WALTER C. RECKLESS MEMORIAL LECTURE
Death and Deterrence Redux: Science, Law and
Causal Reasoning on Capital Punishment
Jeffrey Fagan∗
“Things are seldom what they seem . . . Skim-milk masquerades as cream . . .”
Gilbert and Sullivan
I. THE CURRENT CONTROVERSY
Long before the U.S. Supreme Court restored capital punishment in 1976,
proponents of the death penalty claimed that executions save lives by deterring
would-be murderers from lethal violence. The more recent ascension of deterrence
as a rationale for capital punishment in the 1970s coincided with a series of
landmark Supreme Court cases that first abolished and then reinstated the death
penalty (a list of cases is available), and with the publication of a series of articles
that claimed a scientific basis for the assertion that potential murderers can be
deterred from homicide by the threat of execution. The originator of these claims
was economist Isaac Ehrlich, who (inspired by the theoretical work of the
University of Chicago’s Gary Becker1) developed a theoretical model that
explained crime as a process of rational choice between illegal and legal behavior;
the choices were shaped by how law enforcement reacted to illegal activities.2
Such rationality, Ehrlich argued, would influence would-be offenders to avoid
punishment and forego crime.
Ehrlich published a highly influential article in 1975 that tested this model in
the case of murder and capital punishment. It was a technical piece using
∗

Professor of Law and Public Health, Columbia University. Outstanding research assistance
was provided by Arie Rubinstein, Ethan Jacobs, Michel Werschtenschlag, David Finkelstein and
Jason Stramaglia. Amanda Beth Geller provided excellent assistance in the empirical analyses. I am
indebted to the Criminal Justice Research Center at The Ohio State University for their invitation to
deliver the Walter C. Reckless Lecture in April 2005, which was the basis for this essay. I am also
indebted to Brandon Garrett, Michael Maltz, Christopher Maxwell, Justin Wolfers, Avery Katz and
Franklin Zimring who provided helpful comments and advice on earlier versions of the article.
1
See generally Gary S. Becker, Crime and Punishment: An Economic Approach, 76 J. POL.
ECON. 169 (1968) [hereinafter Becker, Crime and Punishment]; GARY S. BECKER, THE ECONOMIC
APPROACH TO HUMAN BEHAVIOR (1976) [hereinafter BECKER, ECONOMIC APPROACH].
2
Isaac Ehrlich, The Deterrent Effect of Capital Punishment: A Question of Life and Death,
65 AM. ECON. REV. 397 (1975); Isaac Ehrlich, Capital Punishment and Deterrence: Some Further
Thoughts and Additional Evidence, 85 J. POL. ECON. 741 (1977).

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econometric methods, but its influence went way beyond the economics
profession. Ehrlich’s work was cited in Gregg v. Georgia,3 the landmark U.S.
Supreme Court decision restoring capital punishment. No matter how carefully
Ehrlich qualified his conclusions, his article had the popular and political appeal of
a headline, a sound bite and a bumper sticker all rolled into one: “One execution
saves eight innocent lives.” Ehrlich’s work was cited favorably in Gregg, and it
was later cited in an amicus brief filed by the U.S. Solicitor General in Fowler v.
North Carolina.4 Even though Ehrlich’s findings were disputed in academic
journals such as the Yale Law Journal,5 the proponents of deterrence had gained
the upper hand in how this research was interpreted and how its findings were
applied.6
Ehrlich’s work became the focal point for research on deterrence and the
death penalty, launching an era of contentious arguments in the press and in
professional journals.7 Over the next two decades, economists and other social
scientists attempted to replicate Ehrlich’s results using different data, alternative
statistical methods, and other twists that tried to address glaring errors in Ehrlich’s
techniques and data.8 Yet the accumulated scientific evidence from these later

3

428 U.S. 153 (1976).
428 U.S. 904 (1976).
5
See Editors’ Introduction, Statistical Evidence on the Deterrent Effect of Capital
Punishment, 85 YALE L.J. 164 (1975); David C. Baldus & James W.L. Cole, A Comparison of the
Work of Thorsten Sellin and Isaac Ehrlich on the Deterrent Effect of Capital Punishment, 85 YALE
L.J. 170 (1975); William J. Bowers & Glenn L. Pierce, The Illusion of Deterrence in Isaac Ehrlich’s
Research on Capital Punishment, 85 YALE L.J. 187 (1975); Isaac Ehrlich, Deterrence: Evidence and
Inference, 85 YALE L.J. 209 (1975).
6
For critiques of Ehrlich’s work, see Michael McAleer & Michael R. Veall, How Fragile
Are Fragile Inferences? A Re-Evaluation of the Deterrent Effect of Capital Punishment, 71 REV.
ECON. & STATISTICS 99 (1989); Edward E. Leamer, Let’s Take the Con out of Econometrics, 73 AM.
ECON. REV. 31 (1983); Walter S. McManus, Estimates of the Deterrent Effect of Capital Punishment:
The Importance of the Researcher’s Prior Beliefs, 93 J. POL. ECON. 417 (1985); Jeffrey Grogger, The
Deterrent Effect of Capital Punishment: An Analysis of Daily Homicide Counts, 85 J. AM.
STATISTICAL ASSOC. 295 (1990).
For support and extensions of Ehrlich’s work, see Stephen A. Layson, Homicide and
Deterrence: A Reexamination of the United States Time-Series Evidence, 52 S. ECON. J. 68 (1985)
[hereinafter Layson, Homicide and Deterrence]; James P. Cover & Paul D. Thistle, Time Series,
Homicide, and the Deterrent Effect of Capital Punishment, 54 S. ECON. J. 615 (1988); George A.
Chressanthis, Capital Punishment and the Deterrent Effect Revisited: Recent Time-Series
Econometric Evidence, 18 J. BEHAV. ECON. 81 (1989).
7
For an excellent summary of the critique of Ehrlich’s article, see John Lamperti, Deter
Murder? A Brief Look at the Evidence, ¶ 17, available at http://www.math.dartmouth.edu/~lamperti/
capitalpunishment.html (last visited Aug. 18, 2006).
8
See, e.g., Layson, Homicide and Deterrence, supra note 6, at 75, 80; Stephen Layson,
United States Time-Series Homicide Regressions with Adaptive Expectations, 62 BULL. N.Y. ACAD.
MED. 589 (1986).
4

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studies also weighed heavily against the claim that executions deter murders.9
Ehrlich’s findings were challenged by many scholars as to the sample period
and/or the variables he chose, and the murder supply equation and the functional
form of the equations he estimated.10 Also, under Ehrlich’s methodology, the
aggregation of data from all U.S. states led to his conclusion that “a decrease in the
execution risk in one State combined with an increase in the murder in another
State would, all other things being equal, suggest a deterrent effect that quite
obviously would not exist.”11 Within three years of the publication of Ehrlich’s
study, an expert panel appointed by the National Academy of Sciences issued
strong criticisms of his work.12 Despite the weight of technical economic and
other social science evidence condemning Ehrlich’s work, each new study that
followed supporting the deterrence conclusion found uncritical acceptance among
proponents of the death penalty, while the critiques failed to get popular or
political traction.
History is now repeating itself. In the past five years, a new wave of a dozen
or more studies have appeared, reporting deterrent effects of capital punishment
9

For example, Peter Passell and John Taylor showed that Ehrlich’s result relied heavily on
movements from 1963 to 1969. They focused on Ehrlich’s observed negative relation between
executions and homicide rates, and analyzed the impact of a change in the time period chosen for the
model or a change in the assumptions as to the model’s functional form. Both changes showed that
the broad aspects of the model were unchanged, but that the evidence suggesting a particular
deterrent effect from executions had totally vanished. See Peter Passell & John B. Taylor, The
Deterrent Effect of Capital Punishment: Another View, 67 AM. ECON. REV. 445, 450 (1977):
First, we have shown that Ehrlich’s model does not satisfy the statistical requirement of
temporal homogeneity and that the results are sensitive to specification of the variables
and transformation of the data. . . . Second, . . . it is not possible to infer from [Ehrlich’s
murder rate regression function] that a change in legal institutions . . . would reduce
murder rates. . . . [I]t is prudent to neither to accept nor reject the hypothesis that capital
punishment deters murder.
See also Bowers & Pierce, supra note 5, at 187; Richard M. McGahey, Dr. Ehrlich’s Magic Bullet:
Economic Theory, Econometrics and the Death Penalty, 26 CRIME & DELINQ. 485 (1980); Stephen A.
Hoenack & William C. Weiler, A Structural Model of Murder Behavior and the Criminal Justice
System, 70 AM. ECON. REV. 327 (1980); McAleer & Veall, supra note 6, at 99. See generally
Grogger, supra note 6, at 295; see also William C. Bailey, Deterrence, Brutalization, and the Death
Penalty: Another Examination of Oklahoma’s Return to Capital Punishment, 36 CRIMINOLOGY 711
(1998); Jon Sorenson et al., Capital Punishment and Deterrence: Examining the Effect of Executions
on Murder in Texas, 45 CRIME & DELINQ. 481 (1999).
10
H. Naci Mocan & R. Kaj Gittings, Getting Off Death Row: Commuted Sentences and the
Deterrent Effect of Capital Punishment, 46 J. L. & ECON. 453 (2003).
11
Craig J. Albert, Challenging Deterrence: New Insights on Capital Punishment Derived
from Panel Data, 60 U. PITT. L. REV. 321, 356 (1999) (citing Gregg v. Georgia, 428 U.S. 153, 235
(1976) (Marshall, J., dissenting)). Later in the article, the author also adds, after analyzing the same
data as Ehrlich’s, “the data do not support any conclusion that executions deter homicides.” Id. at
363.
12
See Lawrence R. Klein et al., The Deterrent Effect of Capital Punishment: An Assessment
of the Estimates, in DETERRENCE AND INCAPACITATION: ESTIMATING THE EFFECTS OF CRIMINAL
SANCTIONS ON CRIME RATES 336, 336–60 (Alfred Blumstein et al. eds., 1978).

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that go well beyond Ehrlich’s findings. The new deterrence studies analyze data
that spans the entire period since the resumption of executions in the U.S.
following the 1973 decision in Furman v. Georgia.13 The new studies go further,
though, claiming that pardons, commutations, and exonerations cause murders to
increase.14 Some say that even murders of passion, among the most irrational of
lethal acts, can be deterred.15
At least one study, by Professor Zhiqiang Liu, claims that executions not only
deter murders, but they also increase the deterrent effects of other punishments.16
Following this logic, the new deterrence research has been applied to justify
punitive criminal justice policies in several areas: mandatory minimum sentences
and “three strikes” laws, zero tolerance policies for school children and drug
offenders, and mandatory transfer of adolescent offenders from the juvenile court
to the criminal court. Thus, the deterrent effects of capital punishment are
apparently indefinite and offer execution as a cure-all for everyday crime.17
Many of these studies have already appeared in leading academic journals,
while others are working their way through the review process. These studies have
been reported favorably and uncritically by leading newspapers (e.g., Washington
Post, Boston Globe, Wall Street Journal), and they have been broadcast widely by
pro-death penalty advocacy groups to state legislators.18 Many were cited in major
newspapers even before their papers underwent some major changes after
comments and critiques of their peers, while newspapers of record, such as The
Washington Post, quoted in their headlines findings that were later proven to be
wrong.19 Pro-death penalty advocacy groups including Justice for All, The
Criminal Justice Legal Foundation and American Voice, are widely disseminating
the results of the new studies as scientific evidence of the deterrent effects of
capital punishment. State groups in California and North Carolina also are citing
this evidence to oppose local moratorium efforts. As in the Gregg era, these
studies have been cited without challenge in amicus briefs in recent capital cases
13

408 U.S. 238 (1972).
See Mocan & Gittings, supra note 10.
15
Joanna M. Shepherd, Murders of Passion, Execution Delays, and the Deterrence of Capital
Punishment, 33 J. LEGAL STUD. 283 (2004) [hereinafter Shepherd, Murders of Passion].
16
Zhiqiang Liu, Capital Punishment and the Deterrence Hypothesis: Some New Insights and
Empirical Evidence, 30 E. ECON. J. 237 (2004).
17
Id.
18
For example, Mocan’s article received media coverage in inter alia Gene Koretz, Equality?
Not on Death Row, BUSINESS WEEK, June 30, 2003, at 28; Jeff Jacoby, Execution Saves Innocents,
BOSTON GLOBE, Sept. 28, 2003 at H11; Kieran Nicholson, Study: Race, Gender of Governors Affect
Death-Row Decisions, DENVER POST, Dec. 19, 2002, at A17; Richard Morin, Lame Ducks and the
Death Penalty, WASH. POST, Jan. 20, 2002, at B05; Richard Morin, Murderous Pardons?, WASH.
POST, Dec. 15, 2002, at B05. See also Mocan & Gittings, supra note 10.
19
George Lardner, The Role of the Press in the Clemency Process, 31 CAP. U. L. REV. 179
(2003) (pinpointing all the mistakes made in the Mocan’s article and taken at face value by the
Washington Post, without any due review by professional criminologists).
14

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including Schirro v. Summerlin.20 In April 2004, Professor Joanna Shepherd, coauthor of some of these studies, summarized the new deterrence evidence in
testimony before the federal House Judiciary Committee, claiming that there is
sound scientific evidence that each execution deters between three and eighteen
murders.21
Accordingly, the reach of the new deterrence research seems quite long, and
its potential impact on criminal justice politics and policies extends well beyond
the death penalty. This new deterrence research also benefits advocates of capital
punishment by competing with death penalty opponents who cite high rates of
errors in capital cases and wrongful convictions as arguments for state moratoria or
abolition.22 If these claims are true, the new evidence would not only
fundamentally change the roiling discourse on capital punishment, it could have
influence on both the politics and substance of criminal law and policy.
What are we to make of these claims? I answer this question in three ways.
First, we will look at the evidence itself. What claims are made in the various
studies, and what might we conclude about executions and deterrence scanning
across the new body of evidence? What is the structure of the data and what does
the data tell us, even before we look at the modeling process itself? What cautions
should we place on the interpretation and application of this information?
Second, we ask how well these claims stand up to scientific scrutiny. Have
these analyses asked too much of the data? What happens when the data are
subject to alternatives in measurement and analysis? Do the studies pay sufficient
attention to the conceptual details of deterrence, murder itself, and alternate
explanations for the complex relationships that influence changes in murder rates
over time? Here, we consider some serious omissions in the construction of this

20
Summerlin v. Stewart, 341 F.3d 1082 (9th Cir. 2003), rev’d, Schirro v. Summerlin, 542
U.S. 348 (2004).
21
Joanna Shepherd has recently argued before Congress that recent research has created a
“strong consensus among economists that capital punishment deters crime,” going so far as to claim
that “[t]he studies are unanimous.” Terrorist Penalties Enhancement Act of 2003: Hearing on H.R.
2934 Before the Subcomm. on Crime, Terrorism, and Homeland Security of the H. Comm. on the
Judiciary, 108th Cong. 23–28 (2004) (statement of Joanna M. Shepherd, Visiting Assistant Professor,
Emory Law School) [hereinafter Shepard Statement]. This consensus was repeated in recent
testimony by Professor Paul Rubin, co-author on several recent studies also reporting deterrent
effects from executions. An Examination of the Death Penalty in the United States: Hearing Before
the Subcommittee on the Constitution, Civil Rights and Property Rights of the Senate Committee on
the Judiciary, 109th Cong. (2006) (statement of Paul H. Rubin, Samuel Candler Dobbs Professor of
Economics and Law, Emory), available at http://judiciary.senate.gov/testimony.cfm?id=1745
&wit_id=4991 (last visited Mar. 10, 2006) [hereinafter Rubin Statement].
22
See, e.g., Lawrence C. Marshall, The Innocence Revolution and the Death Penalty, 1 OHIO
ST. J. CRIM. L. 573 (2004); Robert Warden, Illinois Death Penalty Reform: How it Happened, What it
Promises, 95 J. CRIM. L. & CRIMINOLOGY 381 (2005). See generally DAVID L. PROTESS & ROBERT
WARDEN, A PROMISE OF JUSTICE (1998) (documenting the media reactions to the exonerations of the
four death row inmates).

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theoretical framework, both conceptually and in the details of some modeling
decisions.
Third, can the causal modeling approach of these studies justify the claims
they make?23 In this section, we offer secondary analyses of data from one of the
new deterrence studies, authored by Professors Naci Mocan and Kaj Gittings,24 in
an effort to replicate the findings.25 Replication is one of the cornerstones of the
scientific process,26 and is essential to vetting the types of claims of causal
inference that are deeply embedded in the new deterrence studies. In this spirit, the
re-analyses in this article apply alternate measurement strategies and model forms
to establish the robustness or fragility of these findings. Already, at least one reanalysis has shown that the estimates are unstable when re-analyzed under
different measurement and analysis conditions.27 The analysis in this article goes
further by re-specifying these models using analytic strategies that account for the
unique temporal dependence in murder rates. Based on the results, I draw
conclusions about the status of this evidence and its utility both in law and policy.
Finally, we consider the tensions at the intersection of science and law that
these episodes raise. Here, we examine the recurring phenomenon of what we
might conveniently call a “rush to judgment” when science—whether behavioral
or natural—dangles the promise of simple answers to urgent but very complex
questions.
The essay shows that the new deterrence studies are fraught with numerous
technical and conceptual errors: inappropriate methods of statistical analysis,
failures to consider several relevant factors that drive murder rates such as drug
epidemics, missing data on key variables in key states, the tyranny of a few outlier
states and years, weak to non-existent tests of concurrent effects of incarceration,
statistical confounding of murder rates with death sentences, failure to consider the
23
For discussion of the complexity of causal analysis in estimating the effects of social
interventions with observational data, see Martin Rein & Christopher Winship, The Dangers of
‘Strong’ Causal Reasoning in Social Policy, 36 SOCIETY 38 (July/August 1999); Michael E. Sobel,
An Introduction to Causal Inference, 24 SOC. METHODS & RES. 353 (1996); Richard A. Berk & David
A. Freedman, Statistical Assumptions as Empirical Commitments, in PUNISHMENT AND SOCIAL
CONTROL 235 (2d ed.) (Thomas G. Blomberg & Stanley Cohen eds., 2003); PAUL R. ROSENBAUM,
OBSERVATIONAL STUDIES (1995).
24
Mocan & Gittings, supra note 10, at 454.
25
Another re-analysis of the Mocan and Gittings data also reported instability in these results.
See John Donohue & Justin Wolfers, Uses and Abuses of Empirical Evidence in the Death Penalty
Debate, 58 STAN. L. REV. 791 (2005) [hereinafter Donohue & Wolfers, Uses and Abuses](reviewing
the main studies cited by Sunstein and Vermeule and finding the empirical support for the claim that
the death penalty deters . . . to be unstable and too unreliable to inform either law or policy).
26
Lee Epstein & Gary King, The Rules of Inference, 69 U. CHI. L. REV. 1 (2002) [hereinafter
Epstein & King, The Rules of Inference]. For examples of how data sharing and independent
replication can advance the scientific process, see Lee Epstein & Gary King, Building an
Infrastructure for Empirical Research in the Law, 53 J. LEGAL EDUC. 311 (2003).
27
Donohue & Wolfers, Uses and Abuses, supra note 25, at 791.

