter-
rence and the Death Penalty to address whether the available evidence
provides a reasonable basis for drawing conclusions about the magnitude of
the effect of capital punishment on homicide rates. At a workshop on April
28-29, 2011, workshop papers commissioned by the committee (which will
be published in a special issue of the Journal of Quantitative Criminology)
were presented and discussed by their authors: Robert J. Apel, University at
Albany, State University of New York; Aaron Chalfin, University of Califor-
nia, Berkeley; Chao Fu, University of Wisconsin–Madison; Justin McCrary,
University of California, Berkeley; Salvador Navarro, University of Western
Ontario, Ontario, Canada; John V. Pepper, University of Virginia; and
Steven Raphael, University of California, Berkeley. The workshop also
included comments on the presentations by Jeffrey Grogger, University
of Chicago; Guido Imbens, Harvard University; Kenneth C. Land, Duke
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
x PREFACE
University; Christopher Sims, Princeton University; and Justin Wolfers,
University of Pennsylvania.
The committee appreciates the contributions of these presenters and
those who commented on them to the development of its report. In ad-
dition, John V. Pepper provided invaluable assistance to the committee
throughout its deliberations. The work of staff members from the Com-
mittee on Law and Justice of the NRC facilitated the committee’s work in
many ways. Thanks are due to Jane L. Ross, study director; Keiko Ono,
senior program associate; Carol Hayes, Christine Mirzayan fellow; and
Barbara Boyd, administrative coordinator.
Many individuals at the NRC assisted the committee. We thank Kirsten
Sampson-Snyder, who shepherded the report through the NRC review pro-
cess, Eugenia Grohman, who edited the draft report, and Yvonne Wise, for
processing the report through final production.
This report has been reviewed in draft form by individuals chosen for
their diverse perspectives and technical expertise, in accordance with pro-
cedures approved by the NRC’s Report Review Committee. The purpose
of this independent review is to provide candid and critical comments that
will assist the institution in making its published report as sound as possible
and to ensure that the report meets institutional standards for objectivity,
evidence, and responsiveness to the study charge. The review comments
and draft manuscript remain confidential to protect the integrity of the
deliberative process. We thank the following individuals for their review of
this report: John Donohue, III, Stanford Law School, Stanford University;
Andrew Gelman, Department of Statistics and Department of Political Sci-
ence, Columbia University; Kenneth C. Land, Department of Sociology,
Duke University; Candice Odgers, School of Social Ecology, University of
California, Irvine; Ricardo Reis, Department of Economics, Columbia Uni-
versity; Greg Ridgeway, RAND Safety and Justice Program, RAND Center
on Quality Policing, RAND Corporation; Robert J. Sampson, Department
of Sociology, Harvard University; Dick Thornburgh, Counsel, K&L Gates,
LLP, and former Attorney General of the United States; Petra E. Todd,
Department of Economics, University of Pennsylvania; and Michael Tonry,
School of Law, University of Minnesota, Minneapolis.
Although the reviewers listed above have provided many constructive
comments and suggestions, they were not asked to endorse the conclusions
or recommendations nor did they see the final draft of the report before its
release. The review of this report was overseen by Gary LaFree, National
Consortium for the Study of Terrorism and Responses to Terrorism, Univer-
sity of Maryland, and John T. Monahan, University of Virginia Law School.
Appointed by the NRC, they were responsible for making certain that an
independent examination of this report was carried out in accordance with
institutional procedures and that all review comments were carefully con-
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
PREFACE xi
sidered. Responsibility for the final content of this report rests entirely with
the authoring committee and the institution.
This report is dedicated to James Q. Wilson. Jim was a valued member
of this and many other NRC committees on which he served over his long
and influential career. Jim’s contributions to scholarship and public service
will stand as enduring testimony to the power of his intellect. He was a
quiet but forceful proponent for balanced and clear-minded assessment of
the evidence. I first met Jim in my role as a staff member of the 1978 NRC
committee that resulted in report Deterrence and Incapacitation: Estimat-
ing the Effect of Criminal Sanctions on Crime Rates. I was deeply impressed
by the clarity of his thought and gift for communication. He served as a
role model for me ever since. I was thus especially honored that he agreed
to serve on this committee, which was greatly aided by his constructive
participation throughout our deliberations.
Daniel S. Nagin, Chair
Committee on Deterrence and the Death Penalty
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
xiii
Contents
SUMMARY 1
Shortcomings in Existing Research, 4
Specification of the Sanction Regime for Homicide, 4
Potential Murderers’ Perceptions of and Responses to
Capital Punishment, 5
Strong and Unverifiable Assumptions, 6
Next Steps for Research, 7
References, 8
1 INTRODUCTION 9
The Current Debate, 9
Committee Charge and Scope of Work, 11
References, 14
2 CAPITAL PUNISHMENT IN THE POST-GREGG ERA 15
Executions and Death Sentences Over Time, 15
Use of the Death Penalty, 20
References, 26
3 DETERMINING THE DETERRENT EFFECT OF
CAPITAL PUNISHMENT: KEY ISSUES 27
Concepts of Deterrence, 28
Sanction Regimes, 32
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
xiv CONTENTS
Data Issues, 36
Variations in Murder Rates, 37
Reciprocal Effects Between Homicide Rates and
Sanction Regimes, 41
Summary, 43
References, 44
4 PANEL STUDIES 47
Panel Studies Reviewed, 48
Methods Used: Overview, 48
The Studies, Their Characteristics, and the Effects Found, 49
Specifying the Expected Cost of Committing a Capital
Homicide: f(Z
it
), 54
Model Assumptions, 63
Benefits of Random Assignment, 64
Fixed Effect Regression Model, 65
Instrumental Variables, 66
Homogeneity, 68
Conclusion, 70
References, 71
5 TIME-SERIES STUDIES 75
Basic Conceptual Issues, 76
Execution Event Studies, 76
Studies of Deviations from Fitted Trends, 78
Vector Autoregressions, 82
Evidence Under Existing Criminal Sanction Regimes, 82
Granger Causality and Causality as Treatment Response, 86
Choice of Variables in VAR Studies, 88
Inferences Under Alternative Sanction Regimes, 89
Event Studies, 90
Time-Series Regressions, 92
Cross-Polity Comparisons, 94
Conclusions, 97
References, 99
6 CHALLENGES TO IDENTIFYING DETERRENT EFFECTS 101
Data on Sanction Regimes, 104
Perceptions of Sanction Risks, 105
Measurement of Perceptions, 107
Inference on Perceptions from Homicide Rates Following
Executions, 110
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
CONTENTS xv
Identifying Effects: Feedbacks and Unobserved Confounders, 111
Feedback Effects, 111
Omitted Variables, 112
The Equilibrium Effect, 113
Addressing Model Uncertainty with Weaker Assumptions, 115
Model Averaging, 116
Partial Identification, 119
References, 121
Appendix: Biographical Sketches of Committee Members and Staff 125
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
1
Summary
I
n 1976, the Supreme Court decision in Gregg v. Georgia (428 U.S. 153)
ended the 4-year moratorium on executions that had resulted from its
1972 decision in Furman v. Georgia (408 U.S. 238). In the immediate
aftermath of Gregg, an earlier report of the National Research Council
(NRC) reviewed the evidence relating to the deterrent effect of the death
penalty that had been gathered through the mid-1970s. That review was
highly critical of the earlier research and concluded (National Research
Council, 1978, p. 9) that “available studies provide no useful evidence on
the deterrent effect of capital punishment.”
During the 35 years since Gregg, and particularly in the past decade,
many additional studies have renewed the attempt to estimate the effect of
capital punishment on homicide rates. Most researchers have used post-
Gregg data from the United States to examine the statistical association
between homicide rates and the legal status, the actual implementation of
the death penalty, or both. The studies have reached widely varying, even
contradictory, conclusions. Some studies conclude that executions save
large numbers of lives; others conclude that executions actually increase
homicides; and still others conclude that executions have no effect on
homicide rate. Commentary on the scientific validity of the findings has
sometimes been acrimonious. The Committee on Deterrence and the Death
Penalty was convened against this backdrop of conflicting claims about the
effect of capital punishment on homicide rates. The committee addressed
three main questions laid out in its charge:
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
2 DETERRENCE AND THE DEATH PENALTY
1. Does the available evidence provide a reasonable basis for drawing
conclusions about the magnitude of capital punishment’s effect on
homicide rates?
2. Are there differences among the extant analyses that provide a ba-
sis for resolving the differences in findings? Are the differences in
findings due to inherent limitations in the data? Are there existing
statistical methods and/or theoretical perspectives that have yet to
be applied that can better address the deterrence question? Are the
limitations of existing evidence reflective of a lack of information
about the social, economic, and political underpinnings of homi-
cide rates and/or the administration of capital punishment that first
must be resolved before the deterrent effect of capital punishment
can be determined?
3. Do potential remedies to shortcomings in the evidence on the de-
terrent effect of capital punishment have broader applicability for
research on the deterrent effect of noncapital sanctions?
CONCLUSION AND RECOMMENDATION: The committee con-
cludes that research to date on the effect of capital punishment on ho-
micide is not informative about whether capital punishment decreases,
increases, or has no effect on homicide rates. Therefore, the committee
recommends that these studies not be used to inform deliberations
requiring judgments about the effect of the death penalty on homicide.
Consequently, claims that research demonstrates that capital punish-
ment decreases or increases the homicide rate by a specied amount
or has no effect on the homicide rate should not inuence policy judg-
ments about capital punishment.
The committee was disappointed to reach the conclusion that research
conducted in the 30 years since the earlier NRC report has not sufficiently
advanced knowledge to allow a conclusion, however qualified, about the ef-
fect of the death penalty on homicide rates. Yet this is our conclusion. Some
studies play the useful role, either intentionally or not, of demonstrating the
fragility of claims to have or not to have found deterrent effects. However,
even these studies suffer from two intrinsic shortcomings that severely limit
what can be learned from them about the effect of the death penalty—as it
has actually been administered in the United States in the past 35 years—on
the death penalty.
Properly understood, the relevant question about the deterrent effect of
capital punishment is the differential or marginal deterrent effect of execu-
tion over the deterrent effect of other available or commonly used penalties,
specifically, a lengthy prison sentence or one of life without the possibility of
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
SUMMARY 3
parole. One major deficiency in all the existing studies is that none specify
the noncapital sanction components of the sanction regime for the punish-
ment of homicide. Another major deficiency is the use of incomplete or
implausible models of potential murderers’ perceptions of and response to
the capital punishment component of a sanction regime. Without this basic
information, it is impossible to draw credible findings about the effect of
the death penalty on homicide.
Commentary on research findings often pits studies claiming to find
statistically significant deterrent effects against those finding no statistically
significant effects, with the latter studies sometimes interpreted as imply-
ing that there is no deterrent effect. A fundamental point of logic about
hypothesis testing is that failure to reject a null hypothesis does not imply
that the null hypothesis is correct.
Our mandate was not to assess whether competing hypotheses about
the existence of marginal deterrence from capital punishment are plausible,
but simply to assess whether the empirical studies that we have reviewed
provide scientifically valid evidence. In its deliberations and in this report,
the committee has made a concerted effort not to approach this question
with a prior assumption about deterrence. Having reviewed the research
that purports to provide useful evidence for or against the hypothesis that
the death penalty affects homicide rates, we conclude that it does not pro-
vide such evidence.
A lack of evidence is not evidence for or against the hypothesis. Hence,
the committee does not construe its conclusion that the existing studies are
uninformative as favoring one side or the other side in the long-standing
debate about deterrence and the death penalty. The committee also empha-
sizes that deterrence is but one of many considerations relevant to rendering
a judgment on whether the death penalty is good public policy.
Even though the scholarly evidence on the deterrent effect of capital
punishment is too weak to guide decisions, this does not mean that people
should have no views on capital punishment. Judgment about whether
there is a deterrent effect is still relevant to policy, but that judgment
should not be justified based on evidence from existing research on capital
punishment’s effect on homicide. Just as important, the committee did not
investigate the moral arguments for or against capital punishment or the
empirical evidence on whether capital punishment is administered in a
nondiscriminatory and consistent fashion. Nor did it investigate whether
the risk of mistaken execution is acceptably small or how the cost of ad-
ministering the death penalty compares to other sanction alternatives. All
of these issues are relevant to making a judgment about whether the death
penalty is good public policy.
Our charge was also limited to assessing the evidence on the deterrent
effect of the death penalty on murder, not the deterrent effect of noncapital
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
4 DETERRENCE AND THE DEATH PENALTY
sanctions on crime more generally. Our negative conclusion on the infor-
mativeness of the evidence on the former issue should not be construed as
extending to the latter issue because the committee did not review the very
large body of evidence on the deterrent effect of noncapital sanctions.
SHORTCOMINGS IN EXISTING RESEARCH
The post-Gregg studies are usefully divided into two categories based
on the type of data analyzed. One category, which we call panel data stud-
ies, analyzes sets of states or counties measured over time, usually from
about 1970 to 2000. These studies relate homicide rates to variations over
time and across states or counties in the legal status of capital punishment
and/or the frequency of executions. The second category, which we call
time-series studies, generally studies only a single geographic unit. The geo-
graphic unit may be as large as a nation or as small as a city. These studies
usually examine whether there are short-term changes in homicide rates in
that geographic unit in the aftermath of an execution.
As noted above, research on the effect of capital punishment on ho-
micide suffers from two fundamental flaws that make them uninformative
about the effect of capital punishment on homicide rates: they do not
specify the noncapital sanction components of the sanction regime for the
punishment of homicide, and they use incomplete or implausible models of
potential murderers’ perceptions of and response to the capital punishment
component of a sanction regime. In addition, the existing studies use strong
and unverifiable assumptions to identify the effects of capital punishment
on homicides.
Specication of the Sanction Regime for Homicide
The sanction regime for homicide comprises both the capital and non-
capital sanctioning options that are available for its punishment and the
policies governing the administration of these options. The relevant ques-
tion regarding the deterrent effect of capital punishment is the differential
deterrent effect of execution in comparison with the deterrent effect of other
available or commonly used penalties. We emphasize “differential” because
it is important to recognize that even in states that make the most intense
use of capital punishment, most convicted murderers are not sentenced to
death but to a lengthy prison sentence—often life without the possibility
of parole.
None of the studies that we reviewed (both those using a panel ap-
proach and those using time-series approaches) accounted for the severity
of noncapital sanctions in their analyses. As discussed in Chapters 4 and 6,
there are sound reasons to expect that the severity of the noncapital sanc-
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
SUMMARY 5
tions for homicide varies systematically with the availability of capital pun-
ishment, the intensity of use of capital punishment, or both. For example,
the political culture of a state may affect the frequency of the use of capital
punishment and also the severity of noncapital sanctions for homicide.
Thus, any effect that these noncapital sanctions have on the homicide rate
may contaminate any estimated effect of capital punishment.
Potential Murderers’ Perceptions of and Responses to Capital Punishment
A by-product of the absence of consideration of the noncapital com-
ponent of the sanction regime is that no studies consider how the capital
and noncapital components of a regime combine in affecting the behavior
of potential murderers. Only the capital component of the sanction regime
has been studied, and this in itself shows both a serious conceptual flaw
and a serious data flaw in the entire body of research.
Several factors make the attempts by the panel studies to specify the
capital component of state sanctions regimes uninterpretable. First, the
findings are very sensitive to the way the risk of execution is specified. Sec-
ond, there is no logical basis for resolving disagreements about how this
risk should be measured.
Much of the panel research simply assumes that potential murderers
respond to the objective risk of execution. There are significant complexities
in computing this risk even for a well-informed researcher, let alone for a
potential murderer. Among these complexities are that only 15 percent of
people who have been sentenced to death since 1976 have actually been
executed and a large fraction of death sentences are subsequently reversed.
None of the measures that are used in the research have been shown to be
a better measure of the risk of execution than any others. Thus, even if one
assumes that a potential murderer’s perceived risk corresponds to the actual
risk, there is no basis for arbitrating the competing claims about what is
the “right” risk measure.
The committee is also skeptical that potential murderers can possibly
estimate the objective risk, whatever it is. Hence, there is good reason to be-
lieve that perceived risk deviates from the objective risk. The research does
not address how potential murderers’ perceptions of capital punishment—
and, more generally, noncapital sanction risks—are formed.
The time-series studies come in many forms—studies of a single ex-
ecution event, studies of many events, and studies with a cross-polity
dimension—but a common feature of the studies is that none of them at-
tempts to specify even the capital component of the overall sanction regime.
This is a crucial shortcoming and is exemplified in the time-series analyses
that examine the association between deviations of number of executions
from a fitted trend line and deviations of homicides from a fitted trend line.
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
6 DETERRENCE AND THE DEATH PENALTY
For potential murderers to possibly be responsive to deviations from the
execution trend line, they have to be attentive to it. The studies are silent on
two key questions: (1) Why are potential murderers attentive to the trend
line in the number of executions? (2) Why do they respond to deviations
from the trend line?
If time-series analyses find that homicide rates are not responsive to
such deviations, it may be that potential murderers are responding to the
trend line in executions but not to deviations from it. For example, a ris-
ing trend in the number of executions might be perceived as signaling a
toughening of the sanction regime, which might deter potential murderers.
Alternatively, if a time-series analysis finds that homicide rates are respon-
sive to such deviations, the question is why? One possibility is that potential
murderers interpret the deviations as new information about the intensity
of the application of capital punishment—that is, they perceive a change
in the part of the sanction regime relating to application of capital punish-
ment. If so, a deviation from the execution trend line may cause potential
murderers to alter their perceptions of the future course of the trend line,
which in turn may change their behavior.
Yet, even accepting this idea, a basic question persists. Why should the
trend lines fit by researchers coincide with the perceptions of potential mur-
derers about trends in executions? Because there are no studies that include
empirical analyses on the question of how potential murderers perceive the
risk of sanctions, there is no basis for assuming that the trend line specified
by researchers corresponds to the trend line (if any) that is perceived by
potential murderers. If researchers and potential murderers do not perceive
trends the same way, then time-series analyses do not correctly identify
what potential murderers perceive as deviations. Because of this basic flaw
in the research, the committee has no basis for assessing whether the find-
ings of time-series studies reflect a real effect of executions on homicides
or are artifacts of models that incorrectly specify how deviations from a
trend line cause potential murderers to update their forecasts of the future
course of executions.
Strong and Unveriable Assumptions
To obtain a single estimate that specifies the effect of capital punish-
ment on homicide, researchers invariably rely on a range of strong and
unverified assumptions. In part (as discussed above), this reflects the lack of
basic information on the relevant sanction regimes for homicide and the as-
sociated perceptions of risk. None of the studies accounts for the noncapital
component of the sanction regime, and potential murderers’ risk percep-
tions are assumed to depend on observable frequencies of arrest, conviction,
and execution. The ad hoc choices of alternative models of risk perceptions
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
SUMMARY 7
lead to very different inferences on the effects of capital punishment, and
none of them is inherently any more justifiable than any other.
Additional data and research on sanction regimes and risk perceptions
may serve to reduce this form of model uncertainty. However, even if these
uncertainties are fully reconciled, a more fundamental problem is that the
outcomes of counterfactual sanction policies are unobservable. That is,
there is no way to determine what would have occurred if a given state
had a different sanction regime. In light of this observational problem, the
available data cannot reveal the effect of capital punishment itself since the
policy-relevant question is whether capital punishment deters homicides
relative to other sanction regimes. That is, the data alone cannot reveal
what the homicide rate in a state without (with) a capital punishment re-
gime would have been had the state (not) had such a regime.
The standard procedure in capital punishment research has been to
impose sufficiently strong assumptions to yield definitive findings on deter-
rence. For example, a common assumption is that sanctions are random
across states or years, as they would be if sanctions had been randomly as-
signed in an experiment. Another common assumption is that the response
of criminality to sanctions is homogeneous across states and years. Some
studies use instrumental variables to identify deterrent effects, but this
requires yet other assumptions. The use of strong assumptions hides the
problem that the study of deterrence is plagued by model uncertainty and
that many of the assumptions used in the research lack credibility.
NEXT STEPS FOR RESEARCH
The earlier NRC committee concluded that it was “skeptical that the
death penalty [as practiced in the United States] can ever be subjected to the
kind of statistical analysis that would validly establish the presence or ab-
sence of a deterrent effect” (National Research Council, 1978, p. 62). The
present committee is not so pessimistic and offers several recommendations
for addressing the shortcomings in research to date on capital punishment.
They include
1. collection of the data required for a more complete specification of
both the capital and noncapital components of the sanction regime
for murder;
2. research on how potential murderers perceive the sanction regime
for murder; and
3. use of methods that makes less strong and more credible assump-
tions to identify or bound the effect of capital punishment on
homicides.
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
8 DETERRENCE AND THE DEATH PENALTY
In addition, the committee suggests research on how the presence of capital
punishment in a sanctions regime affects the administration of the regime
and how the homicide rate affects the statutory definition of the sanction
regime and its administration.
The committee does not expect that advances in new data on sanction
regimes and obtaining knowledge of sanctions risk perceptions will come
quickly or easily. However, data collection on the noncapital component of
the sanction regime need not be entirely complete to be useful. Moreover,
even if research on perceptions of the risk of capital punishment cannot
resolve all major issues, some progress would be an important step forward.
The ultimate success of the research may depend on the specific ques-
tion that is addressed. Questions of interest include
if or how the legal status of the death penalty affects homicide
rates,
if or how the intensity of use of the death penalty affects homicide
rates, and
• iforhowexecutionsaffecthomicideratesintheshortrun.
Some but not all of these questions may be informed by successful applica-
tion of the committee’s suggested lines of research.
Although evaluation of research on the deterrent effect of noncapital
sanctions was not part of the committee’s charge, we note that the methods
and approaches used to study capital and noncapital sanction effects on
crime overlap. We were charged with making suggestions for advancing
research on the latter issue. Thus, the research and data collection sugges-
tions above are framed in the broader context of research on the effect on
crime rates of both capital and noncapital sanctions.
We think this aspect of our charge is particularly important. Although
capital punishment is a highly contentious public policy issue, policies on
prison sanctions and their enforcement are the most important components
of the nation’s response to crime. Thus, even if the research agenda we
outline is not ultimately successful in illuminating some aspects of the ef-
fect of capital punishment on homicide, advancing knowledge on the crime
prevention effects of noncapital sanctions and their enforcement can make
major contributions to important policy issues.
REFERENCE
National Research Council. (1978). Deterrence and Incapacitation: Estimating the Effects of
Criminal Sanctions on Crime Rates. Panel on Research on Deterrent and Incapacitative
Effects. A. Blumstein, J. Cohen, and D. Nagin (Eds.), Committee on Research on Law
Enforcement and Criminal Justice. Assembly of Behavioral and Social Sciences.Washing-
ton, DC: National Academy Press.
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
1
Introduction
I
n 1976 the Supreme Court decision Gregg v. Georgia (428 U.S. 153)
ended the 4-year moratorium on executions that had resulted from its
1972 decision in Furman v. Georgia (408 U.S. 238). In Furman the
Court had ruled that the death penalty, as then administered in the United
States, constituted cruel and unusual punishment in violation of the Eighth
Amendment to the Constitution. Then, in Gregg, it had ruled that the death
penalty is not, in all circumstances, cruel and unusual punishment, thereby
opening the way for states to revise their capital punishment statutes to
conform to the requirements of Gregg.
In the immediate aftermath of Gregg, a National Research Council
report reviewed the evidence relating to the deterrent effect of the death
penalty that had been published through the mid-1970s. That review was
highly critical of the available research, concluding (1978, p. 9):
The flaws in the earlier analyses finding no effect and the sensitivity of
the more recent analysis to minor variations in model specification and
the serious temporal instability of the results lead the panel to conclude
that available studies provide no useful evidence on the deterrent effect of
capital punishment.
THE CURRENT DEBATE
During the 35 years since Gregg, and particularly in the past decade,
many studies have renewed the attempt to estimate the effect of capital
punishment on homicide rates. Most researchers have used post-Gregg
data from the United States to examine the statistical association between
9
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Deterrence and the Death Penalty
10 DETERRENCE AND THE DEATH PENALTY
homicide rates and the legal status or the actual implementation of the
death penalty.
The studies have reached widely varying, even contradictory, conclu-
sions, and commentary on the findings has sometimes been acrimonious.
Some researchers have concluded that deterrent effects are large and robust
across datasets and model specifications. For example, Dezhbakhsh, Rubin,
and Shepherd (2003, p. 344) concluded that:
Our results suggest that capital punishment has a strong deterrent effect;
each execution results, on average, in eighteen fewer murders with a mar-
gin of error of plus or minus ten. Tests show that results are not driven by
tougher sentencing laws and are robust to many alternative specifications.
Similarly, Mocan and Gittings (2003, p. 453) stated the following:
The results show that each additional execution decreases homicides by
about five, and each additional commutation increases homicides by the
same amount, while an additional removal from death row generates one
additional murder.
In 2004 testimony before Congress, Shepherd (2004, p. 1) summarized this
line of evidence on the deterrent effect of capital punishment as follows:
Recent research on the relationship between capital punishment and crime
has created a strong consensus among economists that capital punishment
deters crime.
However, the claims that the evidence shows a substantial deterrent
effect have been vigorously challenged. Kovandzic, Vieraitis, and Boots
(2009, p. 803) concluded that:
Employing well-known econometric procedures for panel data analysis,
our results provide no empirical support for the argument that the exis-
tence or application of the death penalty deters prospective offenders from
committing homicide . . . policymakers should refrain from justifying its
use by claiming that it is a deterrent to homicide and should consider less
costly, more effective ways of addressing crime.
Others do not go so far as to claim that there is no deterrent effect, but
instead argue that the findings supporting a deterrent effect are fragile, not
robust. Donohue and Wolfers (2005, p. 794) reanalyzed several of the data
sets used by the authors who claimed to have found robust deterrent effects
and concluded that:
We find that the existing evidence for deterrence is surprisingly fragile,
and even small changes in specifications yield dramatically different re-
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
INTRODUCTION 11
sults. Our key insight is that the death penalty—at least as it has been
implemented in the United States since Gregg ended the moratorium
on executions—is applied so rarely that the number of homicides it can
plausibly have caused or deterred cannot be reliably disentangled from the
large year-to year changes in the homicide rate caused by other factors.
Berk (2005, p. 328) reached a similar conclusion:
. . . the results raise serious questions about whether anything useful about
the deterrent value of the death penalty can ever be learned from an obser-
vational study with the data that are likely to be available.
Not surprisingly, the criticisms of the research claiming to have found
deterrent effects have generated defenses of the research findings and the
methodologies used, as well as counterclaims about the deficiencies in
the methods used by the critics. For instance, in response to the Kovandzic,
Vieraitis, and Boots (2009) claim of no deterrent effect, Rubin (2009,
p. 858) argued that:
the weight of the evidence as well as the theoretical predictions both argue
for deterrence, and econometrically flawed studies such as this article are
insufficient to overthrow this presumption.
In response to Donohue and Wolfers (2005, 2009), Zimmerman (2009,
p. 396) argued that:
This paper shows that many of D&W’s [Donohue and Wolfers] criticisms
of Zimmerman’s original work do not hold up under scrutiny, and other
authors have also rebutted D&W’s criticisms of their research.
Beyond disagreement about whether the research evidence shows a
deterrent effect of capital punishment, some researchers claim to have
found a brutalization effect from state-sanctioned executions such that
capital punishment actually increases homicide rates (see, e.g., Cochran and
Chamlin, 2000; Thomson, 1999). Evidence in support of a brutalization
effect is mostly the work of sociologists, but it is notable that in her latter
work Shepherd also concluded that brutalization effects may be present
(Shepherd, 2005).
COMMITTEE CHARGE AND SCOPE OF WORK
The Committee on Deterrence and the Death Penalty was organized
against this backdrop of conflicting claims about the effect of capital pun-
ishment on homicide rates, with the following charge:
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
12 DETERRENCE AND THE DEATH PENALTY
This study will assess the evidence on the deterrent effect of the death
penalty—whether the threat of execution prevents homicides. The focus
will be on studies completed since an earlier National Research Council
assessment (National Research Council, 1978). A major objective of this
study is to evaluate underlying reasons for the differing conclusions in
more recent empirical studies about the effects of the legal status and ac-
tual practice of the death penalty on criminal homicide rates. The commit-
tee will develop a report about what can be concluded from these studies
and also draw conclusions about the potential for future work to improve
upon the quality of existing evidence.
Issues and questions to be examined include the following:
1. Does the available evidence provide a reasonable basis for drawing
conclusions about the magnitude of capital punishment’s effect on
homicide rates?
2. Are there differences among the extant analyses that provide a ba-
sis for resolving the differences in findings? Are the differences in
findings due to inherent limitations in the data? Are there existing
statistical methods and/or theoretical perspectives that have yet to
be applied that can better address the deterrence question? Are the
limitations of existing evidence reflective of a lack of information
about the social, economic, and political underpinnings of homi-
cide rates and/or the administration of capital punishment that first
must be resolved before the deterrent effect of capital punishment
can be determined?
3. Do potential remedies to shortcomings in the evidence on the de-
terrent effect of capital punishment have broader applicability for
research on the deterrent effect of noncapital sanctions?
In addressing those questions, we focused on the studies that have been
undertaken since the earlier assessment (National Research Council, 1978).
That assessment has stood largely unchallenged: none of the recent work,
whatever its conclusion regarding deterrence, relies on the earlier studies
criticized in that report or attempts to rehabilitate the value of those studies.
It is important to make clear what is not in the committee’s charge.
Deterrence is but one of many considerations relevant to deciding whether
the death penalty is good public policy. Not all supporters of capital pun-
ishment base their argument on deterrent effects, and not all opponents
would be affected by persuasive evidence of such effects. The case for
capital punishment is sometimes based on normative retributive arguments
that the death penalty is the only appropriate and proportional response
to especially heinous crimes; the case against it is sometimes based on
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
INTRODUCTION 13
similarly normative claims that the sanctity of human life precludes state-
sanctioned killings, regardless of any possible social benefits of capital
punishment. Separate from normative considerations, deterrence is not the
only empirical issue relevant to the debate over capital punishment. Other
considerations include whether capital punishment can be administered in
a nondiscriminatory and consistent fashion, whether the risk of a mistaken
execution of an innocent person is acceptably small, and the cost of admin-
istering the death penalty in comparison with other sanction alternatives.
Although there is empirical evidence on the issues of discrimination,
mistakes, and cost, the charge to the committee does not include these
questions. Nor have we been charged with rendering an overall judgment
on whether capital punishment is good public policy. We have been tasked
only with assessing the scientific quality of the post-Gregg evidence on the
deterrent effect of capital punishment and making recommendations for
improving the scientific quality and policy relevance of future research.
In including recommendations for future research, the study’s statement
of task recognized that potential remedies to shortcomings in the evidence
on the deterrent effect of capital punishment on homicide might also be
used in the study of the crime prevention effects of noncapital sanctions.
Thus, this report also offers recommendations for improving the scientific
quality and policy relevance of that research.
The post-Gregg studies can be divided into two types on the basis of
the type of data analyzed. Panel data studies analyze sets of states or coun-
ties measured over time, usually from about 1970 to 2000. These studies
relate homicide rates over time and the jurisdictions covered to the legal
status of capital punishment or the frequency of executions or both. Time-
series studies generally cover only a single geographic unit, which may be
as large as a nation or as small as a city. These studies usually examine
whether there are short-term changes in homicide rates in that geographic
unit in the aftermath of an execution. We review and critique these two
types of studies separately because their design and statistical methods are
quite different.
Assessing the deterrent effect of the death penalty is much more than
a question of interest to social science research. It is a matter of importance
to U.S. society at large, and we expect that a potentially broad audience
will want to understand how the committee reached its conclusions. Yet
the research that the committee has had to appraise is a body of formal
empirical work that makes use of highly technical concepts and techniques.
The committee has been mindful of the importance of reaching as broad an
audience as possible while meeting the fundamental requirement that the
report be scientifically grounded. With this in mind, Chapters 1, 2, and
3 (as well as the summary) have been written for a broad, largely policy
audience, largely avoiding technical language. In contrast, Chapters 4 and
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
14 DETERRENCE AND THE DEATH PENALTY
5 include some exposition and analyses that are aimed for the researchers
in the field.
Chapter 2 summarizes homicide rates and the legal status and practice
of execution in the United States from 1950 to the present. Chapter 3 pro-
vides an overview of the possible mechanisms by which the legal status and
practice of execution might affect homicide rates and also provides a non-
technical primer on some of the key challenges to making valid inferences
about the deterrent effect of the death penalty. Chapters 4 and 5 review and
assess the panel and time-series studies, respectively. Chapter 6 elaborates
on the theoretical and statistical challenges to drawing valid conclusions
about the deterrent effect of the death penalty, and presents our conclusions
and recommendations for future research.
REFERENCES
Berk, R. (2005). New claims about executions and general deterrence: Déjà vu all over again?
Journal of Empirical Legal Studies, 2(2), 303-330.
Cochran, J.K., and Chamlin, M.B. (2000). Deterrence and brutalization: The dual effects of
executions. Justice Quarterly, 17(4), 685-706.
Dezhbakhsh, H., Rubin, P.H., and Shepherd, J.M. (2003). Does capital punishment have a
deterrent effect? New evidence from postmoratorium panel data. American Law and
Economics Review, 5(2), 344-376.
Donohue, J.J., and Wolfers, J. (2005). Uses and abuses of empirical evidence in the death
penalty debate. Stanford Law Review, 58(3), 791-845.
Donohue, J.J., and Wolfers, J. (2009). Estimating the impact of the death penalty on murder.
American Law and Economics Review, 11(2), 249-309.
Kovandzic, T.V., Vieraitis, L.M., and Boots, D.P. (2009). Does the death penalty save lives?
Criminology & Public Policy, 8(4), 803-843.
Mocan, H.N., and Gittings, R.K. (2003). Getting off death row: Commuted sentences and the
deterrent effect of capital punishment. Journal of Law & Economics, 46(2), 453-478.
National Research Council. (1978). Deterrence and Incapacitation: Estimating the Effects of
Criminal Sanctions on Crime Rates. Panel on Research on Deterrent and Incapacitative
Effects, A. Blumstein, J. Cohen, and D. Nagin (Eds.). Committee on Research on Law
Enforcement and Criminal Justice. Assembly of Behavioral and Social Sciences. Wash-
ington, DC: National Academy Press.
Rubin, P.H. (2009). Don’t scrap the death penalty. Criminology & Public Policy, 8(4), 853-859.
Shepherd, J.M. (2004). Testimony on Crime and Deterrence: Hearing on H.R. 2934, the
Terrorist Penalties Enhancement Act of 2003. Subcommittee on Crime, Terrorism, and
Homeland Security, House Judiciary Committee. Available: http://judiciary.house.gov/
legacy/shepherd042104.pdf [January 2012].
Shepherd, J.M. (2005). Deterrence versus brutalization: Capital punishment’s differing impacts
among states. Michigan Law Review, 104(2), 203-255.
Thomson, E. (1999). Effects of an execution on homicides in California. Homicide Studies,
3(2), 129-150.
Zimmerman, P.R. (2009). Statistical variability and the deterrent effect of the death penalty.
American Law and Economics Review, 11(2), 370-398.
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
2
Capital Punishment in
the Post-Gregg Era
T
he resurgence in the use of the death penalty in the aftermath of
Gregg, which followed the de facto moratorium of the 1960s and
early 1970s, created the empirical basis for the post-Gregg capital
punishment deterrence studies. This chapter provides an empirical summary
of the legal status and use of capital punishment during this period.
EXECUTIONS AND DEATH SENTENCES OVER TIME
Figure 2-1 shows executions in the United States from 1930 through
2010. As can be seen, executions were more common prior to World War II
than in the postwar era. Executions peaked at 199 in 1935. Following the
war, executions steadily declined, from 153 in 1947 to 0 in the late 1960s.
From 1967 to the Furman decision in 1972, there were no executions even
though they were legally permissible. (The Furman rendered executions
legally impossible from 1972 through 1976.) Following the Gregg decision
in 1976, the number of executions rose rather steadily to the 1999 peak
of 98. It then began falling again: by 2005, the number of executions had
nearly halved to 53. Since 2005 the number of executions has remained
stable at about 50 per year. From 1976 to 2010, a total of 1,234 people
were executed.
Also relevant to the evidence on deterrence is the number of death sen-
tences imposed: Figure 2-2 shows the number of those sentences, as well
as the number of executions, for the post-Gregg period. In 1977, the first
full year following the Gregg decision, 137 death sentences were imposed.
Thereafter, death sentences rose to an annual peak of about 300 in the late
15
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
16 DETERRENCE AND THE DEATH PENALTY
0
50
100
150
200
250
1930 1950 1970 1990 2010
Annual Number of Executions in the United States
Year
R02175
Figure 2-1
vectors, editable
FIGURE 2-1 Annual number of executions in the United States from 1930 to 2010.
SOURCE: Bureau of Justice Statistics (2010, Figure 2).
0
50
100
150
200
250
300
350
1976 1981 1986 1991 1996 2001 2006
ExecutionsDeath Sentences
Year
Number
R02175
Figure 2-2
vectors, editable
2009
FIGURE 2-2 Annual number of death sentences and executions in the United States
from 1976 to 2009.
SOURCE: Bureau of Justice Statistics (2010, Tables 13, 19).
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
CAPITAL PUNISHMENT IN THE POST-GREGG ERA 17
1990s. Since then there has been a steady decline, to 112 in 2009. Figure
2-2 makes clear that far more death sentences are imposed than are carried
out.
When a defendant is convicted and sentenced to death, theoretically
what follows is an execution. An execution, however, does not follow a
death sentence very swiftly or at all for a variety of reasons. The Bureau of
Justice Statistics reports that only 15 percent of people sentenced to death
between 1973 and 2009 had been executed by the end of 2009. Of these
cases, 46 percent ended in alternate ways, including reversed convictions,
commuted sentences, or the death of the inmate. Thus, 39 percent of the in-
mates sentenced to death during the 36-year period were still on death row
in December 2009. These inmates, on average, had been under a death sen-
tence for more than 12 years. Because of the smaller number of executions
than death sentences every year, the death row population has increased
steadily over this period. The number of prisoners facing a death sentence
was a little over 400 in 1977 (the first full year after reinstatement); by 2009
it was close to 3,200 (Bureau of Justice Statistics, 2010, Table 18).
These national-level data conceal large differences across states in the
use of the death penalty. During the post-Gregg era, the death penalty was
not legal in all states, and in some states it was only legal for part of the
period. Also, among states authorizing the death penalty, in at least some
cases there were very large differences in the extent of the legal authority for
capital punishment and the frequency with which that authority was used.
Notably, these variations across states and over time in the legal authority
to impose the death penalty and the frequency with which that authority
was exercised created the empirical basis for the deterrence studies reviewed
in this report.
Table 2-1 shows the legal authority for a death sentence by state from
1976 to 2009. A geographically and otherwise diverse group of 10 states
never authorized the use of the death penalty during this period: Alaska,
Hawaii, Iowa, Maine, Michigan, Minnesota, North Dakota, Vermont,
Wisconsin, and West Virginia. Of the other 40 states, 29 provided that au-
thority for the whole period. The remaining 11 states experienced changes
in death penalty authority from 1976 to 2009:
Two states—North Carolina and Wyoming—transitioned in 1977,
immediately after the Gregg decision.
Four states—Kansas, New Hampshire, Oregon, and South
Dakota—transitioned from non–death penalty to death penalty
status after 1977.
Two states—New Mexico and Rhode Island—transitioned from
death penalty to non–death penalty status after 1977.
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
18 DETERRENCE AND THE DEATH PENALTY
TABLE 2-1 Legal Status of Execution in the Post-Gregg Era
State Legal Authority for Death Penalty 1976-2009
Alabama Yes
Alaska No
Arizona Yes
Arkansas Yes
California Yes
Colorado Yes
Connecticut Yes
Delaware Yes
Florida Yes
Georgia Yes
Hawaii No
Idaho Yes
Illinois Yes
Indiana Yes
Iowa No
Kansas No, 1976-1992; Yes, 1993-2009
Kentucky Yes
Louisiana Yes
Maine No
Maryland Yes
Massachusetts No, 1977-1979; Yes, 1980-1983; No, 1984-2009
Michigan No
Minnesota No
Mississippi Yes
Missouri Yes
Montana Yes
Nebraska Yes
Nevada Yes
New Hampshire No, 1976-1989; Yes, 1990-2009
New Jersey No, 1976-1981; Yes, 1982-2005; No, 2006-2009
New Mexico Yes, 1976-2007; No, 2008-2009
New York No, 1976-1994; Yes, 1995-2006; No, 2007-2009
North Carolina No, 1976; Yes, 1977-2009
North Dakota No
Ohio Yes
Oklahoma Yes
Oregon No, 1976-1977; Yes, 1978-2009
Pennsylvania Yes
Rhode Island Yes, 1976-1983; No, 1984-2009
South Carolina Yes
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
CAPITAL PUNISHMENT IN THE POST-GREGG ERA 19
State Legal Authority for Death Penalty 1976-2009
South Dakota No, 1976-1978; Yes, 1979-2009
Tennessee Yes
Texas Yes
Utah Yes
Vermont No
Virginia Yes
Washington Yes
West Virginia No
Wisconsin No
Wyoming No, 1976; Yes, 1977-2009
SOURCES: Data from Bureau of Justice Statistics (2010), Rogers (2002), and Death Penalty
Information Center (2010b).
TABLE 2-1 Continued
• Three states—Massachusetts, New Jersey, and New York—
transitioned from a non–death penalty to a death penalty status and back
to a non–death penalty status over the period.
Thus, from 1976 to 2009 there were 14 transitions in death penalty status
among the 50 states. This fact has important implications for estimating
the deterrent effect of providing the legal authority for the death penalty
independent of the frequency of its use. This issue is discussed at length in
Chapter 5.
There is considerable variation among states that authorize the death
penalty regarding the types of cases in which death is an allowable punish-
ment. While deterrence studies often focus on homicide rates, there are no
states in which the death penalty is available for all intentional homicides.
First, not all intentional homicides are murders: many prosecutions that
begin as homicide cases are mitigated to the lesser crime of manslaughter,
for which capital punishment is never available. Second, even in most states
that authorize the death penalty, capital punishment is only available for
the relatively narrow category of “first-degree” murders, typically those
committed with “premeditation” or those committed during the course of
serious felonies. Finally, even those guilty of first-degree murder can only
be sentenced to death if the jury finds one or more specified aggravating
circumstances. These specified circumstances vary somewhat from state
to state, but typically include such factors as the murder of a police of-
ficer or witness, murder for hire, murder by a sentenced prisoner, multiple
murders or killings that caused a serious risk of death to many people, and
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
20 DETERRENCE AND THE DEATH PENALTY
murders that are especially “heinous, atrocious, or cruel,” which is gener-
ally interpreted to mean killings that inflicted torture or extreme degrees
of physical or psychological pain on the victim beyond that inherent in the
act of killing.
The research reviewed in this report is not always clear in its use of
such terms as “homicide” and “murder.” Homicide is a generic term mean-
ing the killing of one human being by another (as distinct from suicide or
accidental death). Some homicides (e.g., killings in legitimate self-defense or
executions pursuant to judicial judgment) are not criminal at all. Criminal
homicides are subdivided into various categories of crime (e.g., murder,
manslaughter, negligent homicide), depending on whether the person caus-
ing death intended to do so or was merely reckless or negligent and on other
circumstances surrounding the killing, and these categories are often further
subdivided into degrees (e.g., murder in the first degree). Capital punish-
ment is typically only available for the most serious instances of murder.
Most of the studies we reviewed examine the association between
capital punishment and the combined number or rate of all types of non-
negligent homicides. Unless the specific context dictates otherwise, we use
the term “homicide” in describing the findings from the research. When
discussing the effect of capital punishment in a broader or more conceptual
sense, we use the term “murder,” since the conduct that the death penalty
typically aims to deter is unjustified intentional killing, which often (but not
always) falls into that legal category.
We recognize that neither of these usages is entirely precise as a reflec-
tion of legal categories, but the legal complexity (and diversity across the
states) of the legal categories, and the general tendency of the social science
literature to ignore these distinctions altogether, leave us with no entirely
satisfactory alternative.
USE OF THE DEATH PENALTY
As we discuss in Chapter 3, there are no data on the fraction of mur-
ders that are eligible for capital punishment, and studies of this issue have
reached varying conclusions. One nationwide study (Fagan, Zimring, and
Geller, 2006) concluded that about 25 percent of homicides are capital
eligible; in contrast, a Missouri study estimated that more than 70 per-
cent of all intentional homicides were at least theoretically capital eligible
(Barnes, Sloss, and Thaman, 2009). However, these kinds of studies are
inherently problematic. In the absence of an authoritative adjudication,
the “facts” of any given homicide can only be gleaned from police reports
and other accounts that do not necessarily reliably describe the facts that
could be proven sufficiently in a court of law to support a finding of capital
eligibility.
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
CAPITAL PUNISHMENT IN THE POST-GREGG ERA 21
Whatever the percentage of homicides that could hypothetically be
charged as capital, the percentage that are so charged, even at a very early
stage of the criminal process, is much smaller, and the number in which a
capital verdict is handed down, or a defendant actually executed, is minute
in comparison to the homicide rate. Cook (2009) reports that in North
Carolina for the fiscal years 2005 and 2006, 26.5 percent of murder ar-
raignments (N = 1,034) were initially charged as capital offenses, and of
those that were capitally prosecuted 4 percent were ultimately sentenced
to death.
The Cook study also illustrates that, even if a case is initially treated
by prosecutors as capital eligible, it is very unlikely to result in a death
sentence. There were many reasons for the precipitous drop-off in capital
cases between arraignment and sentencing. A small fraction of cases were
dismissed or found not guilty at trial. More commonly, defendants pleaded
guilty and received a noncapital sentence in return for the plea. In jury
trials, some individuals were found guilty of manslaughter or second-, not
first-, degree murder, and among those found guilty of first-degree murder
most juries did not recommend the death penalty.
Table 2-2 shows summary statistics on the frequency of executions
and death sentences from 1973 to 2009 for the 40 states with active death
penalty laws during at least part of the period. We focus on this time period
because it is the one used in most panel studies of deterrence. The table
shows that executions were very concentrated in a few states. Texas ac-
counted for 37.6 percent of executions from 1973 to 2009; Florida, Texas,
and Virginia together accounted for 52.2 percent. This concentration is only
partly attributable to more frequent imposition of the death penalty by the
courts in those states. Other large states, such as California and Pennsylva-
nia, impose relatively large numbers of death sentences. However, the rate
at which death sentences are actually carried out varies greatly across states.
The last column in Table 2-2 is the ratio of total executions to total death
sentences. In California and Pennsylvania, it is only 1.4 percent and 0.8
percent, respectively, compared with 7.0 percent in Florida, 43.0 percent
in Texas, and 70.0 percent in Virginia.
Table 2-2 makes clear that in many states death sentences will either
never be carried out or will only be carried out after a very long delay. This
fact is important for considering the deterrent effect of the death penalty be-
cause the longer the delay the more the death penalty resembles a sentence
of life without parole, the next most severe sanction to execution. It also
complicates the assessment of what features of a capital punishment regime
should be tested for an effect on homicide rates: the legal status of capital
punishment as a potential sanction, the rate of capital sentences, the rate of
executions, or the time to execution. We return to this point in Chapter 3.
Table 2-3 provides perspective on the frequency of executions and
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
22 DETERRENCE AND THE DEATH PENALTY
TABLE 2-2 Number of Death Sentences and Executions by Jurisdiction,
1973-2009
Death Sentences Executions
Executions per
Death Sentence
Federal 65 3 0.0462
Alabama 412 44 0.1068
Arizona 286 23 0.0804
Arkansas 110 27 0.2455
California 927 13 0.0140
Colorado 21 1 0.0476
Connecticut 13 1 0.0769
Delaware 56 14 0.2500
Florida 977 68 0.0696
Georgia 320 46 0.1438
Idaho 42 1 0.0238
Illinois 307 12 0.0391
Indiana 100 20 0.2000
Kansas 12 0 0
Kentucky 81 3 0.0370
Louisiana 238 27 0.1134
Maryland 53 5 0.0943
Massachusetts 4 0 0
Mississippi 190 10 0.0526
Missouri 182 67 0.3681
Montana 15 3 0.2000
Nebraska 32 3 0.0938
Nevada 147 12 0.0816
New Hampshire 1 0 0
New Jersey 52 0 0
New Mexico 28 1 0.0357
New York 10 0 0
North Carolina 528 43 0.0814
Ohio 401 33 0.0823
Oklahoma 350 91 0.2600
Oregon 58 2 0.0345
Pennsylvania 399 3 0.0075
Rhode Island 2 0 0
South Carolina 203 42 0.2069
South Dakota 5 1 0.2000
Tennessee 221 6 0.0271
Texas 1,040 447 0.4298
Utah 27 6 0.2222
Virginia 150 105 0.7000
Washington 38 4 0.1053
Wyoming 12 1 0.0833
TOTAL 8,115 1,188
SOURCE: Bureau of Justice Statistics (2010, Table 20).
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
CAPITAL PUNISHMENT IN THE POST-GREGG ERA 23
death sentences relative to the frequency of homicides in the states that
provided the authority for capital punishment for all or part of the period
from 1990 to 1999, the post-Gregg decade in which the most executions
occurred. The final two columns in the table report the ratios of total death
sentences and total executions, respectively, to the total homicides for the
period. The statistics make clear that relative to total homicides, death
sentences are rare and executions ever rarer. Among states with more than
500 homicides, Oklahoma had the highest ratio of death sentences to homi-
cides, 4.9 percent. Those ratios for Texas and Virginia, the two states that
most frequently impose the death penalty were 2.1 percent and 1.4 percent,
respectively. The ratio of executions to homicides was even smaller. Among
states with more than 500 homicides, the rate never exceeds 1 percent ex-
cept in Virginia.
The data in Table 2-3 highlight two important challenges to inferring
the deterrent effect of the death penalty. Because the fraction of murders
resulting in a death sentence is small and the fraction that results in execu-
tions even smaller, absolute differences in these fractions between the high
and low use states are correspondingly small. It is these small absolute
differences that typically form the basis for statistical inferences about the
deterrent effect of the death penalty in the panel-type studies. The second
problem results from the relative infrequency of homicide in small states.
Eight states in Table 2-3 averaged fewer than 50 homicides per year for
the 1990-1999 period. Overall, in absolute terms, the numbers of death
sentences and executions has been very small. It is these rare events that
are the basis for trying to determine what would-be murderers calculate to
infer the risk of execution.
The infrequency of executions has been interpreted to mean that there
is insufficient variation in the data to detect the effect of capital punishment
(see, e.g., Donohue and Wolfers, 2005, p. 794). However, the problem is
not that a deterrent effect cannot be estimated from the data: as shown in
Table 4-1, there is no shortage of statistically significant results that are re-
ported. Rather, the problem is that the inferences drawn from those data on
the impact of the death penalty rest heavily on unsupported assumptions.
Although many methodological approaches have been used in the research
and analyses, the challenge is to identify credible and informative assump-
tions that can be combined with the data to draw valid inferences on the
deterrent effect of capital sanctions. These issues are discussed further in
Chapter 4 on panel studies.
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
24
TABLE 2-3 Death Sentences, Executions, and Homicides by State: 1990-1999
Jurisdiction Death Sentences Executions Homicides
Death Sentences
per Homicide
Executions
per Homicide
Alabama
a
155 12 3,608 0.0430 0.0033
Arizona 85 19 3,319 0.0256 0.0057
Arkansas 51 21 2,136 0.0239 0.0098
California 334 7 28,781 0.0116 0.0002
Colorado 4 1 1,741 0.0023 0.0006
Connecticut 5 0 1,448 0.0035 0
Delaware 21 10 260 0.0808 0.0385
Florida
b
185 22 5,711 0.0324 0.0039
Georgia 88 8 6,159 0.0143 0.0013
Idaho 11 1 319 0.0345 0.0031
Illinois 113 12 10,775 0.0105 0.0011
Indiana 26 5 3,931 0.0066 0.0013
Kansas
c
0 0 304 0 0
Kentucky 25 2 2,134 0.0117 0.0009
Louisiana 79 6 6,409 0.0123 0.0009
Maryland 18 3 5,040 0.0036 0.0006
Mississippi 67 0 2,953 0.0227 0
Missouri 83 39 4,320 0.0192 0.009
Montana
d
2 2 162 0.0123 0.0123
Nebraska 5 3 491 0.0102 0.0061
New Hampshire
e
0 0 174 0 0
New Jersey 20 0 3,313 0.006 0
New Mexico 5 0 1,450 0.0034 0
New York 5 0 15,227 0.0003 0
North Carolina 237 11 6,123 0.0387 0.0018
Ohio 127 1 5,337 0.0238 0.0002
Oklahoma 109 19 2,226 0.049 0.0085
Oregon 32 2 1,129 0.0283 0.0018
Pennsylvania 151 3 6,410 0.0236 0.0005
South Carolina 63 21 3,007 0.021 0.007
South Dakota 4 0 110 0.0364 0
Tennessee 57 0 4,492 0.0127 0
Texas 343 162 16,120 0.0213 0.01
Utah 5 3 518 0.0097 0.0058
Virginia 62 63 4,562 0.0136 0.0138
Washington 18 3 2,203 0.0082 0.0014
Wyoming 1 1 141 0.0071 0.0071
NOTE: Table includes only states with the legal authority for use of the death penalty for some part of this period.
a
Alabama data include only 1990-1998 because homicide rates were not available for 1999.
b
Florida data include only 1990 and 1992-1996 because homicide rates were not available for 1991 and 1997-1999.
c
Kansas data include only 1991-1992 because homicide rates were not available for 1993-1999.
d
Montana data include only 1991, 1992, and 1995 because homicide rates were not available for 1993 and 1994.
e
New Hampshire data include only 1990-1996 and 1998-1999 because homicide rates were not available for 1997.
SOURCES: Data on executions from Espy and Smykla (2004), data on death sentences from Death Penalty Information Center (2010a), data on
homicides from Bureau of Justice Statistics (2009).
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
25
TABLE 2-3 Death Sentences, Executions, and Homicides by State: 1990-1999
Jurisdiction Death Sentences Executions Homicides
Death Sentences
per Homicide
Executions
per Homicide
Alabama
a
155 12 3,608 0.0430 0.0033
Arizona 85 19 3,319 0.0256 0.0057
Arkansas 51 21 2,136 0.0239 0.0098
California 334 7 28,781 0.0116 0.0002
Colorado 4 1 1,741 0.0023 0.0006
Connecticut 5 0 1,448 0.0035 0
Delaware 21 10 260 0.0808 0.0385
Florida
b
185 22 5,711 0.0324 0.0039
Georgia 88 8 6,159 0.0143 0.0013
Idaho 11 1 319 0.0345 0.0031
Illinois 113 12 10,775 0.0105 0.0011
Indiana 26 5 3,931 0.0066 0.0013
Kansas
c
0 0 304 0 0
Kentucky 25 2 2,134 0.0117 0.0009
Louisiana 79 6 6,409 0.0123 0.0009
Maryland 18 3 5,040 0.0036 0.0006
Mississippi 67 0 2,953 0.0227 0
Missouri 83 39 4,320 0.0192 0.009
Montana
d
2 2 162 0.0123 0.0123
Nebraska 5 3 491 0.0102 0.0061
New Hampshire
e
0 0 174 0 0
New Jersey 20 0 3,313 0.006 0
New Mexico 5 0 1,450 0.0034 0
New York 5 0 15,227 0.0003 0
North Carolina 237 11 6,123 0.0387 0.0018
Ohio 127 1 5,337 0.0238 0.0002
Oklahoma 109 19 2,226 0.049 0.0085
Oregon 32 2 1,129 0.0283 0.0018
Pennsylvania 151 3 6,410 0.0236 0.0005
South Carolina 63 21 3,007 0.021 0.007
South Dakota 4 0 110 0.0364 0
Tennessee 57 0 4,492 0.0127 0
Texas 343 162 16,120 0.0213 0.01
Utah 5 3 518 0.0097 0.0058
Virginia 62 63 4,562 0.0136 0.0138
Washington 18 3 2,203 0.0082 0.0014
Wyoming 1 1 141 0.0071 0.0071
NOTE: Table includes only states with the legal authority for use of the death penalty for some part of this period.
a
Alabama data include only 1990-1998 because homicide rates were not available for 1999.
b
Florida data include only 1990 and 1992-1996 because homicide rates were not available for 1991 and 1997-1999.
c
Kansas data include only 1991-1992 because homicide rates were not available for 1993-1999.
d
Montana data include only 1991, 1992, and 1995 because homicide rates were not available for 1993 and 1994.
e
New Hampshire data include only 1990-1996 and 1998-1999 because homicide rates were not available for 1997.
SOURCES: Data on executions from Espy and Smykla (2004), data on death sentences from Death Penalty Information Center (2010a), data on
homicides from Bureau of Justice Statistics (2009).
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
26 DETERRENCE AND THE DEATH PENALTY
REFERENCES
Barnes, K., Sloss, D., and Thaman, S. (2009). Place matters (most): An empirical study of pros-
ecutorial decision-making in death-eligible cases. Arizona Law Review, 51(2), 305-379.
Bureau of Justice Statistics. (2009). Homicide—State Level Trends in One Variable. Available:
http://bjs.ojp.usdoj.gov/dataonline/Search/Homicide/State/TrendsinOneVar.cfm [January
2011].
Bureau of Justice Statistics. (2010). Capital Punishment, 2009—Statistical Tables. U.S. De-
partment of Justice. Available: http://bjs.ojp.usdoj.gov/index.cfm?ty=pbdetail&iid=2215
[December 2011].
Cook, P.J. (2009). Potential savings from abolition of the death penalty in North Carolina.
American Law and Economics Review, 11(2), 498-529.
Death Penalty Information Center. (2010a). Death Sentences in the United States from 1977
by State and by Year. Available: http://www.deathpenaltyinfo.org/death-sentences-united-
states-1977-2008 [September 2011].
Death Penalty Information Center. (2010b). State by State Database. Available: http://www.
deathpenaltyinfo.org/state_by_state [January 2011].
Donohue, J.J., and Wolfers, J. (2005). Uses and abuses of empirical evidence in the death
penalty debate. Stanford Law Review, 58(3), 791-845.
Espy, M.W., and Smykla, J.O. (2004). Executions in the United States, 1608-2002: The Espy
File. Available: http://www.deathpenaltyinfo.org/executions-us-1608-2002-espy-file [De-
cember 2011].
Fagan, J., Zimring, F.E., and Geller, A. (2006). Capital punishment and capital murder:
Market share and the deterrent effects of the death penalty. Texas Law Review, 84(7),
1803-1867.
Rogers, A. (2002). “Success-at long last”: The abolition of the death penalty in Massachusetts,
1928-1984. Boston College Third World Law Journal, 22(2), 281-354.
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
3
Determining the Deterrent Effect of
Capital Punishment: Key Issues
M
any people have strongly held views on the deterrent effect of
the death penalty. To some a deterrent effect is self-evident—who
would not at least take pause before committing murder when
the potential consequence may be forfeiting one’s own life? To others it is
equally self-evident that there is no deterrent effect due to the rarity of the
imposition of the death penalty and the emotionally charged circumstances
of most murders. Both views may have some merit, as the deterrent effect of
the death penalty may vary across persons and circumstances. This chapter
provides an overview of the difficulties of empirical analysis of the potential
deterrent effect. The difficulties arise both from conceptual issues about
how the death penalty might deter and from statistical issues that must be
successfully overcome to measure the size of that effect, if any.
To argue for the deterrent effect of the death penalty in such ways as
“because the death penalty increases the price of murder, there will be less
of it” is to gloss over critical elements of understanding how it might work.
The magnitude of the deterrent effect of the death penalty, including the
possibility of no effect, will depend both on the scope of the legal author-
ity for its use and on the way that legal authority is actually administered.
It might also depend on such factors as the publicity given to executions,
which are beyond the direct control of the criminal justice system.
One reflection of this complexity is that research on the deterrent ef-
fect of capital punishment in the post-Gregg era has itself examined diverse
issues. Some studies have attempted to assess whether the legal status of
capital punishment is related to the homicide rate. And some of these stud-
ies have addressed whether statewide homicide rates are associated with
27
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
28 DETERRENCE AND THE DEATH PENALTY
whether capital punishment is a legally permissible sanction. Other studies
have examined whether homicide rates are associated with moratoriums
on executions ordered by governors or courts. There is also a distinct set
of studies that have examined whether the frequency of and publicity given
to actual executions are related to homicide rates. One part of this research
has examined whether execution events seem to affect homicide rates; an-
other part has examined whether homicide rates are associated with various
measures of the probability of being executed for homicide.
Our overview of key challenges to making an empirical assessment of
the effect of capital punishment on homicide rates is necessarily selective.
There is an enormous research literature on the mechanisms by which
legal sanctions, of which the death penalty is but one, might affect crime
rates. There is also a very large research literature on the econometric and
statistical methods used to estimate the effect of the death penalty on ho-
micide rates. We focus on those issues that are particularly important to
the reviews and critiques of the panel and time-series literatures in Chapters
4 and 5, respectively. These issues include data limitations, factors beyond
the death penalty that contribute to large differences in murder rates across
place and over time, possible feedback effects by which homicide rates
might affect the administration of the death penalty, how sanction risks are
perceived, and the concept of a sanction regime.
There is also a literature that examines the argument that executions
may actually exacerbate homicide rates through a brutalization effect. This
argument has been studied using the same statistical tools as deterrence,
although the mechanism being studied is different. With one exception, all
of these are time-series studies, and we review them in Chapter 5.
CONCEPTS OF DETERRENCE
Going back at least 200 years to the legal philosophers Cesare Beccaria
in Italy and Jeremy Bentham in England, scholars have speculated on the
deterrent effect of official sanctions. At its most basic level, deterrence is typi-
cally understood as operating within a theory of choice in which would-be
offenders balance the benefits and costs of crime. In the context of murder,
the benefits may be tangible, such as pecuniary gain or silencing a potential
witness, but they may also involve intangibles, such as defending one’s honor,
expressing outrage, demonstrating dominance, or simply seeking thrills. The
potential costs of crime are comparably varied. Crime can entail personal
risk if the victim resists (see, e.g., Cook, 1986). It may also invoke pangs of
conscience or shame (see, e.g., Braithwaite, 1989).