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general performance of the criminal justice system, artifactual results from
truncated time frames, and the absence of any direct test of the components of
contemporary theoretical constructions of deterrence. Social scientists have failed
to replicate several of these studies, and in some cases have produced contradictory
or unstable results with the same data, suggesting that the original findings are
unreliable and perhaps inaccurate. The central mistake in this enterprise is one of
causal reasoning: the attempt to draw causal inferences from a flawed and limited
set of observational data, and the failure to address important competing influences
on murder. Murder is a complex and multiply-determined phenomenon, with
cyclical patterns for over forty years of distinct periods of increase and decline that
are not unlike epidemics of contagious diseases. There is no reliable, scientifically
sound evidence that pits execution against a robust set of competing explanations
to identify whether it can exert a deterrent effect that is uniquely and sufficiently
powerful to overwhelm these consistent and recurring epidemic patterns. These
flaws and omissions in a body of scientific evidence render it unreliable as a basis
for law or policy that generate life-and-death decisions. To accept it uncritically
invites errors that have the most severe human costs.
II. THE NEW DETERRENCE LITERATURE
Over a dozen new studies appeared since the mid-1990s, mainly in economics
journals, with most claiming new evidence that executions have strong and
powerful deterrent effects on homicide.28 The studies have quickly found their
way into the courts. Similar to the immediate citations of Ehrlich’s work in Gregg
and other cases, the new deterrence studies were cited in Schirro v. Summerlin29 in
an amicus brief in a certiorari petition to the United States Court of Appeals for
the Ninth Circuit.30 The studies gained attention in Congress,31 in the popular
press,32 among death penalty advocates,33 and now, among legal scholars.34
28

For a compilation of recent studies, along with abstracts, see CRIMINAL JUSTICE LEGAL
FOUNDATION, ARTICLES ON DEATH PENALTY DETERRENCE, http://www.cjlf.org/deathpenalty/
DPDeterrence.htm (last visited Nov. 11, 2005).
29
542 U.S. 348 (2004).
30
Arguing that “[t]here is grave danger that the ‘annually improvised’ jurisprudence of
capital punishment is killing innocent people through lost deterrence” and that “that a death penalty
which is actually enforced saves innocent lives in large numbers.” Brief of Amici Curiae Criminal
Justice Legal Foundation at 23–24, Schirro v. Summerlin, 542 U.S. 348 (2004) (No. 03-526),
available at http://www.cjlf.org/briefs/Summerlin.pdf.
31
See Shepherd Statemetn, supra note 21; Rubin Statement, supra note 21.
32
See, e.g., Jacoby, supra note 18; see also John Hood, A Deadly Moratorium?, CAROLINA J.
ON-LINE, (2004), http://www.carolinajournal.com/jhdailyjournal/display_ jhdailyjournal.html?id=13
91. Studies such as Mocan & Gittings, supra note 10, were discussed in the Washington Post even
before their publication in peer-reviewed journals. Several of the unreviewed papers received broad
media coverage in, inter alia, BUSINESS WEEK, supra note 18; BOSTON GLOBE, supra note 18;
DENVER POST, supra note 18; and WASH. POST, supra note 18. See also Hashem Dezhbakhsh et al.,
Does Capital Punishment Have a Deterrent Effect? New Evidence from Postmoratorium Panel

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Professors Sunstein and Vermeule find the new deterrence evidence “powerful”35
and “impressive,”36 and they couple it with “many decades of reliable data about
[capital punishment’s] deterrent effects”37 as the “foundation” of their argument
that since “capital punishment powerfully deters killings,”38 there is a moral
imperative to aggressively prosecute capital crimes.
The studies use several designs that conceptualize capital punishment as a
“treatment” that would deter homicides. The studies include classical panel
designs that co-vary homicide rates and deterrence measures that incorporate
executions, quasi-experiments testing the effects of moratoria, natural experiments
comparing homicide rates in death penalty and non-death penalty states, nested
(hierarchical) designs of counties within states that provide more fine-grained
analyses of local homicide rates, and instrumental variables designs that attempt to
disentangle spurious effects due to factors other than deterrence. The estimation
techniques vary from standard Ordinary Least Squares models to complex
equilibrium models with simultaneous equations, to negative binomial estimators
of homicides. Several have used a relatively new dataset on death sentences and
executions to operationalize and measure deterrence. The data are produced by the
U.S. Department of Justice,39 and are updated and revised annually. They include
Data, 5 AM. L. & ECON. REV. 344 (2003), was discussed uncritically in, Jerry Seper, Garza Executed
for Drug Killings: Murderer Makes Deathbed Apology, WASH. TIMES, June 20, 2001, at A3; Paul H.
Rubin, Study: Death Penalty Deters Scores of Killings, ATLANTA J. CONST., Mar. 14, 2002, at 22A,
which led to Professor Shepherd’s testimony before the U.S. House of Representatives, supra note
31. None of these papers sought opinions from criminologists who might have raised questions about
the reliability of many of the new deterrence studies. See, e.g., George Lardner, supra note 19
(pinpointing mistakes made in Mocan & Gittings, supra note 10).
33
See, e.g., CRIMINAL JUSTICE LEGAL FOUNDATION, supra note 28.
34
Cass R. Sunstein & Adrian Vermeule, Is the Death Penalty Morally Required? Acts,
Omissions, and Life-Life Tradeoffs, 58 STAN. L. REV. 703 (2005). See also Richard Posner, The
Economics of Capital Punishment, http://www.becker-posner-blog.com/archives/2005/12/
the_economics_o.html (last visited Dec. 18, 2005); Gary Becker, More on the Economics of Capital
Punishment, http://www.becker-posner-blog.com/archives/2005/12/more_on_the_eco.html (last
visited Dec. 18, 2005).
But see Carol S. Steiker, No, Capital Punishment Is Not Morally Required: Deterrence,
Deontology, and the Death Penalty, 58 STAN. L. REV. 703 (2005) (responding to claim of the “moral
requirement” of Sunstein and Vermeule by stating that “…executions constitute a distinctive moral
wrong (purposeful as opposed to non-purposeful killing), and a distinctive kind of injustice
(unjustified punishment)” and concluding that … “acceptance of ‘threshold’ deontology in no way
requires a commitment to capital punishment even if …deterrence is proven”).
35
Sunstein & Vermeule, supra note 34, at 745.
36
Id. at 713.
37
Id. at 751.
38
Id. at 738.
39
BUREAU OF JUSTICE STATISTICS, U.S. DEP’T OF JUSTICE, CAPITAL PUNISHMENT IN THE
UNITED STATES, 1973–2002, http://webapp.icpsr.umich.edu/cocoon/ICPSR-DAS/03958.xml). See
THOMAS P. BONCZAR & TRACY L SNELL, CAPITAL PUNISHMENT (2002), at

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all death sentences and their dispositions following the resumption of capital
punishment following Furman. The conclusions these studies derive are wedded
to the methods and sources that are used to compile these data. The studies have
appeared both in peer-reviewed journals, primarily in economics, and in law
reviews; a few have been published online as working papers.
The studies are listed in Appendix A. Their claims are strong, far stronger
than results produced in most social policy experiments on education, welfare, or
crime control. A detailed analysis of the methods and results of these studies is not
the purpose here; instead, here is a representative sampling of the results and
claims made by these authors.
• Mocan & Gittings: “[A]n additional execution generates a reduction
in homicide by five, an additional commutation increases homicides by
four to five, and an additional removal brings about one additional
murder.”40
• Dezhbakhsh et al.: “Our results suggest that capital punishment has a
strong deterrent effect; each execution results, on average, in eighteen
fewer murders—with a margin of error of plus or minus ten.”41
• Shepherd (Murders of Passion): “[E]ach execution results in, on
average, three fewer murders….[C]apital punishment deters murders
previously believed to be undeterrable: crimes of passion and murders by
intimates….[L]onger waits on death row before execution lessen the
deterrence. . . . [O]ne less murder is committed for every 2.75-year
reduction in death row waits. Thus, recent legislation to shorten the wait
should strengthen capital punishment’s deterrent effect.”42
• Dezhbakhsh & Shepherd: “Our results indicate that capital
punishment has a deterrent effect, and the moratorium and executions
deter murders in distinct ways. This evidence is corroborated by both the
before-and-after comparisons and regression analysis.”43
• Cloninger and Marchesini: As a result of the unofficial moratorium
on executions during most of 1996 and early 1997, the citizens of Texas
experienced a net 90 additional innocent lives lost to homicide.44
• Liu: From the econometric standpoint, the structure of the murder
supply function depends on the status of the death penalty, which is in
www.ojp.usdoj.gov/bjs/pub/pdf/cp02.pdf for illustrations of the components of the dataset and trends
and patterns over time.
40
Mocan & Gittings, supra note 10, at 469.
41
Dezhbakhsh et al., supra note 32.
42
Shepherd, Murders of Passion, supra note 15.
43
Hashem Dezhbakhsh & Joanna M. Shepherd, The Deterrent Effect of Capital Punishment:
Evidence from a “Judicial Experiment,” 44 ECON. INQUIRY 512, 517–26 (2006).
44
Dale O. Cloninger & Roberto Marchesini, Execution and Deterrence: A Quasi-Controlled
Group Experiment, 33 APPLIED ECON. 568, 575 (2001).

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itself endogenous. Liu goes on to claim that executions deter crimes
other than murder, suggesting collateral benefits of capital punishment
for public safety more broadly.45
• Shepherd (Deterrence Versus Brutalization): The impact of
executions differs substantially among the states. Executions deter
murders in six states, executions have no effect on murders in eight
states, and executions increase murders in thirteen states. Additional
empirical analyses indicate that there is a threshold effect that explains
the differing impacts of capital punishment. On average, the states with
deterrence execute many more people than do the states where
executions increase crime or have no effect. To achieve deterrence,
states must execute several people.46
Readers can easily see the appeal of these findings. Just as the Ehrlich
findings were quickly embraced in popular and political culture, these new studies
make strong claims that have similar appeal. It is not surprising that they have
been quickly embraced and disseminated as a counterweight against the cultural
and political narratives of innocence47 and errors.48
45

Liu, supra note 16, at 238.
Joanna M. Shepherd, Deterrence Versus Brutalization: Capital Punishment’s Differing
Impacts Among States, 104 MICH. L. REV. 203, 205 (2005) [hereinafter Shepherd, Deterrence Versus
Brutalization].
47
See, e.g., BARRY SCHECK ET AL., ACTUAL INNOCENCE: FIVE DAYS TO EXECUTION, AND
OTHER DISPATCHES FROM THE WRONGLY CONVICTED (2000) (citing numerous exonerations from
death row as evidence of the risks of wrongfully executing an innocent person); see also Samuel R.
Gross et al., Exonerations in the United States, 1989 Through 2003, 95 J. CRIM. L. & CRIMINOLOGY
523 (2005); RICHARD C. DIETER, DEATH PENALTY INFORMATION CENTER, INNOCENCE AND THE CRISIS
IN THE AMERICAN DEATH PENALTY (2004), available at http://www.deathpenaltyinfo.org/
article.php?scid=45&did=1149#ExSum (last visited Aug. 18, 2006) (showing that the number of
innocence cases increased by more than fifty percent in an eight year period, from thirty-two in
1989–1996 to forty-nine in 1997–2004); STAFF OF S. COMM. ON THE JUDICIARY, SUBCOMM. ON CIVIL
AND CONSTITUTIONAL RIGHTS, 103D CONG., INNOCENCE AND THE DEATH PENALTY: ASSESSING THE
DANGER OF MISTAKEN EXECUTIONS (OCT. 21, 1993); Joshua Herman, Comment, Death Denies Due
Process: Evaluating Due Process Challenges to the Federal Death Penalty Act, 53 DEPAUL L. REV.
1777 (2004); Joseph L. Hoffmann, Protecting the Innocent: The Massachusetts Governor’s Council
Report, 95 J. CRIM. L. & CRIMINOLOGY 561 (2005); Evan J. Mandery, Innocence as a Death Penalty
Issue, 40 CRIM. L. BULL. 78 (2004); Evan J. Mandery, Massachusetts and the Changing Debate on
the Death Penalty, 40 CRIM. L. BULL. 518 (2004); Michael L. Radelet, William S. Lofquist & Hugo
A. Bedau, Prisoners Released from Death Rows Since 1970 Because of Doubts About Their Guilt, 13
T. M. COOLEY L. REV. 907 (1996); Rob Warden, Illinois Death Penalty Reform: How it Happened,
What it Promises, 95 J. CRIM L. & CRIMINOLOGY 381 (2005); Laurie A. Whitt et al., Executing the
Innocent: The Next Step in the Marshall Hypotheses, 26 N.Y.U. REV. L. & SOC. CHANGE 309 (2001–
2002); Laurie A. Whitt et al., Innocence Matters: How Innocence Recasts the Death Penalty Debate,
38 CRIM. L. BULL. 670 (2002). Newspaper accounts also show that growing support for moratoria on
executions is animated by fears of wrongful executions. See Ken Armstrong & Steve Mills,
O’Connor Questions Fairness of Death Penalty Justice Rethinking Laws She Shaped, CHIC. TRIB.,
July 4, 2001, at 1; Helen Dewar, Support Grows for Execution Safeguards: Exonerations Spur Bills
46

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III. SOCIAL SCIENCE REASONING
These strong claims of powerful deterrent effects are not without
contradictions and serious limitations. When the elements of this scientific
enterprise are decomposed and evaluated, we can identify a series of recurring
challenges in their conceptualization, model specification, measurement, and
causal reasoning. The totality and cumulative weight of these challenges yields
strong reasonable doubts about the reliability of these claims. There are errors
both of commission and omission in this oeuvre of research, as I discuss below. In
addition, some simple empirical exercises reveal problems in the sensitivity of the
results to alternate measurement and model specification assumptions, producing
different results whose instability and fragility undermine the strong claims of
death penalty proponents.
A. The Structure of the Data
The findings of a negative correlation between executions and murder seem to
be structured into the data in a way that weakens generalizations or predictions.
Indeed, executions in most states in most years since Gregg are very rare.
According to the Death Penalty Information Center, there have been 1045
executions since 1976; more than one in three (366) have been in Texas.49 A
simple average of executions per state per year would be deceptive, since state
laws were enacted in different years, but even a simple estimate—there are thirtyeight death penalty states, each with a valid law in effect for an average of twenty
years since Gregg—suggests that on average, there is fewer than one execution per
in Congress, WASH. POST, June 16, 2000, at A1; Sara Rimer, Support for a Moratorium in Executions
Gets Stronger, N.Y. Times, Oct 31, 2000, at A18; Jodi Wilgoren, Citing Issue of Fairness, Governor
Clears Out Death Row in Illinois, N.Y. TIMES, Jan 12, 2003, at A1. In addition to Illinois, popular
and political concerns over innocence have generated creation of an innocence commission in North
Carolina. See Phoebe Zerwick, Innocence Commission: N.C. Creates First In Nation To Backstop
Courts, WINSTON-SALEM JOURNAL, Aug. 20, 2006, at A1.
48
James S. Liebman et al., Capital Attrition: Error Rates in Capital Cases, 1973–1995, 78
TEX. L. REV. 1839 (2000) (showing that 68% of all death sentences since Furman v. Georgia were
reversed either on direct appeal, state direct appeal, or federal habeas review; most (82%) of those
reversed were re-sentenced to non-capital punishments, 7% were exonerated, and the remainder were
re-sentenced to death). See, e.g., David Broder, Broken Justice, WASH. POST, June 18, 2000, at B7;
see also Jonathan Alter, The Death Penalty on Trial: Special Report: DNA and Other Evidence Freed
87 People from Death Row; Now Ricky McGinn is Roiling Campaign 2000. Why America’s
Rethinking Capital Punishment, NEWSWEEK, June 12, 2000, at 24, 26–34 (noting changes in political
rhetoric concerning the death penalty); Alan Berlow, The Broken Machinery of Death, AM.
PROSPECT, July 30, 2001, at 16; David Gergen, Death by Incompetence, U.S. NEWS & WORLD REP.,
June 26, 2000, at 76; James Liebman, The Condemned, and the Mistakes, N.Y. TIMES, July 12, 2000,
at A20; Murder One, THE ECONOMIST, June 17, 2000, at 33.
49
DEATH PENALTY INFORMATION CENTER, available at http://www.deathpenaltyinfo.org/
article.php? scid=8&did=146 (last updated Sept. 1, 2006).

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year per state. In states other than Texas, the median state-year average is far
lower.
In Mocan and Gittings,50 for example, executions between 1976 and 1997
range from 0 to 18, with 859 of the 1000 over the 21 years (86%) equal to 0. As a
result, the median is also 0. There are 78 values (8%) equal to 1. There are but 11
values (1%) larger than 5, ranging from 7 to 18 executions. Obviously, the
distribution is highly skewed, and the mean is dominated by a few extreme values.
Most states in most years execute no one. Accordingly, the low number of events
in most states suggests that there is hardly enough signal to reach a disparate and
heterogeneous population of would-be murderers.51
The problems of both low base rates and the hegemony of Texas in the new
deterrence studies have been illustrated by Professor Richard Berk, who reanalyzed data from Mocan and Gittings to show some simple trends and empirical
facts in the data.52 Berk constructed a simple deterrence measure, lagging
executions one year behind homicides, to show several underlying trends in these
data. First, a deterrent effect—that is, a negative slope in the murder rate relative
to the execution rate—occurs when the number of executions within a state over a
single year is five or more. Figure 1, from Professor Berk’s analysis, illustrates
this point. But even at this extreme tail of the distribution, the confidence intervals
are so large as to render a claim of prediction meaningless.

50

Mocan & Gittings, supra note 10, at 458 fig.1.
Richard Berk, New Claims About Executions and General Deterrence: Déjà Vu All Over
Again?, 2 J. EMPIRICAL LEGAL STUD. 303 (2005) [hereinafter Berk, New Claims]. Not only are
executions clustered in Texas, but most states in most years have no executions, a statistical burden
that none of the new deterrence studies competently address. To address this problem statistically,
one must first estimate a model that explains which states have any executions, and then a second
model to show the factors that predict the frequency of its use. Such models are called “hurdle”
regressions. See, e.g., Christopher J. W. Zorn, An Analytic and Empirical Examination of ZeroInflated and Hurdle Poisson Specifications, 26 SOC. METHODS & RES. 368 (1998); see also Yin Bin
Cheung, Zero-Inflated Models for Regression Analysis of Count Data: A Study of Growth and
Development, 21 STAT. IN MED. 1461, 1462–67 (2002). Statistical methods that fail to account for
this two part process will produce unreliable and inflated results.
52
Berk, New Claims, supra note 51, at 304.
51

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Figure 1. Homicide rate as a function of the number of executions lagged by one year, 1976–
1997.53

Second, Professor Berk shows that after controlling both for the initial and
average murder rate per state over the full twenty-one year study interval and state
population size over time, the trends become unstable and unpredictable.54 Third
and most important, he shows that once Texas is removed from the analysis, all
deterrent effects disappear.55
These extremes have undue “leverage” and “influence” on the data56 Most of
the model-fitting methods in these studies tend to weigh these skewed observations
very heavily, giving them undue leverage in the regression coefficients in complex
models. According to Professor Berk, claims of a deterrent effect reflect these
extreme cases, not the mass of the data.57 The leverage of these cases is
transformed into influence when extreme values of a predictor—executions—are
likely to be paired with extreme values of a response variable—homicides. By
“influence” one means that the potential impact of leverage in a model’s fit
53

Id. (reanalyzing data from Mocan & Gittings, supra note 10). Note: Solid line is smoothed
fitted values. The dotted lines contain the approximate 95% confidence interval. The relationship
between the homicide rate and the lagged number of executions is generally positive for up to five
executions and uncertain thereafter.
54
Id. at 319 fig.13.
55
Id. at 321–24 figs.15–18.
56
Id. at 305.
57
Id. at 318.