In this report we are mainly concerned with the response of would-be
offenders to the sanction costs that may result from the commission of mur-
der. Such sanction costs will typically include lengthy imprisonment. Properly
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
DETERMINING THE DETERRENT EFFECT OF CAPITAL PUNISHMENT 29
understood, the relevant question regarding the deterrent effect of capital
punishment is the differential or marginal deterrent effect of execution over
the deterrent effect of other available or commonly used penalties. We em-
phasize “differential” because it is important to recognize that the alternative
to capital punishment is not no punishment or a minor punishment such as
probation. Instead, it is a lengthy prison sentence—often life without the
possibility of parole.
The theory of deterrence is predicated on the idea that if state-imposed
sanction costs are sufficiently severe, certain, and swift, criminal activity will
be discouraged. Concerning the severity dimension, a necessary condition for
state-sanctioned executions to deter crime is that, at least for some, capital
punishment is deemed an even worse fate than the possibility of a lifetime
of imprisonment.
1
Severity alone, however, cannot deter. There must also be
some possibility that the sanction will be incurred if the crime is committed.
For that to happen, the offender must be apprehended, charged, successfully
prosecuted, and sentenced by the judiciary. As discussed in Chapter 2, none
of these successive stages in processing through the criminal justice system
is certain. Thus, another key concept in deterrence theory is the certainty of
punishment. Many of the studies of the deterrent effect of capital punishment
attempt to estimate whether homicide rates seem to be affected by variation
in various measures of the likelihood of execution beyond the likelihood of
apprehension and conviction.
Across the social science disciplines, the concepts of certainty and severity
have been made operational in deterrence research in very different ways. In
Becker’s (1968) seminal economic formulation of criminal decision making,
individual perceptions of certainty and severity are assumed to correspond to
reality. The decision to commit a crime is also assumed to correspond with
a precisely formulated set of axioms that define rational decision making. In
contrast, among criminologists, models of criminal decision making are less
mathematically formalized and place great emphasis on the role of percep-
tions. These models also explicitly acknowledge that perceptions of certainty
and severity may diverge substantially from reality and are probably heavily
influenced by experience with the criminal justice system (Cook, 1980; Nagin,
1998). More recent theorizing about criminal decision making also incorpo-
rates insights from behavioral economics on biases in risk perceptions to bet-
ter model the linkage between sanction risk perceptions and reality (Durlauf
and Nagin, 2011; Kleiman, 2009; Pogarsky, 2009). For example, prospect
1
Another way sanctions may prevent crime is by making it physically impossible for the
offender to commit another crime. Execution achieves this end by the death of the offender.
Note, however, that a death sentence will not, on the margin, be more effective in preventing
crime (outside a prison) than the incapacitation that accompanies a sentence of life imprison-
ment without parole.
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
30 DETERRENCE AND THE DEATH PENALTY
theory (Kahneman and Tversky, 1979) predicts that low probability events,
such as execution, are either overweighted compared to models based on
objective probabilities or not considered at all. While each of these perspec-
tives on the deterrence process shares a common view that criminal decision
making involves a balancing of costs and benefits, the conceptualization of
how this balancing occurs varies greatly across theories. Most importantly
for our purposes, the different models are based on different conceptions of
how sanction risks are perceived and affect behavior.
A less studied dimension of the classical formulation of deterrence is the
concept of celerity—the speed with which a sanction is imposed. In the case
of the death penalty, celerity may be a particularly important dimension of the
classical formulation. According to the Bureau of Justice Statistics (2010), the
average time to execution for the executions that occurred between 1984 and
2009 was 10 years. This statistic, however, pertains only to the small minor-
ity of persons sentenced to death who have actually been executed. Only 15
percent of death sentences imposed since 1976 have been carried out. Thus,
some individuals have been on death row for decades and indeed may die by
other causes before they can be executed. Indeed, according to the Bureau of
Justice Statistics (2010, Table 11) there have already been 416 such deaths
(1973-2009) among death row inmates. For these offenders, their sentence
was, in fact, equivalent to a life sentence.
The studies we review do little to reveal the underlying mechanisms that
generate the associations that are estimated between the death penalty and the
homicide rate. Indeed, it is possible that these associations reflect social pro-
cesses that are distinct from deterrence in the narrow sense discussed above.
For example, Andenæs (1974) and Packer (1968) speculate that independent
of the sanctions prescribed in the criminal laws, the laws themselves may
reduce the incidence of the prohibited acts by moral education and related
social processes. Thus, providing the legal authority for the use of the death
penalty for a special class of murders might prevent murders of that type by
making clear that these types of murder are deemed particularly heinous.
Alternatively, the brutalization hypothesis predicts the opposite effect.
Given these possible and unknown underlying mechanisms, in the re-
mainder of this report we discuss empirical estimates of the effects of the
death on the homicide rate, not “deterrent” effects. Even more important
than this point of nomenclature are the implications of alternative possible
mechanisms for using empirical findings on the death penalty effects to
predict effects on the crime rate of alternative sanction regimes. As we dis-
cuss below, alternative mechanisms can imply very different inferences and
interpretations. We emphasize this point because the issue of mechanisms is
one of several reasons that inferences about the causal effect of capital pun-
ishment on homicide rates cannot be reduced to a simple statistical exercise:
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
DETERMINING THE DETERRENT EFFECT OF CAPITAL PUNISHMENT 31
the validity of the inferences also depend on the validity of the theories used
to construct the statistical models that generate the estimated effects.
The mechanism by which capital punishment might affect homicide
rates also has implications for the time frame over which the effect oper-
ates. The socialization processes about which Andenæs (1974) and Packer
(1968) speculate would likely take years or even decades to materialize and
if present would probably operate gradually. Gradual change over long time
frames, even if cumulatively large, is often extremely difficult to measure
convincingly.
Another issue related to time frame, to which we return in the conclu-
sions of this report, is the processes by which perceptions of sanction risk
are formed and are influenced by changes in sanction policy. For example,
immediately following the Gregg decision, 33 states had capital punishment
statutes in place (see Chapter 2). Individual states subsequently followed
very different paths in the frequency, relative to the murder rate, with which
death penalties were imposed and carried out. If would-be murderers are re-
sponsive to this relative frequency, it would take time for them to calibrate
the intensity in the state in which they reside and to recognize any changes
in intensity resulting from policy shifts. Thus, any effect on homicide rates
of changes in the frequency of execution may not occur until after some
unknown interval.
The remainder of this chapter lays out key challenges to estimating the
causal effect of capital punishment on murder rates. Many of these chal-
lenges stem from the necessity of using nonexperimental data to estimate
this effect. A useful way of conceptualizing these challenges is to note the
important differences between data generated from experiments and data
generated under nonexperimental conditions. In an experiment, the effec-
tiveness of a treatment is tested by administering the treatment to a ran-
domly selected group of subjects and comparing their outcomes to another
group of randomly selected subjects who receive the control treatment.
Randomization of treatment status is intended to ensure the equivalence of
the treatment and control groups except for treatment status. The purpose
of an experiment is to measure the effect of a specified treatment on one or
more outcomes relative to an alternative treatment, generally referred to as
the control treatment. Experiments are a widely accepted way of scientifi-
cally testing for causal effects: there is general agreement that the findings
are reflective of causal effects.
For obvious reasons, it is not possible to conduct a randomized capital
punishment experiment. Suppose, however, that such an experiment were
possible. In such an experiment, three key features would be relevant: (1)
specification of what constitutes treatment, (2) randomization of the capi-
tal punishment treatment, and (3) experimental control of the treatment.
In addition, in an experiment, the experimental and control treatment al-
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
32 DETERRENCE AND THE DEATH PENALTY
ternatives must be specified prior to the beginning of the experiment, and
treatment status is controlled by the experimenter, not the subjects of the
experiment. We develop below the implications of each of the features of
experiments for the study of the effect of capital punishment with nonex-
perimental data.
SANCTION REGIMES
A sanction regime defines the way a jurisdiction administers a sanc-
tion. In an experiment, the differences between the sanction regimes in the
treatment and control jurisdictions would define what constitutes treat-
ment. In a capital punishment jurisdiction, specification of the sanction
regime would require a delineation of the types of crimes and offenders that
would be eligible for capital punishment and the rules that would be used
to determine whether an eligible offender could be sentenced to death. It
would also require a specification of the appeals and pardon processes. In
addition, sanctions for individuals not sentenced to death would have to
be specified. The sanction regime in a jurisdiction without capital punish-
ment would have to be similarly specified. Such an experiment, therefore,
would not test the efficacy of “capital punishment” in the abstract. Instead,
it would test a particular capital punishment against a specific alternative
regime without capital punishment. Only after specification and assignment
of the capital and noncapital sanction regimes could the experiment begin
and the data collected.
By contrast, in studies based on nonexperimental data, sanction re-
gimes are not specified and assigned prior to data collection. Instead, the
researcher has to make assumptions about the theoretically relevant dimen-
sions of the sanction regimes of the entities administering the punishment,
usually states. Thus, a key question in an assessment of the validity of a
capital punishment study involves those assumptions: How convincingly
does a study specify and explain aspects of the capital punishment sanction
regime it is studying?
The legal status of the death penalty in the jurisdiction is one relevant
dimension of a sanction regime. States with and without the death penalty
have clearly defined differences in their sanction regimes. However, the
numerous differences across states in the types of offenses that are capital
eligible and the administrative processes related to the imposition and ap-
peal of the death sentences (as described in Chapter 2) may be relevant to
defining aspects of the sanction regime that have the potential to influence
deterrence. For example, Frakes and Harding (2009) attempt to examine
whether the explicit delineation of the killing of a child as an aggravating
circumstance for the use of the death penalty deters child murder. Still
another important dimension of the sanction regime is the severity of non-
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
DETERMINING THE DETERRENT EFFECT OF CAPITAL PUNISHMENT 33
capital sanctions for murder in both capital and noncapital punishment
states, a point we return to below.
A sanction regime is also defined by how aggressively the authority
to use the death penalty is actually applied. Among states that provide
authority for the use of the death penalty, the frequency with which that
authority is used varies greatly. As pointed out in Chapter 2, since 1976
three states—Florida, Texas, and Virginia—have accounted for more than
one-half of all executions carried out in the United States, even though 40
states and the federal government provided the legal authority for the death
penalty for at least part of this period. Constructing measures of the inten-
sity with which capital punishment is used in states with that authority is a
particularly daunting problem. In an experiment, the intensity of applica-
tion would have to be specified ex ante by delineating the circumstances in
which capital punishment should be applied. With nonexperimental data,
intensity must be inferred ex post by the rate of application. The panel stud-
ies calculate intensity by an assortment of measures of the probability of ex-
ecution based on variations over time and among states in the frequency of
executions to distinguish, for example, the very different sanction regimes
of Texas and California. Chapter 4 discusses these measures at length.
The concept of deterrence predicts that one relevant dimension of a
sanction regime is the probability of execution given conviction for a capital
eligible murder. However, if deterrence is predicated on the perception of
the risk of execution, short-term or even longer term variations in the rate
of executions may not produce changes in the homicide rate, even if the
death penalty is a deterrent. If such temporal variation in the actual rate
of administration is perceived as confirming stable perceptions about this
probability, rather than signaling change in the probability, such variations
will not be associated with changes in the homicide rate even though the
intensity of the use of capital punishment does deter.
An example from gambling on the outcome of the role of a dice can
illustrate this point. Suppose a person knows that the dice are fair. For that
person, the actual outcomes of successive roles of the dice will not cause the
person to change the estimate that the chance of each number is 1/6. There-
fore, that person’s betting patterns will not change in response to short-term
variations in the frequency of each of the numbers 1 to 6. The analog for
deterrence research is that variations over time in the actual frequency of
executions may not alter would-be murderers perceptions of the risk of
execution and therefore not alter behavior even if there is a deterrent effect.
However, it is possible that perceptions are influenced by the actual
outcomes. If so, a bettor’s betting pattern would change in response to the
outcomes of the dice rolls. But if this is the case, it is necessary to posit
a specific model of how those perceptions change to infer how behavior
changes. For example, the so-called gambler’s fallacy (Gilovich, 1983) pos-
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
34 DETERRENCE AND THE DEATH PENALTY
its that if one number, say 6, is rolled several times in a row, people will
surmise that the probability of a 6 is reduced at least temporarily and thus
reduce their betting on 6. In the context of deterrence, the gambler’s fallacy
model suggests that the event of an execution might increase, not decrease,
murders because people will surmise that the probability of execution has
declined at least temporarily. Alternatively, people may surmise that the
dice is weighted to favor 6 and therefore increase their betting on 6. Under
this model, the event of an execution might cause individuals to increase
their perception of the risk of execution and thereby reduce the murder
rate. We do not specifically endorse any of these models of risk percep-
tion. Our purpose in this discussion is to emphasize that in the analysis of
nonexperimental data, the sanction regime must be constructed ex post on
the basis of the researcher’s assumptions about theoretically relevant con-
structs. In turn, this fact implies that the relevant dimensions of a sanction
regime cannot be specified outside of a model of sanction risk perceptions
and their effect on behavior.
It is a truism that sanction threats cannot deter unless at least some
would-be offenders are aware of the threat. There is a large literature on
sanction risk perceptions that demonstrates that the general public is very
poorly informed about actual sanction levels and the frequency of their im-
position (Apel, in press). These studies might be interpreted as demonstrat-
ing that legal sanctions cannot deter (since people do not really know what
they are). This interpretation neglects the possibility that some would-be
offenders may be deterred by the mere knowledge that there is a criminal
sanction even if the severity of the sanction is not specifically known to
them. Moreover, most people do not commit crimes for a host of reasons
that are unrelated to the certainty and severity of criminal sanctions. These
people have no reason to know, for example, the frequency with which
executions are carried out, because they have no intention of committing
murder. Some degree of deterrence only requires that some people who are
actively considering committing a crime are aware of the penalties and that
their behavior is influenced by this awareness.
Still, as the dice example illustrates, the issue of how the death penalty
sanction is perceived is fundamental to the interpretation of the evidence on
its deterrent effect. Consider an actual, not hypothetical, example. Donohue
and Wolfers (2005) compared trends in homicide rates between states with
and without capital punishment from 1960 to 2000, a period that spans
the 1972 Furman decision that stopped use of the death penalty and 1976
Gregg decision that reinstated it. The time-series data for the two states
closely track each other, with no obvious perturbations at the time of the
Furman and Gregg decisions. From these data one could conclude there
is no obvious evidence that the moratorium on capital punishment or its
reinstatement had an effect on murder rates. However, because the last ex-
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
DETERMINING THE DETERRENT EFFECT OF CAPITAL PUNISHMENT 35
ecution prior to the Furman decision was in 1967 and executions were rare
throughout the 1960s, there are two very different possible interpretations
of the data. One interpretation is that the deterrent effect of the potential
for a death sentence is small or nonexistent. The other is that the near ab-
sence of executions in the decade prior to Furman resulted in people’s stable
perceptions in both abolitionist and nonabolitionist states that there was no
realistic chance of the death penalty being imposed. With such perceptions
there would be no possibility of a deterrent effect even if would-be murder-
ers would otherwise be deterred by the threat of execution.
The issue of how sanction threats are perceived is also important in
correctly interpreting evidence that is taken as reflecting deterrence. For
example, some time-series studies report evidence that suggests reduced
homicides in the immediate aftermath of an execution. Suppose this is, in
fact, a reflection of a causal effect of an execution on murder. Depending
on how the threat of execution is perceived, there are a number of very dif-
ferent interpretations of this evidence. One possible model of perceptions
is that people respond to the event of an execution, with each execution
reducing the number of murders that would otherwise occur according to
a dose-response relationship relating murders averted to number of execu-
tions in a given time frame. A second model is that people respond not
to the event of an execution but to the perceived probability of execution
given commission of a murder, and that the event of an execution causes
them to update this perceived probability. In this model, the number of
both executions and murders is relevant to the updating process. Unlike the
first model, there is no single dose-response relationship between number
of executions and murders. If the frequency of execution does not keep
pace with the rate of increase in murders, would-be murderers might infer
that the probability of execution is declining. Yet a third model of such
time-series evidence is that the event of an execution only alters the timing
of the murder—a murder averted in the immediate aftermath of an execu-
tion occurs at a later date. We do not endorse any of these interpretations:
we offer them to make concrete the proposition that the interpretation of
evidence requires a model of sanction risk perceptions and of the effect of
those perceptions on behavior.
2
2
We also emphasize that this same observation about the need for a model of sanction risk
perceptions and their influence on behavior applies to the interpretation of evidence from an
experiment. Only in an impossibly idealized experiment would it be possible to specify the
sanction regime in such detail to avoid the need to extrapolate from the experimental findings
to explain their implications for unspecified aspects of the sanction regime. Furthermore, even
with a completely specified sanction regime, extrapolation of the findings to other settings or
modified versions of the tested sanction regime would require a theory of perceptions and
behavior.
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
36 DETERRENCE AND THE DEATH PENALTY
DATA ISSUES
In any empirical study it is important to question the adequacy of the
data used in the analysis. In the context of the studies reviewed for this
report a key question is whether the data being used are adequate to pro-
duce credible estimates of the effects of those aspects of the sanction regime
under investigation.
As noted above, most studies of the deterrent effect of capital punish-
ment are based on U.S. data. Although the U.S. data on murder show far
less underreporting than data on other types of crime, the data on murders
contain flaws that are important to recognize in studies on deterrence. The
murder rates used in most studies include murders that are not eligible
for capital punishment, either because of characteristics of the perpetrator
(such as age or IQ) or because of characteristics of the offense (such as the
absence of legally defined aggravating factors). The supplemental homicide
reports, a dataset compiled by the Federal Bureau of Investigation (FBI)
that provides more detailed data on homicide incidents than the agency’s
standardized Uniform Crime Report, in principle provide details of the
perpetrator and the event that allow researchers to exclude murders that
likely are not eligible for capital punishment; but these data have their own
set of problems due to widespread recording errors and omissions about
characteristics of the perpetrator and the event itself (Messner, Deane, and
Beaulieu, 2002; Wadsworth and Roberts, 2008).
As we emphasize above, the deterrent effect of capital punishment is a
meaningful concept only relative to another key dimension of the sanction
regime—the severity of noncapital sanctions. After all, as a practical ques-
tion of public policy, the key question is not whether a hypothetical capital
punishment regime in which execution is the only available sanction for
murder would deter some offenders. Rather, it is whether a plausible capital
punishment regime will have a meaningful incremental effect on homicide
rates in the United States when added to a specific program of lesser sanc-
tions. Hence, state-level data on alternative punishments are necessary,
most specifically, the prison sentence lengths for murders that might also
be candidates for capital punishment.
Such data do not exist. This gap is potentially a serious one for studying
deterrence. If the severity of noncapital sanctions for murder is correlated
with the legal status or the frequency of use of capital punishment, failure
to account for the severity of noncapital sanctions may result in serious
bias in estimates of deterrent effect. If, for example, capital punishment ju-
risdictions tended also to impose more severe imprisonment sanctions than
noncapital jurisdictions, a reduced level of homicide in such jurisdictions
may be attributable to these other features of their sanction regime and not
to the death penalty. Or, if capital punishment jurisdictions are otherwise
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
DETERMINING THE DETERRENT EFFECT OF CAPITAL PUNISHMENT 37
more lenient, any deterrent effect achieved by adding capital punishment
might not translate into a similar effect of adding capital punishment in a
jurisdiction that already imposes severe prison sentences for murder. Or, if
a state relied on the threat of capital punishment to counter an inadequate
budget for investigating and prosecuting crimes, the deterrent effect of capi-
tal punishment might be masked relative to a noncapital punishment state
with more effective crime control policy. Again, we do not endorse any of
these hypotheses, but delineate them to illustrate the difficulty of isolating
deterrent effects of a single component of any sanction regime.
VARIATIONS IN MURDER RATES
The severity of noncapital sanctions is but one example of other factors
that may affect murder rates. If the data being analyzed were the product
of a randomized capital punishment experiment, the question of how other
factors influence murder rates would not have to be addressed. Randomiza-
tion of the capital punishment sanction regime would insure that the use of
capital punishment was uncorrelated with other factors influencing murder
rates. Thus, for example, if a capital punishment sanction regime were
randomized across states, capital punishment would not be more common-
place in the Southern states, as in practice it is. By breaking the correlation
between treatment, in this case capital punishment, and other factors that
may be influencing the outcome of interest, in this case murders, random-
ization ensures that the capital punishment deterrent effect estimate is not
contaminated by the independent influence of these other factors on murder
rates. Because capital punishment research is based on nonexperimental
data, equivalence of states without and without capital punishment on all
other factors is not insured. Hence, consideration of the influence of factors
other than capital punishment on murder rates must be addressed.
Homicide rates in the United States vary enormously over time and
place. In 2009, Louisiana had the highest statewide rate, 11.8 homicides
per 100,000 population; the state with the lowest rate, New Hampshire,
had 0.8 homicides per 100,000 population, 93 percent fewer (Bureau of
Justice Statistics, 2010; Federal Bureau of Investigation, 2010). Variations
over time are also large. Figure 3-1 plots the U.S. homicide rate over the
25-year period from 1974 to 2009. From 1974 to the early 1990s, the rate
rose, then fell, then rose again, and then began declining steadily until level-
ing off in the early 2000s.
As we emphasize throughout this report, these variations are important
to making a valid determination of the deterrent effect of the death penalty,
because if other influences on the murder rate are correlated with the use
of the death penalty, the estimated deterrent effect may be contaminated
by the effect of these other influences on the homicide rates. Such other
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
38 DETERRENCE AND THE DEATH PENALTY
influences may reflect factors related to the criminal justice system. One
has already been described: the severity of noncapital sanctions. Another
is police effectiveness in apprehending murderers. If the probability of ap-
prehension is correlated with the imposition of the death penalty, a finding
that the death penalty seemingly deters murders might actually reflect police
effectiveness in deterring murder. Such contamination may also come from
social, economic, or political factors that affect the homicide rate and that
are outside the criminal justice system.
There have been numerous commentaries on the sources of variation
in U.S. homicide rates, with many focusing specifically on the sharp drop
in homicides since the early 1990s (Blumstein and Wallman, 2000, 2006;
Levitt, 2004; Zimring, 2010; Zimring and Fagan, 2000). However, these
commentaries provide very limited guidance on how to account for other
possible sources of change in homicide rates in a statistical analysis of the
deterrent effect of the death penalty.
To provide a concrete illustration of the challenges of inferring the
deterrent effects of the death penalty, consider Texas, the state that makes
the most frequent use of the death penalty (in absolute numbers). Figure 3-2
plots the annual frequency of executions in Texas from 1974 to 2009.
Texas’s first post-Gregg execution occurred in 1982, and executions re-
0
2
4
6
8
10
12
1974 1979 1984 1989 1994 1999 2004 2009
Homicide Rate per 100,000
R02175
Figure 3-1
vectors, editable
Year
FIGURE 3-1 Homicide rates in the United States: 1974 to 2009.
SOURCES: Data from Bureau of Justice Statistics (2010) and Federal Bureau of
Investigation (2010).
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
DETERMINING THE DETERRENT EFFECT OF CAPITAL PUNISHMENT 39
0
5
10
15
20
25
30
35
40
45
1974 1979 1984 1989 1994 1999 2004 2009
Executions in Texas
R02175
Figure 3-2
vectors, editable
Year
FIGURE 3-2 Executions in Texas: 1974 to 2009.
SOURCES: Data from Espy and Smykla (2004) and Texas Department of Criminal
Justice (2011).
mained relatively infrequent until the early 1990s; the frequency then esca-
lated rapidly to a peak of 40 in 2000. Thereafter, there has been drop-off
to about 20-25 per year. Figure 3-3 plots the homicide rate in Texas (as
well as California and New York) over the same period. The pattern for all
three states closely resembles the U.S. national trend. From 1974 through
the early 1990s the Texas homicide rate rose then fell and then rose again
before falling steadily from 1991 to the early 2000s, when it leveled off. For
the period from 1976 to 1991, there is no apparent relationship between
the homicide rate and the frequency of execution. However, the steady
decline in the homicide rate since 1991 does correspond with the dramatic
increase in executions that occurred in the early 1990s. Thus, if the early
1990s is assumed to be the demarcation of Texas shifting to a dramatically
higher use of capital punishment, the data are consistent with that shift
having a deterrent effect.
However, the data from California and New York challenge that in-
terpretation. The death penalty has been an available sentencing option in
California for the entire post-1976 period, but the frequency of executions
in California is low in comparison with Texas—from 1976 to 2009, Cali-
fornia executed 13 people, and Texas executed 447. Both states, however,
sentenced sizable numbers of people to death. In this regard, New York
offers still another interesting contrast. It sentenced only 10 people to
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
40 DETERRENCE AND THE DEATH PENALTY
death between 1973 and 2009 and had executed none as of 2009 (Bureau
of Justice Statistics, 2010).
3
As shown in Figure 3-3, the California, New York, and Texas homicide
rates move in close unison for the entire 1974-2009 period. Like Texas, the
California and New York rates rise, then fall, and then rise between 1974
and the early 1990s; the rates for all three states then begin a steep decline
to the early 2000s and level out. Thus, even though California, New York,
and Texas have made very different use of the death penalty, particularly
since 1990, their homicide rates are remarkably the same over about three
decades.
Our purpose in reporting these data is not to draw any conclusion
about the deterrent effect of the death penalty. The three states were pur-
posely selected to illustrate the importance of accounting for variations,
across time and place, in factors that influence murder rates other than the
use of capital punishment. If informal comparisons of data from a few self-
selected jurisdictions were sufficient to settle the question of the deterrent
effect of the death penalty, the reviews of the panel studies in Chapter 4 and
the of time-series studies in Chapter 5, which are based on application of
3
In New York, the legal authority for the death penalty was available only from 1995 to
2007.
0
2
4
6
8
10
12
14
16
18
1974 197919841989 1994 1999 2004 2009
Homicide Rates per 100,000
Texas
New York
California
Year
R02175
Figure 3-3
vectors, editable
FIGURE 3-3 Homicide rates in California, New York, and Texas: 1974 to 2009.
SOURCES: Data from Bureau of Justice Statistics (2010) and Federal Bureau of
Investigation (2010).
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
DETERMINING THE DETERRENT EFFECT OF CAPITAL PUNISHMENT 41
formal statistical methods, would be unnecessary. For example, the panel
studies are based on data from all 50 states, not just three selected ones.
In addition, and most critically, any inferences about the effects of the
death penalty that are based on the data reported in Figure 3-3 require
a conception—that is, a plausible hypothesis—of how the death penalty
might affect homicide rates. Suppose, as is assumed in some of the time-
series studies reviewed in Chapter 5, the residents of these three states
respond to deviations away from their state’s long-term trend in executions
or death sentences and not to the trend lines themselves. Informal inferences
based on visual inspection of long-term homicide rates and death penalty
sanction trends cannot provide the basis for detecting such relationships:
in Chapter 5 we apply the formal statistical methods that can detect those
relationship. More generally, if valid inferences about the effect of the death
penalty on homicide rates could be drawn from superficial analysis of data
plots like those in Figure 3-3, the question of its effect would have been
settled long ago. For the committee’s discussion of this point, see the section
on cross-polity comparisons in Chapter 5.
RECIPROCAL EFFECTS BETWEEN HOMICIDE
RATES AND SANCTION REGIMES
In an experiment, one very important consequence of random as-
signment of treatment is that treatment assignment is not affected by the
outcome of interest. For example, in a randomized experiment of the ef-
fectiveness of a therapy in reducing depression, the probability of partici-
pants receiving the experimental treatment is not influenced by their level
of depression at the time of treatment assignment. As a consequence, the
direction of causality is clear—any difference in symptoms of depression
between the experimental and control groups is a consequence of the treat-
ments assigned and not of the level of depression at the time of treatment.
In analyses of nonexperimental data, attribution of direction of causality in
an association between two variables is often far less clear.
Going back to deterrence research in the 1960s, there has been con-
cern about the possibility that estimates of deterrent effects were biased by
reciprocal effects between crime rates and sanction levels. That is, while
sanction levels may be influencing crime rates through the processes of de-
terrence, crime rates may simultaneously be affecting sanction levels. Crime
rates may influence sanctions by a variety of mechanisms. One possibility is
that, in the short run, increases in crime may strain the resources committed
to the criminal justice system and result in a reduction in overall effective
sanction levels. Over the longer term, the political process might respond
to rising crime rates by increasing the resources committed to crime control
and increasing the severity of sanctions.
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
42 DETERRENCE AND THE DEATH PENALTY
The possibility of reciprocal effects greatly complicates estimation of
the deterrent effect of capital punishment. For example, suppose that states
with high rates of executions (as measured by the percentage of homicides
that result in executions) tend also to have lower homicide rates. One in-
terpretation of this negative association is deterrence: that is, more certain
application of the death penalty reduces murders. However, if there are
reciprocal effects of crime rates on sanction levels, this negative association
might just as well reflect the resource saturation effect noted above: that is,
higher murder rates and crime rates tend to overwhelm the capacity of the
justice system to respond to crime. Higher crimes rates may, for example,
reduce the effectiveness of police in apprehending criminals or may make
overburdened prosecutors more receptive to accepting plea bargains for
noncapital sanctions in order to avoid trials. Both such mechanisms could
contribute to reductions in the frequency of executions.
The possibility of reciprocal causation is not addressed in the time-
series research, and only a subset of studies in the panel research make any
attempt to address this very challenging problem. Given enough assump-
tions, it is possible to disentangle empirically causal effects in the presence
of reciprocal causation. Thus, in principle, in the above example, the de-
terrent effect of execution certainty can be distinguished from the effect of
murder rates on execution certainty. However, such analysis requires the
imposition of what are called “identification restrictions.” Identification
restrictions can come in many forms, and isolating the role of any one
restriction is difficult and sometimes impossible.
In the panel studies in which reciprocal causation is addressed, an
important component of identification involves the use of “instrumental
variables.” Chapter 4 includes an extended discussion of the validity of
the assumptions that underlie the instrumental variable applications in
that research. Here we emphasize only that in the presence of reciprocal
causation, estimation of causal effects ultimately depends on more than
just the data. This is still another example of the fact that the validity of
the estimates of the effects of deterrence depends significantly on model-
ing assumptions—in this case the plausibility of untestable assumptions
about identification restrictions. This is not, by itself, a fatal criticism, since
identification restrictions can often be derived from social science theories.
However, not all assumptions are equally plausible, so their validity has to
be judged in context.
The presence of reciprocal effects also complicates the interpretation of
findings on the deterrent effect of the death penalty even if based on plausi-
ble identification restrictions. For example, suppose that a state changes its
death penalty sanction regime by expanding the types of murders that are
eligible for the death penalty and that this change has the desired deterrent
effect, which is estimated, based on plausible identification restrictions, to
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
DETERMINING THE DETERRENT EFFECT OF CAPITAL PUNISHMENT 43
reduce the murder rate by 5 percent. In the presence of feedback effects, the
ultimate reduction in the murder rate will not be 5 percent: it may be more
or it may be less because the change in the murder rate may affect other
aspects of the sanction regime, such as the way prosecutors and defense
attorneys approach plea bargains or the resources available to the criminal
justice system. These changes, in turn, may further influence the murder
rate. Furthermore, the sentencing regime that caused the 5 percent reduc-
tion may differ from a regime without the death penalty, not just because
of the possibility of a death sentence, but also because the availability of
the death penalty as an option provides prosecutors with greater leverage
in plea negotiations (which may result in a greater number of long prison
sentences) and because the extra resources required to try capital cases may
affect the resources available to prosecute and try other crimes.
In North Carolina, for example, 25 percent of first-degree murder cases
are initially prosecuted capitally. Each of these cases requires relatively more
resources because of extra care for due process. The in-kind costs include
the equivalent of nine assistant prosecutors each year, as well as 345 days of
trial court time, approximately 10 percent of the resources of the Supreme
Court, and $11 million in cash outlays (Cook, 2009). Only after all these
feedbacks have played themselves out could the ultimate effect of a change
in sanction regime on the murder rate be determined. This kind of feedback
is still another reason that throughout this report we describe empirical
estimates of the effects of the death penalty as effects on the homicide rate,
not as deterrent effects.
SUMMARY
In this and the preceding chapter we lay out some of the key challenges
to using data from the studies reviewed in the next two chapters to infer
the causal effect of the death penalty on the homicide rate. Some of these
challenges can be resolved empirically. For example, with data on the se-
verity of noncapital sanctions, it is possible to test empirically whether the
inclusion of these data in the analysis alters estimates of the causal effect
of capital punishment on murder rates. More generally, it is also possible
to analyze the sensitivity of findings to a specified set of alternative model
specifications. We discuss examples of such tests in those chapters.
However, it is also important to recognize that inferences about the ef-
fect of alternative capital punishment regimes cannot be reduced to purely
statistical questions. Interpretations will always depend on assumptions
about the underlying mechanisms by which sanction regimes affect be-
havior and how behavior in turn affects sanction regimes and that those
assumptions are not testable with the data used in the analysis. As a con-
sequence, inferences about the effects of capital and noncapital sanction
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
44 DETERRENCE AND THE DEATH PENALTY
regimes on murder rates will depend on more than the data that generate
the estimates: the inferences will also depend on the validity of the theories
used to construct the models on which the estimates rest.
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Wadsworth, T.I.M., and Roberts, J.M. (2008). When missing data are not missing: A new ap-
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Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
4
Panel Studies
I
n this chapter, we discuss the recent research that used panel data and
methods to examine whether the death penalty has a deterrent effect on
homicide and if so, the size of this effect. As noted in Chapter 1, “panel
data” and “panel methods” refer to data from many geographic locations
followed over time—usually annual state-level data—and a particular set
of multiple regression methods. The annual state data include all states,
and the time periods covered are typically from the late 1970s (post-Gregg)
through the late 1990s or into the 2000s. Over this time period, there have
been variations in the frequency of death penalty sentences, executions,
and the legal availability of the death penalty. With these types of data,
the strategy for identifying an effect of the death penalty on homicides has
been, roughly speaking, to compare the variation over time in the average
homicide rates among states that changed their death penalty sanctions
versus those that did not.
This chapter assesses the extent to which the research using panel data
is informative on the question of whether and how much the death penalty
has a deterrent effect on homicide. For this assessment, we compare the
data and methods used in this literature with those that would be avail-
able from an ideal randomized experiment (see Chapter 3). The purpose
of this exercise is to clarify the challenges that face researchers using panel
methods to study the death penalty and deterrence. We then assess the ex-
tent to which this research overcomes these challenges.
This literature is striking in the similarity of the data and methods used
across studies and the diversity of the results. Given this diversity of results
47
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
48 DETERRENCE AND THE DEATH PENALTY
across and in some cases within studies, a central task for this committee
is to assess the validity of the models used in the studies.
We begin the chapter by describing the key features of the studies we
reviewed and giving a brief overview of their data and methods. We then
discuss the primary challenges to researchers using panel data and methods
to inform the question of whether the death penalty affects the homicide
rate: the difficulty in measuring changes over time in the relevant sanction
policies for homicide and the difficulties in establishing that any changes in
homicides that are concurrent with changes in the death penalty are caused
by those changes in the death penalty and not vice versa or by other factors
that affect both—such as other sanctions for murder. We conclude with our
assessment of the informativeness of the panel research.
PANEL STUDIES REVIEWED
Methods Used: Overview
We begin our review of the panel research by briefly describing the
regression models used in the studies. Our intention with this description
is to establish the extent to which the methods are largely consistent across
studies, as context for understanding the particular dimensions on which
the studies differ.
The panel research makes use of multiple regression models involving
“fixed effects” that take the following form:
y
it
= a
i
+ b
it
+ gf(Z
it
) + dX
it
+ e
it
, (4-1)
where y
it
is the number of homicides per 100,000 residents in state i in year
t, f(Z
it
) is an expected cost function of committing a capital homicide that
depends on the vector of death penalty or other sanction variables Z
it
with
corresponding parameter g measuring the effect of the death penalty on the
homicide rate. Importantly, this effect is assumed to be homogeneous across
states i and years t.
A primary benefit of panel data is that one observes homicide and ex-
ecution rates in the 50 states over many years. This allows researchers to
effectively account for unobserved features of the state or of the time period
that might be associated with both the application of the death penalty
and the homicide rate. Some states, for example, might have unobserved
social norms that lead to higher (or lower) execution rates and lower (or
higher) rates or homicide: Texas is arguably different than Massachusetts
in this regard. The panel data model in Equation (4-1) accounts for some
of these differences with a state-specific intercept parameter, a
i
, referred to
as a state fixed effect, that allows the mean homicide rate to vary additively
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
PANEL STUDIES 49
by state, and a time-specific intercept, b
it
,
referred to as a time fixed effect,
that allows the mean homicide rate to vary additively over time. These
fixed effects account for unobserved factors that are state specific but fixed
across time, such as the social norms that make Texas different than Mas-
sachusetts, and factors that are year specific but apply to all states, such as
macroeconomic events that may affect homicide rates across the country.
In addition to these fixed effects, some of the researchers also include state-
specific linear time trends that allow each state’s homicide rate trend to vary
(linearly) from the year-to-year national fluctuations.
The literature also includes a set of covariates, X
it
, that are intended to
control for additional factors that may vary with both state and year. These
sets of covariates are largely similar across studies and include economic
indicators, such as the unemployment rate and real per capita income;
demographic variables, such as the proportion of the state’s population in
each of several age groups; the proportion of the state’s population that
is black; and the proportion of the state’s population that reside in urban
areas. The covariates also include health and policy variables, such as the
infant mortality rate, the legal drinking age, and the governor’s party affili-
ation; and crime, policing, or sanctioning variables, such as the number of
prisoners per violent crime.
Finally, e
it
is a random variable that accounts for the unobserved factors
determining the homicide rate.
1
Researchers make two general assumptions
about the relationship between the death penalty variables, Z
it
, and e
it
.
The most common assumption is that the death penalty, as measured by
the variable Z
it
, is statistically independent of the unobserved factors that
determine homicide, as it would be in an ideal randomized experiment.
An alternative route is to assume that there is some covariate, termed an
instrumental variable, that is independent of e
it
but not of the death penalty.
The Studies, Their Characteristics, and the Effects Found
Table 4-1 lists the studies reviewed in this chapter and a few of their
key characteristics, and briefly notes each one’s results.
2
This list does not
1
In estimating these models, the data are typically weighted by state population.
2
One characteristic that is not highlighted in Table 4-1 is the choice of outcome variable,
y
it
.
All of the studies listed in the table and reviewed in this chapter focused on the overall
homicide rate (or the log-rate). However, there are a few studies in the panel data literature
that examined different outcome measures. Most notably, Fagan, Zimring, and Geller (2006)
focused on all capital murders, and Frakes and Harding (2009) examined child murders which,
depending on the state and year, may or may not be death penalty eligible. Otherwise, the key
characteristics of these two studies are similar to the ones reviewed in this chapter. Interest-
ingly, although both studies focused on the impact of the death penalty on capital eligible
murders, Fagan, Zimring, and Geller found no evidence that the death penalty deters murder,
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
50
TABLE 4-1 Panel Studies Reviewed
Study Legal Status Intensity of Use
Use of an
Instrument
Results: Sign
a
and Significance
b
of Point Estimates
Berk (2005) N Y N All possible results
Cohen-Cole et al. (2009) Y Y Y All possible results
Donohue and Wolfers (2005, 2009) Y Y Y All possible results
Dezhbakhsh and Shepherd (2006) Y Y N
**
Dezhbakhsh, Rubin, and Shepherd (2003)
c
Y Y Y
**
; and –
NS
Katz, Levitt, and Shustorovich (2003) N Y N
**
; –
NS
; and +
NS
Kovandzic, Vieraitis, and Boots (2009) Y Y N
NS
; +
NS
Mocan and Gittings (2003) Y Y N
**
; and –
NS
Mocan and Gittings (2010) N Y N
**
; and –
NS
Zimmerman (2004) N Y Y
*
; and –
NS
a
Sign of the estimated coefficients: –, the estimated effect of capital sanctions on homicide is negative, indicating a deterrent effect; +, the
estimated effect of capital sanctions on homicide is positive, indicating a brutalization effect.
b
Statistical significance levels: NS, no statistical significance at p = 0.05; *, p < 0.05; **, p < 0.01.
c
Dezhbakhsh, Rubin, and Shepherd (2003) estimate 55 different panel data regression models. In 49 of the models, the estimated effect of capital
sanctions on homicide is negative and statistically significant; in 4, the estimates are negative and insignificant; and in 2, the estimates are positive
and insignificant.
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
PANEL STUDIES 51
include every study of deterrence using panel data, but instead provides
information on a set of influential studies that use the different approaches
found in the research and that draw a wide range of different conclusions.
Studies designed to illustrate the fragility of the results reports in the lit-
erature, namely, Donohue and Wolfers (2005, 2009) and Cohen-Cole et al.
(2009), apply the same basic models and thus are included in our review.
The first study characteristic is how researchers specify the expected
cost function of committing a capital homicide f(Z
it
). At the most basic
level, studies seek to determine the effect of changes in the legal status of
the death penalty, changes in the intensity with which the death penalty is
applied, or both. Most studies evaluated the intensity of use, but some also
focused on the legal status of the death penalty. The specification of the
death penalty variables in the panel models varies widely across the research
and has been the focus of much debate. The different specifications assume
that quite different aspects of the sanction regime are salient for would-be
murderers. The research has demonstrated that different death penalty
sanction variables, and different specifications of these variables, lead to
very different deterrence estimates—negative and positive, large and small,
both statistically significant and not statistically significant.
The second characteristic of interest is whether the death penalty mea-
sure is assumed to be randomly applied after controlling for the observed
covariates and the fixed effects. The choice of whether or not to use instru-
mental variables, and the particular variables selected, has led to conten-
tious differences in model assumptions invoked across the literature. In
most of the studies, the researchers have assumed that the death penalty is
unrelated to the unobserved factors associated with the homicide rate. That
is, the unobserved factors, e
it
, are not associated with the death penalty
sanctions. Studies using this independence assumption have drawn conflict-
ing conclusions (see Table 4-1) with some reporting statistically significant
evidence in favor of a deterrence effect, many others finding that capital
punishment has a negative but statistically insignificant association with
homicide, and a few others reporting evidence in favor of a brutalization
effect, that capital punishment increases homicide.
Dezhbakhsh, Rubin, and Shepherd (2003) and Zimmerman (2004) ar-
gue that death penalty sanctions are likely to be correlated with unobserved
determinants of homicide, and instead propose using instrumental variables
to provide variation in the risk perceptions of potential murderers that is
separable from the effects of all of the unobserved factors. The results of
and Frakes and Harding reported substantial deterrent effects. Our review does not consider
the choice of the outcome variable: although this choice may have important implications for
inference, these issues are secondary relative to the more fundamental issues covered in this
chapter.
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
52 DETERRENCE AND THE DEATH PENALTY
studies that do not use such instrumental variables vary from those that
do, and the results of studies that use different instrumental variables vary
from each other.
The fact that the estimated effects of the death penalty on homicide
are sensitive to the different data and modeling assumptions used is not
surprising. Deterrence estimates from the panel models depend on state
changes over time in the legal status of the death penalty or the intensity
with which the death penalty is applied. Since the moratorium was lifted,
such changes have been few and far between (see Chapter 2). Because of the
way in which the death penalty has been implemented in the United States
in the last 30 years, no executions occur in most states in most years (86
percent of state-year observations), and when there are any, the number is
almost always very low. In addition, the executions that do occur are con-
centrated in particular states, with Texas carrying out executions an order
of magnitude more often than any other state. There also tends to be little
variability for states over time in their numbers of or rates of executions
and whether they legally allow executions. Only 11 states experienced
one or more changes in legal status of the death penalty after the national
moratorium was lifted. Overall, in recent decades in the United States the
death penalty has been a rare practice that is concentrated in a few places.
Not only is there low variability in the application of the death pen-
alty, there are only a small number of state-year observations that exhibit
large variations in homicide rates over time. Figure 4-1 illustrates a partial
regression plot with a death penalty sanction measure on the horizontal
axis and the homicide rate on the vertical axis (adjusted for state and year
fixed effects and typical covariates). This plot reflects the data, covariates,
and specification used by Kovandzic, Vieraitis, and Boots (2009).
3
In dis-
playing these regression results, the committee is not endorsing this or any
other particular study.
4
Instead, our purpose is to illustrate how outlier or
influential observations may affect regression results. Since the effect of the
death penalty is estimated as the slope of the ordinary least squares regres-
sion line between the bulk of the data near zero and the location of the
small set of influential values, the estimates in the research studies can vary
widely (Berk, 2005). For example, if the particular state-year observations
that are influential depend on the death penalty intensity measure used, then
the slope of the regression line will vary with this measure. If one believes in
the validity of the underlying model applied in Figure 4-1, then the outlier
3
The execution measure is computed using the number of executions the year before the
period year divided by the number of death sentences 7 years prior to the period year. For full
model specification, see Figure 4-1 notes in the figure caption.
4
In particular, we note that alternative but similar specifications result in a positive sloping,
rather than a negative sloping line.
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
PANEL STUDIES 53
FIGURE 4-1 Illustration of influential data points.
NOTES: The plot reflects the data, covariates, and specification used by Kovandzic,
Vieraitis, and Boots (2009), Table 3, Model 6 with the addition of two common
sanction variables: death sentences divided by homicide arrests 2 years prior and
homicide arrests divided by homicides. These additional variables required a mea-
sure of arrests for homicide, which was obtained from J. Wolfers’ web page and was
not available for years after 1998.
The horizontal axis represents the adjusted execution measure (residuals of execu-
tion measure regressed on all the rest of the regressors in the model). The execution
measure is defined as the number of executions the prior year per number of death
sentences 7 years prior, with missing values set to zero.
The vertical axis represents the adjusted homicide rate (residuals of the homicide
rate regressed on all the regressors except the execution rate variable). The homi-
cide rate is homicides per 100,000 residents. The regression was run on data for
1984-1998, weighted by state population share, and standard errors were clustered
by state.
The coefficient of the ordinary least squares line between these two sets of ad-
justed variables—and hence the coefficient on the execution measure in the multiple
linear regression of homicide rates on the execution measure and all covariates—is
–0.183 (p = 0.173).
SOURCES: Data from T.V. Kovandzic (personal communication) and J. Wolfers.
Wolfers’ data are available at http://bpp.wharton.upenn.edu/jwolfers/DeathPenalty.
shtml.
–4 –2 0 2 4
Adjusted Homicide Rate
–1 0 1 2 3
Adjusted Execution Measure
R02175
Figure 4-1 revised
vectors, editable
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
54 DETERRENCE AND THE DEATH PENALTY
observations are informative. But if there is uncertainty about the validity
of the model, the outliers can make the estimates highly sensitive to the
underlying assumptions.
As noted in Chapter 2, the infrequency of executions does not mean
that there is insufficient variation in the data to detect the effect of capital
punishment. In fact, as shown in Table 4-1 (above), there is no shortage of
statistically significant results reported in the literature. Rather, the problem
is that inferences on the impact of the death penalty rest heavily on unsup-
ported assumptions.
SPECIFYING THE EXPECTED COST OF
COMMITTING A CAPITAL HOMICIDE: f(Z
it
)
In light of the variability in the estimated effects of the death penalty
on homicide, a central question is whether the correct specification is being
used and can be identified. We evaluate this question below by first focus-
ing on measures of the perceived cost of murder and then taking up more
generic issues associated with the panel data models in equation (4-1).
A vital component to evaluating the effect of the death penalty on ho-
micide is to properly specify the expected cost function, f(Z
it
), in Equation
(4-1). Yet, researchers have failed to measure the relevant sanction regime
and have relied on seemingly ad hoc measures of the relevant sanction
probabilities.
What is the relevant treatment? Researchers have struggled to clearly
specify and measure the incremental cost of a particular sanction policy. As
noted in Chapter 3, there is little information on the sanction regime, and
thus the counterfactual policy of interest. In particular, the research aims to
determine the effect of an increase (or decrease) in the risk of receiving the
death penalty or being executed relative not to no sanction, but rather rela-
tive to the other common sanctions for murder—lengthy prison sentences
(with or without the possibility of parole). Moreover, these other aspects
of the sanction regime may be changing over time, and any changes in the
risks of the death penalty have to be evaluated relative to the varying but
always higher risks associated with prison sentences. Two mechanisms that
could plausibly create associations between changes in death penalty and
prison sentence sanctions for homicide are the plea bargaining process,
through which the threat of the death penalty may change the likelihood
of sentences of different lengths, including life without parole, and the
punitiveness of a state’s culture, which influences the severity of the capital
and noncapital aspects of the sanction regime.
None of the studies we reviewed made any use of information on other
sanction risks for murder or the ways in which they may be changing over
time. For this reason, it is not possible to tell if any “treatment” effects
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
PANEL STUDIES 55
found in these models are due to death penalty sanction changes or to
changes in other more frequently used sanctions that are part of a state’s
sanction regime for homicide. If changes in the death penalty are part of a
larger “law and order” program, then concurrent changes in other much
more heavily used sanctions could be at the root of any associated change
in homicide rates.
A related problem in specifying a cost function is the ad hoc and in-
consistent measures of subjective sanction probabilities. How do potential
offenders measure the expected cost of committing a capital offense? The
difficulty in answering this question stems from two interrelated problems:
first, there is little information on how offenders perceive the relevant prob-
abilities of arrest, conviction, and execution; and second, in practice, these
probabilities may be difficult to measure.
In the studies we reviewed, one or both of just two features of the death
penalty are assumed to be salient for deterring homicide: the legal status
of the death penalty (in each state and year) and what are described as
measures of the intensity with which the death penalty is applied (in each
state and year). A variety of different and complex temporal structures are
used to measure the probabilities of arrest, death sentence, and execution.
Consider, for example, the specifications used for variables described
as the risk of execution given a death sentence:
• the number of executions in the prior year (prior to the current
year’s homicide rate);
• thenumberofexecutionsintheprioryeardividedbythenumber
of death sentences in the same prior year (or a variant, using a
12-month moving average of these counts for both the numerator
and denominator);
• thenumberofexecutionsinthecurrentorprioryeardividedbythe
number of death sentences in an earlier prior year (3, 4, 5, 6, and
7 years prior have all been implemented and similar specifications
using executions from the first three quarters of the current year
and last quarter of prior year divided by death sentences 6 years
prior);
• thenumberofexecutionsintheprioryeardividedbythenumber
of death row inmates in the prior year;
• thenumberofexecutionsinthecurrentyeardividedbythenumber
of homicides in the prior year;
• thenumberofexecutionsintheprioryeardividedbythenumber
of prisoners in the prior year (or 2 or 3 years prior); and
• thenumberofexecutionsintheprioryeardividedbythepopula-
tion of the state in the prior year.
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
56 DETERRENCE AND THE DEATH PENALTY
There is no empirical basis for choosing among these specifications, and
there has been heated debate among researchers about them, particularly
on the number of years that should be lagged for the numerator and, even
more so, for the denominator in order to best correspond to the relevant
risk of execution given a death sentence in each state and year.
This debate, however, is not based on clear and principled arguments
as to why the probability timing that is used corresponds to the objective
probability of execution, or, even more importantly, to criminal perceptions
of that probability. Instead, researchers have constructed ad hoc measures
of criminal perceptions. Consequently, the results have proven to be highly
sensitive to the specific measures used. Donohue and Wolfers (2005) find,
for example, that when reanalyzing the results in Mocan and Gittings
(2003), using a 7-year lag implies that the death penalty deters homicide
(4.4 lives saved per execution) but using a 1-year lag implies that the death
penalty increases the number of homicides (1.2 lives lost per execution).
Donohue and Wolfers (2005) question whether would-be murderers are
aware of the number of death sentences handed down 7 years prior. Re-
sponding to these concerns, Mocan and Gittings (2010) argue that because
executions do not take place the same year as a sentence is imposed, models
with a 1-year lag are meaningless.
Whether any of these measures accurately reflect the relevant risk prob-
abilities is uncertain. The basic problem is that little is known about how
those who may commit murder perceive the sanctions for this crime. If
the death penalty is going to have an effect on the behavior of this group,
it is their perceptions of the sanction regime for murder that matter. It is
not known whether the current legal status of the death penalty is salient
to potential murderers; other relevant factors could include how often the
legal status of the death penalty has changed in recent years and the pres-
ence of high-profile cases, which create greater awareness of the legality
of the death penalty in a state. Similarly, it is not known whether specific
state and year information is salient to potential murderers; no evidence or
theory is presented in the studies we reviewed to argue that the particular
measures are valid or that alternative measures—such as executions in sur-
rounding states or in one’s own county or executions in the last 5 years or
the last 3 months—are not equally valid. As potential murderers may be
attempting to predict the effective sanction regime several or many years
into the future, when they might be sentenced or executed, it is particularly
unclear what the relevant geographic or time horizon is for obtaining a
salient measure.
Suppose that when deciding whether to commit a crime, potential
murderers weigh the benefits and risks that committing murder may bring
them along with the likelihood of those benefits or risks occurring. In this
setting, the probability of being sentenced to death and henceforth being
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
PANEL STUDIES 57
executed are theorized to be among these perceived risks. The sanction
risks are necessarily based on the individual’s perceptions. Either implicitly
or explicitly, researchers in this field typically make an additional assump-
tion that the risk perceptions of potential murderers are accurate and thus
the perceived risks of receiving a death sentence, being executed, or being
executed within a particular time period, are equivalent to the objective
measures of these risks. The accuracy of this assertion that the risk percep-
tions of potential murderers are correct is questionable. There is no clear
enforcement mechanism or learning process that would create such accu-
racy over time in potential murderers’ perceptions of the risk of incurring
the death penalty.
Even if potential murderers’ risk perceptions are accurate, research-
ers must carefully specify the probabilities that might affect behavior and
must confront the practical difficulties involved in measuring the relevant
probabilities. The studies to date, however, have failed to address either
of these issues. Because the post-Gregg panel research has not developed
models based on the potential offender’s decision problem, the studies may
mis-specify the relevant risk probabilities.
Much of this research considers how different conditional probabilities—
say, the probability of execution given capital sanctions—each separately
affects behavior (see, e.g., Dezhbakhsh, Rubin, and Shepherd, 2003). Yet, in
standard decision models in which potential offenders weigh the uncertain
benefits and costs of committing a crime, the joint probability of execu-
tion, capital sanctions, and arrests are germane. In this expected utility
framework, Durlauf, Navarro, and Rivers (2010) show that the effect of the
conditional probability of execution given a death sentence cannot be un-
derstood separately from the effects of the conditional probability of being
caught and being sentenced to death if caught. Moreover, under a rational
choice assumption, what will matter is the expected execution rate at time
t + 6, which is not necessarily equal to the t – 6 years used in the literature.
Aside from this important issue of modeling and functional form, re-
searchers also encounter practical obstacles in measuring the objective risks.
Consider the risk of being executed given a death sentence, the risk that
has been most focused on in the research, and consider how this risk could
be objectively measured and updated each year for those in each state, as
is assumed relevant in these models. In 1977, the first full year after the
Gregg decision, 31 states provided the legal authority to impose the death
penalty. In 1977, there were no data on the actual use of the death penalty
in any state to create an estimate of the risk of execution. Some people
might have predicted that Texas would be more vigorous in its actual use
of the death penalty than California or Pennsylvania, but there were as yet
no data to confirm such a prediction. Thus, it is unclear what the objective
risk of receiving a death sentence or consequently being executed was in
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
58 DETERRENCE AND THE DEATH PENALTY
any state for which the death penalty was legal in 1977. Only over time
could an objective risk be based on data. Thus, over time one would expect
divergent risks to develop in different states as data on the actual use of the
death penalty in each state accumulated.
The process of forming and revising objective measures of the risks
associated with the death penalty, however, would then be complicated
by additional factors. One is that the volume of data on death sentences
and executions available for calculating estimates of risk depends on
the size of the state. By various measures of execution risk reported in
Chapter 2, Delaware was at least as aggressive in its use of the death
penalty as Texas. However, over the period from 1976 to 2000, Delaware
sentenced 28 people to death and carried out 11 executions, while Texas
sentenced 753 people to death and carried out 231 executions. Thus,
potential murderers have far more data on the actual practice of capital
punishment each year in Texas than in Delaware. As a consequence, even
for well- informed potential murderers living in states with similar sanc-
tion regimes, one would expect sanction risk perceptions to evolve along
different paths that would depend, among other things, on the size of the
state.
Perhaps in an environment in which sanction regimes were plausibly
stable, the objective risk of execution could be precisely estimated even in
small states with low murder rates. However, sanction regimes do not ap-
pear to be uniformly stable in large states for which it is feasible to obtain
precise measures of year-to-year variation. Indeed, it is changes in the sanc-
tion regime for murder that the panel models use to inform their estimates
of deterrence. Moratoriums and commutations may signal changes in re-
gimes, particularly when accompanied by high-visibility announcements
such as that by former Illinois Governor George Ryan in 2000. As noted
in Chapter 2, Texas appears to have shifted to a higher intensity execu-
tion sanction regime during the 1990s. Thus, in an environment in which
sanction regimes are changing, the value of older data in forming a correct
estimate of the prevailing sanction regime deteriorates. Moreover, the value
of current data in forming a correct estimate of the future sanction regime
also deteriorates. This forecast is particularly relevant as those consider-
ing murder now would face the sanction regime of the state in which the
homicide is prosecuted some significant time in the future. These factors
raise the question of whether year-to-year variation in a measure, such as
the number of people executed in a state, has any bearing on the risk of
execution for someone committing a murder today. Overall, the degree to
which this, or other proposed measures of execution risk, predicts later
executions has not been established.
To illustrate the problems associated with these different measures,
consider using the number of executions in a state 1 year prior to the
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
PANEL STUDIES 59
year in which the homicide rate is measured divided by the number of
death sentences in that state 7 years earlier. Those at risk for execution in
any particular year are all those on death row at some point in that year.
Those who were sentenced to death 7 years earlier could be executed at
any time after their sentence, with different probabilities of being executed
in each year based on the particulars of their crime, the appeals process,
their health, the current governor, etc. In the early years after the national
death penalty moratorium ended, on a national level, those who were
executed had spent an average of 6-7 years on death row (Snell, 2010).
There are several problems with using this information to justify lagging
the denominator of a risk of execution measure by 7 years. First, only 15
percent of those sentenced to death in the United States since 1977 have
been executed, with close to 40 percent leaving death row for other reasons
(vacated sentences or convictions, commutations, a successful appeal, or
death by other causes), and 45 percent are still on death row (Snell, 2010).
Moreover, these figures vary substantially across states and over time.
Table 4-2 displays the number of inmates removed from death row in
each state by the reasons for removal. First, there is substantial variation
in the execution rates across states. For example, of the 150 people in
Virginia sentenced to death from 1973 to 2009, 105—70 percent—have
been executed. In contrast, in North Carolina, only 8 percent of the 528
people sentenced to death have been executed. Not only do these rates vary
across states, but they also vary over time (see, e.g., Cook, 2009). Clearly,
the number of years those executed have spent on death row is not an ac-
curate measure of the number of years those on death row will spend there
before they are executed, if they are ever executed. Second, the time spent
on death row by those executed has varied over time at the national level,
and it varies considerably by state (Snell, 2010). Third, no evidence has
been given or arguments made to suggest that death sentences that come
to some resolution earlier than others are indicative of the resolution for
death sentences that have not yet come to resolution. Thus, using a fixed
number of years of lag between those sentenced and those executed means
that for many states and years this lag will have an uncertain relationship
to the objective risk of execution given a death sentence.
The fact that there is a mismatch between the numerator and denomi-
nator in the models used is perhaps best illustrated by the many state-year
cases in which there are one or more executions the prior year but there
were no death sentences imposed 7 years earlier. Researchers have made a
variety of ad hoc removals or substitutions for these undefined cases includ-
ing: replace with zero or treat as missing (Kovandzic, Vieraitis, and Boots,
2009); numerator set to zero regardless of denominator and non-zero
numerator and zero denominator considered missing at random (Donohue
and Wolfers, 2005; Mocan and Gittings, 2003, 2010); replace with most
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
60
TABLE 4-2 Death Sentences and Removals, by Jurisdiction and Reason for Removal, 1973-2009
Jurisdiction
Total Sentenced
to Death,
1973-2009
Removals
Sentence or
Conviction
Overturned
Sentence
Commuted
Other
Removals
Under Sentence of
Death, December 31,
2009Executed Died
U.S. Total 8,115 1,188 416 2,939 365 34 3,173
Federal 65 3 0 6 1 0 55
Alabama 412 44 31 135 2 0 200
Arizona 286 23 14 110 7 1 131
Arkansas 110 27 3 38 2 0 40
California 927 13 73 142 15 0 684
Colorado 21 1 2 15 1 0 2
Connecticut 13 1 0 2 0 0 10
Delaware 56 14 0 25 0 0 17
Florida 977 68 53 447 18 2 389
Georgia 320 46 16 147 9 1 101
Idaho 42 1 3 21 3 0 14
Illinois 307 12 15 96 156 12 16
Indiana 100 20 4 54 6 2 14
Kansas 12 0 0 3 0 0 9
Kentucky 81 3 6 35 2 0 35
Louisiana 238 27 6 114 7 1 83
Maryland 53 5 3 36 4 0 5
Massachusetts 4 0 0 2 2 0 0
Mississippi 190 10 5 112 0 3 60
Missouri 182 67 10 52 2 0 51
Montana 15 3 2 6 2 0 2
Nebraska 32 3 4 12 2 0 11
Nevada 147 12 15 36 4 0 80
New Hampshire 1 0 0 0 0 0 1
New Jersey 52 0 3 33 8 8 0
New Mexico 28 1 1 19 5 0 2
New York 10 0 0 10 0 0 0
North Carolina 528 43 21 297 8 0 159
Ohio 401 33 20 168 15 0 165
Oklahoma 350 91 12 165 3 0 79
Oregon 58 2 2 23 0 0 31
Pennsylvania 399 3 24 148 6 0 218
Rhode Island 2 0 0 2 0 0 0
South Carolina 203 42 5 98 3 0 55
South Dakota 5 1 1 1 0 0 2
Tennessee 221 6 15 105 4 2 89
Texas 1,040 447 38 167 56 1 331
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
61
TABLE 4-2 Death Sentences and Removals, by Jurisdiction and Reason for Removal, 1973-2009
Jurisdiction
Total Sentenced
to Death,
1973-2009
Removals
Sentence or
Conviction
Overturned
Sentence
Commuted
Other
Removals
Under Sentence of
Death, December 31,
2009Executed Died
U.S. Total 8,115 1,188 416 2,939 365 34 3,173
Federal 65 3 0 6 1 0 55
Alabama 412 44 31 135 2 0 200
Arizona 286 23 14 110 7 1 131
Arkansas 110 27 3 38 2 0 40
California 927 13 73 142 15 0 684
Colorado 21 1 2 15 1 0 2
Connecticut 13 1 0 2 0 0 10
Delaware 56 14 0 25 0 0 17
Florida 977 68 53 447 18 2 389
Georgia 320 46 16 147 9 1 101
Idaho 42 1 3 21 3 0 14
Illinois 307 12 15 96 156 12 16
Indiana 100 20 4 54 6 2 14
Kansas 12 0 0 3 0 0 9
Kentucky 81 3 6 35 2 0 35
Louisiana 238 27 6 114 7 1 83
Maryland 53 5 3 36 4 0 5
Massachusetts 4 0 0 2 2 0 0
Mississippi 190 10 5 112 0 3 60
Missouri 182 67 10 52 2 0 51
Montana 15 3 2 6 2 0 2
Nebraska 32 3 4 12 2 0 11
Nevada 147 12 15 36 4 0 80
New Hampshire 1 0 0 0 0 0 1
New Jersey 52 0 3 33 8 8 0
New Mexico 28 1 1 19 5 0 2
New York 10 0 0 10 0 0 0
North Carolina 528 43 21 297 8 0 159
Ohio 401 33 20 168 15 0 165
Oklahoma 350 91 12 165 3 0 79
Oregon 58 2 2 23 0 0 31
Pennsylvania 399 3 24 148 6 0 218
Rhode Island 2 0 0 2 0 0 0
South Carolina 203 42 5 98 3 0 55
South Dakota 5 1 1 1 0 0 2
Tennessee 221 6 15 105 4 2 89
Texas 1,040 447 38 167 56 1 331
continued
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
62
Jurisdiction
Total Sentenced
to Death,
1973-2009
Removals
Sentence or
Conviction
Overturned
Sentence
Commuted
Other
Removals
Under Sentence of
Death, December 31,
2009Executed Died
Utah 27 6 1 9 1 0 10
Virginia 150 105 6 14 11 1 13
Washington 38 4 1 25 0 0 8
Wyoming 12 1 1 9 0 0 1
Percentage 100 14.6 5.1 36.2 4.5 0.4 39.1
NOTE: Some inmates executed since 1977 or currently under sentences of death were sentenced prior to 1977. For those inmates sentenced to death
more than once, the numbers are based on the most recent death sentence.