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becomes a reality, reinforcing the illusion of a statistical relationship which—in
this case—actually is simply a product of one small set of observations. When he
eliminates Texas, where these extremes are concentrated, Professor Berk shows
that the relationship between execution and homicide disappears.58
Some analysts have tried to overcome these difficulties by disaggregating
murders to the county level,59 but the extreme cases still unduly influence the
execution-homicide trends. No matter how deterrence is measured, the analyses
remain captives of the structure of the data, and that structure ordains a particular
result. If there is an effect of executions on homicides, it is the result of eleven
extreme values, and from the influence of Texas. Generalizations from the eleven
observations to the remaining ninety-nine percent would be unstable and
inappropriate.
B. Theory and Specifications
The current set of deterrence tests typically takes the form of a regression
model predicting murder rates. The predictors include measures of deterrence in
the form of executions per death sentence, a lag function expresses assumptions
about the delay from sentence to execution; and from execution to the deterrent
effect on murder. At least one study includes “announcement effects” of
executions by including newspaper reports of executions.60 Controls are
sometimes introduced to account for different assumptions about the production of
the “supply” of offenders eligible for execution: murder arrests, population size
and demography. Rarely are there measures that capture the punitiveness of the
criminal justice system or its incapacitative effects. Some try to estimate the risks
of detection by indexing the number of police. Few estimate the aggressiveness of
law enforcement by looking at the general behavior of legal institutions toward
crime generally. Socio-economic contexts associated with homicide appear via
measures of the age distribution of the population, poverty and unemployment
rates, and the extent of urbanization of the population. These structural factors
have been identified as homicide risks over time and across different units of
analysis including states, cities, and neighborhoods.61 Most of the new deterrence
58
Id. at 322 fig.16. The confidence intervals in Figure 16 suggest that there may be a positive
relationship between the homicide rate and the lagged number of executions when Texas is removed
from the data set.
59
Shepherd, Deterrence Versus Brutalization, supra note 46, at 223. One of the problems
that Shepherd faced in this analysis was disaggregating death sentences and executions to the county
level. Her solution was to apply the statewide measures for each year to each county within the state,
creating an ecological fallacy that biases estimates of deterrence.
60
Id. at 253.
61
See, e.g., Kenneth C. Land et al., Structural Covariates of Homicides Rates: Are There Any
Invariances Across Time and Social Space? 95 AM. J. SOC. 922 (1990); Robert J. Sampson & Janet
Lauritsen, Violent Victimization and Offending: Individual-, Situational-, and Community-Level Risk
Factors, in UNDERSTANDING AND PREVENTING VIOLENCE: SOCIAL INFLUENCES 1, 48–63 (A. Reiss &

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studies measure both murder and social structural risk at the state level, but others
are based on a county-within-state analysis.62
The typical approach in the new deterrence studies involves estimation of
regressions with different combinations of predictor variables, with sensitivity or
robustness estimated from variation in the size of the regression coefficient for
execution or the statutory presence of the death penalty in different configurations
of predictors. Covariates associated with the production of homicides are
included, but often are manipulated to form a sensitivity test for the specifications.
However, these predictor sets often omit a range of other important factors that
have stable and recurring effects on murder rates. These omissions in turn create
specification errors that tend to inflate the significance of the deterrence factors.
As we shall see below, some omissions are more important than others, but the
cumulative effect of these omissions is a distortion and inflation of execution
effects.
1. Deterrence, Incapacitation, and Life Without Parole
Perhaps the most important theoretical misspecification in the new deterrence
studies is the omission of the incapacitative effects of imprisonment generally, and
Life Without Parole (LWOP) sentences in particular. Of the thirty-eight states that
currently have valid death penalty statutes, thirty-seven also have LWOP statutes.
Only New Mexico does not. Of the twelve states without the death penalty, eleven
have life without parole. Only Alaska does not.63 Even if LWOP were available
as a sentencing option in cases other than capital trials, incarceration of persons
with lengthy histories of violent crimes for non-capital offenses would likely exert
some prophylactic effect on murder, given the prevalence of felony murders such
as robbery-homicides.64 Accordingly, the omission of LWOP from research on
legal interventions to reduce homicide is a potentially biasing omission.
But how much of an effect might LWOP have on homicide rates? Systematic
data on the extent to which juries return LWOP sentences capital cases is difficult
to obtain; when available, it often is only for periods beginning in 1990 or later.
J. A. Roth eds., 1994); Lauren J. Krivo & Ruth D. Peterson, The Structural Context of Homicide:
Accounting for Racial Differences in Process, 65 AM. SOC. REV. 547 (2000).
62
Shepherd, Deterrence Versus Brutalization, supra note 46.
63
Julian H. Wright, Jr., Life-Without-Parole: An Alternative to Death or Not Much of a Life
at All?, 43 VAND. L. REV. 529, 546 (1990); J. Mark Lane, “Is There Life Without Parole?” A Capital
Defendant’s Right to a Meaningful Alternative Sentence, 26 LOY. L.A. L. REV. 327 (1993); DEATH
PENALTY INFORMATION CENTER, LIFE WITHOUT PAROLE
(2000),
available
at
http://www.deathpenaltyinfo.org/ article.php?did=555&scid=59 [hereinafter DPIC]; BUREAU OF
JUSTICE STATISTICS, U.S. DEP’T OF JUSTICE, STATE COURT ORGANIZATION (1998), available at
http://www.ojp.usdoj.gov/bjs/pub/pdf/sco9807.pdf.
64
Jeffrey Fagan et al., Capital Punishment and Capital Murder: Market Share and the
Deterrent Effects of the Death Penalty, 84 TEX. L. REV 1803 (2006) [hereinafter Fagan et al., Capital
Punishment and Capital Murder].

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Information is available on when each state passed its LWOP statute or modified it
to make it a sentencing alternative in capital cases,65 so the effects at least of the
availability of LWOP as a sentencing option could be modeled and estimated.
None of the new deterrence studies do so.
Yet data from a small number of states shows ample evidence that LWOP is
used far more often than are death sentences in capital cases and cannot be ignored
in estimating reasons for the decline in homicide rates.66 For example, data from
the Pennsylvania Department of Corrections shows that there were 139 LWOP
sentences in Pennsylvania in 1999, compared to 15 death sentences. 67 In 2000,
there were 121 life sentences compared to 12 death sentences.68 In California,
there were 3163 inmates serving life without parole on February 29, 2004,
compared to 635 on death row, and zero executions.69 In South Carolina, 485
defendants have received LWOP sentences since 1996, compared to 27
executions.70 One final illustration comes from Georgia. Georgia has sentenced
369 persons to death since passing its LWOP statute in 1993, while death
sentences have declined from about ten per year to four during this time.71 Georgia
has executed 21 persons since passing its LWOP statute.72 Overall, data from the
National Judicial Reporting Program in 2002 shows that LWOP sentences were
more than three times more frequent in murder cases than were death sentences,
and nearly ten times more common than executions.73
Obviously, LWOP has incapacitative effects, as does execution, and the two
are difficult to disentangle empirically. The 1978 National Research Council Panel
65

DPIC, supra note 63.
Id.
67
PA. DEP’T OF CORRECTIONS, ANNUAL STATISTICAL REPORT 18 (1999), available at
http://www.cor.state.pa.us/stats/lib/stats/ASR1999.pdf.
68
PA. DEP’T OF CORRECTIONS, ANNUAL STATISTICAL REPORT 19 (2000), available at
http://www.cor.state.pa.us/stats/lib/stats/Annual%20Report%202000.pdf.
69
CAL. DEP’T OF CORRECTIONS, FACTS AND FIGURES (Third Quarter 2004), available at
http://www.corr.ca.gov/DivisionsBoards/AOAP/FactFiguresArchive/FactsFiguresArchive.html.
Fewer than 100 of the LWOP sentences were “Three Strikes Convictions.” See FRANKLIN ZIMRING
ET AL., PUNISHMENT AND DEMOCRACY: THREE STRIKES AND YOU’RE OUT IN CALIFORNIA (2001).
70
S.C. DEP’T OF CORRECTIONS, INMATE POPULATION STATISTICS AND TRENDS, SENTENCE
LENGTH DISTRIBUTION FY-01-05 (2005), available at http://www.doc.sc.gov/PublicInformation/
StatisticalReports/InmatePopulationStatsTrend/AsOfTrendSentenceLengthDistributionFY01-05.pdf.
For sentence length distributions for 1996–2001, data are available from the author at
http://www2.law.columbia.edu/fagan/researchdata/osjcl_deter/.
71
Associated Press, Georgia: Number of Death Penalty Cases Decline, Dec. 28, 2003,
available at http://www.democracyinaction.org.dia/organizations/ncadp/news.jsp?key=374&t=.
72
GA. DEP’T OF CORRECTIONS, INMATE STATISTICAL PROFILE, available at
http://www.dcor.state.ga.us/pdf/ lwop04-10.pdf (last visited Oct. 21, 2004).
73
U.S. DEP’T. OF JUSTICE, BUREAU OF JUSTICE STATISTICS NATIONAL JUDICIAL REPORTING
PROGRAM 2002, INTER-UNIVERSITY CONSORTIUM FOR POLITICAL SCIENCE AND SOCIAL RESEARCH,
http://www.icpsr.com.
66

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on Research on Deterrence and Incapacitation noted the complex relationship
between the two and the difficulty of separating the effects of each.74 Using a
lengthy time series, Professors Katz, Levitt and Shustarovich compared deterrence
(executions per 1000 prisoners) with incapacitation and conclude that the death
rate among prisoners, which they view as a proxy for prison conditions, has a
significant deterrent effect on violent crime rates, but they find no robust evidence
of a deterrent effect of capital punishment.75 And in one study that does compete
incarceration and deterrence, Mocan and Gittings report larger regression
coefficients for incarceration (-.0354) than executions (-.0063).76 Mocan and
Gittings call no attention to this very interesting finding that competes well with
execution as an explanation for the decline in murders. Few other studies in the
new deterrence literature report incarceration effects, and when they do, the effects
either compete with or overwhelm execution effects.
To claim that executions deter homicides when there may be equally strong
simultaneous effects from incarceration—whether incapacitative or deterrent—
introduces an omitted variable bias that potentially inflates the effects of execution.
Indeed, with the exceptions noted above, most of the new deterrence studies
simply ignore incarceration or understate its effects.77 Incarceration effects argue
against the marginal deterrent effects of execution threats. Felony murder
offenders should be deterred both by the threat of prison and the threat of
execution. But when both are included in multivariate models, there seems to be
no greater marginal threat from execution than from a generalized effect from
incarceration. Indeed, one sensitivity test that was not conducted by Mocan and
Gittings is a model that includes incarceration but not execution.
Parsing the deterrent effects of incarceration from its incapacitative effects is
a task for another article. But for this essay, it is important to note that high
incarceration rates across most states are exerting a significant downward pressure
on homicide rates.78 Moreover, these rates are highest for violent crimes.79 This is
74

See generally Klein et al., supra note 12.
Lawrence Katz et al., Prison Conditions, Capital Punishment, and Deterrence, 5 AM. L. &
ECON. REV., 318, 327 (2003) [hereinafter Katz et al., Prison Conditions].
76
Mocan & Gittings, supra note 10, at 464 tbl.2 col.1.
77
For example, Shepherd’s analysis of state-by-state “Deterrence Versus Brutalization”
effects includes prison admissions in one of the estimating equations in her model of deterrence, but
the effects are not reported. See Shepherd, Deterrence Versus Brutalization, supra note 46.
78
Prison sentences and prison populations have been increasing dramatically since 1978. See
Alfred Blumstein & Allen J. Beck, Population Growth in U.S. Prisons, 1980–1996, 26 CRIME &
JUST. 17 (1999). The largest segment of the prison population is inmates convicted of violent crimes.
See PAIGE M. HARRISON & ALLEN J. BECK, BUREAU OF JUSTICE STATISTICS, U. S. DEP’T OF JUSTICE,
PRISONERS IN 2004 (2005), available at http://www.ojp.usdoj.gov/bjs/pub/pdf/p04.pdf. At year end
in 2004, there were 2.1 million persons incarcerated in state prisons, including an estimated 624,900
prisoners serving time for a violent offense, and the nationwide incarceration rate in state prisons was
486 per 100,000 population. See, e.g., MARK R. DUROSE & PATRICK A. LANGAN, BUREAU OF JUSTICE
STATISTICS, U. S. DEP’T OF JUSTICE, FELONY SENTENCES IN STATE COURTS, 2002 (2005), available at
http://www.ojp.usdoj.gov/bjs/pub/pdf/fssc02.pdf. In 2002, the average state prison sentence for a
75

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important for two reasons. First, most capital-eligible homicides are felony
murders: homicides committed in the course of other crimes, specifically robbery
and rape.80 No offense category has grown faster in the run-up of incarceration
than violent crimes.81 Removing a segment of serious offenders through
incarceration inevitably will reduce the base rate of robbery and assault, and
reduce the portion of such crimes that escalate to homicides. While Shepherd
controls for the robbery rate in one of the new deterrence studies, she does not
control for robbery incarcerations or any other incarceration category.82 Second,
the high rate of incarceration and the increasingly lengthy sentences imposed for
violent offenses may leave little margin for additional deterrent effects from the
threat of execution. Certainly, a robust test of deterrence, as well as a fully
specified conceptual theory, would address the separate if not conditional effects of
incarceration on murder rates. Unfortunately, the current crop of deterrence
studies overlooks this question.
2. Policing and Deterrence
Deterrence theorists emphasize the importance of perceived punishment risk
in dissuading would-be offenders from committing crimes. Such risks depend on
the efficiency of the police in detecting wrongdoing and responding quickly and
efficiently, or alternately, the risk of punishment after having been caught and
prosecuted. Research both with offenders and general population samples suggests
that (subjectively) perceived risk weighs heavily on the decisions of would-be
offenders to engage in or avoid crime.83 But only a small minority of the new
deterrence studies include measures of risk of detection, especially as constructed
through effective and efficient policing.
For example, Mocan and Gittings include “the subjective probabilities that
potential offenders are apprehended, convicted, and executed” in their estimation
models, but restrict their policing and conviction estimates to murders.84 This is a
fairly typical strategy in the few studies that do consider policing. Others focus on
police expenditures,85 or the number of police officers.86 But with the exception of
violent offense was eighty-four months, a rate that excludes life sentences. The average time served
was 5.4 years. Id.
79
See Durose & Langan, supra note 78.
80
See Fagan et al., Capital Punishment and Capital Murder, supra note 64.
81
See Durose & Langan, supra note 78.
82
Shepherd, Deterrence Versus Brutalization, supra note 46, at 225.
83
Daniel S. Nagin, Criminal Deterrence Research at the Outset of the Twenty-First Century,
23 CRIME & JUST. 1 (1998).
84
Mocan & Gittings, supra note 10, at 457–58.
85
See Shepherd, Murders of Passion, supra note 15; Shepherd, Deterrence Versus
Brutalization, supra note 46.
86
See, e.g., Dezhbakhsh et al., supra note 32.

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Katz and his colleagues, there is little attention to the contributions of policing to
reductions or variations in homicide rates.
This is an error not just in understanding how crime rates vary, but also it misspecifies the theoretical pathway and mediating effects of how policing affects
deterrence and homicide. The locus of deterrent effects may reside either in the
threat of execution or in the threat of apprehension and punishment. A century of
deterrence theory and research shows that punishment risk outweighs punishment
costs in a general deterrence heuristic,87 suggesting that the margin for deterrence
from execution may be rather thin when compared to punishment risks that have a
higher present-value to offenders. Clearance rates for murder are a simple metric
for establishing these risks. Clearance rates usually are expressed as the percent of
homicides that result in an arrest of a suspect leading to a prosecution. Although
plea bargaining often reduces the conviction charge and punishment cost for the
offense, homicide arrests are still quite likely to generate a sentence of some
lengthy spell of incarceration, achieving either a deterrent or incapacitative effect,
if not both. The question, then, is whether there is a marginal deterrent effect of
execution.
The clearance rate for felonies that creates punishment risk also attenuates the
supply of potential homicide offenders. The ability of local law enforcement to
identify homicide offenders or high rate offenders generally will reduce their
prevalence and in turn the risks of homicides, especially felony murders.
Examining errors in capital sentences, Professor James Liebman and his colleagues
showed that from 1976 to 1995 inefficient criminal justice systems seemed to
overly rely on the death penalty to respond to homicides compared to jurisdictions
with more efficient and effective policing regimes.88 This signals that the death
penalty was compensatory in these locales for poor policing. The court
jurisdictions that used the death penalty more often were prone to higher rates of
serious reversible error.89
Recent studies also show that the police have a prophylactic effect on crime.90
This effect goes beyond simply the expenditure on policing or the number of
police. Police efficiency and strategy exert strong influences on crime rates,
87

Nagin, supra note 83.
JAMES S. LIEBMAN ET AL., A BROKEN SYSTEM, PART II: WHY THERE IS SO MUCH ERROR IN
CAPITAL CASES, AND WHAT CAN BE DONE ABOUT IT (2002), available at
http://www2.law.columbia.edu/brokensystem2/report.pdf [hereinafter LIEBMAN ET AL., A BROKEN
SYSTEM, PART II].
89
Id.
90
See, e.g., Hope Corman & H. Naci Mocan, A Time-Series Analysis of Crime, Deterrence,
and Drug Abuse in New York City, 90 AM. ECON. REV. 584 (2000); Steven D. Levitt, Using Electoral
Cycles in Police Hiring to Estimate the Effect of Police on Crime, 87 AM. ECON. REV. 270 (1997);
Jeffrey Grogger, Certainty vs. Severity of Punishment, 29 ECON. INQUIRY 297 (1991); Jonathan Klick
& Alexander Tabarrok, Using Terror Alert Levels to Estimate the Effect of Police on Crime, 48 J. L.
& ECON. 267 (2005); Steven D. Levitt, Understanding Why Crime Fell 1990s: Four Factors that
Explain Decline and Six that Do Not, 18 J. ECON. PERSP. 163 (2004).
88

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including gun-related crimes that carry a special risk of escalating to lethality. For
example, Professor Jacqueline Cohen’s analysis of aggressive police interdiction
strategies in Pittsburgh showed strong reductions in gun crimes and gun injuries.91
Local police departments allocate and deploy their resources to reflect
strategic analyses of crime problems and the tactics best suited to their control.
These decisions, and policing effects generally, are not accurately captured through
measures of police force size or police expenditures that are typically used in the
new deterrence studies. In general, the inconsistent and atheoretical attention to
policing as a competing source of deterrence or crime control is another form of
omitted variable bias that weakens the claims of the new deterrence studies.
3. Co-Morbid Epidemics
Homicide was not the only epidemic social problem in the United States in
the years following Furman. Furman was decided just as a five year epidemic of
heroin use had begun to wane in the United States in the early 1970s,92 an era when
homicide rates also rose sharply across American cities.93 The sharp rise in
homicides was linked temporally and spatially to an epidemic of heroin use.94
Over the next two decades, homicide rates rose and fell concurrently with other
drug epidemics. Homicide rates spiked again from 1979 to 1981, concurrent with
the emergence of street drug markets in major cities where powdered cocaine was
openly sold.95 Record homicide rates in American cities in the early 1990s
coincided with the crack epidemic that lasted nearly a decade after 1986.96
91

Jacqueline Cohen & Jens Ludwig, Policing Crime Guns, in EVALUATING GUN POLICY:
EFFECTS ON CRIME AND VIOLENCE 217 (Philip J. Cook & Jens Ludwig eds., 2003). See generally
FAIRNESS AND EFFECTIVENESS IN POLICING: THE EVIDENCE (Wesley Skogan & Kathleen Frydl eds.,
2004) (citing empirical evidence that specialized policing targeting specific crime problems is more
effective than general reactive policing, and discounting evidence reporting that larger police forces
are more effective at crime deterrence).
92
See DAVID F. MUSTO, THE AMERICAN DISEASE: ORIGINS OF NARCOTIC CONTROL (3d ed.
1987). See generally David F. Musto, Perception and Regulation of Drug Use: The Rise and Fall of
the Tide, 123 ANNALS INTERNAL MED. 468 (1995).
93
See FRANKLIN ZIMRING & GORDON HAWKINS, CRIME IS NOT THE PROBLEM: LETHAL
VIOLENCE IN AMERICA (1997); see also Alfred Blumstein & Richard Rosenfeld, Explaining Recent
Trends in U.S. Homicide Rates, 88 J. CRIM. L. & CRIMINOLOGY 1175 (1998); Richard Rosenfeld,
Patterns in Adult Homicide: 1980–1995, in THE CRIME DROP IN AMERICA 130 (Alfred Blumstein &
Joel Wallman eds., 2000).
94
See LEON G. HUNT & CARL D. CHAMBERS, THE HEROIN EPIDEMICS: A STUDY OF HEROIN
USE IN THE UNITED STATES, 1965–1975, 73–113 (1976); James A. Inciardi, Heroin Use and Street
Crime, 25 CRIME & DELINQ. 335 (1979); D.J. Egan & D.O. Robinson, Models of a Heroin Epidemic,
136 AM. J. PSYCHIATRY 1162 (1979); Michael Agar & H.S. Reisenger, A Heroin Epidemic at the
Intersection of Histories: The 1960s Epidemic Among African Americans in Baltimore, 21 MED.
ANTHROPOL. 115 (2002).
95
See, e.g., Bruce D. Johnson et al., Drug Abuse in the Inner City: Impact on Hard Drug
Users and the Community, in DRUGS AND CRIME 9 (Michael Tonry & James Q. Wilson eds., 1990);
TERRY WILLIAMS, THE COCAINE KIDS (1989); Audio Tape: Lloyd Johnston et al., National Trends in

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The temporal and spatial dependence of murder and drugs is an
epidemiological fact that deserves serious attention as a competing influence on
the murder rate. One might see drug epidemics and murder as simply co-morbid
problems that share common etiologies or that combine to weaken the resources
needed to resist such social problems. Or, one might see them as causally related,
in which case the rise and fall of one epidemic would predict concurrent or closely
spaced changes in the other.97 The latter view dominated criminological research
through the 1990s. Through mechanisms that connect drug sales and gun violence,
the crack epidemic exerted a strong push on murder rates and spread across
American cities in a pattern similar to a contagious disease.98
The decline in homicides through the late 1990s and into the early part of this
decade has been linked to the decline in the crack epidemics, specifically changes
in street markets where drugs had been openly sold amidst much violence a decade
earlier.99 Drug sales declined in volume and moved indoors as demand shrunk and
also as police focused on drug sales. Competition between sellers waned, reducing

Drug Use and Related Factors Among American High School Students and Young Adults, 1975–86
(1987) (DHS ADM 87–1535); LYNN ZIMMER, OPERATION PRESSURE POINT: THE DISRUPTION OF
STREET-LEVEL DRUG TRADE ON NEW YORK’S LOWER EAST SIDE (1987); Lynn Zimmer, Proactive
Policing Against Street-Level Drug Trafficking, 9 AM. J. POLICE 43 (1990).
96
Eric Baumer et al., Poverty, Crack, and Crime: A Cross-City Analysis, 31 J. RES. CRIME &
DELINQ. 311 (1994); Eric Baumer et al., The Influence of Crack Cocaine on Robbery, Burglary and
Homicide Rates: A Cross-City Longitudinal Analysis, 35 J. RES. CRIME & DELINQ. 316 (1998); Jeff
Grogger & Michael Willis, The Emergence of Crack Cocaine and the Rise in Urban Crime Rates, 82
REV. ECON. & STAT. 519, 526 (2000); Roland G. Fryer et al., Measuring the Impact of Crack Cocaine
1–65 (Nat’l Bureau of Econ. Research, Working Paper No. 11318, 2005), available at
http://papers.nber.org/papers/w11318.pdf (last visited Mar. 13, 2006).
97
See, e.g., Jan M. Chaiken & Marcia R. Chaiken, Drugs and Predatory Crime, in DRUGS
AND CRIME 203 (Michael Tonry & James Q. Wilson eds., 1990); ROBERT J. MACCOUN & PETER
REUTER, DRUG WAR HERESIES: LEARNING FROM OTHER VICES, TIMES AND PLACES (2003).
98
See Alfred Blumstein, Youth Violence, Guns, and the Illicit-Drug Industry, 86 J. CRIM. L. &
CRIMINOLOGY 10 (1995); Daniel Cork, Examining Space-Time Interaction in City-Level Homicide
Data: Crack Markets and the Diffusion of Guns Among Youth, 15 J. QUANTITATIVE CRIMINOLOGY
379 (1999); see also Paul J. Goldstein et al., Crack and Homicide in New York City, 1988: A
Conceptually Based Event Analysis, 16 CONTEMP. DRUG PROBS. 651 (1989) (showing that in 1988 in
New York City, 85% of crack-related crimes were caused by the market culture associated with illicit
crack sales, primarily territorial disputes between rival crack dealers); Roland G. Fryer et al., supra
note 96. The Fryer crack index is specific to cocaine and specifically crack, and emphasizes
homicide victimization and drug overdose deaths. However, since most drug-related violence,
including homicide, is associated with drug trafficking, the index is of less utility in explaining longterm variation in drug market trends and their effects on homicides. See Jeffrey Fagan, Intoxication
and Aggression, in DRUGS AND CRIME 241 (Michael Tonry & James Q. Wilson eds., 1990). See
generally U.S. SENTENCING COMMISSION, Chapter 5: Cocaine and Crime, in REPORT ON COCAINE
AND FEDERAL SENTENCING POLICY, available at http://www.ussc.gov/crack/chap5.htm (last visited
Mar. 22, 2006).
99
See, e.g., Richard Curtis, The Improbable Transformation of Inner-City Neighborhoods:
Crime, Violence, Drugs and Youth in the 1990s, 88 J. CRIM. L. & CRIMINOLOGY 1233 (1998).

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the incidence of disputes implicated in many murders during the height of the
epidemic.100
None of the new deterrence studies consider the epidemics of drug use and
related violence, especially murder. Perhaps the declines in drug markets were due
to police efforts to deter drug selling through intensive drug enforcement and high
volumes of drug arrests, or to sentencing laws that targeted drug sellers. But these
direct or indirect effects of policing were also not given close attention. As in
policing, the inattention to the effect of drug epidemics on violence is an omission
that challenges, if not impeaches, the conclusions of the new deterrence studies of
a singular effect of execution on homicide.
4. Are all Homicides Deterrable?
Most of the new deterrence studies regard homicide as a homogeneous
criminal behavior. With one exception, these studies make no distinctions between
homicides committed in varying contexts or with different motivations. The
assumption is that all are equally deterrable. This logic is challenged in at least
two different ways. First, several decades of empirical research on homicide that
cut across the social sciences suggests that homicides are variably rational; some,
such as crimes of jealousy or unplanned and highly contingent events, are simply
poor candidates for deterrence. Second, the law makes these distinctions explicit
in felony murder rules, and carves out a particular set of homicides—such as
homicides committed in the course of other crimes—as eligible for capital
punishment. The most accurate test of the underlying rationale for deterrence
would be the sensitivity of these homicides to the threat of execution.
Only one among the new studies, by Professor Joanna Shepherd,101 offers
estimates of the deterrent effects of execution on specific categories of
homicide.102 Shepherd reports that executions deter all types of murder, including
domestic or marital homicides, or other “crimes of passion” that so often are
considered to be irrational and spontaneous acts that are beyond the rational reach
of execution threats.103
100

Id. See also NAT’L INSTITUTE OF JUSTICE, 1998 ANNUAL REPORT ON COCAINE USE AMONG
ARRESTEES, NCJ 175657, available at http://www.ncjrs.gov/pdffiles1/175657.txt (last visited Mar.
16, 2006).
101
Shepherd, Murders of Passion, supra note 15.
102
Information about the circumstances of events is provided by the Federal Bureau of
Investigation in the Supplemental Homicide Reports, a data file of homicide records that includes
information on victims, offenders (where known via arrest), and the circumstances of the homicide
event. See BUREAU OF JUSTICE STATISTICS, U.S. DEP’T OF JUSTICE, HOMICIDE TRENDS IN THE U.S.,
available at http://www.ojp.usdoj.gov/bjs/homicide/homtrnd.htm#contents (last visited Sept. 1,
2006); JAMES A. FOX, INTER-UNIVERSITY CONSORTIUM FOR POLITICAL SCIENCE AND SOCIAL
RESEARCH, UNIFORM CRIME REPORTS [UNITED STATES]: SUPPLEMENTARY HOMICIDE REPORTS, 1976–
2003 (2005), available at http://webapp.icpsr.umich.edu/cocoon/ICPSR-STUDY/04351.xml.
103
Shepherd, Murders of Passion, supra note 15.

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The high rate of murder-suicides in domestic homicides is one clue to the
irrationality if not mental illness of this subset of murderers, limiting the prospects
for deterrence.104 The gradient of uncontrolled rage that precedes many domestic
homicides also suggests the inelasticity of motivation and arousal among men who
kill or nearly kill their intimate partners.105 The steady decline over nearly 30
years in “domestic” or intimate partner homicides106 suggests a secular trend that is
insensitive to fluctuations in the number of executions since capital punishment
was reinstated following Gregg.
The literature on homicide events shows that many homicide offenders are
simply unresponsive to punishment threats.107 Professor Jack Katz offers an
analysis of homicide events and offenders that portrays some as “stone cold
killers” while others simply take pleasure from killing, even as they remain
indifferent to punishment threats or even death by retaliation in the moment of the
homicide.108 Using a social interactionist framework, several sociologists conclude
that most homicide events are largely unplanned products of complicated social
interactions—disputes that escalate from minor conflicts into threatening conflicts
where the fear of injury or death motivates lethally violent responses to even minor
provocations.109 Deanna Wilkinson and I suggest that the presence of firearms
104
See, e.g., Jacquelyn C. Campbell et al., Risk Assessment for Intimate Partner Homicide, in
CLINICAL ASSESSMENT OF DANGEROUSNESS: EMPIRICAL CONTRIBUTIONS 136 (Georges-Franck Pinard
& Linda Pagani eds., 2001); Lauren Bennett et al., Risk Assessment Among Batterers Arrested for
Domestic Assault: The Salience of Psychological Abuse, 6 VIOLENCE AGAINST WOMEN 1190 (2000);
Arlene N. Weisz et al., Assessing the Risk of Severe Domestic Violence: The Importance of
Survivors’ Predictions, 15 J. INTERPERSONAL VIOLENCE 75 (2000).
105
See KENNETH POLK, WHEN MEN KILL: SCENARIOS OF MASCULINE VIOLENCE (1994); see
also Jeffrey Fagan & Angela Browne, Violence toward Spouses and Intimates: Physical Aggression
between Men and Women in Intimate Relationships, in 3 UNDERSTANDING AND PREVENTING
VIOLENCE 115 (Albert J. Reiss, Jr., & Jeffrey A. Roth eds., 1994); Angela Browne et al., Homicide
Between Intimate Partners, in HOMICIDE: A SOURCEBOOK OF SOCIAL RESEARCH 149 (M. Dwayne
Smith & Margaret A. Zahn eds., 1999).
106
See, e.g., Laura Dugan et al., Explaining the Decline in Intimate Partner Homicide: The
Effects of Changing Domesticity, Women’s Status, and Domestic Violence Resources, 3 HOMICIDE
STUD. 187 (1999) (attributing the two-decades-long decline in the intimate partner homicide rate in
the United States as a function of three factors that reduce exposure to violent relationships: shifts in
marriage, divorce, and other factors associated with declining domesticity; the improved economic
status of women; and increases in the availability of domestic violence services).
107
See JACK KATZ, SEDUCTIONS OF CRIME: THE MORAL AND SENSUAL ATTRACTIONS OF DOING
EVIL (1988) [hereinafter KATZ, SEDUCTIONS OF CRIME] (describing “stone cold killers” who are
insensitive to punishment threats, and whose homicides can only be described as the pursuit of
domination and pleasure); see also NATHANIEL J. PALLONE & JAMES J. HENNESSY, TINDER-BOX
CRIMINAL AGGRESSION: NEUROPSYCHOLOGY, DEMOGRAPHY, PHENOMENOLOGY (1996).
108
KATZ, SEDUCTIONS OF CRIME, supra note 107.
109
See Richard B. Felson & Henry J. Steadman, Situational Factors in Disputes Leading to
Criminal Violence, 21 CRIMINOLOGY 59, 59–60 (1983); David F. Luckenbill, Criminal Homicide as a
Situated Transaction, 25 SOC. PROBS. 176 (1977); Richard B. Felson, Impression Management and
the Escalation of Aggression and Violence, 45 SOCIAL PSYCHOLOGY Q. 245 (1982); David F.

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short circuits the decision stages where the perceived cost of not killing a possibly
armed opponent is one’s own death from the opponent’s firearm.110 There is no
planning in these events; the emotional arousal in the moment trumps all restraint
and compromises the type of reasoning and calculation necessary for deterrence.111
The use of total homicides has always been an aggregation error in the
deterrence debate in the United States.112 Under common law, only the top grade
of murder was ever eligible for the death penalty. However, the traditional legal
framework on the criteria that made criminal homicide potentially capital was far
from clear until the U.S. Supreme Court imposed minimum constitutional
standards for death eligibility in Gregg v. Georgia and its companion 1976
cases.113 Shepherd’s was one of the few projects to attempt to disaggregate
homicides into separate categories to assess their deterability. However, she did
not use legally relevant categories; her partitioning of the data was not indexed to
statute, but to a set of categories descriptive of “different types of murders”114 that
were defined neither by statute nor, with the exception of “crimes of passion,” by
theory. More importantly, none of these categories were narrowed according to
statutory criteria that bound the circumstances and conditions that qualify a murder
as “capital.”115
In fact, when one narrows the search for deterrence by focusing not on
general homicide trends and rates, but on the subset of homicides that are eligible
for the death penalty, any evidence of deterrence disappears. If execution risk is
the core element in deterrence, these types of homicides should provide a more
sensitive test than the overall homicide rate index for detecting a deterrent effect
Luckenbill & Daniel P. Doyle, Structural Position and Violence: Developing a Cultural Explanation,
27 CRIMINOLOGY 422, 422–23 (1989); WILLIAM OLIVER, THE VIOLENT SOCIAL WORLD OF BLACK
MEN 138–40 (1994).
110
Deanna L. Wilkinson & Jeffrey Fagan, A Theory of Violent Events, in THE PROCESS AND
STRUCTURE OF CRIME: CRIMINAL EVENTS AND CRIME ANALYSIS 169 (Robert F. Meier & Leslie
Kennedy eds., 2001). See also DEANNA L. WILKINSON, GUNS, VIOLENCE, AND IDENTITY AMONG
AFRICAN AMERICAN AND LATINO YOUTH (2004); Jeffrey Fagan & Deanna L. Wilkinson, Guns, Youth
Violence, and Social Identity in Inner Cities, in YOUTH VIOLENCE 105 (Michael Tonry & M.H.
Moore eds., 1998) [hereinafter Fagan & Wilkinson, Guns, Youth Violence].
111
PALLONE & HENNESSY, supra note 107.
112
See THORSTEN SELLIN, THE DEATH PENALTY: A REPORT FOR THE MODEL PENAL CODE
PROJECT OF THE AMERICAN LAW INSTITUTE (1959). Sellin’s classic studies of more than 50 years ago
included particularly high risk categories of homicides, such as killings of police officers and prison
guards.
113
Gregg v. Georgia, 428 U.S. 153 (1976).
114
Shepherd, Murders of Passion, supra note 15, at 292 (sorting murders into categories of
victim-offender relationship including intimates, acquaintances, and strangers, crime-of-passion
murders and murders committed during other felonies, and murders of African-American and white
people).
115
For the distinction between felony murder and capital murder, see 40A AM. JUR. 2D
Homicide § 551 (2006).

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from execution.116 After all, felony murder carries strict liability, a consequence of
the intent-based retributivism that guides most of the capital murder statutes in
effect in 38 states today.117
However, when partitioned according to these legal categories, there seems to
be no evidence of deterrence based on lagged executions. Analyses of homicide
trends from 1976 to 2003 in death penalty states, using a variety of econometric
models, show that there is no significant effect of executions on the rate of capitaleligible murders. 118 One deterrence story is that the threat of execution should
affect the subset of homicides eligible for executions more than other homicides.
Accordingly, the “market share” of homicides that are capital-eligible should
decline as the overall homicide rate declines, while non-capital homicides should
remain unaffected by the threat of execution. But, together with colleagues
Franklin Zimring and Amanda Geller, I find just the opposite: the market share is
rising, since capital-eligible homicides remain stable over time while the rate of
other homicides declines. This also is true when we isolate county-level trends in
Texas, the state that has carried out more than one third of all executions in the
United States since Gregg.119 This is the opposite of what would be predicted from
economic theories of death penalty deterrence.
If capital eligible homicides are insensitive to deterrent threats, even as other
homicides are declining, then the prospects for a more generalized pattern of
deterrence of homicide are not good. As non-capital eligible homicides decrease
in number, it would be logical that police and prosecutors would devote more
attention to the smaller number of capital-eligible cases. Greater resources would
be available for police investigations and clearance rates should improve.
Prosecutors also would have more time and greater resources to devote to these
cases, increasing the likelihood of lengthy prison sentences, if not capital
sentences. Yet even this concentration of criminal justice resources on capitaleligible cases has not leveraged the rate of capital-eligible homicides.
C. Measurement and Specification Errors
Three types of measurement error undermine the claims of the new deterrence
studies: large amounts of missing data on key indices of murder, over-inclusion of
persons who are eligible for capital punishment in the estimates of deterrence, and
arbitrary and artifactual temporal truncation in the panel designs. Each source of
error independently leads to inflated estimates of deterrence.
116

See, e.g., Franklin Zimring & Gordon Hawkins, Deterrence and Marginal Groups, 5 J.
RES. CRIME & DELINQ. 100 (1968).
117
Kevin Cole, Killings During Crime: Toward a Discriminating Theory of Strict Liability, 28
AM. CRIM. L. REV. 73 (1990).
118
Fagan et al., Capital Punishment and Capital Murder, supra note 63.
119
Id.

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1. Missing Data
To measure both homicides and homicide arrests, most of the new deterrence
studies rely on data published by the Federal Bureau of Investigation through its
Uniform Crime Reporting (UCR) program.120 However, the UCR data have large
amounts of missing data from critical states. For example, data on homicide and
robbery arrests in Florida are missing for many local police departments in 1988
and 1989 and again in 1997 through 2002.121 A more recent analysis by Professors
Michael Maltz and Harald Weiss of monthly data on crimes reported to the police
shows that many years have only partial data: reports in fewer than the full twelve
months of the calendar year.122 For example, Florida reported homicides to the
UCR system for no months in 1988, five months in 1989, and no more than two
months in 1997 through 1999.123 Yet Florida is one of the nation’s most active
death penalty states, with fifty-seven executions from Gregg through 2003, so the
importance of its omission and the potential bias in estimating the deterrent effects
of execution due to incomplete data is obvious. In general, non-reporting by police
agencies is a recurring problem in the UCR program. For example, from 1992–
1994, 3516 of the 18,413 (19%) agencies participating in the UCR system made no
reports at all to the UCR program. 124 According to Professor Michael Maltz, the
non-reporting agencies included the primary police agencies in three counties and
cities with populations greater than 100,000, and also the primary agencies in 200
cities with populations greater than 10,000. By 1995, the percent of the U.S.
population covered by agencies reporting crimes to the UCR system declined from
nearly 100% in 1980 to less than 90%.125 By 1997, the percent of the U.S.

120
FED. BUREAU OF INVESTIGATION, UNIFORM CRIME REPORTS DEP’T OF JUSTICE, UNIFORM
CRIME REPORTS FOR THE UNITED STATES: CRIME IN THE UNITED STATES, 1973–2003, available at
http://bjsdata.ojp.usdoj.gov/dataonline/ (last visited Aug. 18, 2006).
121
See, e.g., INTER-UNIVERSITY CONSORTIUM FOR POLITICAL SCIENCE AND SOCIAL RESEARCH,
UNIFORM CRIME REPORTING PROGRAM DATA [UNITED STATES]: OFFENSES KNOWN AND CLEARANCES
BY ARREST (1999) available at http://www.icpsr.umich.edu/cgi-bin/bob/newark?study=3158&
path=NACJD (last visited July 21, 2006). Data for each state and year are available at
http://www.icpsr.umich.edu/NACJD/ucr.html (last visited July 21, 2006).
122
MICHAEL D. MALTZ & HARALD E. WEISS, CREATING A UCR UTILITY: FINAL REPORT TO THE
NATIONAL INSTITUTE OF JUSTICE (2006), available at http://www.ncjrs.gov/pdffiles1/nij/grants/
215341.pdf.
123
Id. Data for Florida and all other states from 1960–2002 are available in spreadsheets from
http://sociology.osu.edu/people/mdm/UCR_Utility.zip.
124
See MICHAEL MALTZ, BUREAU OF JUSTICE STATISTICS, U.S. DEP’T OF JUSTICE, BRIDGING
GAPS IN POLICE CRIME DATA (1999), available at http://www.ojp.usdoj.gov/bjs/pub/pdf/bgpcd.pdf, at
9 tbl.1 and accompanying text. The percent of the population covered by police agencies reporting
arrests statistics declined from 95% in 1977 to 73% by 1997. Id. at fig.10.
125
Id. at fig.3.