SOURCE: Snell (2010), Table 20.
TABLE 4-2 Continued
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
PANEL STUDIES 63
recent defined ratio (Zimmerman, 2004). These (and other) ad hoc adjust-
ments highlight the general problem that the people who were sentenced
to death 7 years earlier may be executed before or after the year in which
executions are counted, and they are not the only people at risk for being
executed in the current or prior year. Overall, the interpretation of this ratio
is not clear at all, whether the denominator is lagged any particular number
of years, and its relevance to the objective risk of execution for each state
and year, let alone to the risk perceptions of potential murderers, is highly
questionable.
Basing execution risk measures only on data on executions that have
actually been carried out, as has been done in the research being discussed,
could result in a serious underestimate of the eventual probability of ex-
ecution for those given a death sentence. In addition, this fact raises seri-
ous questions about whether the risk of ever being executed after a death
sentence is the most salient measure or whether additional information is
salient, such as measures that consider expected time to death, expected
living conditions while on death row, and in comparison, expected time
to death during a long prison sentence and conditions while in prison in
that state. (Of course, one can only speculate about which, if any, of these
variables is salient for potential murderers.)
These many complications make clear that even with a concerted effort
by dedicated researchers to assemble and analyze relevant data on death
sentences and executions, assessment of the actual and changing objective
risk of execution that faces a potential murderer is a daunting challenge.
Given the obstacles to obtaining an objective measure of this risk, the com-
mittee does not find any of the measures used in the studies to be credible
measures of the objective risk of execution given a death sentence. We also
reiterate that it is not known whether there is a relationship between any
of these measures or any more credible objective measure of execution risk,
and the execution risk as perceived by potential murderers.
MODEL ASSUMPTIONS
The conceptual and measurement concerns raised thus far, which are
somewhat unique to studies on the effects of the death penalty on homi-
cides, make it difficult to even to envision how one could draw valid infer-
ences on the deterrent effect using the existing data. There is a complete
lack of basic information on the noncapital component of the sanction
regime, on how offenders perceive sanction risks, and on how to accurately
measure those risks.
Even if these measurement problems are some day fully addressed,
all studies using observational data must also address the counterfactual
outcomes problem that arises because the data cannot reveal the outcome
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
64 DETERRENCE AND THE DEATH PENALTY
that would occur if the death penalty had not been applied in treatment
states and had been applied in control states. The data alone cannot reveal
the effect of the death penalty. Rather, researchers must combine data with
assumptions.
In the studies we reviewed, variations of the model in Equation 1 have
been used to identify the impact of the death penalty on homicide. In this
section, we consider the credibility of the four assumptions that have been
applied in this literature: (1) that the death penalty measures are inde-
pendent of the unobserved factors influencing homicide; (2) that certain
observed covariates, called instrumental variables, are correlated with the
death penalty but not with the unobserved factors that influence homicide;
(3) that the effect of the death penalty is the same for all states and years;
and (4) that the sanction regimes of adjacent states do not have any bear-
ing on the effect of the death penalty in a particular state. We begin with a
brief discussion of the benefits of random assignment.
Benets of Random Assignment
As discussed in Chapter 3, random assignment of treatment to large
samples of subjects leads the distributions of all other characteristics of
treatment and control subjects, whether observed or unobserved, to be
approximately the same across the two groups. With small samples of
subjects, this feature will hold on average, meaning that if a given set of
subjects is repeatedly randomly assigned to treatment or control conditions,
then the features of the subjects over all possible treatment groups and all
possible controls groups would be exactly equal. In any particular ran-
domization, however, there may be some features that differ by chance for
the subjects in the treatment condition and those in the control condition.
This “balancing” of the characteristics of treatment and control subjects
justifies the attribution of any difference in outcomes between the treatment
and control groups to the treatment and not to other factors that may differ
between the treatment and control subjects. Without randomization, the
threat of misattributing the cause of any observed differences in outcomes
to the treatment when it is actually due to other factors that differ between
the groups is always present. In the remainder of this section we focus on
the specific challenges this concern raises with regard to the death penalty
and deterrence research, discuss the methodological strategies proposed to
overcome these challenges, and assess whether these strategies have been
successful.
In research on the death penalty and deterrence, the sanction regime
for murder (including the legal status of the death penalty and the inten-
sity with which the death penalty is applied) is, for obvious reason, not
randomly assigned to state-by-year units. Hence, the possibility is present
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
PANEL STUDIES 65
that other factors may be the actual causes of any changes seen in homicide
rates. Mechanically, what is required for this misattribution to occur is for
death penalty changes to occur at similar times and places as changes in the
true underlying causal factors. An example is a shift to a political leader
with a “law and order” approach, which could both increase death-penalty-
related risks and increase the perceived or actual arrest rates, either or both
of which could bring down the homicide rate.
Fixed Effect Regression Model
Two methodological strategies are used to try to identify changes in
the homicide rate that are caused by changes in the sanction regime for
murder and not by other factors. The first methodological strategy is a fixed
effect multiple regression (described above), in which fixed state and year
effects are used to account for unobserved determinants of homicide. Given
these fixed effects, researchers assume that the death penalty measures are
statistically independent of the unobserved determinants of homicide, as
would be the case in a randomized experiment. The second methodologi-
cal strategy is to add an instrumental variables analysis to the fixed effect
multiple regression models.
The fixed effects multiple regression models rely on state level variation
in death penalty measures over time to attempt to identify a causal effect of
death-penalty-related changes on homicide after controlling for the effects
of the other variables in the models. But even if one provisionally assumes
that the death penalty measures used in these models are correctly specified
(i.e., are the salient factors for potential murderers), that the state-year unit is
the unit at which potential murderers are assessing death-penalty-associated
risks, and that the specification of all other variables and of the functional
form of the model are correct, additional strong assumptions are still required
for panel models to deliver estimates of a deterrent effect of the death penalty.
In the fixed effect models, states that do not apply the death penalty
sanction are used to estimate the missing counterfactual for states that do
experience different death penalty sanction levels. This approach identifies
a causal effect only if there are no other factors besides the death penalty
causing homicide rates to change differently in states that do and do not
experience changes in death penalty sanctions. Many such factors may
well exist—such as changes in economic conditions, crime rates, public
perceptions or political regimes—and there is no reason to believe that
these variables are fixed over time or across states. Moreover, the com-
mittee considers the omission from these models of other changes in the
sanction regime for murder especially problematic. As discussed above,
other changes in the sanction regime for murder, such as the likelihood of
life without parole or the average sentence length, may well change con-
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
66 DETERRENCE AND THE DEATH PENALTY
currently with death-penalty-related changes and so affect homicide rates.
If states that do not experience changes in the death penalty also did not
experience comparable changes (on average) in other aspects of the sanc-
tion regime for murder, then the required assumption is violated, and those
states cannot provide the missing counterfactual information for states that
do experience changes in the death penalty.
A related concern is that while death penalty sanctions may be af-
fecting the homicide rate, the homicide rate may also be affecting death
penalty sanctions and statutes. Since factors causing changes in observed
in death penalty sanctions are unknown, one cannot rule out that changes
in the homicide rate are among such factors. One way this could occur
is that an increase in homicides may influence policy makers to increase
the seriousness of sanctions or the likelihood of more serious sanctions
for murder. Given this possibility, it is interesting to note that states in an
available sanction have higher homicide rates on average than states that
do not have the death penalty. Alternatively, an increase in the homicide
rate may decrease the intensity with which the death penalty is applied as
death penalty proceedings require more resources than non-death-penalty
proceedings (Alarcón and Mitchell, 2011; California Commission on the
Fair Administration of Justice, 2008; Cook, 2009; Roman, Chalfin, and
Knight, 2009). This potential reverse causality problem—termed simultane-
ity in econometrics and feedback from output to input in the literature on
causality—is particularly thorny to overcome. It was a major concern of the
earlier National Research Council (1978) report on deterrence.
Instrumental Variables
In light of these concerns, Dezhbakhsh, Rubin, and Shepherd (2003)
and Zimmerman (2004) have added an additional identification strategy,
the use of instrumental variables. The idea behind an instrument is to
separate out the part of any observed relationship between the death pen-
alty and homicide that is spurious (i.e., resulting from the relationship of
both to other factors) from the part of the relationship between the death
penalty and homicide that is causal. The success of an instrument and the
consequent instrumental variables analysis depends on the ability of the
instrument to identify the portion of the variation in the treatment that is
not contaminated by other causal factors that covary with the treatment
and affect the outcome.
The success of an instrument depends on the degree to which it meets
two requirements: (1) the death penalty sanction must vary with the value
of the instrument, and (2) the average outcome must not vary as a function
of the value of the instrument conditional on the treatment and levels of
other covariates. A sufficient condition for this to hold is that the instru-
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
PANEL STUDIES 67
ment affects the homicide rate only through its effect on the death penalty
sanctions, that is, that the instrument has no direct effect of its own on ho-
micide rates. The first of these requirements can be checked empirically. The
second requirement typically cannot be established using data and empirical
analysis; it requires, instead, logic or theory to establish its credibility.
In the studies of death penalty and deterrence, the challenge is to find
a variable that predicts death penalty sanctions but does not have a direct
effect on the homicide rate. Although successful instrumental variables are
notoriously difficult to come up with, making an argument for a particular
instrument in this setting is complicated by the same fact that makes a spu-
rious correlation very difficult to rule out. Little is known about the factors
that actually affect homicide rates and, thus, the relevant factors may not
be observed, measured, and controlled for. Compounding the problem, even
less is known about factors that are associated with death-penalty-related-
changes in the sanction regime for murder, or more relevantly, changes
in perceptions of sanction risks. As noted above, factors contributing to
changes in the legal status of the death penalty or the intensity with which
the death penalty is applied could include economic, crime, or political
changes that may also have direct consequences for the homicide rate.
These two gaps in knowledge—of factors that contribute to the homi-
cide rate and factors that contribute to changes in the legality or practice of
the death penalty and of risk perceptions—combine to heighten the concern
that any association observed between death penalty changes and homicide
rate changes may well be due to other factors. Thus, it is particularly dif-
ficult to convincingly establish that a proposed instrument does not directly
affect the homicide rate, as is required.
A couple of examples of credible instruments in other settings may be
useful to compare with those proposed in the studies of the death penalty
and deterrence. In studies of crime and justice, Lee and McCrary (2009)
use the age at which an offender can be tried as an adult as an instrument
to identify the deterrent effect of incarceration; and Klick and Tabarrok
(2005) use terror alerts in Washington, DC, as an instrument to identify
the deterrent effect of police on crime on the Washington Mall. In the field
of labor economics, a person’s Vietnam draft number has been used as
an instrument to identify the effect of military service on future earnings
because one’s draft number affects military service but does not have any
direct effect on future earnings (Angrist, 1990). Month of birth has been
used as an instrument to identify the effect of number of years of schooling
on earnings because month of birth affects the academic year in which high
school students of similar ages may legally leave school, but it is unlikely to
have any direct effect on earnings (Angrist and Kreuger, 1991).
In contrast, the instruments proposed in the panel studies of the death
penalty often appear to clearly violate the second requirement and some-
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
68 DETERRENCE AND THE DEATH PENALTY
times violate the first. The instruments that have been used include police
payroll, judicial expenditures, Republican vote share in each separate presi-
dential election, prison admissions, the proportion of a state’s murders in
which the assailant and victim are strangers, the proportion of a state’s
murders that are nonfelony, the proportion of murders by nonwhite offend-
ers, an indicator (yes/no) for whether there were any releases from death
row due to a vacated sentence, and an indicator (yes/no) for whether there
was a botched execution. The specific death penalty variables for which
these instruments are proposed are measures of the risk for murderers of be-
ing arrested, the risk for those arrested for murder of receiving a death sen-
tence, and the risk for those receiving a death sentence of being executed.
The studies offer very little justification for why these instruments are
believed to be unrelated to the unobserved determinants of homicide, and in
many cases the committee does not find the assumptions to be credible. To
take two examples, it seems highly unlikely that police expenditures or the
Republican vote share in a particular presidential election affect homicide
rates only through the intensity with which the death penalty is exercised.
To the contrary, police expenditures are likely to have a direct effect on ho-
micide rates, and Republican vote shares may be related to a host of factors
that are thought to influence crime (e.g., “get tough on crime” policies and
a state’s demographic composition).
The idea of using instrumental variables to help identify the effect of
the death penalty on homicides is sensible. The problem, however, is find-
ing variables that are related to the sanction regime but not directly related
to homicide rates. In general, the committee finds that the instruments
proposed in the research are not credible and, as a result, this identifica-
tion strategy has thus far failed to overcome the challenges to identifying a
causal effect of the death penalty on homicide rates.
5
Homogeneity
Still another assumption of the panel regression model in Equation (4-1)
is that any effect that the death penalty has on homicide rates is the same
5
In addition to these fundamental problems with the instruments, Donohue and Wolfers
(2005) document that the results are highly sensitive to the specification of the instruments.
For example, the results of Dezhbakhsh, Rubin, and Shepherd (2003) notably vary depend-
ing on whether and how one specifies the Republican vote share instrument: when using vote
shares from six different elections, Dezhbakhsh, Rubin, and Shepherd (2003) report that each
additional execution saves an average of 18 lives; when using a single vote share measure from
the most recent election, Donohue and Wolfers (2005, p. 826) find that “instead of saving
eighteen lives, each execution leads to eighteen lives lost.” Moreover, Donohue and Wolfers
find that when the partisanship variables are not included among the instruments, more execu-
tions lead to substantially more homicides.
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
PANEL STUDIES 69
in every state and every year. This assumption of a homogeneous treat-
ment effect is unlikely to hold in practice. This assumption relies on “unit
exchangeability,” which requires that if the change in the death penalty
measure observed in a particular state and year were instead to be observed
in a different state and year, then the effect seen on homicide would be the
same. For the legal status of the death penalty, this assumption would mean
that the death penalty would have the same effect on homicides in the first
year a low-crime state instituted the death penalty by legislative action as
it would in the 15th year in Texas, a state in which it is widely used. The
assumption would also mean that the effect would be the same in the year
before the death penalty was removed as a possible sanction due to the
courts’ determining the state’s death penalty law was unconstitutional in
a state that had the death penalty but did not implement it. The death-
penalty-intensity models also invoke this assumption. These models assume
that every possible death-penalty-intensity level would have the same effect
on homicide rates in every state and year if it was present in that state and
year, regardless of the prior sanction regime, a state’s history with the death
penalty, or any other factor.
Although this homogeneity assumption is commonly invoked in regres-
sion models, no support is offered for it in studies of the death penalty,
and on its face it appears unlikely to hold. In fact, there is some evidence
to the contrary. Figure 4-2 displays the distribution of estimates found by
Donohue and Wolfers (2005, p. 810, Figure 4) when they estimate state-
specific parameters using the same basic specification as in Dezhbakhsh
and Shepherd (2006). They find that reinstatement of the death penalty in
1976 is associated with an increased homicide rate in 17 states and a lower
rate in 24 states. Similarly, when Shepherd (2005) estimated state-specific
deterrence parameters using the same basic specifications as in Dezhbakhsh,
Rubin, and Shepherd (2003), she finds that executions deterred murder in 8
states, and increased murders in 13 states. The committee does not endorse
these state-specific models and estimates, but the findings do suggest the po-
tential for substantial heterogeneity in the effect of the death penalty across
states, which violates a basic assumption of the panel data model in Equa-
tion (4-1). Moreover, relaxing this homogeneity assumption can lead to
very different inferences on the effect of the death penalty (see Chapter 6).
Finally, we note that the panel regression models also rely on the as-
sumption that the sanction regimes of adjacent states do not have any bear-
ing on the effect the death penalty in a particular state. In other words, the
assumption asserts that the effect of the legalization of death penalty (or
an increase to a higher death-penalty-intensity level) is the same for a state
regardless of whether it is surrounded by states with a death penalty that
is rarely implemented or is adjacent to, say, Texas. Although it is possible
that the legal status of the death penalty (or an increase to a higher death-
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
70 DETERRENCE AND THE DEATH PENALTY
penalty-intensity level) may have the same effect in each of these scenarios,
it is also plausible that in the first setting the change in the sanction regime
for murder would be perceived as small to potential murderers and in the
second it would seem large. No research to date has explored whether the
assumption that the treatment effect is insensitive to context created by
other states is likely to hold, but violations of this assumption are known
to lead to biased inferences (see, e.g., Rubin, 1986, p. 961). While account-
ing for social interactions is known to be difficult, Manski (in press) points
to constructive ways of further addressing some of the problems that have
been identified in the research to date.
CONCLUSION
The committee finds the failure of the panel studies we reviewed to
address or overcome the primary challenges discussed above sufficient
reason to view this research as noninformative with regard to the effect
of the death penalty on homicides. The sanction regime is insufficiently
specified and the measures of the intensity with which the death penalty
is applied are flawed. No connection has been established between these
measures and the perceived sanction risks of potential murderers. Neither
0
.05 .1
.15
.2 .25
Density
-6 -4 -2 0 2 4 6
Estimated Effect on Homicide Rate
Annual Murders per 100,000 People
Death Penalty Reinstatement
0 .05 .1 .15
.2 .25
Density
-6 -4 -2 0 2 4 6
Estimated Effect on Homicide Rate
Annual Murders per 100,000 People
Death Penalty Abolition
R02175
Figure 4-2
vectors, editable
taken from original source
(Donohue & Wolfers, 2006)
FIGURE 4-2 Distribution of regression-estimated effects across states.
SOURCE: Donohue and Wolfers (2005, p. 810, Figure 4). Used by permission.
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
PANEL STUDIES 71
the fixed effects multiple regression models nor the proposed instruments
are credible in overcoming challenges to identifying a causal link between
the death penalty and homicide rates. The homogeneous response restric-
tion that the effects are the same for all states and all time periods seems
patently not credible.
Some researchers have argued that fixed effect models without instru-
ments may provide valuable information, although not perfect information
about the impact of death penalty on crime. One reason given is that they
do not suffer from the defects that attend the use of manifestly invalid
instrumental variables (see, for example, Donohue and Wolfers, 2009, and
Kovandzic, Vieraitis, and Boots, 2009). This assessment of the informative
value of the fixed effects models is dubious for several reasons. Most no-
tably, these models do not address the data and modeling issues discussed
throughout this chapter. The fixed effects models estimated in the literature
do not specify the noncapital component of the sanction regime and setting
aside the issue of how sanction risks are actually perceived, the measures
of execution risk that are used do not appear to bear any resemblance to
the true risk of execution. In addition, the key assumption that the death
penalty sanction is independent of other unobserved factors that might in-
fluence homicide rates seems untenable. For these reasons, the fixed effects
models are no more informative about the effect of the death penalty on
homicide rates than other types of model.
Some studies play the useful role, either intentionally or not, of dem-
onstrating the fragility of claims to have or not to have found deterrent
effects (e.g., see Cohen-Cole et al., 2009; Donohue and Wolfers, 2005,
2009). However, even these studies suffer from the intrinsic shortcomings
that severely limit what can be learned about the effect of the death penalty
on homicide rates by using data on the death penalty as it has actually been
administered in the United States in the past 35 years.
The challenges discussed here are formidable, and breakthroughs on
several fronts would be necessary to overcome them. Only then might panel
models, with or without instruments, be a fruitful methodology for study-
ing the deterrent effects associated with the death penalty.
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Berk, R. (2005). New claims about executions and general deterrence: Déjà vu all over again?
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Deterrence and the Death Penalty
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
5
Time-Series Studies
T
ime-series studies of the effect of capital punishment on homicides
study the statistical association of executions and homicides over
time. As noted in the preceding chapter, panel studies also contain a
time dimension, so the division between the two approaches is not perfect.
Indeed, time-series studies can be thought of as a particular type of panel
study, characterized by a small number of cross-sectional units, often only
one or two. Some time-series studies analyze executions and homicides over
a large number of periods; others examine the aftermath of single execution
events. Whatever the length of the series, the intuition undergirding the
analysis is that the presence of an effect of executions on homicide rates can
be seen from the association of fluctuations of executions over time with
fluctuations of homicides over time.
The time-series and panel studies we reviewed differ in several other
important respects.
First, the unit of time in time-series studies is usually months,
weeks, or even days; in contrast, the unit of time in panel studies
is usually a year. Thus, results from time-series studies are generally
interpreted as measuring short-term effects of capital punishment.
Second, time-series studies generally examine the association be-
tween execution events and homicides; panel studies generally mea-
sure the association of homicide rates with ratios that are intended
to measure the probability of execution.
75
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
76 DETERRENCE AND THE DEATH PENALTY
Third, while most panel studies use very similar regression meth-
ods, time-series studies use a wide assortment of specialized time
series methods.
Fourth, the designs of time-series studies are more varied than
are those of panel studies. Perhaps the most important difference
among time-series studies is the number of execution events ex-
amined. Some time-series research focuses on the effect of a single
execution event, and other studies combine data on many execu-
tion events and analyze their temporal association with homicide
rates in a single statistical model.
The variation of research methods in the time-series studies makes it
challenging to organize a cohesive discussion of the subject. It also is chal-
lenging to describe and critique the studies in a way that is understandable
to audiences who do not have expertise in time-series methods. Methods
for analysis of time-series data are specialized and often very technical. We
address the second challenge by beginning this chapter with a nontechnical
discussion of some relatively transparent problems of the studies. We then
continue with further criticisms that of necessity are more technical.
BASIC CONCEPTUAL ISSUES
Execution Event Studies
Studies of single execution events attempt to identify whether a change
in the homicide rate occurs in the immediate aftermath of a single execution.
A decline is interpreted as evidence of deterrence; an increase is interpreted
as evidence of a brutalization effect, whereby state-sanctioned executions
“legitimate” homicide to some in the citizenry. If either such effect could
be convincingly demonstrated, it would establish a threshold requirement
for capital punishment to affect behavior, namely that “someone is seem-
ingly listening.” However, as detailed below, the committee concluded that
no existing study has successfully made such a demonstration and that the
obstacles to success for a future study are formidable. As importantly, the
committee concluded that a successful demonstration would have limited
informational value.
Studies of a single execution event are subject to the same problem that
bedevils most before-after studies. Because the execution is not conducted
in the context of a carefully controlled experimental setting, other factors
that affect the homicide rate may coincide with the execution event. Some
event studies attempt to deal with this problem by examining changes over
very short periods of time, days or a week. Although shortening the time
window of observation may provide some protection from the effects of
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
TIME-SERIES STUDIES 77
other sources (but see discussion below), it opens other possible interpreta-
tions of the result. Even if a short-term effect could be established, it would
be difficult to determine whether homicides were actually prevented or
simply displaced in time. This possibility creates a fundamental conundrum:
the study of short time frames increases the plausibility of the displacement
in time interpretation, and the study of longer time frames increases the risk
of confounding by other factors.
It is vital to understand that event studies do not speak to the ques-
tion of whether and how a state’s sanction regime affects its homicide rate.
The simplest illustration of this point involves the interpretation of a study
that fails to find evidence that an execution event affects the homicide rate.
Consider, for example, a study of the first execution after an extended
moratorium. Suppose that the study convincingly demonstrated that the
execution was not followed by any change in the homicide rate. One inter-
pretation of this result is that capital punishment has no deterrent effect.
However, another possibility is that the deterrent effect is large but that it
was anticipated in advance of the execution due to the publicity given to
the upcoming event. Both possibilities are logical and plausible, but they
are not distinguishable by the event study methodology.
Alternatively, suppose that an event study found that homicides are
reduced in the immediate aftermath of an execution and not just displaced
in time. To generalize from this single execution requires consideration of
the context in which the execution occurred. If it was the first execution
after an extended moratorium, it is problematic to assume that such an
effect would recur for subsequent executions. More generally, the effect of
any given execution may depend on the proximity in time of that execution
to other executions and to the frequency of executions more generally. For
example, if an execution event study established convincingly that it averted
one homicide that week, it does not follow that each additional execution
would avert one more homicide. To complicate matters further, the effect
of any one execution may depend on the identity of the person executed
(e.g., an infamous serial killer or a person for whom there is some public
sympathy) and the amount of publicity given to the execution.
The problem of generalizing from the findings of even a convincing
event study is indicative of still another fundamental committee concern
with all the time-series studies. The researchers who carry out such studies
never clearly specify why potential murderers respond to execution events.
Do potential murderers respond to the shock value of execution? If so,
would the magnitude of the shock value change with each additional ex-
ecution? One possibility is that the shock value might increase, perhaps be-
cause of reinforcement. Alternatively, it might decrease, perhaps because a
potential murderer becomes inured to executions. Still another possibility is
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
78 DETERRENCE AND THE DEATH PENALTY
that potential murderers respond to sanction risk probabilities and that ex-
ecution events cause them to update their perceptions of those probabilities.
Studies of Deviations from Fitted Trends
This issue of why and how potential murderers react to executions is
equally important to the interpretation of studies that combine data on
executions and homicides over multiple time periods, deploying subtle
time-series methods to analyze these data. Consider Figures 5-1 and 5-2,
which plot executions and homicides, respectively, in Texas from 1990 to
2008. The most obvious way to examine the association of executions and
homicides in Texas is to correlate these two time series. Over the period,
this correlation is –0.68. However, there are innumerable obvious objec-
tions to interpreting this negative association as deterrence because many
factors that influence the homicide rate were also changing over this time
period. One manifestation of this observation can be seen in Figure 3-3 (in
Chapter 3), which shows the close correspondence over time in the homi-
0
5
10
15
20
25
30
35
40
45
1990 1992 1994 1996 1998 2000 2002 2004 2006 2008
Number of Executions in Texas
Year
R02175
Figure 5-1
vectors, editable
FIGURE 5-1 Executions in Texas from 1990 to 2008.
SOURCE: Data from Texas Department of Criminal Justice (2011).
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
TIME-SERIES STUDIES 79
cide rates of three states with very different capital punishment sanction
regimes—California, New York, and Texas.
Studies of executions and homicides over multiple time periods do
not examine the raw time-series association between the homicide rate
and number of executions. Instead they analyze the association between
deviations from fitted statistical trend lines that summarize these two time
series. One technical adjustment sometimes used to in these studies is that
the data series be detrended. By “detrended” it is meant that the time series
does not vary systematically with time (e.g., does not increase over time).
As a consequence the time-series studies analyze the association between
deviations from statistical trend lines that summarizes the execution time
series and the homicide rate time series
As an illustration, consider again Figures 5-1 and 5-2. Superimposed on
the raw time-series plots of executions and homicides are regression equa-
tions fit to the execution and homicide data. In the case of the execution
time series, the regression uses a quadratic function of time to fit the raw
0
2
4
6
8
10
12
14
16
18
1990 1992 1994 1996 1998 2000 2002 2004 2006 2008
Homicide Rate in Texas per 10,000
Year
R02175
Figure 5-2
vectors, editable
FIGURE 5-2 Texas homicide rate from 1990 to 2008.
SOURCES: Data from the Federal Bureau of Investigation (2011).
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
80 DETERRENCE AND THE DEATH PENALTY
data. In the case of the homicide time series, the regression uses a cubic
function of time to fit the data.
The time-series literature views the fitted regressions as “trends” that
should be subtracted from the raw data prior to analysis. After that subtrac-
tion, researchers analyze the statistical association between deviations from
the respective trends to draw inferences about the effect of executions on
homicides. For example, in 1998, during the peak period of executions in
Texas, the deviation of the actual number of executions from the fitted
trend line is negative. A time-series researcher might examine the statistical
association between this negative deviation and corresponding deviations of
the homicide rate from its fitted trend line in 1999 and later years.
Unfortunately, the researchers who carry out these studies do not ex-
plicitly state their rationale for analyzing deviations in this fashion. They
may believe that this form of analysis provides a basis for causal inter-
pretation of findings that is more credible than analysis of raw data on
homicides and executions. However, the committee concludes that analysis
of deviations from fitted trends, at least as conducted in the published stud-
ies, does not provide a valid basis for inferring the effects of executions on
homicides.
One reason for our conclusion is that the study of deviations from fitted
trend lines, even with high frequency data, may not avoid the confounding
problem that affects analyses of the raw correlation of executions and ho-
micide rates over time. For example, the publicity given to executions may
still be systematically related to deviations from an execution trend line.
Indeed, one of the studies we reviewed (Stolzenberg and D’Alessio, 2004)
reports that, even in deviation form, the execution and publicity time series
were highly correlated.
A more fundamental concern is that execution event studies do not
clearly specify why potential murderers respond to execution events. For
potential murderers to react to a deviation from a fitted trend line re-
quires that they recognize it as a deviation. To recognize it as a deviation
requires that they be aware of the trend line from which deviations are
measured. However, none of the studies discusses why potential murderers
might be attentive to the trend lines fit by time-series researchers and, if so,
how they might react to deviations from fitted trends. Indeed, the studies do
not even ask whether potential murderers perceive the time-series evidence
on executions in terms of a trend and deviations from the trend.
If potential murderers are attentive to the trend line, there would
have to be a reason for giving it their attention. One possibility is that
their behavior is affected by the trend line. For example, the escalation of
executions in Texas during the 1990s might have been interpreted as an
intensification of the state’s capital punishment sanction regime. Conven-
tional deterrence theory would predict that such an escalation would reduce
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
TIME-SERIES STUDIES 81
homicides, assuming that intensification of the use of capital punishment
did not alter other aspects of the sanction regime. But the brutalization
theory might predict that this escalation increases murders. Yet neither of
these predictions speaks to the question of how potential murderers react
to deviations from the trend.
Consider, for example, the conventional economic model of criminal
decision making. This model assumes that potential murderers respond
to their perceptions of the probability of capture and punishment, which
in this context is execution. Under this model, unless potential murderers
perceive a deviation from trend as signaling a change in the probability of
execution, they will not change their behavior even though their behavior
is affected by the probability of execution. Thus, from the perspective of
the economic conception of deterrence, a finding of no association between
deviations from fitted execution and homicide trends is not indicative of a
lack of deterrence.
In making this point, it is important to emphasize that the committee
is not endorsing this deterrence-based model of behavior. We pose it to il-
lustrate that the results of time-series analyses are not interpretable in the
absence of a behavioral model.
Another possible behavioral model might build from the assumption
that potential murderers react in fear to the shock value of executions and
are thereby dissuaded from committing a murder. This assumption, how-
ever, does not suffice to interpret the results of time-series analyses of de-
viations from fitted trends. Why should deviations from a fitted trend have
shock value separate from the trend itself? If there is no apparent shock
value to a deviation from the trend line, does that mean that the trend line
itself has no shock value?
The idea that potential murderers perceive and react to deviations from
fitted execution time trends presupposes that they are attentive to trends
and have mental models of how trends are formed. Moreover, their percep-
tions of trends must coincide with those of the researchers who fit trend
lines to raw execution data. Otherwise, potential murderers would have no
basis for recognizing deviations as such.
If time-series analysis finds that homicide rates are responsive to such
deviations, the question is why? One possibility is that potential murderers
interpret a deviation as new information about the intensity of the appli-
cation of capital punishment—that is, that the deviation signals a change
in the part of the sanction regime that relates to the application of capital
punishment. If so, a deviation from the execution trend line may cause po-
tential murderers to alter their perceptions of the future course of the trend
line, which in turn may change their behavior.
Yet, even accepting this idea, a basic question persists. Why should the
trend lines fit by researchers coincide with the perceptions of potential mur-
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
82 DETERRENCE AND THE DEATH PENALTY
derers about trends in executions? If researchers and potential murderers do
not perceive trends the same way, then time-series analyses do not correctly
identify what potential murderers perceive as deviations. However, the pub-
lished time-series studies do not ask whether and how potential murderers
perceive trends. Moreover, no study performs an empirical analysis that
tries to learn how potential murderers perceive the risk of sanctions. Hence,
the committee has no basis for assessing whether the findings of time-series
studies reflect a real effect of executions on homicides or are artifacts of
models that incorrectly specify how deviations cause potential murderers
to update their forecasts of the future course of executions.
VECTOR AUTOREGRESSIONS
Evidence Under Existing Criminal Sanction Regimes
One methodology used in time-series studies of deterrence is known
as vector autoregressions (VARs). Research of this type estimates dynamic
regressions that relate current homicide and execution rates to previous
realizations of these two variables. The estimated relationships are then
used to make inference about deterrence. Although this methodology has
only recently been applied in studies of capital punishment and deterrence,
it has been long used in studies of imprisonment and crime: see Durlauf
and Nagin (2011) for a review. We extensively discuss its limitations as a
source of information on deterrence because it is the methodological state
of the art in time-series approaches to deterrence, and it seems poised to
become widespread in capital punishment studies, despite the shortcomings
we discuss.
VARs were originally developed by macroeconometricians to describe
the time-series evolution of an economy (Granger, 1969; Sims, 1972, 1980;
Sims, Goldfeld, and Sachs, 1982). The methodology was motivated by the
idea that the evolution of an economy can usefully be represented as the
superposition of short-run cyclical fluctuations on long-run trends. This
idea suggests a three-step analysis. One first uses the raw time-series data
on the economy to estimate the trends. One then “detrends” the raw data
by subtracting the estimated trends. The detrending step also subtracts the
means of each variable, to produce residuals that have no trend and zero
mean. One finally estimates a VAR on the detrended and “demeaned” re-
sidual data to study the time-series properties of the short-run fluctuations.
VARs are commonly specified to be linear regressions. The use of linear
regression is motivated by a statistical idea rather than a substantive one.
That is, under relatively weak technical conditions, any stationary time-
series can be represented as a dynamic linear relationship that is recoverable
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
TIME-SERIES STUDIES 83
from observation of the series.
1
The detrending step of the VAR methodol-
ogy is intended to render the residual time series stationary.
Some criminologists have used VARs to study deterrence. An immediate
question is whether it makes sense to think of the time-series evolution of
homicides and executions as the superposition of short-run cyclical fluctua-
tions on long-run trends. The researchers have used various definitions of
trends, assuming them to be either linear or nonlinear functions of time.
The absence of a consensus approach to detrending reflects the absence
of any persuasive theory of the generation of the purported trends. In any
case, after detrending is somehow accomplished, VARs are estimated on the
detrended residual data and used to describe short-run cyclical fluctuations
in homicides and executions.
To illustrate the methodology, denote the detrended and demeaned ho-
micide and execution rates in political unit i at time t as h
i,t
and e
i,t
, respec-
tively, and suppose that there are multiple observations on these variables
over time.
2
The VAR representation of these rates is a two equation system
of linear regressions
h
i,t
= a
1
h
i,t–1
+
a
2
h
i,t–2
+ . . . + b
1
e
i,t–1
+ b
2
e
i,t–2
+ . . . + e
i,t
e
i,t
= c
1
h
i,t–1
+
c
2
h
i,t–2
+ . . . + d
1
e
i,t–1
+ d
2
e
i,t–2
+ . . . + h
i,t
(5-1)
Thus, a VAR linearly relates current executions and homicides to previous
executions and homicides, as well as to the current values of the random
variables e
i,t
and h
i,t
. The choice of how many lagged terms to use is made
with the intention that e
i,t
and h
i,t
be random variables that are uncorrelated
across time. That is, these two random variables may be correlated at a
point in time, but future and previous values cannot be correlated. For-
mally, e
i,t
and h
i,t
are the one-period-ahead prediction errors for homicides
and executions given that predictor variables are restricted to the linear
histories of these variables.
3
In the relatively simple case in which only finite
lags appear in (1), the coefficients of the VAR may be estimated by ordinary
least squares.
In studies of the deterrent effect of capital punishment, systems such as
(5-1) have focused on the coefficients b
1
, b
2
,…, which relate lagged levels
of execution rates to the time t homicide rate. If the b
i
coefficients are all
equal to 0, then execution rates are said not to “Granger-cause” homicide
rates. That term comes from econometrician Clive Granger, who proposed
1
This is known as the autoregression form of the Wold representation theorem: see Ash and
Gardner (1975) for a fully rigorous treatment.
2
Some studies use levels rather than rates, but this distinction is not essential for understand-
ing the methodology.
3
By linear, we refer to the fact that prediction of homicides and executions are not allowed to
depend on more complicated functions of their joint histories than the additive structure in (1).
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
84 DETERRENCE AND THE DEATH PENALTY
this statistical definition of causality as a way to summarize the dynamic
relationships between time series. It is essential to understand that use of
the word “cause” notwithstanding, a finding that the b
1
coefficients are
all equal to 0 is only a statement about the absence of a linear statistical
relationship between current homicides and lagged executions, condition-
ing on lagged homicides. It is not a statement about causality as it is com-
monly understood in social science research that distinguishes statistical
association from causation. The absence of Granger causality from execu-
tion rates to homicide rates only means that the best linear prediction of
homicide rates, given the joint histories of homicide and execution rates,
does not require knowledge of the history of execution rates; the history
of homicides rates is sufficient. The absence of Granger causality does not
imply that a counterfactual change in executions because of a change in the
sanction regime facing potential murderers would fail to generate changes
in homicides at later dates.
Despite the fact that Granger causality is only a statistical concept,
findings on the statistical question of whether executions Granger-cause
homicides have been used to make substantive claims about the deterrent
effect of capital punishment. The absence of Granger causality has been
interpreted by some researchers as evidence that capital punishment does
not have a deterrent effect on homicides. In studies in which the estimates
of the b
i
coefficients are negative, such findings have been alleged to be evi-
dence of a deterrent effect, with higher execution rates in the past generat-
ing lower homicide rates in the future. In studies in which estimates of the
b
i
coefficients are positive, those findings have been alleged to be evidence
of a brutalization effect, with higher execution rates in the past generating
higher homicide rates in the future.
In a study of the time-series relationships between homicides and execu-
tions, as well as the relationship between homicides and execution public-
ity in Houston, Stolzenberg and D’Alessio (2004) use this approach. The
authors find that neither actual executions nor publicity about executions
Granger-cause homicides and conclude that neither deterrence nor brutal-
ization effects are present in the Houston data.
Land, Teske, and Zhang (2009) provide a particularly sophisticated
analysis of this type, using data from Texas, by focusing directly on how
a one-unit increase in h
i,t
affects homicides at t + 1, t + 2, etc. In order to
render this a well-posed question, it is necessary to address the contem-
poraneous correlation between h
i,t
, the one-step-ahead prediction error to
executions, and e
i,t
the one-step-ahead prediction error to homicides. In
essence, Land, Teske, and Zhang resolve this contemporaneous correlation
by assuming that e
i,t
= rh
i,t
+
n
i,t
such that e
i,t
and n
i,t
are contemporaneously
uncorrelated, and so treat n
i,t
as the shock to homicides. Thus, the con-
temporaneous correlation between h
i,t
and e
i,t
is resolved by assuming that
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
TIME-SERIES STUDIES 85
the shock to homicides is due to the shock to executions and some other
unspecified factor. The researchers do not provide a model of the timing of
executions, so it is difficult to assess this assumption.
4
They find a negative
association between executions and homicide and conclude that there is a
net small deterrent effect from an additional execution. However, they also
find that executions appear to displace homicides in time. Thus, the long-
run deterrent effect is smaller than the short-run effect.
Taken on their own terms, Stolzenberg and D’Alessio (2004) and Land,
Teske, and Zhang (2009) provide contradictory evidence on deterrence.
Even though each paper uses monthly data from Texas, the papers reach
opposite conclusions about the evidence of a deterrent effect. This does not
mean that either paper contains errors, as the data sets used and the choice
of VAR specification differ across the papers. Nonetheless, the papers’
contradictory findings illustrate that conclusions about a deterrent effect
can be very sensitive to the choice of model and details as to how data are
transformed prior to estimation. What might be thought to be relatively
innocuous assumptions can matter greatly.
This observation leads to a broader critique of both papers. Neither
asks what conclusions about deterrence can be drawn when one does not
assume a particular time-series specification or when one allows for differ-
ent deterrent effects in different time periods. Neither the time-series speci-
fication nor the appropriate data range are known a priori to a researcher.
Although both papers engage in model selection exercises in order to gen-
erate specific VAR forms, this approach is inadequate for policy purposes.
Model selection methods in essence assign a weight of 1 to the “best”
model, given some criterion, but the data themselves do not necessarily
assign such a weight. In other words, neither paper appropriately accounts
for model uncertainty in providing deterrence estimates. The committee
returns to this issue in Chapter 6.
A more basic question is whether evidence of the type presented in
the Land, Teske, and Zhang (2009) and Stolzenberg and D’Alessio (2004)
analyses actually speaks to the question of the deterrent effect of capital
punishment. VARs only measure statistical associations in data. Thus, the
fundamental question is the relationship between the statistical concept of
Granger causality and the policy-relevant concept of causality as treatment
response. The remainder of this section mainly discusses this basic issue. We
then raise a second concern about criminological research that uses VARs.
4
One might plausibly argue that the assumption holds when time increments are short.
However it may be that the judicial system’s willingness to grant stays of execution is affected
by recent homicide activity, particularly when the homicides generate publicity.
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
86 DETERRENCE AND THE DEATH PENALTY
Granger Causality and Causality as Treatment Response
The idea that Granger causality speaks to a deterrent effect of capital
punishment is not a logical implication of social science theory. There may
perhaps be theories of deterrence in which the presence of a deterrence
effect would be equivalent to the statistical concept of Granger causality,
but no such theory has yet been advanced. However, there already exist
standard models of criminal behavior under which Granger causality tests
are uninformative about deterrence.
For the sake of concreteness, we focus on the model of rational criminal
behavior that has been the workhorse of much of the modern theory of de-
terrence, that of Becker (1968). This model, which assumes that the choice
of whether to commit a crime (in this case, homicide) can be understood as
a purposeful choice in which costs and benefits are compared, is controver-
sial among some criminologists, sociologists, and economists. A particular
concern has been the common assumption that potential criminals not only
behave rationally, but also have so-called rational expectations; that is, that
they correctly perceive the sanctions risk that they face. The discussion be-
low should not be interpreted as a committee endorsement of this specific
assumption or of the idea of rational criminal behavior more broadly. The
discussion is meant to illustrate how this widely used theoretical formula-
tion sharply delimits what can be learned from standard VAR estimates.
Put simply, the rational-criminal model places no restrictions on the
presence or absence of Granger causality from executions to homicides.
The reason the model does not imply such time-series restrictions on the
relationship between executions and homicides is not a function of its spe-
cific rationality assumptions; rather, the central point is that the rational-
criminal model supposes that individual beliefs about sanctions risks derive
from their perception of the criminal sanction regime in which they live, not
from the occurrence of executions per se.
The idea of a sanction regime is that a potential murderer faces a prob-
ability distribution of outcomes that will stem from the choice of committing
murder. The first uncertain outcome is whether the murderer will be caught.
Conditional on being caught, the potential murderer then faces a probability
distribution of punishments. With some simplification of the way the criminal
justice system works, the beliefs of a potential murderer about three probabil-
ities matter: (1) the probability of not being caught, P
NC
, (2) the probability
of being caught and serving a prison sentence, P
P
,
5
and (3) the probability of
being caught and being executed, P
E
. It is standard to regard P
C
= 1 – P
NC
as the certainty of punishment. The outcomes of imprisonment and execu-
5
In this example, we assume that there is a single prison sentence length for murder. In
practice, there are many potential prison sentence lengths and a rational criminal will account
for the probabilities of each of the sentences.
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
TIME-SERIES STUDIES 87
tion constitute the severity of punishment. The criminal sanction regime is
defined by those probabilities and the two outcomes, sentence length if not
executed and execution.
From the vantage of the rational-criminal model, short-run fluctuations
in the occurrence of executions are irrelevant to murder decisions unless
they cause individuals to revise their beliefs about the certainty and sever-
ity of punishment if a murder is committed. Although one can construct
theories as to why the occurrence of executions would lead to revisions in
beliefs (and one can find examples of such theories in the literature), tests
of Granger causality as they have so far been used do not speak to the
deterrence question. In particular, they ignore the distinction between the
criminal sanction regime and the time-series realizations of one of the po-
tential punishments under that regime, namely, executions. We emphasize
that this point does not depend on the assumption that potential murderers
rationally weigh the costs and benefits of murder. Rather, it rests on the
much weaker assumption that potential murderers respond to their beliefs
about sanction risks and not about execution events per se.
More specifically, a potential murderer makes the decision to commit a
homicide against the background of a set of uncertain outcomes to that act.
In a rational-criminal model, beliefs about sanction risk are not necessarily
affected by the occurrence of a relatively high or low number of executions
during the previous month or during any other time period. A potential
murderer may simply interpret time-series fluctuations in the occurrence of
executions as a reflection of time-series fluctuations in the number of people
convicted of murder several years earlier, each execution taking place under
a stationary sanction regime. Thus, execution events themselves need not
alter perceptions of the sanction regime. It follows that an empirical finding
of no Granger causality does not necessarily imply the absence of a deter-
rence effect to capital punishment.
Furthermore, if the candidate explanations for criminal behavior are
either that criminals are not subject to deterrent effects or that potential
murderers obey a rational model of criminal behavior, then Granger causal-
ity from executions to homicides does not necessarily provide support for
the deterrence explanation. For example, suppose the rational choice theory
of deterrence, which does not embody any explanation of the timing of ex-
ecutions, is correct. For the rational choice models under a stable sanction
regime, Granger causality from fluctuations in executions to fluctuations in
homicides tautologically occurs because of factors outside of changes in the
sanction regime. Hence, Granger causality from executions to homicides
cannot be attributed to the deterrence mechanism of the rational choice
model. The upshot is that the validity of the claim of deterrence cannot
alone be assessed by either the presence or the absence of Granger causal-
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
88 DETERRENCE AND THE DEATH PENALTY
ity from executions to homicides. It must be assessed in the context of a
behavioral model whether of the rational choice variety or not.
Under the rational-criminal model, one can potentially connect execu-
tion events to behavior if one discards the specific assumption of rational
expectations and instead supposes that people use data on the occurrence
of executions to update their subjective beliefs about the sanction regime in
which they live. Suggestions of such updating appear in the some studies,
but the committee is unaware of any formal model of beliefs and behavior
that make tests of Granger causality that have interpretable implications for
deterrence. Furthermore, as we emphasized earlier in the report, remarkably
little is known about the perceptions of would-be murderers or about how
their perceptions may change in response to executions.
Choice of Variables in VAR Studies
The use of vector autoregressions in the empirical studies of capital
punishment and deterrence suffers from a second important limitation:
insufficient attention to the choice of variables in the systems under study.
The studies that use Granger causality to study deterrence have been al-
most exclusively focused on bivariate relations of the type described by
equation (5-1). Although bivariate systems are relatively straightforward
to analyze, especially when one is interested in the effects of shocks to one
series on the behavior of another, they are not nearly as sophisticated as
the form of vector autoregression analysis that is now conventionally used
in macroeconomics, the field from which these methods are taken. In fact,
the evolution of atheoretical models in macroeconomics has illustrated the
importance of thinking about the time-series relationships among differ-
ent collections of variables. Modern vector autoregression analysis works
with far more complex systems than the bivariate ones found in studies of
capital punishment.
6
Without carefully specifying the set of relevant variables, findings from
the VAR studies on deterrence and capital punishment may be an artifice of
the choice of executions as the only variable that can affect homicides. For
capital punishment, there is an obvious lacuna when focus is restricted to
executions and homicides: entirely omitted are variables that measure the
severity of punishment for murderers who are not executed. Virtually any
behaviorally plausible formulation of deterrence would suggest that these
variables are an essential part of the sanction regime relevant to a would-be
murderer’s behavior.
The omission of time series of data that describe the noncapital pun-
6
For example, Leeper, Sims, and Zha (1996) analyze systems that use 13 and 18 distinct vari-
ables to study monetary policy and draw explicit contrasts with more parsimonious systems.
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
TIME-SERIES STUDIES 89
ishments meted out for homicides means that the bivariate systems omit
critical variables necessary for complete description of a sanction regime.
Therefore, even if people use observations of realized fluctuations in pun-
ishments to update their perceptions of sanction regimes, bivariate models
cannot be interpreted as giving evidence of the deterrent effect of capital
punishment per se. Fluctuations in the occurrence of executions may be
correlated with fluctuations in the severity of the prison terms received
by murderers who do not receive the death penalty, generating a classic
problem of omitted variables. The omitted variables problem affects vector
autoregressions just as it affects other types of regressions: spurious correla-
tions may be produced and parameter estimates may be biased.
This argument can be generalized. Crime rates are well understood
to vary with a host of demographic and socioeconomic variables. Land,
Teske, and Zhang (2009) and Stolzenberg and D’Alessio (2004) omit such
variables from their analyses. Findings of Granger causality or its absence
depends on the set of variables under consideration. Therefore, by the
standards of the modern use of vector autoregressions, neither of these
studies considers a rich enough system of variables to justify interpreting
their findings in terms of deterrence.
Inferences Under Alternative Sanction Regimes
The discussion above has concerned inference on deterrence under
existing sanction regimes. A distinct question concerns the capacity of
atheoretical time-series methods in general and Granger causality tests in
particular to provide information on the deterrent effect of capital punish-
ment under alternative sanction regimes from those that have existed and
currently exist in the United States. As described elsewhere in this report,
the historical capital punishment regime is one in which executions are very
infrequent in comparison with the numbers of homicides. Furthermore,
when a murderer is apprehended, execution typically does not occur even
when the murderer receives the death penalty in trial. Liebman, Fagan,
and West (2000) found that two-thirds of capital sentences are reversed
on appeal. As we note elsewhere in the report, only 15 percent of capital
sentences meted out between 1973 and 2009 have ended in an actual
execution.
The alleged strength of atheoretical time-series methods—which is
evinced in their reliance on the properties of the historical data as opposed
to a priori assumptions on how people or groups behave—has the necessary
consequence that these methods cannot speak to the deterrent effects of
substantively different criminal sanction regimes. Alternative criminal sanc-
tion regimes would imply different coefficients for the vector autoregression
system (5-1) if the individuals’ decision making or the process generating
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
90 DETERRENCE AND THE DEATH PENALTY
executions was different under an alternative regime. In other words, the
relationship between homicides and executions may depend on the criminal
sanction regime. Hence, the historical relationships that are estimated when
a system such as (5-1) is applied to data may change with the regime.
In macroeconomics, this dependence of statistical relationships on the
underlying policy regime (in this case, the sanction regime for murder) is
known as the Lucas critique (Lucas, 1976), although the idea goes back to
Marschak (1953). In the case of capital punishment, the force of the Lucas-
Marschak critique is self-evident. The available data on executions and
homicides are generated in a context in which actual executions are quite
unusual. As such, they are unlikely to provide useful information on hypo-
thetical regimes under which capital sentences are regularly carried out.
7
EVENT STUDIES
A second time-series approach used to study deterrence is what we
will call the “event study” because it focuses on the association between
homicide and a single execution or particular executions. This work takes
seriously the idea that an execution is an unusual event and implicitly as-
sumes that the event is of sufficient importance, considered relative to the
background of other determinants of homicide, that it leaves a discernible
footprint in the homicide time series.
This type of analysis was first performed by Phillips (1980), who identi-
fied 22 executions of “notorious murderers” in England in the period 1858-
1921. For each execution, he studied the number of homicides in London in
the weeks before and after the execution. He found a statistically significant
difference between homicide rates in the week prior to an execution and the
week after an execution. A more detailed analysis found that this reduction
was subsequently reversed, so that homicides were displaced in time rather
than reduced. In light of these results, Zeisel (1982) argued that Phillips’
evidence should be thought of as a delay rather than a deterrent effect.
Phillips (1982) did not dispute this alternative interpretation in his rejoinder.
In our view, the Phillips study is not useful in assessing deterrence ef-
fects. One issue, raised by Zeisel, is that the narrow time horizon studied
before and after the executions makes it hard to distinguish displacement
from deterrence. Another serious problem is Phillips’ assumption that in the
absence of a deterrent effect of execution, the process generating homicides
7
This distinction is well understood in the macroeconomic literature using vector autore-
gressions. Leeper and Zha (2003), for example, explicitly define criteria for “modest” policy
interventions under which VARs may be used for policy evaluation. The explicit objective of
their work is to identify vectors of shocks that occur with high enough probability that their
effects may be evaluated under the assumption that the policy regime generating the shocks
is unchanged.
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Deterrence and the Death Penalty
TIME-SERIES STUDIES 91
is stationary over time. This assumption motivates his test of the null hy-
pothesis that the homicide rate in the week before an execution is the same
as in the week after it. There is little reason to believe this null hypothesis
given that there are many potential sources of time variation in the deter-
minants of homicides beyond the effects of executions. As a stark example
of how Phillips’ approach can lead to spurious inferences, suppose that
England experienced a long-run decline in homicide during the 1858-1921
period that Phillips studied. In that situation, the data would tend to show
lower homicide rates in the week after executions than in the week before
simply because the week after occurs later than the week before. Without a
full specification of the properties of the total homicide process, one cannot
understand the effects of individual executions.
Another limitation of Phillips’ analysis concerns external validity. It is
not clear that the homicide process for England in 1858-1921 is the same
as that for the modern United States. By analogy, one would not use data
on the effects of changes in fiscal policy from 1858-1921 to evaluate current
macroeconomic policy proposals.
A second example of this style of analysis is Cochran, Chamblin,
and Seth (1994), which analyzed the effects of a particular execution on
homicides in Oklahoma. The execution studied was that of Charles Troy
Coleman. Coleman’s execution was the first in Oklahoma in 25 years. In
addition to sharing the same limitations as those in Phillips’ study, the
Oklahoma study has a fatal flaw in the research design. To see this, we
describe some of the details of the model used.
The raw data for the study were weekly homicides in Oklahoma, which
we denote as H
OK,t
. Prior to their analysis, the authors detrended and
demeaned this time series. The researchers next regressed the residuals on
lagged residuals. The result was a white-noise data series, e
OK,t
which repre-
sents the one-step-ahead forecast errors when H
OK,t
is regressed against its
history, after any constant term and trends are removed. They then defined
an intervention time series, I
t
, which equals 0 prior to the execution and 1
afterward. Finally, they estimated the equation
e
OK,t
= a
0
I
t
+ a
1
I
t–1
+ . . . +
x
OK,t
(5-2)
where x
OK,t
is a prediction error. They interpreted the coefficient a
1
as mea-
suring the effects of the execution. Different restrictions on this coefficient
were considered. For example, if the a
1
is required to sum to 0, this imposes
the restriction that there can be no permanent effect of the execution on
homicide rates, only a displacement effect.
The key conceptual problem with this approach is that it is logically
impossible for a white-noise stochastic process to be correlated with an in-
tervention series as it is defined here—there may be a correlation in a finite
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
92 DETERRENCE AND THE DEATH PENALTY
data sample but not in the population. The reason is simple: the white-noise
series has a mean of 0 and the intervention series does not. Hence, there is
nothing that can be learned from the exercise involving specifications that
do not impose the restriction that the long-run effect of the execution on
homicides is zero. In terms of the underlying time-series mathematics, the
“pre-whitening” described in the study assumes statistical properties for
the homicide series that are inconsistent with equation 5-2 (see Charles
and Durlauf, in press, for details). The authors argue the best specification
for 5-2 is one that does not impose the requirement that the a
1
coefficient
sums to 0. In other words, the authors argue that the best specification for
the effect of an execution on homicides is one that cannot in a population
produce the result they assert holds in the finite sample.
A more persuasive example of an event study of deterrence is
Hjalmarsson (2009). Methodologically, the approach in this paper origi-
nated in Grogger (1990), who proposed an appropriate statistical model for
such an analysis, treating the homicide level as a count variable. We focus
on the Hjalmarsson paper because it uses daily data and specifically focus
on cities in which capital punishment is relatively common.
The analysis considered very short-run effects of executions in Dallas,
Houston, and San Antonio, Texas. For the study, the daily counts of homi-
cides in the cities were analyzed to see whether homicide rates varied in the
days before and after an execution. Hjalmarsson found little evidence of a
“local” (in time) deterrence effect. She was careful not to extrapolate her
results to broader concepts of deterrence, recognizing that her limited time
horizon does not allow one to distinguish between displacement and deter-
rence. As such, the analysis suffers from one of the same flaws as Phillips
(1980), but her use of daily homicide counts may be useful to discern the
immediate visceral effect of an execution.
We caution, however, that even this extremely short-run analysis may
be susceptible to the problem that events relevant to homicide may co-occur
with executions. To give one simple example, police departments may alter
deployments of personnel in the periods immediately following executions
that draw public attention. If so, one cannot interpret fluctuations in ho-
micides immediately before and after an execution in terms of the deterrent
effect of the execution.
TIME-SERIES REGRESSIONS
Another strand of the literature estimates time-series regressions that
relate homicide rates or levels to executions and other covariates. Although
VARs are also time-series regressions, the work discussed in this section dif-
fers in several respects from the work discussed above. First, the regressions
are estimated using raw homicide and execution data rather than detrended
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
TIME-SERIES STUDIES 93
and demeaned data. Second, lagged homicides are not included among the
variables used to predict current homicides. Third, various other covari-
ates than lags of executions and homicides are used among the predictor
variables.
One example is the study by Bailey (1998), which considered the
Coleman execution in Oklahoma, but it modifies some aspects of Cochran,
Chamblin, and Seth (1994). In particular, this paper works with the time
series of the level of homicides rather than a transformation of the time
series into a white noise process, and it further includes various predictor
variables in addition to the event of the execution to model the homicide
level. Unfortunately, the paper does not report any equations, but the de-
scription it provides suggests that the analysis is based on the regression
H
OK,t
= k + aI
t
+ b
0
E
US,t
+ b
1
E
US,t–1
+ . . . g
0
P
OK,t
+ g
1
P
OK,t–1
+ . . . + dX
t
+ e
t
(5-3)
In this regression, E
US,t
is a measure of the number of executions in
the United States. The idea is that the public may be aware of these execu-
tions through various channels. P
OK,t
is a measure of the publicity given
to executions throughout the country, as measured by days of newspaper
coverage in the Oklahoman in a given week. This variable is intended to
measure public information about executions; it is distinct from E
US,t
in
that it measures a particular information source. X
t
is a vector of control
variables, which include socioeconomic and demographic characteristics, as
well as month-specific dummy variables; these dummies are included for ad
hoc reasons. The study finds that the overall level of murders is positively
associated with the publicity variables. When focus is limited to overall kill-
ings of strangers, as well as subsets of this category, the results are mixed,
with some regressions finding a brutalization effect, others finding no effect,
and some cases finding a deterrence effect.
Despite these mixed results, Bailey concludes that “No prior study has
shown such strong support for the capital punishment and brutalization
argument” (Bailey, 1998, p. 711). The author, in our view, overstates his
findings by focusing on regressions with statistically significant coefficients.
Other regressions, in which statistical significance fails, are not accounted
for in the author’s strong conclusions. As noted in Chapter 4, a finding that
an estimate is statistically insignificant does not imply that the true deter-
rent effect is zero or even that it is small. In other words, the study does
not properly account for the dependence of the brutalization findings on
particular regression specifications.
Beyond the specifics of Bailey’s study, this type of regression analy-
sis, although still common in the social sciences, does not support causal
claims. Regressions of this type are based on many arbitrary assumptions,
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
94 DETERRENCE AND THE DEATH PENALTY
such as linearity of the effects of executions and other variables on homi-
cides, as well as particular choice of control variables, without attention to
the effects of alternative choices. Furthermore, despite the author’s claims,
the execution of Coleman does not constitute a quasi-experiment. The tim-
ing of the execution is likely to be an endogenous outcome of the criminal
justice system and should be modeled as such.
A different type of time-series regression analysis has been used by
Cloninger (1992) and Cloninger and Marchesini (2001, 2006). These pa-
pers in essence estimate time-series regressions of the form
DH
i,t
= k + bDH
US,t
+ e
i,t
(5-4)
Here DH
i,t
denotes the change across years in the homicide rate in place I,
and DH
US,t
denotes the similar change in the United States as a whole. The
researchers attempt to motivate this regression specification by analogy to
the capital asset pricing model (CAPM) of finance.
8
These studies, for peri-
ods with executions, evaluate deterrence by asking whether b, the average
of DH
i,t
, and the average of e
i,t
is smaller in periods in which capital punish-
ment either is possible or actually occurs. Taken as a whole, these studies
find a deterrent effect for a capital punishment regime.