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population covered by agencies reporting UCR arrest records had declined from
95% in 1977 to 73%.126
The new deterrence studies are generally silent on the patterns of missing data
and offer no adjustments that might compensate the biases from excluding key
states and years. When not silent, the adjustments for missing data are often
puzzling, but more worrisome is their potential for introducing bias. In one study,
Professor Shepherd takes heart in the fact that over 90% of the homicides are
reported by the FBI, ignoring the weighting and distribution of the missing
homicide statistics. Instead, she simply dropped those data points “so that the
missing data do not bias my results.”127 Quite the contrary, simply leaving out
these state-months raises doubts about the accuracy and absence of bias in her
results. The 10% of the population that is not included in the UCR’s crime reports
is not normally distributed, nor is the 27% that is not included in the arrest
statistics. The bias from ignoring the processes generating such large amounts of
missing data is potentially quite large.
Even within states, the omission of these key agencies and years in places like
Florida introduces a selection bias that is likely to distort both the regression
coefficients and the standard errors. Professor Jon Sorenson showed an
undercounting of 137 homicides in a two year span from 1996 to 1997 by
Cloninger and Marchesini128 in their analysis of the impacts on homicide of the
short moratorium on executions in Texas in the mid-1990s.129 Similarly, Mocan
and Gittings use a substitution algorithm to replace cases where division by zero
(in computing executions per lagged death sentence) with .99, a decision that
increases the size of the deterrence coefficient by approximating a value of one
rather than a value of zero.130 In Section IV, I show that when I run the Mocan and
Gittings regression models correcting this coding decision, the deterrence variable
is no longer statistically significant.131
The new deterrence studies also fail to address the missing data problems or
investigate alternate data sources that might fill in important gaps in annual
homicide rates. One such data set is available from the mortality and morbidity

126

Id. at fig.10.
Shepherd, Murders of Passion, supra note 15, at 304.
128
Cloninger & Marchesini, supra note 44.
129
Jon Sorensen et al., Capital Punishment and Deterrence: Examining the Effect of
Executions on Murder in Texas, 45 CRIME & DELINQ. 481 (1999) (finding no evidence of deterrence
resulting from capital punishment using Texas execution and murder rate data from 1984 through
1997); see also JON SORENSON & ROCKY LEANN PILGRIM, LETHAL INJECTION: CAPITAL PUNISHMENT
IN TEXAS DURING THE MODERN ERA (2006) (re-analyzing claim that the moratorium resulted in an
increase in homicides).
130
Mocan & Gittings, supra note 10. See also Donohue & Wolfers, Uses and Abuses, supra
note 25.
131
See infra Part IV.A., tbl.1; see also Donohue & Wolfers, Uses and Abuses, supra note 25.
127

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files of the National Center for Health Statistics (NCHS).132 Information on all
deaths classified as homicides by local coroners or medical examiners are
compiled by NCHS and reported annually. The data are available for counties as
well as states, and have been used in research on capital punishment to develop a
metric of the use of the death penalty relative to local homicide rates.133 The
extent of the missing data bias is evident when we substitute a complete record of
homicides in regression models estimating the deterrent effects of capital
punishment. For example, when the complete NCHS homicide victimization data
set is substituted for the incomplete FBI homicide data in the Mocan and Gittings
data set, regression model results change dramatically and the magnitude of a
putative deterrent effect is significantly reduced.134
2. Deterring Which Murders?
Most of the new deterrence studies use global measures of murder that
include persons or types of murders that are ineligible for execution. For example,
global measures of homicide offenses include murders committed by persons
whose ages are below the threshold of eligibility for capital punishment in most
death penalty states. Since Gregg, only eleven persons below the age of sixteen at
the time of their crime were sentenced to death, and none were executed.135
Moreover, the practice was barred by the 1988 U.S. Supreme Court decision in
Thompson v. Oklahoma136 exempting juveniles below the age of sixteen from
capital punishment. Yet despite the exclusion (at first by socio-legal norm and
later by law) of youths below the age of sixteen from capital punishment, the new
deterrence studies include all homicides in their estimates. Yet between 1976 and
2003, 8312 of the 339,187 homicides since Gregg (where the offender’s age is
132
State homicide and victimization data, including by race, are from the Vital Statistics of the
United States or other data compilations generated by the Centers for Disease Control and Prevention
National Center for Health Statistics. Data for 1973–1992 are from Vital Statistics of the United
States, Mortality Detail Files, 1968–1992, Inter-University Consortium for Political Science and
Social Research, Study No.7632, 6798. Data for 1993–1998 are from Centers for Disease Control
and Prevention National Center for Health Statistics, Compressed Mortality File, 1989–98 CD-ROM
Series 20, No 2C ASCII Version. Data after 1998 are from CDC Wonder, the Centers for Disease
Control data extraction engine at http://wonder.cdc.gov. Through 1992, the relevant data sources list
homicide victims by State of death. After 1993, the relevant data source lists homicide victims by
state of residence. Data for 2001 excludes all victims from the events of September 11, 2001.
133
John Blume & Theodore Eisenberg, Judicial Politics, Death Penalty Appeals, and Case
Selection: An Empirical Study, 72 S. CAL. L. REV. 465 (1999); LIEBMAN ET AL., A BROKEN SYSTEM,
PART II, supra note 88.
134
See infra Part IV. & tbl.1.
135
VICTOR STREIB, THE JUVENILE DEATH PENALTY TODAY: DEATH SENTENCES AND
EXECUTIONS FOR JUVENILE CRIMES, JANUARY 1, 1973—FEBRUARY 28, 2005 (2005), available at
http://www.law.onu.edu/faculty/streib/documents/juvdeath.pdf.
136
487 U.S. 815 (1988) (plurality opinion).

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known) were committed by persons below the age of sixteen.137 In Texas, where
more than one in three executions in the U.S. have taken place of the homicides (of
the 36,630 where information is available on the offender’s age) during these years
were committed by persons below the age of sixteen. During the years of the
highest homicide rates in the United States, juveniles were the fastest growing
group of homicide offenders from 1985 through 1993.138
The extent of potential bias depends on several factors. If the number of
juvenile homicide offenders is small and stable over time, then this poses little
threat. From 1976–2003, among homicides where the offender’s age was known,
a small subset of homicides (2.6%) were committed by persons under the age of
sixteen.139 But offender age is unknown in about one in three cases in this
interval,140 and there is no reliable way to estimate the age distribution of offenders
in unknown cases. Yet, assuming that the age distribution of the unknown cases
approximates the age distribution of the known cases, there may be no reason to
suspect that the parameter estimates of deterrence are inflated due to the inclusion
of murders by very young offenders in the homicide rate. Whatever noise these
cases introduce into the econometric models is negligible and unlikely to be
correlated with any of the predictors. But this is obvious neither empirically nor
theoretically, especially since homicides by and of adolescents increased more
rapidly than every other category of homicides for nearly a decade beginning in
1985.141
The instability over time in the number of homicides committed by persons
below sixteen, and also instability over time in the number of cases where the
offender age is unknown, create measurement problems that invalidate the
invariance assumptions needed to ignore such trends. If these two parameters are
fluctuating over time, and their correlation with other predictors is changing
simultaneously, then we have to ask additional questions to assess whether these
shifts are inconsequential in their effects on the estimates of the homicide rates. 142
137
See INTER-UNIVERSITY CONSORTIUM FOR POLITICAL SCIENCE AND SOCIAL RESEARCH,
UNIFORM CRIME REPORTING PROGRAM DATA [UNITED STATES]: SUPPLEMENTARY HOMICIDE REPORTS,
1976–2003, available at http://webapp.icpsr.umich.edu/cocoon/ICPSR-STUDY/04351.xml (last
visited Dec. 15, 2005). The Supplementary Homicide Reports are filtered to exclude the deaths in
New York associated with the attacks of September 11, 2001, but include those associated with the
Oklahoma City bombing of April 19, 1995.
138
Philip J. Cook & John H. Laub, The Unprecedented Epidemic of Youth Violence, in 24
CRIME AND JUSTICE: A REVIEW OF RESEARCH 27 (Michael Tonry & Mark H. Moore eds., 1998).
139
Fagan et al., Capital Punishment and Capital Murder, supra note 64, at tbl.1.
140
Id.
141
Cook & Laub, supra note 138.
142
For example, these correlates were changing simultaneously with the changes in homicide
rates by adolescents. From 1985–1992, the percentage of homicides committed by firearm rose more
quickly among adolescents than other population groups. So too did the demography of homicide:
the concentration of perpetrators and victims among African Americans rose steadily throughout this
period. Id. See also Lois A. Fingerhut et al., Firearm and Nonfirearm Homicide Among Persons 15

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First, is the timing of the fluctuations related to the peaks and valleys in the
homicide rate, and second, is the timing of these changes correlated with any of the
control variables that also are predictors of homicide? For example, if the number
of homicide offenders below sixteen rises during periods of intense drug activity
and increases in the violence associated with drug markets, then the error terms in
the homicide estimates and the predictors may be correlated, biasing the standard
errors and distorting the significance of the estimates of the size of a putative
deterrent effect of execution. At the least, the timing and magnitude of increases in
the youth homicide rate and increases in the number of offenders whose ages are
unknown should raise cautions in interpreting the magnitude of deterrent effects in
the types of panel series econometrics that populate the new deterrence studies.
3. Early Cutoffs in Panel Designs
A third concern is the artifactual truncation of observations that excludes data
points where execution and homicide show no relationship. What would happen if
there were five to eight more years added to these panels, years when homicide
rates were stable while executions were sharply declining? That is the case in the
new deterrence studies, and the result is that the current estimates suffer from
period effects that produce artifactual and elevated estimates of deterrence.
Many of the studies include data from 1977 through 1996143, 1997144, or
1999.145 Only one panel study extended the observational window through
2000.146 But the pattern of executions and homicides in the five years following
these studies suggests that murder was insensitive to the levels of execution in this
interval: executions declined nationwide from ninety-eight in 1999 to fifty-nine in
2004, but the murder rate remained nearly stable, varying between 5.5 and 5.6 per
100,000 population. Perhaps there were changes in the predictors of homicide in
that period that helped stabilize the murder rate, such as shifts in demography,
incarceration patterns, drug epidemics, or other factors such as the robbery rate that
influences the crimes that typically lead to capital-eligible felony murders. But
there is no reason to believe that homicide rates had become insensitive to the pace
of change in these externalities. Nor did these factors decline at a rate greater than
Through 19 Years of Age: Differences by Level of Urbanization, United States, 1979 Through 1989.
267 J. AM. MED. ASS’N 3048 (1992); Lois A. Fingerhut et al., Firearm Homicide Among Black
Teenage Males in Metropolitan Counties: Comparison of Death Rates in Two Periods, 1983 Through
1985 and 1987 Through 1989, 267 J. AM. MED. ASS’N 3054 (1992).
143
Shepherd, Deterrence Versus Brutalization, supra note 46.
144
See, e.g., Mocan & Gittings, supra note 10; Paul R. Zimmerman, State Executions,
Deterrence, and the Incidence of Murder, 7 J. APPLIED ECON. 163 (2004); James A. Yunker, A New
Statistical Analysis of Capital Punishment Incorporating U.S. Postmoratorium Data, 82 SOC. SCI. Q.
297 (2001).
145
Shepherd, Murders of Passion, supra note 15.
146
Zimmerman, supra note 144.

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the 40% decline in executions. If homicides were sensitive to executions, we
would expect an uptick in the homicide rate as executions declined. But this
distinctive footprint of deterrence is not evident in the patterns of murder through
2004, which remained nearly flat across the nation since 1999.
The flat pattern of homicides and executions since 1999 is likely to influence
both the regression coefficient for any of the measures of execution-based
deterrence, as well as the standard errors of the estimates. Whatever the form of
the model before 2000, it is now different. Throughout the late 1990s, as
executions increased while homicides declined, there was nearly a linear
relationship between execution and murder. But the addition of five more years
with a different pattern of executions and homicides, where the relationship is no
longer tightly defined, makes the earlier model at a minimum less accurate because
the overall fit of the trend line is no longer comfortable. In other words, the shape
of the curve is now different, and so too should be the functional form of the
equation that predicts it.
4. Computation and Model Specification Errors
Other computational and model specification errors have been noted in two
articles by Professors John Donohue and Justin Wolfers,147 including conceptual
and measurement errors in the selection of instrumental variables by Dezhbakhsh
et al.148 Instrumental variables should be correlated with the predictor—in this
case, executions—but not with the dependent variable murders. This technique
allows analysts to conduct quasi-experiments that simulate the conditions of true
experiments. Dezhbakhsh and colleagues use instruments that are in all likelihood
correlated with executions: prison admissions, Republican voters, and police
payrolls. It is hard to imagine that the same social and political dynamics,
including higher crime rates, that contribute to higher prison admissions do not
also contribute to harsher criminal justice policies including the aggressive
application of the death penalty. Indeed, Professor Liebman and his colleagues
show that these measures—political dynamics, punitive criminal justice policies,
high murder rates, and aggressive use of the death penalty—are correlated with
errors in death sentences.149
When Donohue and Wolfers make minor adjustments to avoid the
confounding of the instruments with the other design elements, the estimates of
deterrence become very unstable and range so widely (from 429 lives saved per

147

Donohue & Wolfers, Uses and Abuses, supra note 25; John Donohue & Justin Wolfers,
The Death Penalty: No Evidence for Deterrence, THE ECONOMIST’S VOICE 1 (2006), available at
http://bpp.wharton.upenn.edu/jwolfers/Press/DeathPenalty(BEPress).pdf [hereinafter Donohue &
Wolfers, The Death Penalty].
148
Dezhbakhsh et al., supra note 32.
149
LIEBMAN ET AL., A BROKEN SYSTEM, PART II, supra note 88.

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execution to 86 lives lost) as to become meaningless.150 They also show, as I do in
Section IV of this article, that when computational errors by Mocan and Gittings
are corrected, their estimates are no longer statistically significant. Overall, these
types of computational errors lead to biased if not inaccurate estimates. The biases
affect both the size of the regression coefficients and the standard errors. Both
biases suggest that the published estimates are unacceptably sensitive to even
minor modifications in measurement and, as we see below, estimation techniques.
This is the opposite of robustness, and shows the risks of a utilitarian approach to
vetting claims of deterrence.
D. Estimation Techniques
The new deterrence studies share a common econometric language and
preferences for analytic strategies. All the studies use panel data examining
murder rates over time within states or counties over a number of years. The
general analytic form is a regression equation where the murder rate in each state
and year in the time series (or panel) is the dependent variable, and the predictors
are a linear combination of factors including the presence of a death penalty law in
a given state, the predictability of execution given a death sentence in some
previous era, state effects that account for differences between the states, and year
effects that account for national time trends that affect the states. Most studies
estimate models with states as the unit of analysis, while others include models
where county murder rates are predicted from a combination of state- and countylevel predictors.151
As discussed earlier, most designs include statistical controls or covariates
that represent factors within states or counties that may affect both the homicide
rate including demographic and socio-economic conditions, law enforcement
indicia and political forces that may encourage use of the death penalty.152 But
these factors also influence the presence and use of the death penalty, introducing
an analytic confound that can bias results and give misleading and inflated
estimates of deterrence.153 To avoid this, and to approximate an experiment where
experiments are not possible, some studies use instrumental variables designs,
where variables are included that might affect the use of the death penalty but not
150
151
152

Donohue & Wolfers, The Death Penalty, supra note 147, at 3.
See, e.g., Dezhbakhsh et al., supra note 32.
The model form generally is expressed as:

See Donohue & Wolfers, Uses and Abuses, supra note 25, at 804.
153
For a discussion of how this endogeneity problem affects estimates of deterrence, see
Richard A. Berk, Knowing When to Fold 'Em: An Essay on Evaluating the Impact of CEASEFIRE,
COMPSTAT, and EXILE, 4 CRIMINOLOGY & PUB. POL’Y 451 (2005).

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necessarily murder.154 These studies assume that this strategy can produce
accurate and unbiased results, however, we saw earlier that measurement and
model specification errors can produce misleading, if not inaccurate, results
regardless of how sound the instruments may be.155
Put that aside for the moment, and consider the analytic strategy on its own
terms. Two connected assumptions in this strategy may undermine the stability
and accuracy of the claims of the new deterrence studies. First, the state-fixed
effects strategy assumes that any variance that is not accounted for by the
covariates remains stable over time. In other words, state- or county-level factors
that might produce initial differences are assumed to be invariant. This is probably
incorrect, especially for longer time periods: the assumption that the states or
counties are invariant with respect to stability in these exogenous factors places a
huge burden on the covariates to do all the work in accounting for meaningful
change within the states over time. Accordingly, the assumption of stability is
only as good as the selection of the covariates. Earlier, I discussed limitations and
errors in these predictors and covariates that are likely to produce biased and
inaccurate estimates. So, analytic strategies that rely on the assumptions of
stability (or the absence of cross-sectional heteroskedacity) in the unmeasured
variance in the predictors are quite risky and probably wrong.
Second, using fixed effects for years treats each year as a separate
experimental period that is independent from the previous year’s outcomes. The
year-fixed effects may account for national trends over time, but it ignores the
effects of time within states. In effect, this approach to understanding time in
panel data ignores the fact that murder rates within states vary through time, and
that murder rates within states or counties are serially correlated over time. This is
the problem of autoregression, or serial correlation.156 Autoregression is the
154
Instrumental variables or instruments are necessary when the predictors or independent
variables are correlated with the error terms of the dependent variable. A valid instrument is a
variable that would be correlated with the explanatory variable (in this case, executions or the
presence of a death statute) and is uncorrelated with the error term of the dependent variable, or the
murder rates. See, e.g., Dezhbakhsh et al., supra note 32 (using several instruments including prison
admissions, police payrolls, judicial expenditures, and the statewide Republican vote).
Misspecification of instruments can produce misleading results by introducing factors that might be
correlated not just with the execution rate, but also with the error term in the crime rate. Donohue
and Wolfers point out that Republican voters are more likely to elect legislators who will pass toughon-crime measures such as mandatory minimum sentences, which would also affect the murder rate.
See Donohue & Wolfers, The Death Penalty, supra note 147, at 3. In classic experimental terms, this
is an endogeneity problem, where the “treatment” condition (in this case, executions) is correlated
with other predictors (Republican votes) of the dependent variables (murders). See, e.g., PAUL
ROSENBAUM, OBSERVATIONAL STUDIES (2d ed. 2002).
155
See discussion supra Parts III.C.1–3.
156
County murder rates are also spatially correlated. The murder rates in a particular county,
may reflect processes that are taking place in the adjacent counties, such that they are simply picking
up the effects of causal factors operating nearby but not necessarily within the county itself. See
SPATIAL STATISTICS : METHODOLOGICAL ASPECTS AND APPLICATIONS (Marc Moore ed., 2001).

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tendency of trends in longitudinal or time series data to be heavily influenced by
the trends in preceding years.157 In other words, the best predictor of what the
murder rate will be next year is what it was last year. Statistically and
conceptually, it is unlikely that effects of extremely rare events, such as
executions, can impact trends that are so heavily influenced by their own
history.158 The problem is compounded when there are patterns of missing
observations in time series models when the data evidence autoregressive
structures.159 The problem is compounded again when there is serial correlation in
the treatment variable, as is the case when estimating the effects of the presence of
a death penalty statute, which nearly always is constantly present from year to year
once a valid statute passes and goes into effect.160
Many of the studies underplay the question of when and where executions
take place and the differences between death penalty and non-death penalty states.
Several of the studies include non-death penalty states as comparisons, but fail to
address statistically the differences between the two groups of states. Simple
contrasts between death penalty and non-death penalty states, even with covariates
that characterize some of the differences, make strong identifying assumptions that
in the absence of a treatment, the average murder rates for states in each group
would have followed parallel paths over time. But if the murder rates are higher in
death penalty states, then the antecedents of homicides are probably unbalanced in
the two groups, and the estimates of treatment effects are biased. Simply
controlling for state differences via state fixed effects, or inserting a variable for
whether a valid death penalty statute was in effect in any year, raises a series of
connected endogeneity problems that require an integration of econometrics with
methods more familiar in the analysis of data in natural experiments.161
Most of the new deterrence studies use standard errors computed from simple
Ordinary Least Squares (OLS) regressions, but without correcting for
autoregression, the standard errors in the estimates of the effects of execution are
157

See, e.g., WILLIAM GREENE, ECONOMETRIC ANALYSIS (5th ed. 2003).
See Berk, New Claims, supra note 51; see also BADI H. BALTAGI, ECONOMETRIC ANALYSIS
OF PANEL DATA (2001); Badi H. Baltagi & Qi Li, Testing AR(1) Against MA(1) Disturbances in an
Error Component Model, 68 J. ECONOMETRICS 133 (1995); Robert C. Jung & A.R. Tremayne, Testing
for Serial Dependence in Time Series Models of Counts, 24 J. TIME SERIES ANALYSIS 65 (2003).
159
K.D.S. Yound & L.I. Pettit, The Effect of Observations on Bayesian Choice of an
Autoregressive Model, 27 J. TIME SERIES ANALYSIS 41 (2006).
160
See JEFFREY M. WOOLDRIDGE, ECONOMETRIC ANALYSIS OF CROSS SECTION AND PANEL
DATA (2002); see also Marianne Bertrand et al., How Much Should We Trust Differences-inDifferences Estimates?, 119 Q. J. ECON. 249 (2004).
161
See, e.g., Alberto Abadie, Semiparametric Difference-in-Differences Estimators, 72 REV.
ECON. STUD. 1 (2005). For classic examples of the use of natural experiments to detect the presence
of deterrent effects of executions, see Hans Zeisel, The Deterrent Effect of the Death Penalty: Facts
v. Faiths, 1976 SUP. CT. REV. 317 (1976). See also Thorsten Sellin, Homicides in Retentionist and
Abolitionist States, in CAPITAL PUNISHMENT 135 (Thorsten Sellin ed., 1967); Thorsten Sellin,
Experiments with Abolition, in CAPITAL PUNISHMENT 122 (Thorsten Sellin ed., 1967).
158

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well understated.162 In at least two studies in the new deterrence literature, when
the standard errors are corrected for autoregression, the standard errors increase,
and the execution variable is no longer statistically significant.163 Such instability
in the coefficients under different measurement and analytic conditions should be a
serious warning sign to those who would uncritically embrace the new deterrence
evidence. In section IV., I show that statistical modeling techniques that account
for the strong year-to-year correlation of murder rates over time produces dramatic
changes in the statistical significance and effect size of executions on murder
rates.164
E. Deterrence
Death sentences are rare, as are executions. One reason is that capital
punishment is limited by a jurisprudence that recognizes that “death is different”
and should, therefore, be reserved for only the most heinous murders.165 This
jurisprudence leads to a necessary scarcity: most states have narrowly tailored
capital punishment laws to constrain the number and types of homicides that are
eligible for the death penalty.166 This scarcity undermines the logic of deterrence:
is it reasonable to expect that rare execution events will have salience across large
heterogeneous pools of potential offenders?
This problem is not just a matter of social science, but also of law. The
Supreme Court concluded in Furman that when only a tiny fraction of persons who
162
See, e.g., Bertrand et al., supra note 160. In general, to produce accurate standard errors
when there is serial correlation or autoregression in the outcome variables, we need to estimate
standard errors that are robust to autocorrelation as well as heteroskedasticity, otherwise known as
Heteroskedasticity and Autocorrelation-Consistent (HAC) standard errors, or Newey-West standard
errors.
See Whitney Newey & Kenneth D. West, A Simple, Positive Semi-Definite,
Heteroskedasticity and Autocorrelation Consistent-Covariance Matrix, 55 ECONOMETRICA 703
(1987); see also WOOLDRIDGE, supra note 160.
163
See Donohue & Wolfers, Uses and Abuses, supra note 25, at 835 (reporting that when they
correct Zimmerman’s (2004) analysis for serial clustering or correlation, the confidence interval on
his estimates widens to a range of twenty-three homicides caused by each execution to fifty-four
homicides prevented by each execution); see also infra Part IV.
164
See infra Part IV.B; see also Donohue & Wolfers, Uses and Abuses, supra note 25, at 835.
165
HUGO ADAM BEDEAU, DEATH IS DIFFERENT: STUDIES IN THE MORALITY, LAW, AND POLITICS
OF CAPITAL PUNISHMENT 55–59 (1987); Jeffrey Abramson, Death-is-Different Jurisprudence and the
Role of the Capital Jury, 2 OHIO ST. J. CRIM. L. 117 (2004).
166
But see Jonathan Simon & Christina Spaulding, Tokens of Our Esteem: Aggravating
Factors in the Era of Deregulated Death Penalties, in THE KILLING STATE: CAPITAL PUNISHMENT IN
LAW, POLITICS, AND CULTURE 81 (Austin Sarat ed., 1999) (showing that state legislatures steadily
expanded death penalty eligibility for two decades starting in the early 1980s by adding a wide range
of aggravators). Scarcity has been eroded by a gradual expansion of the categories of murders that
are subject to felony murder rules and classification as capital-eligible. Simon and Spaulding note
that these elements of homicides provide a “currency through which states seek to recognize various
concerns and valorize certain kinds of subjects and situations.” Id.

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commit murder are sentenced to death, capital punishment is unconstitutionally
irrational because it serves no identifiable penal function.167 Assuming rationality,
for the moment, rare executions are unlikely to influence decision processes by
motivating would-be killers to adjust to these punishment threats. A death penalty
that is almost never used serves no deterrent function, because no would-be
murderer can reasonably expect to be executed.168 In his concurrence in
Furman,169 Justice White recognized that:
[A] major goal of the criminal law—to deter others by punishing the
convicted criminal—would not be substantially served where the penalty
is so seldom invoked that it ceases to be the credible threat essential to
influence the conduct of others. . . . [C]ommon sense and experience tell
us that seldom-enforced laws become ineffective measures for
controlling human conduct and that the death penalty, unless imposed
with sufficient frequency, will make little contribution to deterring those
crimes for which it may be exacted.170
The heart of the matter, then, is whether the criminal law can deter murder
and if so, under what conditions. The contours of the modern deterrence argument
in capital punishment were constructed by Professor Gary Becker in theoretical
work that preceded and informed Ehrlich’s 1975 empirical application to the death
penalty.171 Becker’s framework was a decision heuristic informed by rational
choice and information processing: “All human behavior can be viewed as
involving participants who (1) maximize their utility (2) form a stable set of
preferences and (3) accumulate an optimal amount of information and other inputs
in a variety of markets.”172 In the decades following Ehrlich’s publication, these
theoretical propositions formed the core of discourse, theory and research on
deterrence. Accordingly, the new deterrence studies are minor extensions of
Becker’s and Ehrlich’s original theoretical formulations that lean heavily on price
theory.173
167

408 U.S. 238 (1972).
See, e.g., Paul Slovic et al., Decision Processes, Rationality and Adjustment to Natural
Hazards, in PERCEPTION OF RISK 1 (Paul Slovic ed., 2000).
169
408 U.S. 238 (1972).
170
Id. at 312 (White, J., concurring).
171
Becker, Crime and Punishment, supra note 1.
172
Id. See also BECKER, ECONOMIC APPROACH, supra note 1, at 14. Becker continues to
advance price theory as a supplement to, if not a substitution for, the limitations of the new deterrence
research, noting that “most people have a powerful fear of death” that ultimately will deter their
homicidal behavior. See Gary S. Becker, On the Economics of Capital Punishment, 3 THE
ECONOMIST’S VOICE 1166 (2006), available at http://www.bepress.com/ev/vol3/iss3/art4 (last visited
April 16, 2006) [hereinafter Becker, On the Economics of Capital Punishment].
173
When confronted with unstable and noisy data from the current studies, proponents of
deterrence, such as Becker, lean on price theory, claiming that since most people have a strong fear of
168

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Until recently, the crossfire between death penalty deterrence advocates and
opponents focused not on the moving parts of deterrence theory, but on three
methodological concerns: the econometrics to estimate deterrence, data and
measurement concerns, and model specification problems such as those discussed
earlier.174 Despite advances in theorizing deterrence in the context of public
enforcement of law, including the addition of constructs such as tastes for risk or
imperfect knowledge,175 empirical research on capital punishment has not been
updated to test these propositions. In fact, there still have been no direct tests of
deterrence among groups whose responses could be reasonably generalized to
violent offenders. No studies have shown that murderers are aware of executions
in their own state, much less in far-away states, and that they rationally decide to
forego homicide and use less lethal forms of violence in the face of risk of
execution.
No one doubts that the criminal law, as well as other types of legal sanctions,
have deterrent effects, but the evidence suggests that such effects may be confined
to risk groups atypical of homicide offenders.176 Deterrence research in the last
half century is equivocal on the robustness of deterrent effects, and quite modest
when extending deterrence rationales to groups of high-rate or serious offenders.177
Professor Daniel Nagin’s detailed review shows that deterrent effects in the
criminal law are conditioned on the social position of the person and the type of
death, they will avoid murder. See Becker, On the Economics of Capital Punishment, supra note
172.
174
For example, one of the primary critiques of Ehrlich’s 1975 article was the leverage that
was exerted on homicide trends by the final seven years of his time series (1963–1969), while
ignoring contemporaneous trends in non-death penalty states. See, e.g., Peter Passell & John B.
Taylor, The Deterrent Effect of Capital Punishment: Another View, 67 AM. ECON. REV. 445 (1977);
see also Walter S. McManus, Estimates of the Deterrent Effect of Capital Punishment: The
Importance of the Researcher’s Prior Beliefs, 93 J. POL. ECON. 417 (1985); Zeisel, supra note 161, at
317.
175
See A. Mitchell Polinsky & Steven Shavell, The Theory of Public Enforcement of Law, in 1
HANDBOOK OF LAW AND ECONOMICS (forthcoming 2006); see also Owen Bar-Gill & Alon Harel,
Crime Rates and Expected Sanctions: The Economics of Deterrence Revisited, 30 J. LEGAL STUD.
485 (2001).
176
Nagin, supra note 83. See, e.g., Jeff T. Casey & John T. Scholz, Beyond Deterrence:
Behavioral Decision Theory and Tax Compliance, 25 LAW & SOC’Y REV. 821 (1991); Karly A.
Kinsey et al., Framing Justice: Taxpayer Evaluations of Personal Tax Burdens, 25 LAW & SOC’Y
REV. 845 (1991); Greg Pogarsky & Alexis R. Piquero, Can Punishment Encourage Offending?
Investigating the “Resetting” Effect, 40 J. RES. CRIME & DELINQ. 95 (2003) (exploring the relevance
of judgment and decision making research on gambler’s fallacies in probabilistic reasoning for crime
decision making); see also D.L. McArthur & J.F. Kraus, The Specific Deterrence of Administrative
Per Se Laws in Reducing Drunk Driving Recidivism, 16 AM. J. PREVENTIVE MED. 68 (Supp. 1999);
Donald S. Kenkel & Steven F. Koch, Deterrence and Knowledge of the Law: The Case of Drunk
Driving, 33 APPLIED ECON. 845 (2001).
177
See Nagin, supra note 83; see also Daniel S. Nagin & Greg Pogarsky, Integrating Celerity,
Impulsivity, and Extralegal Sanction Threats into a Model of General Deterrence: Theory and
Evidence, 39 CRIMINOLOGY 865 (2001).

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crime. The evidence cannot be reliably extended to murderers, since the more
persuasive deterrence experiments have been done using experimental paradigms
with lower risk groups.178 Obviously, in experimental paradigms, it is unrealistic
to simulate the contexts where lethal aggression tends to occur. But one could
doubt that extreme violence might be deterred: Nagin reports no evidence of valid
tests for deterrence of injury aggression.
With these limitations in mind, what conditions are necessary to reliably
extend deterrence theory to the case of murder and capital punishment? Professors
Paul Robinson and John Darley identify three conceptual and practical
prerequisites to deterrence that are necessary to establish a plausible link between
punishment contingencies and behavioral outcomes: rationality, knowledge, and
choice.179 They characterize each as a conceptual hurdle that deterrence theory
must overcome to attain empirical validity and conceptual legitimacy.
1. Rationality
The rationality test asks whether offenders, assuming they possess knowledge
of the risks of detection and punishment, will apply their understanding to the
decision to engage in homicide at the moment when they are making the choice.
Studies that directly examine the reactions of individuals to punishment threats
consistently show the limits of rationality, especially in the case of aggression or
violence. For example, violence often is embedded in the contexts of the moment,
where choices among alternatives are skewed by the demands of the situation. For
murder, these contingencies include revenge, retaliation, fear of lethal attack, and
nonnegotiable demands of peers or network cohorts.180 Consequently, many
situations that could end in lethal violence are highly volatile, where decisions are
made under conditions of arousal, whether anger or fear.181 Rationality may be

178

See, e.g., Daniel Nagin & Raymond Paternoster, Personal Capital and Social Control: The
Deterrence Implications of Individual Differences in Criminal Offending, 32 CRIMINOLOGY 581, 584
(1994) (reporting results of research with a sample of college students showing that “individuals who
commit crimes place little weight on the future consequences of their actions”).
179
Paul H. Robinson & John M. Darley, Does Criminal Law Deter? A Behavioral Science
Investigation, 24 OXFORD J. LEGAL STUD. 173 (2004) (reviewing evidence from criminology and
other behavioral sciences and concluding that the deterrent effects of the criminal law are quite
limited).
180
See, e.g., LEE ROSS & RICHARD NISBETT, THE PERSON AND THE SITUATION: PERSPECTIVES
OF SOCIAL PSYCHOLOGY (1991). See also Luckenbill & Doyle, supra note 109; Andrew V.
Papachristos, Murder Markets: Network Contagion and the Social Order of Gang Homicide,
Abstract, available at http://ssrn.com/abstract=855304 (last visited May 15, 2006) [hereinafter
Papachristos, Murder Markets].
181
See, e.g., PALLONE & HENNESSY, supra note 107; Fagan & Wilkinson, Guns, Youth
Violence, supra note 110.

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further impaired by cognitive, organic and neuropsychological factors that may
occlude punishment risk from rational calculations.182
The underlying assumptions of rationality depend on clarity and objectivity
among offenders in cognition, risk analysis, cost measuring, future orientation and
premeditation.183 Such attributes are unknown in research on murder and
murderers, except perhaps among the very small percentage of murder-for-hire and
premeditated killings.184 Rather, murderers are more likely to discount punishment
risks, and inflate the present value of whatever gains the crime may offer.185 This
amounts to economics minus the rationality assumptions.186
The limitations in unreconstructed rationality lead Professors Russell
Korobkin and Thomas Ulen to recommend replacing the rationality assumption
with a multi-disciplinary understanding of human behavior, drawing from such
fields as cognitive psychology, sociology, and decision sciences.187 Along the
same lines, Professor Robert Cooter says that economic theories of deterrence need
a theory of endogenous preferences that will integrate cognitive psychology to
incorporate motives and values into the deterrence calculus.188 These theories are
unified in prospect theory, an alternate decision framework that describes how
people actually make decisions.189 Like rational choice theory, prospect theory
assumes that decision makers will seek to maximize their outcomes, but in
182
See, e.g., Adrian Raine et al., Reduced Prefrontal and Increased Subcortical Brain
Functioning Assessed Using Positron Emission Tomography in Predatory and Affective Murderers,
16 BEHAV. SCI. & L. 319 (1998); Lisa M. Gatzke-Kopp et al., Temporal Lobe Deficits in Murderers:
EEG Findings Undetected by PET, 13 J. NEUROPSYCHIATRY & CLINICAL NEUROSCI. 486 (2001);
Dorothy Otnow Lewis et al., Ethics Questions Raised by the Neuropsychiatric, Neuropsychological,
Educational, Developmental, and Family Characteristics of 18 Juveniles Awaiting Execution in
Texas, 32 J. AM. ACAD. PSYCHIATRY & L. 408 (2004); Dorothy Otnow Lewis et al., Neuropsychiatric,
Psychoeducational, and Family Characteristics of 14 Juveniles Condemned to Death in the United
States, 145 AM. J. PSYCHIATRY 584 (1988); D. Michael Bitz & Jean Seipp Bitz, Incompetence in the
Brain Injured Individual, 12 ST. THOMAS L. REV. 205, 260 (1999).
183
Jon Elster, When Rationality Fails, in THE LIMITS OF RATIONALITY 19 (Karen Schweers
Cook & Margaret Levi eds., 1990).
184
KATZ, SEDUCTIONS OF CRIME, supra note 107 (citing anecdotal evidence to build a theory
of criminal motivation in killings).
185
See, e.g., PALLONE & HENNESEY, supra note 107; see also KATZ, SEDUCTIONS OF CRIME,
supra note 107; POLK, supra note 105; ELIJAH ANDERSON, THE CODE OF THE STREET (1999)
[hereinafter ANDERSON, CODE OF THE STREET].
186
Christine Jolls, Cass R. Sunstein & Richard Thaler, A Behavioral Approach to Law and
Economics, 50 STAN. L. REV. 1471 (1998).
187
Russell Korobkin & Thomas S. Ulen, Law and Behavioral Science: Removing the
Rationality Assumption from Law and Economics, 88 CAL. L. REV. 1051 (2000).
188
Robert Cooter, Treating Yourself Instrumentally: Internalization, Rationality and the Law,
in THE LAW AND ECONOMICS OF IRRATIONAL BEHAVIOR 95 (Franco Parisi & Vernon L. Smith eds.,
2005).
189
Chris Guthrie, Prospect Theory, Risk Preference, and the Law, 97 NW. U. L. REV. 1115,
1116–19 (2003).

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unpredictable ways. The theory assumes that people will make risk-averse
decisions when deciding among options that seem to be gains, but will make riskseeking decisions when faced with losses.190 Offenders will value losses more than
gains of a similar magnitude, and they will overvalue certainty.191 In other words,
most people, perhaps including criminal offenders, are more likely to take risks to
avoid losses than to accumulate gains.
This challenge to rationality and the movement toward disciplinary
integration exposes the fault lines in assumptions of rationality among criminal
offenders. As a group, offenders often are risk-seekers and prone to thrill
seeking,192 and their impulsivity tends to be significantly higher than nonoffenders.193 They value social rewards and status from crime over the social
rewards of conventional roles and behaviors,194 and they often are impaired
cognitively from extensive careers of drug and alcohol abuse.195 Future
consequences are either ignored or postponed, giving way to an orientation to
consider only present contingencies.196 In one of the few studies with samples of
criminal offenders, Professor Charles Dean and his research collaborators report
that the stability of present orientation over a long developmental period explains
long criminal careers.197 These irrational orientations tend to co-exist in a cascade
of organic and cognitive impairments to further weaken cognition and decision
making.198
Under these conditions, when faced with uncertainty, decision makers are
likely to systematically depart from the rational actor model.199 Nevertheless,

190

Id. at 1116.
Daniel Kahneman & Amos Tversky, Prospect Theory: An Analysis of Decisions Under
Risk, 47 ECONOMETRICA 263 (1979) [hereinafter Kahneman & Tversky, Prospect Theory].
192
Nagin & Paternoster, supra note 178.
193
But see Cooter, supra note 188.
194
Jeffrey Fagan & Deanna L. Wilkinson, Social Contexts and Functions of Adolescent
Violence, in VIOLENCE IN AMERICAN SCHOOLS: A NEW PERSPECTIVE 55 (D.S. Elliott, B. Hamburg &
K.R. Williams eds., 1998) [hereinafter Fagan & Wilkinson, Social Contexts]; Deanna L. Wilkinson &
Jeffery Fagan, The Role of Firearms in Violence “Scripts”: The Dynamics of Gun Events Among
Adolescent Males, 59 LAW & CONTEMP. PROBS. 55 (1996) [hereinafter Wilkinson & Fagan, Role of
Firearms].
195
Chaiken & Chaiken, supra note 97.
196
Nagin & Paternoster, supra note 178.
197
Charles Dean, Robert Brame & Alex Piquero, Criminal Propensities, Discrete Groups of
Offenders, and Persistence in Crime, 34 CRIMINOLOGY 547 (1996).
198
But see Stephen J. Morse, Brain Overclaim Syndrome and Criminal Responsibility: A
Diagnostic Note, 3 OHIO ST. J. CRIM. L. 397 (2006) (facetiously addressing the tendency among some
social scientists and legal scholars to apply limited research from neuroscience to explain a wide
range of antisocial and violent behaviors).
199
Amos Tversky & Daniel Kahneman, Rational Choice and the Framing of Decisions, 59 J.
BUS. S251, S251–54 (1986) [hereinafter Tversky & Kahneman, Rational Choice]. The failure of
191

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rationality is a familiar comfort zone for the law.200 But rationality as a descriptive
term for cognition has given way in social science to the concept of “bounded
rationality.” 201 Professor Herbert Simon uses “bounded rationality” to describe
the process of making decisions using decision making heuristics, limited time,
and incomplete information. A rational choice would be one which maximizes
utility, but Simon points out that in many cases the decision maker will aim to
make only a satisfactory choice (Simon calls this “satisficing”).202
These shortcomings in rationality remind us that even when facts are known,
they may be neither recalled in a particular event nor mobilized accurately as part
of a decision heuristic. The facts themselves may or may not be relevant to the
situation,203 and even if recalled, they may be interpreted incorrectly given the
context. If a criminal offender is prone to discounting costs that create cognitive
dissonance with the perceived benefits or their preferences, the facts that
communicate those costs will be distorted if not ignored.204

rationality under conditions of uncertainty suggests the need to distinguish between rationality and
rational choice. The latter is the topic of later sections in this essay. See infra Part III.E.3–4.
200
See, e.g., Richard A. Posner, The Economic Approach to Law, 53 TEX. L. REV. 757, 761
(1973) (“The basis of an economic approach to law is the assumption that the people involved with
the legal system act as rational maximizers of their satisfactions’”); see also Richard A. Posner,
Values and Consequences: An Introduction to Economic Analysis of Law, in CHICAGO LECTURES IN
LAW AND ECONOMICS 189, 191 (Eric A. Posner ed., 2000) (“Most economic analysis consists of
tracing out the consequences of assuming that people are more or less rational in their social
interactions”); Jeanne L. Schroeder, Rationality in Law and Economics Scholarship, 79 OR. L. REV.
147 (2000) (providing an alternate foundation for the basis of rationality in the law while critiquing
Posner's model of rationality); Herbert Hovenkamp, Rationality in Law & Economics, 60 GEO.
WASH. L. REV. 293 (1992); MELVIN ARON EISENBERG, THE NATURE OF THE COMMON LAW (1988)
(setting forth the case for internal rationality in the common law).
201
Herbert A. Simon, Theories of Bounded Rationality, in 2 MODELS OF BOUNDED
RATIONALITY: BEHAVIORAL ECONOMICS AND BUSINESS ORGANIZATION 408 (1982).
202
Herbert A. Simon, Rational Choice and the Structure of the Environment, in MODELS OF
MAN: SOCIAL AND RATIONAL 261, 270–71 (1957). The difference between “satisficing” and
optimizing can be understood by the following analogy: optimizing is searching for the sharpest
needle in the haystack, and satisficing is searching for a needle that is sharp enough for sewing. See
Melvin Aron Eisenberg, The Limits of Cognition and the Limits of Contract, 47 STAN. L. REV. 211,
214 (1995).
203
See ROSS & NISBETT, supra note 180.
204
See, e.g., David Anderson, The Deterrence Hypothesis and Picking Pockets at the
Pickpocket’s Hanging, 4 AM. L. & ECON. REV. 295 (2002), cited in Robinson & Darley, supra note
179, at 176.