The committee concludes that the findings of these studies are not in-
terpretable as providing evidence of a deterrent effect. The basic problem
is that the analogy between a portfolio of assets and a portfolio of crimes
is specious. The homicide model under study is constructed exclusively by
analogy with finance. It pays no attention to the criminal justice system as
an input in criminal decisions, time constraints on the part of criminals,
differences in the reasons for crimes, etc. The various studies that use this
methodology assert that all such factors are incorporated in the coefficient
b, but there is no reason to believe that this is true. Because CAPM is
predicated on investors’ optimally investing in financial instruments in the
context of competitive markets for these products, for Cloninger’s specifica-
tion to be sensible he would have to demonstrate that potential murderers
engage in an analogous optimization problem that is aggregated to produce
state-level homicide rates. No attempt is made to demonstrate this analogy.
CROSS-POLITY COMPARISONS
Yet another time-series approach to measuring the deterrent effect of
capital punishment is comparison of time series for homicides in two coun-
tries, one of which has capital punishment and the other of which does not,
8
The capital asset pricing model describes the relationship between risk and expected return
for different assets. See Brennan (2008) for a description.
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
TIME-SERIES STUDIES 95
to see whether one can identify differences between the time series that may
be plausibly attributed to capital punishment. In Chapter 3, for example,
the committee displays homicide rates in, California, New York, and Texas,
from 1974 through the early 1990s (see Figure 3-3) to illustrate the impor-
tance of accounting for variations, across time and place, in factors that
influence murder rates other than the use of capital punishment. Donohue
and Wolfers (2005) use this method and argue that the close tracking of
the U.S. and Canadian homicide rates calls into question any deterrence
effect to the death penalty, since this punishment only exists in the United
States. Their argument is at best suggestive because they do not account
for common trends in the two series, let alone common factors, such as the
interdependence of the Canadian and American economies. It also does
not take into account the de facto moratorium in the death penalty in the
United States prior to the Furman decision. Thus, the fact that the U.S. and
Canadian homicide series are highly correlated is not a legitimate basis for
concluding that there is no deterrent effect of capital punishment in the
United States.
In examining the cross-country differences in the homicide series in
Singapore and Hong Kong, Zimring, Fagan, and Johnson (2010), to their
credit, recognized that an informal comparison from two selected entities
alone is not sufficient to draw inferences. Unfortunately, their more system-
atic efforts cannot address the data and modeling flaws in the study.
The basic idea of the Zimring, Fagan, and Johnson (2010) study is to
see whether differences in the Singapore and Hong Kong homicide rates
can be explained by execution rates in Singapore, none having occurred
in Hong Kong over the time frame of the analysis. Letting h
S,t
denote the
Singapore homicide rate in year t and h
HK,t
the Hong Kong homicide rate in
year t, the paper examines whether h
S,t
– h
HK,t
, once trends are accounted
for, is associated with either the execution rate for Singapore or the execu-
tion level in Singapore. Both contemporaneous and lagged effects of these
execution variables are considered.
Singapore and Hong Kong were chosen on the basis that they are very
similar polities, so that differences in the homicide rates between them can-
not be attributed to differences in demographics or socioeconomic factors.
The researchers further argue that the relative commonality of executions
in Singapore in contrast with the United States makes the analysis of the
two cities particularly informative. The study concludes that executions do
not have predictive power for homicide differences between the two cities.
The committee concludes that this study fails to provide evidence on
the deterrence question. One problem with the analysis has already been
raised in our critical discussion above of the vector autoregression approach
to deterrence: the failure to distinguish between the effects of a sanction
regime on homicides and the effects of fluctuations in the rate of execu-
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
96 DETERRENCE AND THE DEATH PENALTY
tions. The researchers argue that “Singapore is a best case for deterrence
because a death sentence is mandatory for murder and because of celerity
in the appeals process” (Zimring, Fagan, and Johnson, 2010, p. 2). In other
words, Singapore, like Hong Kong, has a constant sanction regime over the
sample. The authors (pp. 9-10) raise the idea that the execution rate matters
for a potential murderer’s beliefs about the likelihood of being executed, but
this assertion is rendered less plausible by their claims of regime stability
for Singapore. If one thinks that deterrence depends on perceptions of the
sanction regime, then the authors’ own argument about regime stability
undermines a role for executions in learning. Such stability eliminates one
channel by which executions might be informative about deterrence.
A distinct reason that this study is not informative about the deter-
rent effect of capital punishment is that the key assumption underlying the
analysis—that any systematic or predictable component of the homicide
rate difference, h
HK,t
h
S,t
, can only be due to capital punishment—is not
credible. The paper’s own regressions lead inevitably to this conclusion. In
addition to studying the difference h
HK,t
h
S,t
, the researchers also perform
regressions of the Singapore homicide rate h
S,t
on the Hong Kong homicide
rate h
HK,t
and their various execution measures. The logic of their thought
experiment would require that h
HK,t
is a statistically significant predictor of
h
S,t
, with a regression coefficient of 1. The validity of their analysis, in other
words, is predicated on the assumption that the homicide rate in Hong
Kong is a sufficient statistic for the homicide rate in Singapore, except for
the presence of capital punishment in Singapore. In fact, the study found
that the homicide rate in Hong Kong fails to predict the homicide rate in
Singapore: the coefficient is far from 1 in value and far from statistical
significance. Hence, the researchers’ own analysis indicates that the key
assumption that justifies their analysis is not valid.
The study by Zimring, Fagan, and Johnson (2009) also suffers from
first-order data problems. As the researchers note, the government of Sin-
gapore does not publish statistics on executions, and it routinely executes
individuals convicted of a wide variety of crimes other than homicide. This
leads the researchers to rely on constructed measures of executions and
executions for murder. However, there are problems in the use of these con-
structed series. First, measurement error in independent variables produces
biased estimates of coefficients; in the standard bivariate regression model,
this bias reduces coefficient magnitude toward 0. Hence, their finding of a
lack of evidence may be due to defects in their measure. The best the re-
searchers can say about their estimated overall homicide series is that “we
have developed a reliable minimum estimate of Singapore executions since
1981” (Zimring, Fagan, and Johnson, 2009, p. 7). This is uninformative as
to what the degree of bias is in their estimates.
Second, the authors end up in an incoherent position in terms of map-
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
TIME-SERIES STUDIES 97
ping executions to the perceptions of potential murderers. In response to
the lack of data on the split between executions for murder and executions
for other crime, they argue that “But, of course, no data are available to the
citizens of Singapore either, so the gross execution rate may be the appro-
priate risk for homicide to the extent that potential homicide offenders are
aware of executions” (p. 6). The authors give no explanation as to how the
potential murderers could possibly be aware of the overall execution rate
but have no knowledge of the execution rate for particular offenses. Since
the researchers conclude that data limitations prevent them from providing
“stable and robust estimates of the unique effects of murder executions on
murder” (p. 22), it is not clear why their negative findings on deterrence
are informative about deterrence for murder.
The issue is not whether the authors did the best they could with the
limited data, but whether the limited data allow one to draw inferences
about deterrence. Note as well that given the researchers’ own description
of capital punishment in Singapore—“The secret nature of both individual
executions and aggregate murder statistics must be a deliberate choice of
the highly centralized and statistically meticulous Singapore government”
(p. 10)—there is no good reason to believe that any results from their study
are informative about capital punishment in the United States, where in-
formation available to the public is of course completely different, leaving
aside all other differences between the two countries.
CONCLUSIONS
The committee analysis of the different strategies for using time series
to uncover deterrent effects for capital punishment has consistently found
the inferential claims to be flawed, whether the study in question does
or does not find evidence of a deterrence effect. A common theme in our
critiques of individual studies is that the underlying “decision theory” of
potential murderers is consistently un- or underspecified, so that the impli-
cations of the time-series relationships between executions and homicide
rates is unclear. Why should actual executions, as opposed to the sanction
regime, matter? As discussed above, following the logic of the strong form
of the rational-criminal model that assumes rational expectations, there
should be no effect from executions by themselves, since the sanction re-
gime entirely determines the deterrence effect. This fact means that the time-
series studies suffer from a common identification problem: the existence
of plausible theories of the behavior of potential murderers for which the
time-series relationships are uninformative about the presence or absence
of a deterrence effect, let alone its magnitude.
Of course, it is possible that the correct behavioral model for potential
murderers is one for which the time-series relationships are informative.
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
98 DETERRENCE AND THE DEATH PENALTY
One possibility is that actual executions affect a potential murderer’s sub-
jective probability of being executed if he commits the crime. If this is the
rationale for the exercises, then Texas is not the ideal context for a study
because executions are sufficiently routine in Texas that one would expect
the informational content of a specific occurrence to be low. Yet because of
the state’s high fraction of executions nationally, Texas data are frequently
used for studies. Texas might have experienced changes in the execution
sanction regime, which would be useful for identifying deterrent effects,
but this perspective has not been systematically explored, despite some oc-
casional references to regime shifts in Texas.
9
In this respect, we think that
the focus on Texas in the time-series literature may be misguided.
Another behavioral framework under which these exercises are infor-
mative is one in which an execution renders the possibility of the punish-
ment more salient to a potential murderer. But such a framework would
appear to imply that the effects of an execution will exhibit heterogeneity
across types of potential murderers. For example, when murder is a crime
of passion, one might argue that executive mental functioning is impaired.
Hence, in this case salience comes into play because of a diminished capac-
ity in thinking about consequences. Alternatively, one could argue that the
impairment is such that the consequences of the action do not affect choice.
This example illustrates that the implications of salience claims are far from
obvious. Furthermore, we are unaware of any work that directly addresses
salience as a source of deterrence and does so in a way that respects the fact
that one needs a model of behavior, whether of the rational choice type or
not, to interpret statistical findings.
Finally, we note that it is not even clear that executions per se are the
source of salience. Is it obvious that actual executions are the main source
of salience of the death penalty rather than, say, highly publicized death
sentences? How do changes in the law or Supreme Court decisions affect
salience? In the committee’s search of relevant studies, we did not find any
in which the sources of salience were explored. Hence, although it is a
perfectly logically coherent idea that executions make capital punishment
salient and provides a deterrence effect for this reason, there is no empiri-
cal work to justify the claim. One of the recommendations in Chapter 6
will involve the collection of data on perceptions of sanction regime, which
would facilitate such empirical work.
Another distinct problem with the time-series studies is that they do
9
Land, Teske, and Zheng (2009) should be commended for distinguishing between periods
in Texas when the use of capital punishment appears to have been erratic and when it appears
to have been systematic. But they fail to integrate this distinction into a coherently delineated
behavioral model that incorporates sanctions regimes, salience, and deterrence. And, as
explained above, their claims of evidence of deterrence in the systematic regime are flawed.
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
TIME-SERIES STUDIES 99
not provide a logical basis for linking the statistical findings back to a
state’s capital punishment sanction regime. Suppose, for example, that an
execution event study was conducted that provided credible evidence that
the execution either increased or decreased homicides that are eligible for
capital punishment. Such a study would not provide the basis for altering
the sanction regime to either increase or decrease the number of executions
because it would not be informative about what aspect of the regime caused
the execution to have the effect identified by the study.
In summary, the committee finds that adequate justifications have not
been provided to demonstrate that the various time-series-based studies of
capital punishment speak to the deterrence question. It is thus immaterial
whether the studies purport to find evidence in favor or against deterrence.
They do not rise to the level of credible evidence on the deterrent effect of
capital punishment as a determinant of aggregate homicide rates and are
not useful in evaluating capital punishment as a public policy.
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Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
6
Challenges to Identifying
Deterrent Effects
R
esearchers from diverse disciplines have contributed to the capital
punishment literature, with prominent contributions by economists,
criminologists, and sociologists. Although researchers’ disciplinary
backgrounds have affected the methods used and the framing of the re-
search questions, the failings of the capital punishment literature are not
rooted in the use of particular empirical methods or theoretical models
of criminal decision making. Rather, the failings are rooted in manifest
deficiencies related to the research data and methods and the researchers’
interpretations of results. Chapters 4 and 5 call attention, respectively, to
fundamental deficiencies in panel and time-series studies. Both approaches
share two basic deficiencies and also manifest two others to some degree.
One shared deficiency is grossly incomplete specification of the sanction re-
gime for homicide. Even in states that make the most frequent use of capital
sanctions, noncapital sanctions are the most common sanction imposed for
a homicide conviction. No study of either type accounts for the noncapi-
tal component of the sanction regime in states with and without capital
punishment. The second basic deficiency is failure to pose a credible model
of the sanction risk perceptions of potential murderers and the behavioral
response to such perceptions. In the absence of such a model, it is difficult,
at best, to interpret data relating sanction regimes to homicide rates.
As discussed in Chapters 4 and 5, these two deficiencies are sufficient
to make existing studies uninformative about the effect of capital punish-
ment on homicide. Both of these deficiencies are potentially correctable.
However, even if the research and data collection initiatives discussed in
this chapter are ultimately successful, research in both literatures share a
101
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
102 DETERRENCE AND THE DEATH PENALTY
common characteristic of invoking strong, often unverifiable, assumptions
in order to provide point estimates of the effect of capital punishment on
homicides. A point estimate may offer the appearance of desirable certitude,
but only at a high cost in credibility. Still another deficiency is inattention
to potential feedbacks through which homicide rates, and crime rates more
generally, may affect the specification and administration of a sanction
regime while the regime simultaneously affects homicide rates. Recogni-
tion of potential feedbacks is relevant both to identify the direct effect of
capital punishment on homicide rates and to predict the ultimate effect after
feedbacks occur. Feedbacks affect the time-series and panel studies differ-
ently because of differences in the time frames of the data typically used in
the two approaches—monthly, weekly, or even daily data in the time-series
studies and annual data in the panel studies.
In light of these deficiencies, the committee has reached the following
conclusion and recommendation:
CONCLUSION AND RECOMMENDATION: The committee con-
cludes that research to date on the effect of capital punishment on homi-
cide is not informative about whether capital punishment decreases,
increases, or has no effect on homicide rates. Therefore, the committee
recommends that these studies not be used to inform deliberations re-
quiring judgments about the effect of the death penalty on homicide.
Consequently, claims that research demonstrates that capital punish-
ment decreases or increases the homicide rate by a specied amount or
has no effect on the homicide rate should not inuence policy judgments
about capital punishment.
The committee was disappointed to reach the conclusion that research
conducted in the 30 years since the National Research Council (1978)
report on this subject has not sufficiently advanced knowledge to allow
a conclusion, however qualified, about the effect of the death penalty on
homicide rates. Yet this is our conclusion. Some studies play the useful role,
either intentionally or not, of demonstrating the fragility of their claims to
have found—or not to have found—deterrent effects. However, even these
studies suffer from two intrinsic shortcomings that severely limit what can
be learned from them about the effect of the death penalty on homicide
rates from an examination of the death penalty as it has actually been ad-
ministered in the United States in the past 35 years.
Commentary on research findings often pits studies claiming to find
statistically significant deterrent effects against those finding no statistically
significant effects, with the latter studies sometimes interpreted as imply-
ing that there is no deterrent effect. A fundamental point of logic about
hypothesis testing is that failure to reject a null hypothesis does not imply
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Deterrence and the Death Penalty
CHALLENGES TO IDENTIFYING DETERRENT EFFECTS 103
that the null hypothesis is correct. For the evidence of even a small effect to
be credible, it requires a demonstration, first and foremost, that the effect is
based on a sound research design. Estimates that lack credibility are not in-
formative regardless of the consistency of their estimated size. The amount
of the effect must also be small in size and estimated with good precision,
for example, by being contained within a tight confidence interval.
Our mandate was not to assess whether competing hypotheses about
the existence of marginal deterrence from capital punishment are plausible,
but simply to assess whether the empirical studies that we have reviewed
provide scientifically valid evidence. In its deliberations and in this report,
the committee has made a concerted effort not to approach this question
with a prior assumption about deterrence. Having reviewed the research
that purports to provide useful evidence for or against the hypothesis that
the death penalty affects homicide rates, we conclude that it does not pro-
vide such evidence.
We stress, however, as noted above, that a lack of evidence is not evi-
dence for or against the hypothesis. Hence, the committee does not construe
its conclusion that the existing studies are uninformative as favoring one
side or the other side in the long-standing societal debate about deterrence
and the death penalty.
In this chapter, we elaborate on these deficiencies that form the basis
for this conclusion and cautiously offer some ideas on potential remedies.
With regard to remedies, our report provides a somewhat less pessimistic
perspective than did the earlier National Research Council (1978, p. 63)
report: “[T]he Panel considers that research on this topic is not likely to
produce findings that will or should have much influence on policymakers.”
The committee does not expect that advances in collecting data on
sanction regimes and obtaining knowledge of sanctions risk perceptions
will come quickly or easily. However, data collection on the noncapital
component of the sanction regime need not be entirely complete to be use-
ful. And even if research on perceptions of the risk of capital punishment
cannot resolve all major issues, some progress would be an important step
forward. Even if these advances prove unsuccessful in providing useful
information on the incremental deterrent effect of capital punishment in
relation to a lengthy prison sentence, the committee believes that there are
potentially major benefits from new data collection, theory, and methodol-
ogy for study of the effect of noncapital sanctions on crimes not subject
to the death penalty. As discussed in Chapter 1, because of the overlap in
the methods and data used in studies of capital punishment and in broader
studies on the effects of sanctions on crime, our charge included a provi-
sion for recommending research that might advance that broader research
literature, and we do so in the rest of this chapter.
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Deterrence and the Death Penalty
104 DETERRENCE AND THE DEATH PENALTY
DATA ON SANCTION REGIMES
Incomplete and inaccurate data have marred research on the effect of
capital punishment on homicides. The most important data problem is that
studies have been based on a very incomplete specification of state sanction
regimes. Part of the difficulty has been lack of conceptual agreement on
how to measure the intensity of use of capital punishment. However, we
see the primary problem as a complete absence of data on the noncapital
sanctions that might be applied to offenders convicted of homicide. A study
of capital punishment in North Carolina by Cook (2009) illustrates the im-
portance of the problem of the absence of information on noncapital sanc-
tions. Of 274 cases prosecuted as capital cases, only 11 resulted in a death
sentence. Another 42 resulted in dismissal or a verdict of not guilty, which
left 221 cases that resulted in convictions and received noncapital sanctions.
As discussed at length in Chapter 4 and below, there are sound reasons
for predicting a correlation between the capital and noncapital components
of a state’s sanction regime. Two examples of how this might occur are the
plea bargaining leverage that the threat of capital punishment may afford
prosecutors and the influence of the state’s political culture on the legislated
design and administration of both the capital and noncapital components
of the regime. Such a correlation would bias the estimated deterrent effect
of capital punishment.
None of the studies we reviewed sought to measure the availability
and intensity of use of the noncapital sanction alternatives for the punish-
ment of homicide. Such alternatives may include a life sentence without
the possibility of parole, a life sentence with the possibility of parole, and
sentences of less than life. It would also be important to have data on the
time actually served for convicted murderers who are paroled or who serve
less than a life sentence.
It is currently not possible to measure noncapital sanction alternatives
at the state level because the required data are not available. The data that
are available include those from the Bureau of Justice Statistics (BJS), which
publishes nationwide statistics on sentences for prison admissions and time
served for prison releases, based on data collected as part of the National
Corrections Reporting Program (NCRP) initiated in the early 1980s. More
than 40 states now report annual data on sentences for admissions and
time served for releases. Individual-level demographic characteristics are
also reported. In principle, these data could be used to measure the actual
administration of the legally authorized dimensions of most state sanction
regimes, not only for murder but also for other types of crimes. The dif-
ficulty is that the data are often extremely incomplete.
In some years, states fail to report any data. Just as important, the
data that are sent to BJS are often so incomplete that it is impossible to
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Deterrence and the Death Penalty
CHALLENGES TO IDENTIFYING DETERRENT EFFECTS 105
construct valid state-level measures of the administration of the sanction
regime. Indeed, the committee attempted to use these data for the purposes
of this report but concluded that the data gaps made their use infeasible.
More complete data on the actual administration of sanction regimes might
be obtained by expanding the NCRP to include all 50 states and filling the
data gaps due to incomplete reporting. Alternatively, an entirely new data
collection system might be desirable. Either way, the collection of more
complete data on sanction regimes for murder and other crimes is feasible.
The data are available: the challenge is designing and implementing an ef-
fective system for their collection.
Even if data on the actual administration of state sanction regimes were
complete, they could only be used to measure how sanction regimes are
actually administered. The data do not specify the potential sanction regime
in a state—the range of sanction alternatives that are legally authorized.
We are not aware of any ongoing effort to assemble data on the legislated
sanction regimes of the states for murder and other crimes. Data on the
legislated regime are important because they define the range of penalties
that can potentially be imposed. Thus, the measurement of legally autho-
rized sanctions by the states for homicides and other crimes may require a
new data collection system.
The committee did not explore the benefits and costs of alternative ap-
proaches for measurement of state-level sanction regimes for murder. We
only emphasize the vital importance of collecting these data.
RECOMMENDATION: The committee recommends that a concerted
effort be made to collect data on the sanctions regimes faced by poten-
tial murderers, with particular attention to xing the current absence
of data on noncapital sanctions.
As noted above, because the methods and data used to study the effect
of noncapital sanctions on crimes other than murder are similar to those
used in research on capital punishment, the committee’s charge includes a
provision that we make recommendations for advancing research on the
broad effects of sanctions on crime. Thus, we also stress the vital impor-
tance of an expanded effort to collect data suitable not only for measuring
sanction regimes for murder, but also for measuring sanction regimes for
other major crimes.
PERCEPTIONS OF SANCTION RISKS
As emphasized in Chapter 3, it is not possible to interpret empirical
evidence on the relationship of homicide rates to sanctions without un-
derstanding how potential murderers perceive sanction regimes. The com-
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Deterrence and the Death Penalty
106 DETERRENCE AND THE DEATH PENALTY
mittee’s review of the time-series and panel studies identified fundamental
deficiencies in this regard.
In the case of the time-series studies, none of them explicitly articulates
a model of sanction risk perceptions. The studies are silent on whether
execution events and their frequency alter perceptions of sanction regimes.
Moreover, the studies do not ask whether the trend lines specified by
researchers correspond to the trend line (if any) perceived by potential
murderers.
Panel studies typically suppose that people who are contemplating mur-
der perceive sanctions risks as subjective probabilities of arrest, conviction,
and execution. Lacking data on these subjective probabilities, researchers
presume that they are somehow based on the observable frequencies of ar-
rest, conviction, and execution.
The fundamental problem is that perceptions of the risk of sanction
are subjective, but researchers have no direct measurements of the percep-
tions of potential murderers. In the absence of data on risk perceptions,
the research practice in the panel studies has been to use publicly available
data on homicides and executions to construct statistics that purport to
measure the objective risk of execution. Then, having done that, many
researchers assume that potential murderers have “rational expectations.”
The word “rational” suggests that potential murderers carefully assess the
risk of execution. What “rational expectations” actually means in practice
is that researchers construct their own measures of execution risk and as-
sume that potential murderers perceive the risk in the same way. However,
the assumption of rational expectations of execution risk has no empirical
foundation. Indeed, it hardly seems credible.
In Chapter 4, we discuss in detail the complications of calculating the
objective risk of execution. One of these complications is that only 15 per-
cent of individuals sentenced to death have actually been executed (since
the resumption of the death penalty in 1976) and that a large fraction of
death sentences are subsequently reversed. Another complication is that
the volume of data on death sentences and executions available for form-
ing perceptions depends on the size of the state. By various measures of
execution risk, Delaware was at least as aggressive as Texas in its use of the
death penalty. However, over the period 1976 to 2000, Delaware sentenced
28 people to death and carried out 11 executions, while Texas sentenced 753
people to death and carried out 231 executions. Still another complication
is that sanction regimes are not stable due to changes in a state’s political
leadership, moratoriums on executions, and legal decisions. Yet another
complication is that there are within-state differences in the risk of execu-
tion due to differences across counties in prosecutorial vigor in the use of the
death penalty and local differences in receptivity to its application.
These many complications make clear that even with a concerted effort
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
CHALLENGES TO IDENTIFYING DETERRENT EFFECTS 107
by careful, conscientious researchers to assemble and analyze relevant data
on death sentences and executions, assessment of the evolving objective
risk of execution facing a potential murderer is a daunting challenge. It is
also clear that perceptions of this risk among potential murderers must at
best be highly impressionistic. To make headway on whether and to what
degree the death penalty affects the behavior of potential murderers, it is
imperative to have knowledge about how their perceptions of execution
risk are formed and then possibly revised on the basis of new information.
RECOMMENDATION: The committee strongly recommends that a
concerted effort be made to research the origins and nature of execu-
tion sanctions risk perceptions specically and of noncapital sanctions
risks more broadly.
Measurement of Perceptions
The essential task is to measure the perceptions of sanctions risks that
potential murderers actually hold. How might this be done?
One possibility is to take seriously the presumption in the panel stud-
ies that people who are contemplating murder perceive sanctions risks as
subjective probabilities of arrest, conviction, and execution. This possibil-
ity suggests that the risk perceptions of potential murderers be measured
probabilistically.
Researchers have developed considerable experience measuring beliefs
probabilistically in broad population surveys. Manski (2004) reviews the
history in several disciplines, describes the emergence of the modern litera-
ture, summarizes applications, and discusses open issues. Among the major
U.S. platforms for collection of such data, the Health and Retirement Study
(HRS) has periodically elicited probabilistic expectations of retirement,
bequests, and mortality from multiple cohorts of older Americans (see,
e.g., Hurd and McGarry, 1995, 2002; Hurd, Smith, and Zissimopoulos,
2004). The Survey of Economic Expectations (SEE) has asked repeated
population cross sections to state the percent chance that they will lose
their jobs, have health insurance, or be victims of crime in the year ahead
(see, e.g., Dominitz and Manski, 1997; Manski and Straub, 2000). The
National Longitudinal Survey of Youth 1997 has periodically asked young
people about the chance that they will become a parent, be arrested, or
complete schooling (see, e.g., Fischhoff et al., 2000; Lochner, 2007). Ex-
amples of victimization and arrest questions include, “What do you think
is the percent chance that your home will be burglarized in the next year?”
“What do you think is the percent chance that you will be arrested in the
next year?” Researchers have learned from these and other surveys that
most people have little difficulty, once the concept is introduced, in using
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
108 DETERRENCE AND THE DEATH PENALTY
subjective probabilities to express the likelihood they place on future events
relevant to their lives.
However, success in measuring beliefs probabilistically within the gen-
eral public does not imply that survey research could similarly measure
the sanction risk perceptions of potential murderers. A major issue when
initiating study of this type is to obtain data from the relevant population,
in this case, the population of potential murderers. Theoretically, most
people who would be legally eligible to be executed (e.g., are not juveniles
or of very low intelligence) are also physically capable of committing a
murder and thereby are potential murderers. The reality, however, is that
the probability of most people committing a murder is so small that as a
practical matter it can be treated as zero. Even the probabilities of people
committing other serious crimes, such as robbery and burglary, while likely
greater, are still extremely small. Thus, when using the term “potential
murderer,” one means that part of population with a non-negligible risk of
committing murder.
Thus, the first step and an important prerequisite for a program of
research on sanction risk perceptions is to define the relevant population of
potential murderers and, more generally, potential criminals. Such a defini-
tion will be required to devise cost-effective sampling strategies for inter-
viewing people with nontrivial risks of committing crimes. We expect that
one important segment of the relevant population is people with criminal
records. The correlation between past and future offending is among the
best documented empirical regularities in criminology (National Research
Council, 1986; West and Farrington, 1973; Wolfgang, 1958). In the case
of murder, for example, Cook, Ludwig, and Braga (2005) found that 43
percent of murderers in Illinois had a felony conviction.
Some may question the feasibility of collecting data on the sanction risk
perceptions and criminal behavior of individuals with prior histories of seri-
ous crimes, especially if subjects are repeatedly interviewed for the purpose
of obtaining longitudinal data. Longitudinal data are useful to study how
offending experience and external events, such as police crackdowns or
policy changes, affect sanction risk perceptions. However, experience dem-
onstrates that, with sufficient diligence, it is feasible to collect longitudinal
data on highly crime-prone people.
A leading example is the Pathways to Desistance Project (Mulvey,
2011), a two-site longitudinal study of desistance from crime among seri-
ous adolescent offenders. The project recruited 1,354 adolescents from the
Philadelphia and Phoenix juvenile and adult court systems who had been
adjudicated as delinquent or found guilty of a serious felony and were 14
to 17 years old at the time that they committed the offense. For the first 4
years of the study, interviews were conducted at 6-month intervals and for
the next 3 years the interviews were annual. The retention rate was quite
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
CHALLENGES TO IDENTIFYING DETERRENT EFFECTS 109
high, with 87 percent of the subjects interviewed in at least 8 of the 10
interview cycles. Respondents were asked about their perceptions of sanc-
tions risks, among other things. The success of this project indicates that
collection of data on sanction risk perceptions from crime-prone popula-
tions is feasible with a sustained commitment among a cadre of researchers
and with the availability of funding.
Apel (in press) reviews the existing research that measures perceptions
of sanction risks. Although there have been a scattering of suggestive stud-
ies, there has not yet been systematic large-scale research on the subject.
Moreover, there has been no research at all on the specific question of per-
ceptions of the sanction risk associated with commission of murder.
With so much to learn, we think it prudent for research to proceed
sequentially. A good beginning would be small-scale studies that include
one-on-one cognitive interviews with respondents in the relevant popula-
tion of potential murderers. These interviews, taking the form of structured
conversations, would explore the feasibility and usefulness of probabilistic
and other modes of questioning about sanction risk perception. The lessons
learned from this exploratory research would inform the design of larger
studies, the aim being to eventually develop a program of survey research
that would regularly measure the perceptions of the sanction risk held by
potential murderers and by potential criminals more generally.
The committee is not confident that measurement of the sanctions risk
perceptions of potential murderers can succeed in producing information
useful to the study of deterrence, but one cannot be sure unless the effort is
made. As demonstrated by the discussion in Chapters 4 and 5, the alterna-
tive of continuing to make unfounded assumptions about these perceptions
is not useful. Measurement of sanction risk perceptions may enable deter-
rence research to make progress that thus far has not been possible in the
absence of data.
The committee is more optimistic about the feasibility and usefulness
of measuring perceptions of sanctions risks among potential criminals more
broadly. This greater optimism has two bases. First, homicide is the least
frequent of the crimes included in the “Part 1-Crime Index” of the Federal
Bureau of Investigation (FBI), which also includes rape, robbery, aggravated
assault, burglary, larceny, and auto theft. More people commit all the other
crimes than commit homicides. Thus, it will probably be easier to survey
sizable numbers of potential perpetrators of these crimes than of potential
murderers. The National Survey of Youth, for example, already surveys
youth and young adults about their involvement in such crimes as theft,
selling drugs, and assault.
Second, perpetrators who are apprehended for crimes less serious than
murder are far less likely to receive lengthy prison sentences, particularly if
they are juveniles. Thus, these people have more opportunity to learn about
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
110 DETERRENCE AND THE DEATH PENALTY
sanction risk on the basis of personal experience, a source of information
that may be vital to formation of sanction risk perceptions.