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2. Knowledge
The second hurdle is knowledge: does the offender know and understand the
implications of the law?205 Does the offender know which actions are criminalized
and at what schedule, or which actions will excuse one’s crime or otherwise
mitigate one’s culpability?
There is little attention to this question in the new deterrence literature. For
example, Professor Joanna Shepherd elaborates on the early deterrence theoretical
framework, maintaining that executions deter all types of murder by allowing all
would-be murderers to update their expectations of punishment risk, compensating
for the uncertainty about whether the murder they are about to commit would be
charged and prosecuted capitally.206 Such uncertainty, she claims, has less to do
with the motivations of murderers than with their capacity to internalize exogenous
factors such as prosecutorial discretion, quality of defense counsel, and juror
preferences. There are no assumptions in her study nor in the other studies in this
oeuvre about where or how potential murderers acquire the information to do so.
Instead, the new deterrence studies seem to assume, incredibly, that murderers
have perfect knowledge about the probability and magnitude of sanctions, and that
their decisions about risk are neither discounted nor variable. One study, for
example, includes measures of newspaper stories and other media reports of
executions.207 It is a causal story that assumes much about the reading habits and
television viewing preferences of would-be murderers. Quite the opposite is
probably true given literacy levels among most prison inmates. The new studies
fail to show that murderers are aware of executions in their own state, much less in
far-away states, and that they rationally decide to forego homicide and use less
lethal forms of violence.
The rules—whether one faces execution for one type of murder versus
another, or whether one faces execution at all given the circumstances producing a
death—are too abstract and removed from the moment to be salient, even
assuming that there is a small number of murderers or would-be murderers who
have such knowledge. There is no evidence that information markets among
would-be murderers are dense, efficient, or fueled by accurate information.208
First, there is no evidence to suggest that there are networks among persons who
commit murder. They may be embedded in social networks where violence is
common—for example, in street gangs or drug selling networks—but homicide is

205

Robinson & Darley, supra note 179, at 176.
Shepherd, Murders of Passion, supra note 15, at 292.
207
Shepherd, Deterrence Versus Brutalization, supra note 46.
208
See, e.g., Cass R. Sunstein, Group Judgments: Deliberations, Statistical Means, and
Information Markets, 80 N.Y.U. L. REV. 962 (2005) (showing that network connectedness and group
deliberation are prerequisites for efficiency in information markets and in both individual and
collective decisions).
206

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far from a primary motivator of social cohesion in these groups.209 Cass Sunstein
also claims that in such markets, competition among group members may lead to
gaming where some may withhold information or not disclose what they know.
This has the unfortunate effect of propagating errors and corroding group cohesion.
While experience—whether direct or vicarious—may substitute for
knowledge, these experiences may not be transferable to the specific situations that
may lead to murder. Robinson and Darley suggest that offenders are unlikely to do
the calculations necessary to decide correctly which rules apply in which
situations.210 Indirect or vicarious knowledge is prone to error as well, as it is
fueled by gossip and misinformation about the rules of law and the probabilities of
detection and punishment.
3. Choice and Preferences
Assuming knowledge and rationality, will an offender make a behavioral
choice consistent with deterrence? Robinson and Darley refer to this as the
Perceived Net Cost Hurdle.211
Decisions themselves—as a matter of human development and not just
antisocial behavior—suggest that even in a “rational” estimation of costs and
benefits, decision makers are more likely to use intuitive heuristics, shortcuts
which may or may not result in wise decision making.212 Professors Amos
Tversky and Daniel Kahneman note that although heuristics sometimes work well,
they can also lead to irrational decisions or decisions that may not maximize utility
but instead maximize short-term preferences that are framed by situational
contingencies and present circumstances.213 “In general, these heuristics are quite
useful, but sometimes they lead to severe and systematic errors.”214 The moving
parts in biased decision making heuristics include two dimensions: fallacies and
skewed adjustments.215
Additionally, decisions are skewed by emotions.
Preferences for utility, cognition and heuristics under conditions of arousal are all
vulnerable to distortion under conditions of arousal or fear.
209

See, e.g., Papachristos, supra note 180.
Robinson & Darley, supra note 179, at 178.
211
Id. at 182.
212
RICHARD THALER, QUASI RATIONAL ECONOMICS (1991).
213
Kahneman & Tversky, Prospect Theory, supra note 191, at 263–91; Daniel Kahneman,
Reference Points, Anchors, Norms, and Mixed Feelings, 51 ORG. BEHAV. & HUM. DECISION
PROCESSES 296 (1992).
214
Amos Tversky & Daniel Kahneman, Judgment Under Uncertainty: Heuristics and Biases,
185 SCI. 1124 (1974).
215
See Korobkin & Ulen, supra note 187, at 1086; see also Pamela K. Lattimore et al., The
Influence of Probability on Risky Choice: A Parametric Estimation, 17 J. ECON. BEHAV. & ORG. 377
(1992) (applying the prospect theory principle of nonlinear probability weighting to crime decision
making).
210

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a. Availability, Representativeness and the Base Rate Fallacy
Tversky and Kahneman suggest that rational decision makers would take into
account general information about population characteristics, and especially
information about the chance of a specific event occurring, but rarely do. The
failure to consider relevant information to make a probability judgment is a logical
fallacy known as the base rate fallacy. 216 The representativeness fallacy refers to
the tendency of decision makers to ignore base rates and overestimate the
correlation between what something is and what it appears to be. The availability
heuristic, like the representativeness heuristic, can lead to irrational decision
making in ignoring base rates.217 The availability heuristic, on the other hand,
refers to the tendency of decision makers to overestimate the relevance of
significant or memorable incidents, and underestimate the base rates.218
b. Anchoring and Adjustment
In the estimating process, decision makers are likely to form an arbitrary
“anchor” that serves as the starting point for estimation, and then adjust from this
anchor but still remain too close to it.219 Professors Russell Korobkin and Chris
Guthrie conducted a series of experiments to show, among other things, how this
irrational tendency to anchor and adjust can affect settlements in litigation.220 In
one experiment, subjects were assigned to two groups and were given almost
identical scenarios, at the end of which they were asked whether they would settle
with the defendant, or go to trial (with the prospect of winning more but the risk of
losing everything). The only difference in the scenarios was the anchor—one
group was given an extremely low settlement offer (the “low ball initial offer”
group) and the other was given a reasonable settlement offer (the “reasonable

216
See Daniel Kahneman & Amos Tversky, On the Psychology of Prediction, 80 PSYCHOL.
REV. 237 (1973); see also Maya Bar-Hillel, The Base-Rate Fallacy in Probability Judgments, 44
ACTA PSYCHOLOGICA 211 (1980); Matthew C. Schneider, Deterrence and the Base Rate Fallacy: An
Examination of Perceived Certainty, 18 JUST. Q. 63 (2001).
217
See Korobkin & Ulen, supra note 187, at 1087. For example, most people believe that
there are more words that begin with the letter “k” than words in which “k” is the third letter. This is
probably because it is easier to think of words beginning with “k”; i.e., such words are more readily
available. However, there are actually two times as many words that have “k” in the third letter than
in the first. Similarly, most people believe that homicides and car accidents kill more people in the
United States than diabetes and stomach cancer, because the former events receive more media
attention and are thus more available.
218
See, e.g., REID HASTIE & ROBYN M. DAWES, RATIONAL CHOICE IN AN UNCERTAIN WORLD:
THE PSYCHOLOGY OF JUDGMENT AND DECISION MAKING, 112–13 (2001).
219
Tversky & Kahneman, Rational Choice, supra note 199.
220
Russell Korobkin & Chris Guthrie, Psychological Barriers to Litigation Settlement: An
Experimental Approach, 93 MICH. L. REV. 107, 139–42 (1994).

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initial offer” group)—but both groups were given an identical “final” settlement
offer.221
Rational choice theory would predict that, given identical choices, the two
groups would either accept the settlement offer or reject it and proceed to trial in
the same proportions. However, the initial settlement offer had a strong effect on
the option chosen by subjects in each group. Subjects who were made the
reasonable initial offer were more likely to reject it than to accept it, whereas
subjects who were made the low initial offer were more likely to accept it. This
difference between the groups was statistically significant.222 Thus, as Korobkin
and Guthrie note, “When choosing between a concrete settlement offer and an
uncertain trial result, our subjects faced cognitive biases that prevented at least
some of them from acting in what decision theorists would consider a rational
manner….Together, the results suggest that litigants—who are not always rational
actors—may fail to reach settlement on some occasions when settlement makes
good economic sense.”223
c. Emotion
One’s emotional state plays a role in decision making, and can influence a
person to act in ways that are not maximally optimal (or rational).224 Obviously,
anger and other forms of arousal can skew judgment in several ways, changing
both rationality and also reshaping the estimation of costs and benefits. Professor
Anne Dailey argues that lawyers should focus more on the source of an
individual’s needs, feelings, and motives, which may be unconscious, irrational, or
both.225 One example of how emotions can lead to irrational decision making is
illustrated by the finding that, in general, people are willing to pay more for an
emotionally meaningful item than for an equally valuable but emotionally neutral
item. Professor Russell Korobkin calls this the endowment effect.226
d. Weighing Net Costs
Assume that knowledge is internalized and a would-be murderer will put this
information to work accurately and rationally. Theorists from Becker227 to
221

Id.
Id.
223
Id. at 142.
224
Anne C. Dailey, The Hidden Economy of the Unconscious, 74 CHI.-KENT L. REV. 1599,
1604–06 (2000).
225
Id. at 1606–08.
226
Russell Korobkin, The Endowment Effect and Legal Analysis, 97 NW. U. L. REV. 1227,
1228 (2003). This also is an example of risk aversion. See also Richard Birke, Reconciling Loss
Aversion and Guilty Pleas, 1999 UTAH L. REV. 205, 212.
227
Becker, Crime and Punishment, supra note 1.
222

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Polinsky and Shavell228 have posited a calculus of decision making where actors
weigh costs and benefits prior to action (or inaction). The decision making is
complex, of course, with different actors assigning different utilities and
preferences to the components of cost and return. For example, postponing reward
is an expression of preference, as is discounting past (sunk) costs or postponing
present costs. Deterrence will take place, to put it simply, when punishment is a
cost worth avoiding—that is, when the costs of punishment outweigh the perceived
rewards of the act. Put another way, is the offender likely to choose compliance as
the more beneficial option?
Beginning with Bentham, deterrence theorists have disaggregated costs into
three dimensions: probability, severity, and delay. 229 While there is no debate on
severity,230 there is strong evidence that death is delayed punishment owing to due
process and the numerous errors in capital sentences.231 Probability also is low: no
more than one homicide in four is capital-eligible,232 few of these are selected for
prosecution,233 and the percentage of death row cases that proceed to execution for
states other than Texas remains very low.234 As mentioned earlier, scarcity
228

Polinsky & Shavell, supra note 175.
JEREMY BENTHAM, AN INTRODUCTION TO THE PRINCIPLES OF MORALS AND LEGISLATION
(1789). See also Robinson & Darley, supra note 179.
230
Although there may be some debate on the severity of life imprisonment without the
possibility of parole compared to execution, and the marginal deterrence of capital punishment
relative to such life sentences is unknown. See supra Part III.B.1.
231
See JAMES LIEBMAN ET AL., A BROKEN SYSTEM, PART I: ERROR RATES IN CAPITAL CASES,
1973–1995 (2000), available at http://www2.law.columbia.edu/instructionalservices/liebman/
[hereinafter LIEBMAN ET AL., A BROKEN SYSTEM, PART I] (citing the average time from sentence to
execution of 9 years for death sentences imposed between 1973 and 1995, and an average of 7.6
years until death sentences are reversed and defendants are re-sentenced, exonerated, pardoned or
their sentences commuted). See also Alex Kozinski & Sean Gallagher, Death: The Ultimate Run-On
Sentence, 46 CASE W. RES. L. REV. 1, 2, n.10 (1995).
232
See Fagan et al., Capital Punishment and Capital Murder, supra note 64.
233
See, e.g., Raymond Paternoster et al., Justice by Geography and Race: The Administration
of the Death Penalty in Maryland, 1978–99, 4 MD. L.J. RACE, RELIGION, GENDER & CLASS 1 (2004)
(examining 1311 death-eligible cases from 1978 to 1999 based on the Maryland statute, MD. CODE
ANN., CRIM. LAW § 2-201 & 2-205m, which defines murder in the first degree as: (a) a deliberate,
premeditated, and willful killing, (b) committed by lying in wait, (c) committed by poison, (d)
committed in the perpetration of or an attempt to perpetrate arson, burglary, carjacking, escape from
prison, kidnapping, mayhem, rape, robbery, sexual offense, sodomy, bomb-making, and (e) if they
willfully, deliberately, and with premeditation intended the death of a law enforcement officer.)
Although the Maryland study generated statistical information on which statutory aggravating factors
were most often present among cases selected for capital prosecution: murders committed during
other crimes, murders with multiple victims, murders committed while the perpetrator was in a
correctional institution, contract killings, and murders committed while fleeing capture by police. Id.
234
As a simple index for comparison, Texas courts have issued 776 death sentences since 1976
and executed 364 inmates, nearly half those sentenced. In Florida, Pennsylvania, and California,
three states whose courts also issue high numbers of death sentences, the comparable number of
death sentences and executions are: 60 of 235 (Florida), 13 of 652 (California), and 3 of 316
(Pennsylvania). See DEATH PENALTY INFORMATION CENTER, DEATH SENTENCING RATE BY STATE,
229

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undermines the deterrent threat of death, and the marginal deterrence from this
weak threat compared to the certainty and harshness of incarceration undermines
this utilitarian argument for capital punishment.
The benefit side of the equation is more complex. Together with Professor
Richard Freeman, I analyzed a series of empirical studies on the tradeoffs between
legal work and illegal income-producing criminal activity for young men in inner
cities.235 When faced with sharply escalating incarceration risks throughout the
late 1980s and 1990s, robbers and drug dealers consistently valued the economic
returns of illegal work over either the foregone opportunities for legal income or
the punishment costs that jail would exact. Similar tradeoffs were reported by
burglars236 and robbers237 in ethnographic studies of their crime decision making.
Other studies have shown that drug offenders will heavily value the combined
reward of relief from withdrawal symptoms and the pleasure of addiction over the
risk of detection and punishment.238
Scholars of homicide have long known that murder is the result of complex
social interactions that increase the present value of benefits and push costs to the
background.239 Recent studies on violence in situ confirm the salience of reward,
and introduce an element of risk that attaches when extreme violence is not used.
In interviews with 125 young males ages sixteen to twenty-four who were involved
in over 300 incidents of gun violence in New York City from 1995–1997, I
collaborated with Professor Deanna Wilkinson to understand decision making
within violent events where guns were used, and other events where guns were
almost used but avoided at some point during a confrontation.240 In these settings,
lethal violence has both instrumental and intrinsic rewards that trumped what these
young men perceived inaccurately as a distal risk of detection and punishment. In
available at http://www.deathpenaltyinfo.org/article.php?scid=67&did=915 (last visited May 15,
2006); DEATH PENALTY INFORMATION CENTER, NUMBER OF DEATH EXECUTIONS BY STATE AND
REGION SINCE 1976, available at http://www.deathpenaltyinfo.org/article.php?scid=8&did=186 (last
visited May 15, 2006).
235
Jeffrey Fagan & Richard B. Freeman, Crime and Work, in 25 CRIME AND JUSTICE: A
REVIEW OF RESEARCH 225 (1999).
236
RICHARD T. WRIGHT & SCOTT H. DECKER, BURGLARS ON THE JOB: STREETLIFE AND
RESIDENTIAL BREAK-INS (1994).
237
RICHARD T. WRIGHT & SCOTT H. DECKER, ARMED ROBBERS IN ACTION: STICKUPS AND
STREET CULTURE (1997) [hereinafter WRIGHT & DECKER, ARMED ROBBERS IN ACTION]. Wright and
Decker interviewed men whose criminal careers included repeated robberies. Robbers were
committed to a street culture that emphasized the materials rewards and social status attendant to
being a successful “stickup boy,” while minimizing or heavily discounting punishment risk.
238
JOHN KAPLAN, THE HARDEST DRUG: HEROIN AND PUBLIC POLICY (1983).
239
See, e.g., MARVIN E. WOLFGANG, PATTERNS IN CRIMINAL HOMICIDE (1958); KATZ,
SEDUCTIONS OF CRIME, supra note 107; POLK, supra note 105; JAMES O’KANE, WICKED DEEDS:
MURDER IN AMERICA (2005).
240
Fagan & Wilkinson, Guns, Youth Violence, supra note 110. See also KATZ, SEDUCTIONS OF
CRIME, supra note 107.

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fact, there was greater fear of retaliation from victims’ families or friends than
from what was perceived as the remote possibility of police involvement. Extreme
violence was an expected and valued behavior and, for some, thought to be
necessary to ensure their survival.241 Chance encounters with others in these
neighborhoods were seen as potentially threatening or lethal—unknown others
were widely thought to harbor hostile intentions and capacity to inflict harm.
Extreme violence and toughness was the currency of respect, and respect had both
strategic value and offered strong social reward. Violence was a public
performance, designed to maintain a social identity that deters attack and
reinforces a self-presentation of "toughness." Other acts of violence also were
pathways to social status. For example, robbery not only generated material goods
or cash and was helpful in sexual conquests, but it also established one’s status in a
social hierarchy where respect was a finite commodity.242 Of course, the danger
that a robbery could escalate into a homicide was always present. Violence also
functions as social control in these contexts, redressing grievances or peremptorily
ending them before they ever begin.
In a similar study, Andrew Papachristos interviewed gang members in the
Austin and North Lawndale neighborhoods of Chicago.243 Most had been involved
either as witnesses or accomplices in murders committed in gang disputes. The
risk of a death sentence was simply not a reality among gang members despite
Illinois’ high rate of death sentences prior to 2000. This is not to say that
rationality is not part of their decisions about crime and violence: gang members
often think rationally about crimes, especially drug dealing, but usually as a matter
of business details such as packaging, marketing and selling drugs to maximize
their returns. Their knowledge of law clearly passed the knowledge hurdle.244
241

WILKINSON, GUNS, VIOLENCE, AND IDENTITY, supra note 110 (illustrating the dynamics of
violent events, including their “spark” or motivation, and their ending). In social interactions in this
context, violence is an expected and valued behavior, shaped by a normative code. It is but one
response in a toolkit of behaviors and responses to danger that evolves within these social worlds.
Teenagers select from this toolkit according to their cognitive reading of a situation, with the level of
danger and lethality their primary consideration. The presumption of hostile intent is both an
accurate reading of potential danger and a reflection of socialization within this ecology. Cognitive
appraisals occur within a setting of witnesses (bystanders) who judge and announce the actor's level
of toughness under conditions of arousal, perhaps while high or drunk, very likely while armed, and
with an adversary whose intentions are either hostile or unknown. See also Jeffrey Fagan, Context
and Culpability in Violent Events, 6 VA. J. SOC. POL’Y & L. 507 (1999).
242
See ANDERSON, CODE OF THE STREET, supra note 185; ELIJAH ANDERSON, STREETWISE:
RACE, CLASS AND CHANGE IN AN URBAN COMMUNITY (1990).
243
Andrew V. Papachristos, Gang Violence as Social Control (unpublished manuscript, on file
with the University of Chicago, Department of Sociology). See also Papachristos, Murder Markets,
supra note 180.
244
See Papachristos, Murder Markets, supra note 180. In one organized drug location,
Papachristos observed an intricate ten man selling system that used walkie-talkies, look-outs, and
multiple “drive-through” locations. Moreover, the “leaders” of this operation had detailed knowledge
of gun and narcotic laws. They made sure that the guns and dope were kept separately to ensure that,

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But the perceptions of risk and benefit were different for interpersonal
violence, including murder. Compared with drug selling, gang members do not
necessarily act “rationally” or weigh the prospects of execution in the course of
violence. Although most of these gang members had been in and out of jail quite
often, very few know anyone on “death row” or who has been executed. Rather,
the greatest risk in murder was retaliation by members of rival gangs, not
retribution by the state. A much broader and more pressing “threat of violence”
looms over the gang world. Even more so than in “street culture” more generally,
the consequences of victimization is the chief concern and is to be avoided at all
costs. Self-protection and mutual protection are often key determinants in carrying
weapons and engaging in violence. Violence was often reactionary and retaliatory,
serving as a deterrent against future victimization, a form of self-protection, or a
mechanism of social control. State sanctions, and especially the death penalty,
rarely entered into the means-ends calculus of gang members on the street. Quite
the opposite was true: gang members see prison sentences as “worth it” in order to
maintain face and self-respect to deter the possibility of victimization. Often,
receiving a prison sentence for maintaining personal honor can, in fact, increase
one’s personal reputation.245
There are numerous other examples of perceived benefits eclipsing risk in
homicide: murders by violent spouses aimed at dominating and controlling
intimate partners, retaliation and reprisal, or even robbery-homicides. 246 In fact,
punishment costs may be discounted even more in the modal category of capitaleligible crimes: felony murders—homicides committed in the course of other
crimes, especially robbery. Robbery is not a crime that is committed casually, nor
are robbers a random sample of the criminal population: most have prior arrest
records and many have completed spells in prison.247 In felony murders, especially
robbery-homicides which are more than half the capital-eligible murders,248
struggles for weapons or fear of identification may escalate the crime to a
homicide. There is a weak prospect that a risk heuristic of punishment will enter
into the volatile and unpredictable street dynamics of robbery interactions to

in the possibility of an arrest, they would not get enhanced sentences for “criminal conspiracy cases”
(in Cook County, the presence of weapons and drugs implies on on-going drug operation and carries
stiffer penalties). In one instance, a gang leader made sure that any members carrying weapons near
his drug operation were juveniles to ensure that the leaders could avoid gun charges if caught. See
also Steven Levitt & Sudhir A. Venkatesh, Growing Up in the Projects: The Economic Lives of a
Cohort of Men Who Came of Age in Chicago Public Housing, 91 AM. ECON. REV. 79 (2001).
245
Id.
246
KATZ, SEDUCTIONS OF CRIME, supra note 107.
247
See, e.g., WRIGHT & DECKER, ARMED ROBBERS IN ACTION, supra note 237. Most
acknowledge the risk of punishment as intrinsic to their work, yet tend to either discount the cost of
punishment or over-value the present benefits of the robbery, or both.
248
Fagan et al., Capital Punishment and Capital Murder, supra note 64.