Inference on Perceptions from Homicide Rates Following Executions
As a complement to research that directly measures perceptions, some
committee members believe that study of homicide rates immediately fol-
lowing execution events might also provide useful evidence of the percep-
tions of potential murderers. As discussed in Chapter 5, the time-series
research has largely been devoted to the question of whether homicide
rates change in the immediate aftermath of an execution. For the reasons
detailed in that chapter, the committee concluded that existing studies were
not informative about whether capital punishment affects homicide rates,
in part because of the absence of any measure of perceptions.
The committee considered at length whether future research on execu-
tion events, if properly conducted, might be informative about whether
homicide rates, at least in the short term, are responsive to execution events.
We concluded that at best the information to be gleaned from this type of
research would be limited and fall far short of establishing whether capital
punishment increases, decreases, or has no effect on homicide rates. Even if
a short-term impact could be established, it would be difficult to determine
whether homicides were actually prevented or simply displaced in time.
More fundamentally, execution event studies cannot speak to the question
of whether and how the state’s overall sanction regime affects the homicide
rate. For example, a null finding from an event study would leave open the
possibility that a death penalty regime had a deterrent effect relative to a
regime that precluded the death penalty or more narrowly prescribed its
applicability. It is important to note that any one execution would only
have a deterrent effect if it changed potential murderers’ perceptions of the
likelihood of an execution, which is not necessarily the case.
Acknowledging these limitations, some committee members nonethe-
less argue that if a well-done event study did produce evidence of an
effect—whether positive or negative and no matter how temporary—that
result would be of considerable interest. It would demonstrate that po-
tential murderers as a group are actually paying attention to the state’s
actions and are influenced by them. In short, it would confirm a threshold
condition for there to be a deterrent or brutalization effect and invite fur-
ther inquiry. Other committee members are not convinced of the value of
establishing this threshold condition or are not convinced that any study
of this sort could make a convincing case that it had isolated a causal ef-
fect of executions.
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
CHALLENGES TO IDENTIFYING DETERRENT EFFECTS 111
IDENTIFYING EFFECTS:
FEEDBACKS AND UNOBSERVED CONFOUNDERS
Even with better data and information on sanction regimes and per-
ceptions of sanction risks, formidable difficulties remain to understanding
the impact of the death penalty on homicide. With only observational
(nonexperimental) data on capital punishment and homicides, researchers
must face the fundamental problem that the data alone cannot reveal the
counterfactual question of interest: What would have happened if the death
penalty not been applied in a “treatment” state or if the death penalty had
been applied in a “control” state? Although this counterfactual-outcomes
problem is common to all observational studies of cause and effect, it has
long been understood to be particularly problematic for understanding the
deterrent effect of the death penalty. A capital punishment regime evolves
over time as a result, among other things, of a complex interplay of crime
trends, social norms, criminal justice budgets, and election results. This
context makes it very difficult to identify the effects of the capital sanction
regime alone.
To better understand these issues, we highlight three related identi-
fication problems that complicate efforts to draw credible inferences on
the effect of capital punishment on homicides. The first, referred to as a
feedback effect, arises when homicide rates may directly affect the capital
sanction regime. The second, referred to as the omitted variable problem,
arises when variables that are jointly associated with the sanction regime
and homicide rate are either unknown or unobserved. The third, referred
to as an equilibrium effect, arises when the capital sanction regime may
directly affect other aspects of the criminal justice system, including, most
notably, noncapital sanction policies.
Feedback Effects
Deterrence research conducted in the early 1970s (Carr-Hill and Stern,
1973; Ehrlich, 1975; Sjoquist, 1973) recognized the possibility of feedbacks
or simultaneity whereby crime rates may affect the sanction risk and sever-
ity even as the sanction risk and severity may affect crime rates. The nature
of such feedbacks is not well understood, but there are good reasons for
believing that feedbacks are present and may be substantial.
To illustrate the problem, suppose that in a particular state during a
particular year there is an exogenous increase in the rate of homicide. If,
given the additional workload and resulting strain on resources, district
attorneys were more reluctant to pursue the death penalty, a continu-
ing upward trend in homicides would appear to show that a reduction
in the probability of a death sentence is associated with an increase in
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
112 DETERRENCE AND THE DEATH PENALTY
homicides—a result compatible with a deterrent effect. But suppose instead
that the upward trend in homicides resulted in greater public concern about
violence and hence a greater willingness on the part of juries in capital cases
to choose a death sentence rather than a life sentence. A continuing upward
trend in homicides would then appear to show that an increase in capital
sanctions is associated with an increase in homicide, a result compatible
with a “brutalization” effect. In both these scenarios, the important fact is
that the homicide trends influenced the sanction regime. These particular
feedbacks are hypothetical, and indeed the very presence of feedbacks has
yet to be documented. Still, there are plausible reasons for believing that
feedbacks are present and possibly substantial in magnitude. If so, they
increase the difficulty of identifying deterrent effects.
Omitted Variables
The second and related problem arises when unobserved changes in the
social, political, and economic environment may have an impact on both
capital sanctions and other aspects of the sanction regime. For example,
a political shift that results in the election of “law and order” legislators
may increase criminal justice resources and produce a broad shift toward
greater severity in sentencing, with some effects on the homicide rate. In
this case, changes in the capital sanction regime may be spuriously related
to the changes in the homicide rate through the associated changes in the
noncapital sanction regime. If variables that are jointly associated with the
sanction regime and homicide rates are omitted from statistical models of
the effect of capital punishment on homicide, then estimates of the deterrent
effect will be biased.
The panel research includes studies that recognize and attempt to ad-
dress the inferential consequences of feedback effects and omitted variable
problems. As discussed in Chapter 4, these attempts have not been suc-
cessful in advancing plausible identification strategies to these problems. In
particular, the instrumental variables used in these analyses do not plausibly
meet criteria for a valid instrument. The two key criteria are that (1) on
average, sanction levels vary as a function of the instrumental variable but
(2) on average, the crime rate at a given sanction level does not vary as
a function of the instrumental variable. In Chapter 4, we argue that the
instrumental variable used in the studies do not meet the second test. This
criticism echoes the conclusions of the earlier National Research Council
report (1978). Thus, the same elementary error in identification is being
made in contemporary research on the deterrent effect of capital punish-
ment that was made decades ago by early deterrence researchers.
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Deterrence and the Death Penalty
CHALLENGES TO IDENTIFYING DETERRENT EFFECTS 113
The Equilibrium Effect
We now turn to a third causal process that makes identification prob-
lematic, one that has been largely ignored in the research yet is of unique
salience to studying the deterrent effect of capital punishment. For capital
punishment, changes in the probability of capital sanctions may cause
changes to other aspects of the sanctions regime. To illustrate the prob-
lem, consider two examples. First, a district attorney who can credibly
threaten an accused homicide defendant with the death penalty may have
greater bargaining leverage than one who lacks this threat; as a result, the
defendants in the former situation may be more willing to plead guilty
to first-degree murder with an agreement that their sentence will be life
imprisonment rather than death (Cook, 2009; Kuziemko, 2006). Thus, a
district attorney who is willing to devote resources to capital prosecutions
may end up achieving more severe noncapital sentences, and the two types
of sentences are intrinsically linked.
There may also be a negative linkage, if, for example, a district attor-
ney’s proclivity to seek the death penalty in homicide cases comes at the
cost of reduced prosecutorial resources available for other cases.
1
Due to
resource constraints and the additional costs of prosecuting capital murder
cases rather than noncapital murder cases, emphasis on capital cases may
diminish prosecutorial effectiveness in noncapital cases. The result in that
situation may be that the more intense capital regime is achieved at the cost
of reduced sentencing (and more dismissals) for the majority of homicide
cases that are not capital. These potential links between capital and non-
capital sentences make it difficult to isolate the deterrent effect of the threat
of execution for homicide.
The equilibrium process, whereby capital and noncapital sanction poli-
cies are jointly related and jointly influence the outcome of interest, poses
a qualitatively different challenge to identification than the first two. In
principle, if the probability that a homicide case would result in a death
sentence was randomly assigned across jurisdictions, then the identification
problems resulting from feedbacks or omitted variables (discussed above)
would be solved. What would remain, however, is the potential difficulty in
isolating the deterrent effect of the death penalty by itself from the changes
in the overall sanction regime that are influenced by the availability and
use of the death penalty.
1
Numerous studies have documented that the prosecution of capital homicide cases is far
more costly than noncapital homicide cases: see, for example, Roman, Chalfin, and Knight
(2009) in Maryland; Cook (2009) in North Carolina; and Alarcón and Mitchell (2011) and
the California Commission on the Fair Administration of Justice (2008) in California. Due
to resource constraints, emphasis on capital cases may diminish prosecutorial effectiveness in
noncapital cases.
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Deterrence and the Death Penalty
114 DETERRENCE AND THE DEATH PENALTY
Knowledge of the entire system, however, is not a necessary require-
ment for learning about the overall impact of the capital sanction regime.
For some questions, the effects of the death penalty on sentence bargain-
ing and on administrative resource constraints are an intrinsic part of the
mechanism by which a capital regime affects murder rates. Consider, for
example, a case in which a judicial ruling terminates the use of the death
penalty for some category of homicides. It would be of considerable interest
to have a reliable estimate of the overall effect of this reform on the murder
rate, even if it is not possible to distinguish among the various mechanisms
(reduction in the probability of a death sentence, weaker bargaining posi-
tion by the district attorney, or increased court resources available for the
average case) that led to that effect. Still, this sort of “black box” estimate
is not satisfactory if the goal is to estimate the effect of the threat of execu-
tion, in part because the ancillary effects of the administration of the death
penalty can be generated by other means, such as changes in court budgets.
Is a more reliable approach to identifying the deterrent effect of capital
punishment possible? Part of the solution may be to develop a better un-
derstanding of the factors that affect sanction regimes, including possible
feedbacks from homicide or other crime patterns. The earlier National
Research Council report (1978, p. 47) observed: “Knowledge of the effect
of crime on the behavior of the criminal justice system is still extremely
limited.” This conclusion is still true today, 30 years later. The 1978 report
went on to observe: “While the seeming dearth of untainted identification
restrictions may reflect the fact that none exist, it is certainly as likely that
it simply reflects our ignorance of the determinants of sanctions” (p. 48).
Three decades later this committee observes that both of these assessments
apply to contemporary research on deterrence.
As noted above, the 1978 report urged more research on the sanction-
generation process for the purpose of accumulating a knowledge base that
might reveal approaches to plausible identification. Although knowledge of
the sanction-generation process is not required for identification of overall
effects of certain relevant regime changes, that knowledge may be useful
in determining the validity of a proposed identification method. Also, as
a practical matter, some committee members believe that without better
knowledge of sanction generation, the prospects for credible identifica-
tion are small. Committee members holding this perspective argue that a
deeper institutional and theoretical knowledge of sanction process would
materially increase the chances of researchers’ becoming aware of credible
sources of identification and that without such knowledge the chances for
credible identification are remote. Other committee members are less pes-
simistic that a chance event or insight might provide a basis for credible
identification.
However credible identification might ultimately be achieved, the com-
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
CHALLENGES TO IDENTIFYING DETERRENT EFFECTS 115
mittee fully endorses another observation from the earlier report (National
Research Council, 1978, p. 49):
It must be noted, however, that identification restrictions cannot be manu-
factured. If the process generating the data is truly one that leaves the
crime function unidentified, then persistent attempts to produce identifying
restrictions because of the desire to estimate the deterrent effect will only
produce different kinds of error. Even if all such attempts found a “deter-
rent” effect, no conclusion would be warranted unless some of them used
validly based identification restrictions.
ADDRESSING MODEL UNCERTAINTY
WITH WEAKER ASSUMPTIONS
The persistent problems that researchers have had in providing mean-
ingful answers about the deterrent effect of capital punishment is unsur-
prising once one recognizes that this body of empirical research rests on
strong and unverified assumptions. Although, in practice, researchers often
recognize and acknowledge that their assumptions may not hold, they are
defended as necessary to provide meaningful answers and in order to make
inferences. But the use of strong assumptions hides the problem that very
little is understood about the process that may link capital punishment to
future crimes.
The different findings in the deterrence research reflect different choices
of assumptions, most of which cannot be supported by strong a priori
justifications. As documented throughout this report, many of the assump-
tions used in the research on the deterrent effect of capital punishment are
not credible. Furthermore, the state of social science knowledge does not
support a unique model that can be used to identify the effects of capital
punishment under the current U.S. sanction regime or to permit the evalu-
ation of deterrence under alternative regimes. The study of deterrence is
plagued by model uncertainty.
The failure of the existing research to address the issue of model un-
certainly is evident in the debate initiated by Donohue and Wolfers (2005),
who challenged claims of deterrence by a broad set of researchers. Much of
their challenge involved demonstrations of how small changes in the models
used in the various studies led to very different estimates of deterrence ef-
fects, in some case changing from positive to negative or vice versa, and in
others eliminating statistical significance. Some of their exercises altered the
set of observations over which the analysis had been conducted; in other
cases they changed the choice of control or instrumental variables.
Although Donohue and Wolfers provide useful evidence of the sensitiv-
ity of many claims of deterrence to model assumptions, their demonstra-
tion begs the question of how to adjudicate their findings relative to the
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
116 DETERRENCE AND THE DEATH PENALTY
papers they critique. This may be seen in two of the rejoinders that have
been written to their study. Dezhbakhsh and Rubin (2011) and Mocan and
Gittings (2010) provide a large number of modifications of their baseline
homicide regressions and argue that deterrence effects generally appear in
them. However, they fail to provide any guidance as to what is learned
from the specifications that are inconsistent with their claim of evidence
of deterrence. Rather, the authors’ claims are based on ad hoc choices of
alternative model specifications; there is no systematic construction of the
models from which to draw inferences. That changes in a given statistical
model change the output of the model is hardly unique to the studies of
capital punishment and deterrence literature. The problem is that there have
been almost no serious attempts to reconcile the many different findings
reported in the research.
Given this existing uncertainty, how might research proceed? Certainly,
research aimed at reducing model uncertainty would be useful. To that
end, the committee proposed, above, developing data and research on
sanction regimes and perceptions of sanction risk. Another complementary
and potentially useful approach would be to explicitly account for model
uncertainty when drawing inferences on the impact of capital punishment.
Rather than continue with the conventional practice of assuming whatever
it takes to achieve point identification, and then providing ad hoc justifica-
tions for particular sets of assumptions to justify a given model, deterrent
studies might instead consider what can be learned when explicitly rec-
ognizing model uncertainty. Although the resulting inferences may reflect
a certain degree of ambiguity about the effects of capital punishment on
homicides, those inferences will necessarily possess greater credibility.
To explore the idea of addressing model uncertainty, the committee
commissioned papers illustrating application of two complementary re-
search paradigms—the model averaging approach and the partial identifi-
cation approach.
Model Averaging
Model averaging, though based on earlier work (Bates and Granger,
1969; Leamer, 1978), developed theoretically, algorithmically, and as an
applied technique in the mid-1990s (examples include Chatfield, 1995;
Draper, 1995; Draper et al., 1993; Raftery, Madigan, and Hoeting, 1997).
The model averaging approach constructs a probability distribution for a
range of estimates of the deterrent effect of capital punishment, and the
researcher constructs this distribution to reflect the researcher’s own or
others experts’ prior beliefs about the probability that a given model is
valid. By asking what can be learned by combining the information ob-
tained across a wide range of models, model averaging methods provide
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
CHALLENGES TO IDENTIFYING DETERRENT EFFECTS 117
a natural way to make empirical claims robust to the details of uncertain
model specifications.
This technique has recently been used in two studies of capital punish-
ment: Cohen-Cole et al. (2009) and Durlauf, Fu, and Navarro (in press).
These studies apply the modeling average approach to various specifications
that have appeared in the research on capital punishment and deterrence.
Cohen-Cole et al. (2009) use this method to adjudicate the different find-
ings of Dezhbakhsh, Rubin, Shepherd (2003) and Donohue and Wolfers
(2005). Durlauf, Fu, and Navarro (in press), whose paper was written for
this committee, consider a range of models based on alternative substantive
assumptions that have appeared in the research, including, for example,
how to measure subjective arrest, sentencing, and execution probabilities
and whether the deterrent effect of capital punishment differs across states.
These two papers aim to understand how different assumptions matter
and whether differences in assumptions render deterrence estimates fragile.
In both papers, the researchers find that model uncertainty swamps the
informational content about deterrent effects. That is, after accounting for
the modeling uncertainty, the empirical evidence does not reveal whether
capital punishment increases or decreases homicides.
As an example of this result, consider the Cohen-Cole et al. (2009)
analysis of the models in Dezhbakhsh, Rubin, and Shepherd (2003) and
Donohue and Wolfers (2005). Dezhbakhsh, Rubin, and Shepherd (2003)
report, under their preferred specification, a statistically significant point
estimate of 18 lives saved for each execution. However, when all of the
different specifications spanned in the two papers are given probability
weights, Cohen-Cole et al. estimate an approximate 95 percent confidence
interval on the number of lives saved per execution of [–24, 124]: see Fig-
ure 6-1, which is from Cohen-Cole et al. The figure illustrates the model
uncertainty by providing a weighted histogram of the estimated net lives
saved for all of the models considered. For the case illustrated in this histo-
gram, the posterior probability for the models with point estimates suggest
that deterrence is 72 percent, but there is substantial bunching around 0,
the individual estimates vary widely, and there is a nontrivial probability
on models that suggest a large increase in homicides associated with ex-
ecutions (a probability 0.15 of point estimates of 20 or more homicides).
Thus, the heterogeneity of the model-specific estimates makes it impossible
to draw strong qualitative conclusions about the deterrent effect of capital
punishment.
The model averaging approach provides a formal and elegant Bayesian
method for incorporating uncertainty about the correct modeling assump-
tions into inferential methods. This approach can be effectively used to
illustrate the importance of different assumptions and the fragility of the
estimates to these assumptions, as is done in Cohen-Cole et al. (2009) and
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
118 DETERRENCE AND THE DEATH PENALTY
Durlauf, Fu, and Navarro (in press). The approach depends on research-
ers’ specifications of the model space and prior over that model space, over
which there may be disagreement. Such disagreement should not obscure an
essential strength of the model averaging approach: model averaging pro-
vides an approach for systematically exploring sensitivity over an explicitly
defined model space.
Ultimately, this approach might also be used to infer the effect of the
death penalty on homicides. However, for this purpose, a key challenge
would be selecting a set of models to include in the averaging and provid-
ing a prior probability distribution over this set that is plausible. The ap-
proach presumes that the range of models included in the averaging routine
includes the correct model that accurately describes the real world and,
-200 -100 0 100 200 300 400
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Net Lives Saved: Weighted Histogram
DRS Estimate
DW Estimate
R02175
Figure 6-1
vector, editable
obtained from original source
(Cohen-Cole et al, 2007)
FIGURE 6-1 Weighted histogram of the net lives saved by the death penalty.
NOTES: The figure includes models for each of the DRS (Dezhbakhsh, Rubin,
and Shepherd, 2003) categories. The weights are the posterior model probabilities
(Bayes factors). The DRS and DW (Donohue and Wolfers, 2005) lines correspond to
the individual model from each with the largest and smallest number of lives saved,
respectively. The unweighted histogram is similar.
SOURCE: Cohen-Cole et al. (2009, Figure 1). Used with permission.
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
CHALLENGES TO IDENTIFYING DETERRENT EFFECTS 119
moreover, that the researcher can provide informed prior beliefs about the
probability that each model is valid. In the context of the research on capi-
tal punishment, we have found no reason to believe that the existing range
of point-identified models includes the correct one, and there is currently
little basis for assigning probabilities to the correctness of each model in the
literature. As discussed in Chapter 4, the committee did not find the instru-
mental variables used in the existing research to be credible. If the existing
models are all invalid, using the modeling averaging approach to produce
interpretable deterrence estimates can be problematic.
2
With uncertainty
about the model space and the prior probabilities, either research efforts
to construct informative priors or research showing the sensitivity of the
posterior to different prior distributions may be useful.
Partial Identication
Partial identification methods provide an alternative approach for re-
ducing the dependence of claims of a deterrence effect on arbitrary assump-
tions. Rather than start with a particular set of point-identified models and
prior beliefs about the probability that each model is valid, both as defined
by the researcher, one might instead begin by directly considering what
can be inferred under a set of weak assumptions that may possess greater
credibility. A natural starting point, for example, is to examine what can be
learned in the absence of any assumptions. What do the data alone reveal?
Under these weaker assumptions, deterrent effects may not be point iden-
tified, but they will be partially identified, with bounds rather than point
estimates. Thus, the partial identification approach formalizes the inherent
tradeoff between the strength of the maintained assumptions and the cred-
ibility of inferences (see Manski, 2003).
The partial identification methodology has been developed and applied
over the past 20 years, beginning with Manski (1989, 1990). In an early
application to criminal justice policy, Manski and Nagin (1998) studied
sentencing and recidivism of juvenile offenders in the state of Utah and
demonstrated how partial identification can be used to produce more cred-
ible inferences than had previously been produced. Youth in Utah faced a
policy that gave judges the discretion to order varying sentences. Using this
discretion, judges sentenced some offenders to residential confinement and
sentenced other offenders to no confinement. A policy question of potential
2
The Cohen-Cole et al. exercise (2009) was narrow in that it considered the smallest model
space one could generate around the different assumptions in Donohue and Wolfers (2005)
and Dezhbakhsh, Rubin, and Shepherd (2003). One can easily argue that for a full model av-
eraging analysis, other models warrant a priori consideration. However, one could also argue
that some of the models considered in Cohen-Cole et al. should not have been included, given
a prior probability of 0.
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
120 DETERRENCE AND THE DEATH PENALTY
interest was to compare recidivism under that policy with the recidivism
that would occur under a policy proposal that removed judicial discretion
and instead mandated that all offenders be sentenced to confinement. The
study showed how bounds of varying width on the existing treatment effect
which allows judges’ discretion could be achieved by combining data on
outcomes under the status quo with relatively weak assumptions regarding
the manner in which (1) judges have made sentencing decisions and (2)
criminality was affected by sentencing.
More recently, in a paper written for this committee, Manski and Pepper
(in press) illustrate the partial identification approach in a relatively simple
setting by examining the effect of death penalty statutes on the national
homicide rate (per 100,000) over 2 years, 1975-1977: 1975 was the last
full year of the federal moratorium on death penalty, and 1977 was the
first full year after the moratorium was lifted. In 1975, the death penalty
was illegal throughout the country; and in 1977, 32 states had legal death
penalty statutes. Over this 2-year period, homicide rates in the 32 states
that had adopted a death penalty statute in 1977 decreased by 0.6; in the
remaining states, the homicide rates decreased by 1.1. It has been common
in the relevant research to report the difference-in-difference estimate, which
in this case is 0.5 (–0.6 + 1.1), as a point estimate of the effect of capital
punishment on the national homicide rate. This interpretation suggests that
the death penalty increases crime, but Manski and Pepper (in press) show
that this difference-in-difference form only point identifies the impact of the
death penalty under a number of strong assumptions, most notably that the
effect is assumed to be homogeneous across states and dates. Under weaker
assumptions that allow the deterrent effect to vary across states, the average
effect of the death penalty is only partially identified, and it was found to lie
in the interval [–1.9, 8.3]. Under still weaker assumptions under which the
effect of the death penalty is allowed to vary over time, the bounds widen
further. Thus, under these weaker models, the average treatment effect of
capital punishment is bounded, but the data do not identify whether the
death penalty increases or decreases homicides.
The committee does not endorse the specific findings of the recent
studies applying the model averaging or partial identification approaches.
These studies are largely illustrative and do not address many of the key
problems identified throughout this report. Most notably, they do not
define the counterfactual sanction regime and do not address the issue of
how potential murderers perceive sanction risks. Still, these studies serve
as a starting point for future research that might inform the debate on the
death penalty. Rather than imposing the strong but unsupported assump-
tions required to identify the effect of capital punishment on homicides in a
single model or an ad hoc set of similar models, approaches that explicitly
account for model uncertainty may provide a constructive way for research
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
CHALLENGES TO IDENTIFYING DETERRENT EFFECTS 121
to provide credible albeit incomplete answers. The basic insight is that with
model uncertainty, the identification of deterrent effects need not be an all-
or-nothing undertaking: the available data and credible assumptions may
yield partial conclusions.
Some people may find partial conclusions unappealing and be tempted
to impose strong assumptions in order to obtain definitive answers. We
caution against this reaction. Imposing strong but untenable assumptions
cannot truly resolve inferential problems. Rather, it simply replaces the
modeling uncertainty with uncertainty associated with the underlying as-
sumptions. We have seen this repeatedly in the literature on the death
penalty. The earlier Panel on Research on Deterrent and Incapacitative Ef-
fects recognized this when it concluded (National Research Council, 1978,
p. 63) “research on this topic is not likely to produce findings that will or
should have much influence on policymakers.” Today, more than 30 years
later, perhaps the primary lesson learned from the latest round of empirical
research on the deterrent effect of the death penalty is that researchers and
policy makers must cope with ambiguity. Explicitly recognizing and ac-
counting for this uncertainty seems like the only hope of moving forward.
RECOMMENDATION: The committee recommends further inves-
tigation of the effects of capital punishment using assumptions that
are weaker and more credible than those that have traditionally been
invoked by empirical researchers.
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Deterrence and the Death Penalty
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
Appendix
Biographical Sketches of
Committee Members and Staff
Daniel S. Nagin (Chair) is Teresa and H. John Heinz III university professor
of public policy and statistics in the Heinz College at Carnegie Mellon Uni-
versity. His research focuses on the evolution of criminal and antisocial be-
haviors over the life course, the deterrent effect of criminal and non criminal
penalties on illegal behaviors, and the development of statistical methods
for analyzing longitudinal data. His work has appeared in such diverse out-
lets as the American Economic Review, the American Sociological Review,
the Journal of the American Statistical Association, Archives of General
Psychiatry, Psychological Methodology, Law & Society Review, and Stanford
Law Review. He is an elected fellow of the American Society of Criminol-
ogy and of the American Association for the Advancement of Science, and
he was the 2006 recipient of the American Society of Criminology’s Edwin
H. Sutherland Award. He holds a Ph.D. from the H. John Heinz III School
of Public Policy and Management at Carnegie Mellon University.
Kerwin K. Charles is the Edwin and Betty L. Bergman distinguished service
professor in the Harris School of public policy studies at the University
of Chicago and a research associate at the National Bureau of Economic
Research. His research focuses on a range of subjects in the broad area of
applied microeconomics, including how mandated minimum marriage ages
affects young people’s marriage and migration behavior; the effect of racial
composition of neighborhoods on the social connections people make;
differences in visible consumption across racial and ethnic groups; the ef-
fect of retirement on subjective well-being; and the propagation of wealth
across generations within a family. His recent work has studied the degree
125
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Deterrence and the Death Penalty
126 DETERRENCE AND THE DEATH PENALTY
to which prejudice can account for wages and employment differences by
race and gender. He has a Ph.D. from Cornell University.
Philip J. Cook is the ITT/Sanford professor of public policy and professor
of economics and sociology at Duke University. Previously, he served as
director and chair of Duke’s Sanford Institute of Public Policy, and he has
been a visiting scholar at the Kennedy School of Government at Harvard
University. He has served as a consultant to the U.S. Department of Justice
(Criminal Division) and the U.S. Department of the Treasury (Enforcement
Division). He has published on a wide range of topics, including punish-
ment, deterrence of crime, the costs of crime, homicide and economic
conditions, and the epidemic in youth violence of the late 1980s and early
1990s. His other research interests include evaluation methods; public
health policy; and the regulation of alcohol, guns, and gambling. He is a
member of the Institute of Medicine. He holds a Ph.D. in economics from
the University of California at Berkeley.
Steven N. Durlauf is the Kenneth J. Arrow and Laurents R. Christensen
professor of economics at the University of Wisconsin–Madison and a re-
search associate of the National Bureau of Economic Research. Previously,
he served as director of the economics program at the Santa Fe Institute and
as general editor of the revised edition of the New Palgrave Dictionary of
Economics. His primary research interests involve the integration of the so-
cial influences into the theoretical and statistical analysis of economic phe-
nomena, and he has also studied issues related to racial profiling, deterrence
and imprisonment, and deterrence and death penalty. He is a fellow of the
Econometric Society. He holds a Ph.D. in economics from Yale University.
Amelia M. Haviland holds the Anna Loomis McCandless chair at the Heinz
College at Carnegie Mellon University, and she is a senior statistician at
RAND. Her research focuses on causal analysis with observational data and
analysis of longitudinal and complex survey data with applications in health,
criminology, and economics. Her methodological work has included new
methods to combine semi-parametric mixture modeling for longitudinal data
with propensity score approaches to causal modeling and methods for creat-
ing minimum mean squared error composite estimates from a combination
of probability and nonprobability samples. She is a recipient of the Thomas
Lord Scholarship Award from the RAND Institute for Civil Justice. She holds
a Ph.D. in statistics and public policy from Carnegie Mellon University.
Gerard E. Lynch is a judge on the U.S. Court of Appeals for the Second
Circuit, and he is the Paul J. Kellner professor of law at the Columbia Uni-
versity School of Law. Previously, he served on the U.S. District Court for
Copyright © National Academy of Sciences. All rights reserved.
Deterrence and the Death Penalty
APPENDIX 127
the Southern District of New York. Prior to his appointment to the bench,
he served as vice dean of the Columbia University School of Law. His main
areas of expertise include sentencing and criminal law and procedure. He
is a recipient of the Edward Weinfeld Award for Distinguished Contribu-
tions to the Administration of Justice from the New York County Lawyers’
Association and of the Wien Prize for Social Responsibility from Columbia
University. He holds degrees from Columbia College and the Columbia Uni-
versity School of Law.
Charles F. Manski is a Board of Trustees professor in economics at North-
western University. Previously, he served on the faculties of the University
of Wisconsin–Madison, the Hebrew University of Jerusalem, and Carnegie
Mellon University. His research spans econometrics, judgment and decision,
and the analysis of social policy. He is an elected member of the National
Academy of Sciences and an elected fellow of the Econometric Society, the
American Academy of Arts and Sciences, and the American Association for
the Advancement of Science. He holds a B.S. and a Ph.D. in economics from
the Massachusetts Institute of Technology.
John V. Pepper is associate professor of economics at the University of
Virginia. His research focuses on program evaluation methods, applied
econometrics, and public economics. He has published widely on a range
of topics, including evaluation of criminal justice data and programs, food
assistance programs, health and disability programs, and welfare programs.
He is on the board of the Michigan Retirement Research Center and of
the Southern Economics Association. He is a coeditor of the Southern
Economic Journal, and he served as a guest editor for a special issue of
the American Journal of Law and Economics, which focused on empirical
research on the death penalty. He holds a Ph.D. in economics from the
University of Wisconsin–Madison.
James Q. Wilson was the Reagan professor of public policy at Pepperdine
University and a distinguished scholar in the Department of Political Sci-
ence and senior fellow at the Clough Center at Boston College. Previously,
he was the Shattuck professor of government at Harvard University and
the James Collins professor of management and public policy at the Uni-
versity of California at Los Angeles. His national positions related to issues
of public policy included chair of the White House Task Force on Crime,
chair of the National Advisory Commission on Drug Abuse Prevention,
member of the Attorney General’s Task Force on Violent Crime, member
of the President’s Foreign Intelligence Advisory Board, and member of the
board of directors of the Police Foundation. He held a Ph.D. from the
University of Chicago.
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Deterrence and the Death Penalty