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reduce the risk of lethality,249 especially when a gun is present. Accordingly, the
presence of a gun in a robbery further increases not just the risk of lethality but the
decision by the robber to use it.250 In other words, there is a strong risk of
cognitive errors in situations of intense arousal, errors that are likely to overwhelm
the evaluations of the benefits of crime and the risks and costs of punishments.251
4. Cumulative and Conditional Corrosion
In the Robinson-Darley framework, “[s]etting any one of the variables to zero
means that there is no deterrent effect whatever.”252 Of course, none of these
values reach zero in reality, except perhaps in the case of the mentally ill.253
Nevertheless, the parts of this framework are neither exchangeable nor separate.
Rather, they interact conditionally and multiplicatively to produce a robust
deterrent effect, and weakness in any one domain will drag down the salience of
the others. So, for example, prison may be worth avoiding if there is a positive
benefit from compliance. If detached from conventional social worlds via
joblessness or addiction, the exposure of violent offenders to the actuarial benefits
of compliance declines, and their perception of detection risks—not inaccurately,
from their perspective—declines with it.254 The scarcity of execution, however
salient executions may be, is unlikely to disturb their risk assessment. How
deterrence works in this social system and in skewed information markets is
uncharted territory. Having said that, there is a large body of social science
evidence that in the case of murder, each of the three hurdles in this framework
becomes far higher than in the case of less complex or serious crimes, and their
reciprocal and multiple effects are likely to militate against deterrence. That is, the
cumulative effect of these hurdles for deterring murder is considerable, and their
height casts doubt on the streamlined version of deterrence argued in the new
deterrence studies.

249

Id. See also Franklin Zimring, Determinants of the Death Rate from Robbery: A Detroit
Time Study, 6 J. LEGAL STUD. 317 (1977); Franklin Zimring & James Zuehl, Victim Injury and Death
in Urban Robbery: A Chicago Study, 15 J. LEGAL STUD. 1 (1986)[hereinafter Zimring & Zuehl,
Victim Injury and Death]; Jack Katz, The Motivation of the Persistent Robber, in 14 CRIME AND
JUSTICE: A REVIEW OF RESEARCH 277 (1991).
250
Zimring & Zuehl, Victim Injury and Death, supra note 249; Fagan & Wilkinson, Social
Contexts, supra note 194; Wilkinson & Fagan, Role of Firearms, supra note 194.
251
See, e.g., Daniel Kahneman & Amos Tversky, Choice, Values, and Frames, 39 AM.
PSYCHOLOGIST 341 (1984).
252
Robinson & Darley, supra note 179, at 196.
253
See, e.g., Bruce G. Link et al., Psychotic Symptoms and Violent Behaviors: Probing the
Components of “Threat/Control-Override” Symptoms, 33 SOC. PSYCHIATRY & PSYCHIATRIC.
EPIDEMIOLOGY S55 (Supp. 1998).
254
Robinson and Darley tell a similar story. See Robinson & Darley, supra note 179, at 197.

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IV. RE-ESTIMATING DETERRENCE
One of the highest hurdles of causal inference is the replication
requirement.255 In the conduct of social inquiry, it is commonplace if not
imperative for investigators to subject their data to testing under alternate
measurement and analytic conditions. Obtaining consistent evidence is a sign of
reliability and robustness256 of the central theoretical and empirical finding. Some
of the researchers whose work is central to the claims of the “new deterrence” have
followed these norms and made not only their data available for further testing and
replication, but also their statistical programming that produced the results they
reported. To assess the robustness and stability of the empirical deterrence claims,
I chose one of these datasets, from Mocan and Gittings257 (hereafter, MG), for
statistical analyses with a set of alternate measurement and analytic specifications.
The results are shown in Tables 1 and 2.

255

Epstein & King, The Rules of Inference, supra note 26.
A finding is considered to be robust when it is insensitive to variation among the inputs and
can be reproduced under a variety of sampling and measurement conditions.
257
Mocan & Gittings, supra note 10.
256

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Table 1. Original and Alternate Specifications for Analysis of Deterrent Effects of
Execution from Mocan and Gittings Dataa
CI
Model

B

SE

p(t)

Exp B

1. Original
Specification

- .006

.003

.028

.994

-.011

-.001

680

2. Alternate Data
Sources1

-.004

.001

.004

.996

-.007

-.001

682

3. Original Specification,
Recoding2

.000

.000

.762

1.000

.000

.000

680

4. Original Specification
without Texas

-.005

.003

.074

.995

-.010

.000

666

-.00002

.000

.639

1.000

-.0001

.0001

666

.000

.000

.340

1.000

.000

.000

682

7. Original Specification,
Recoding 0=0

-.006

.004

.084

.994

-.014

.001

359

8. Alternate Data Sources1,
Recoding, 0=0

-.003

.001

.048

.997

-.006

.000

364

9. Alternate Data Sources,
No Texas

-.003

.001

.021

.997

-.006

-.001

668

10. Original Specification
without state-time trend

-.002

.003

.497

.998

-.008

.004

680

11. Original Specification,
-.001
.000 .065
.999
-.002
.000
Alternate Deterrence
Index3
a
Source: Naci Mocan & Kai Gittings, Getting Off Death Row: Commuted Sentences
and the Deterrent Effect of Capital Punishment, 46 J.L. & ECON. 453 (2003).
1
Homicides: NAT’L CTR. FOR HEALTH STATISTICS, MORBIDITY FILE; Death Sentences:
BUREAU OF JUSTICE STATISTICS, U.S. DEP’T OF JUSTICE, CAPPUN2003; Executions:
DEATH PENALTY INFORMATION CENTER.
2
Recoding years with zero death sentences to .01 instead of .99.
3
Executions lagged one year and Death Sentences lagged two years.

879

5. Original Specification
without Texas, Recoding2
6. Alternate Data Sources1,
Recoding2

Lower

Upper

N

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Table 2. Growth Curve Models of Effects of Execution and Incarceration on
Murder Rates, Using Mocan and Gittings Execution Index and Incarceration Dataa
Time
Time and Time2
Effect
B
p(t)
B
p(t)
Execution

-.003

.826

-.007

.829

Custody

-.004

.797

.051

.088

Time * Execution

-.0003

.677

.0005

.916

Time * Custody

-.002

.016

-.010

.018

-.00003

.853

.0003

.030

Time2 * Execution
2

Time * Custody
Ratio of Custody to Execution Coefficients
β (Custody) | β (Execution)

1.50

-6.99

β (T*Custody) | β (T*Execution)

7.13

-19.72

2

2

β (T *Custody) | β(T * Execution)

-10.37

Model Fit
-2LL

-3404

-3342

AIC

-3398

-3336

BIC

-3385

-3323

a

All models estimated with random intercepts and both fixed and random effects for time.
Estimates are population-averaged with AR(1) covariance structure. Execution measure
derived from H. Naci Mocan & R. Kaj Gittings, Getting off Death Row: Commuted
Sentences and the Deterrent Effect of Capital Punishment, 46 J.L. & ECON. 453, tbl.2, panel
A (2003).

The replication is done in two steps. The first set of analyses accepts the
functional form of the regressions that are reported by MG in their 2003 article, but
substitutes alternate data sources and also makes a series of adjustments to handle
missing data in ways that differ from MG’s strategies. In the second set of
analyses, reported in Table 2, I vary the functional form of the regression equation
and adopt an analytic strategy that responds to concerns discussed earlier about the
panel structure of the data and appropriate statistical tests to detect changes over
time when observational data are heavily correlated from one year to the next.

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A. Sensitivity Tests
The columns in Table 1 show the results of estimates for the deterrence
measure reported by MG in Table 2. In the original MG analysis, the deterrence
measure is computed as the ratio of executions in the past year to death sentences
six years preceding. Table 1 shows only the regression results for that deterrence
variable, using the original code and data generously provided by Professors
Mocan and Gittings.258 The columns include a standard set of statistics to
characterize the results in each model. Of particular interest is the regression
coefficient, the standard error, the probability or statistical significance of the
estimate (p(t)), and the number of cases included in the analysis.259
The first step is a replication of the original MG analysis. Model 1 shows
results identical to those reported by MG in several regression estimates in Table 2,
row 1. Model 2 uses the original MG specification, but substitutes alternate data
sources to measure homicides and executions. MG used homicide statistics
obtained from the Uniform Crime Reports, a crime accounting system maintained
by the Federal Bureau of Investigation, U.S. Department of Justice. There are
well-known limitations in that system, including large amounts of missing data.260
We use data from the Morbidity and Mortality Files of the National Center for
Health Statistics. Homicide counts are generated from death certificates filed by
each county’s coroner or medical examiner. Cases are classified as homicides
pursuant to a separate investigation and decision making process. More important,
there is complete coverage in these records for all years in the time series (1976–
1998). The second alternate measure is the count of executions in each state. MG
used reports of executions obtained from the U.S. Justice Department in an archive
that is updated each year based on death row cases. The current version of this
dataset is publicly available as Capital Punishment 2003,261 and is updated
annually with new information supplied by the states. The alternate data source is

258

Mocan and Gittings include several other predictors simultaneously with the deterrence
variable. So, these results show the estimated effects of the deterrence variable, controlled
statistically for other variables including population characteristics and urbanization, incarceration
rates, income and unemployment, infant mortality, other causes of removal from death row
(commutations and pardons), prison death rates, the presence of a Republican governor in the state,
and state minimum drinking age laws. They also include a dummy variable to account for the spike
in homicides in Oklahoma City in 1995 from the bombing of the Murrah Federal Office Building.
259
Readers familiar with regression analyses will be interested in the confidence intervals,
which show the range in which the coefficient could vary, and the exponentiated coefficient, which
describes the magnitude of the effects of the deterrence variable.
260
See Maltz, supra note 124.
261
BUREAU OF JUSTICE STATISTICS, U.S. DEP’T OF JUSTICE, CAPITAL PUNISHMENT IN THE
UNITED STATES, 1973–2003 (2004).

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a count of executions generated by the Death Penalty Information Center,262 a
private not-for-profit organization that closely monitors capital punishment
legislation and activity across the states and in the federal courts. With these
alternate data, the results are again statistically significant, though the regression
coefficient is smaller compared to Model 1.
Model 3 uses the original MG data, but applies an alternate computation to
estimate deterrence for cases when the denominator in the original measure was
zero. Recall that deterrence is measured as the number of executions in a given
state divided by the number of death sentences six years earlier. For some
observations, this required division by zero, which would produce an infinite
result. For these observations, MG replaced the incomputable zero value with .99.
The alternate measure was to replace the problem observation with .01, a value
that is closer to the true value of zero in the denominator.263 The result here is a
dramatic change from Models 1 and 2. The coefficient is now close to 0 (it is
rounded to .000 in the table), and deterrence is no longer statistically significant.
Model 4 repeats Model 1—a replication of the original MG analysis—but
excludes Texas. The hegemony of Texas in the estimates of deterrence was
discussed earlier, and its influence on the distributions suggests that specifications
without Texas might show different results. The results here are mixed. The
coefficient is in the same range as in Models 1 and 2, but it no longer is statistically
significant (p=.074) at the conventional p<.05 threshold.264 Model 5 repeats Model
4, excluding Texas while adopting the alternative coding procedures of Model 3.
The results closely resemble the results in Model 3, and deterrence here is not
statistically significant (p=.639). Model 6 repeats Model 2, but adopting the
recoding conventions of Model 3; deterrence again is not statistically significant
(p=.340).
Models 7 and 8 use a different strategy for addressing the problem of
division-by-zero, this time by substituting a true zero for the zero value. The
deterrence estimate in Model 7 is the same as in the original MG analysis, but it no
longer is statistically significant, with (p=.084). In Model 8, using the alternate
data sources, the coefficient is smaller but it once again is significant (p=.048).
262

DEATH PENALTY INFORMATION CENTER, EXECUTIONS IN THE UNITED STATES, 1976–2006
(2006), available at http://www.deathpenaltyinfo.org/article.php?did=414&scid=8.
263
MG recode all state-years with 0 death sentences as having 0.99 death sentences. Thus for
non-executing states, the probability of execution is 0.99. When there are zero executions, there is no
difference whether one uses 0.99 or 0.01, because the ratio of executions to death sentences remains
zero. However, they intended to drop those cases, based on their computer code, so there is no effect
on their estimates when they substitute for zero. For the state-years when there are positive (greater
than zero) executions, they assume that the denominator is 0.99, but it does influence their estimates
because they dropped cases at a lag of six years, not seven. See Donohue & Wolfers, Uses and
Abuses, supra note 25. In the estimates in this article, both these errors are corrected, and several
models are estimated with full data and a denominator of 0.01 for years when there are no executions.
264
See Epstein & King, The Rules of Inference, supra note 26 for a discussion of this
convention.

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However, note the sample size is nearly halved: the decrease in the number of
cases that are eliminated when true zeros replace the artifactual values of either .01
or .99 for the cases with division-by-zero. In Model 9, using alternate data sources
but excluding Texas, the coefficient is half of the original estimate (Model 1), and
it is significant (p=.021).
Model 10 omits one predictor from the MG models—a within-state time
parameter that is meant to capture variance in the models that is attributable to
state-specific time trends within each death penalty state.265 The contribution of
this time trend is not obvious, and possibly is redundant with the linear time trend
for the aggregate panel, with state and year fixed effects in the original MG model.
Without this time trend, the coefficient for deterrence in Model 10 is not
significant (p=.497).
Finally, Model 11 replicates Model 1 but shortens the time lag for executions.
Here, deterrence is computed as the number of executions in the previous year
divided by the number of death sentences two years prior. This specification
emphasizes the temporal proximity of punishment by assuming a shorter duration
between death sentences and executions. MG assume that six years266 temporal
proximity brings the importance of the celerity of punishment to the forefront in
estimating deterrent effects, since offenders may be less likely to discount
punishments that are not postponed far into the future; in other words, celerity
increases the present value of a deterrent threat. It also provides a better
approximation of how offenders update their information, since they are unlikely
to recall the frequency of death sentences in their state from six or seven years
earlier. When we substitute this measure, the coefficient becomes very small (β=.001) and is not statistically significant (p=.065).267
The sensitivity of these analyses to alternate specifications undermines the
claims by MG of robust deterrence findings. The coefficient for deterrence varies
from 0 to -.006 in the 10 alternate models, and only four of the 10 are statistically
significant at the conventional threshold of p<.05. Note also that in Models 3
through 8 and again in Model 10, the upper bound on the confidence interval is
zero or above. This suggests that it is possible that the regression coefficients may
be zero or positive, suggesting either no deterrent effect, or a positive or
“brutalization” effect of executions. The sensitivity of these analyses to wide
265
See Mocan & Gittings, supra note 10, at 461 (providing a more detailed explanation of this
time trend).
266
In some models, they intended to estimate a seven year lag, although close inspection of the
MG programming code shows that they actually estimated a six year lag. Both time intervals are
well shorter than the measured lag between sentence and execution, averaging approximately nine
years for death sentences handed out from 1973–1995. See LIEBMAN ET AL., A BROKEN SYSTEM,
PART II, supra note 88.
267
We also increase the sample size in this model to 879 cases, since the shorter lag time
means that fewer years are censored due to truncation from lagged denominator in the MG deterrence
measure.

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swings in the estimates of deterrence when alternate data sources are used and
when coding errors are corrected weakens the case for deterrence and introduces
uncertainty and fragility when the policy questions demand stability and
consistency.
B. A Different Accounting of Time
The panel structure of the data in most of the deterrence studies lends itself to
a class of statistical models that explicitly examine change over time and identify
the effects of time-varying events that may alter trajectories of homicide. Earlier, I
noted the advantages and appropriateness of such models for data with repeated
measures over time, where the events in one year are highly correlated with the
events in both the preceding and the following years. In this section, I use this
functional form to re-estimate the effects of deterrence using the MG dataset.268
One class of models that is designed for these circumstances is hierarchical or
mixed effects regressions. These regression models can identify the parameters
that shape a trajectory or pattern or sequence of behaviors over time, and estimate
the effects of interventions or treatments that might influence these patterns.269
The models are “mixed” in the sense that some variables are considered fixed and
others random. Variables are “fixed” when we assume that they are measured
without error, or that they are constant across studies. So, for example, variables
such as population, the number of executions or death sentences, or the
incarcerated population are fixed effects. We assume that “random” variables have
measurement error, and that models with random effects are making inferences or
generalizations within some probability distribution.
In mixed effects growth curve modeling, time is usually modeled as both a
fixed effect, to control for the effects of specific years in the time series, and a
random effect, to estimate change over time in the dependent variable. Of
particular interest in this class of models is the interaction of time with each of the
fixed effects. This interaction allows the influence of a fixed effect to vary over
268
The models were estimated using the MIXED procedure in SPSS 13.0. The programming
commands and the output are available at http://www2.law.columbia.edu/fagan/researchdata/
osjcl_deter/. This package was selected because it offered options to specify an autoregressive
covariance structure. See supra Part III.D. and notes 155–58. Other options to adjust regression
estimates in analyses of panel data include the use of Newey-West standard errors. Since
observations in panel data often are highly correlated over time, this temporal dependence results in
serial correlation and thus downwardly biased standard errors. For an illustration using crime data,
see Klick & Tabarrok, supra note 90. For the derivation of Newey-West standard errors, see Newey
& West, supra note 162, at 703–08. See also Jeremy Smith & Michael McAleer, Newey-West
Covariance Matrix Estimates for Models with Generated Regressors, 26 APPLIED ECON. 635 (1994).
269
See, e.g., ANTHONY BRYK & STEPHEN RAUDENBUSH, HIERARCHICAL LINEAR MODELS:
APPLICATIONS AND DATA ANALYSIS METHODS (1992); JUDITH SINGER & JOHN B. WILLETT, APPLIED
LONGITUDINAL DATA ANALYSIS: MODELING CHANGE AND EVENT OCCURRENCE (2003); Sophia RabeHesketh et al., Maximum Likelihood Estimates of Limited and Discrete Dependent Variables with
Nested Random Effects, 128 J. ECONOMETRICS 301 (2005).

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time as the fixed effect itself changes. Accordingly, the interactions show whether
and how the rate of change in the dependent variable over time is affected by the
values of the predictor or independent variable at different points in time. Finally,
because of “serial correlation,” the estimates in Table 2 use an adjustment for
autoregression.270
The general composite two-level model follows the form:
Yij = γ00 + γ10TIME + γ01EXECUTION + γ11(EXECUTION* TIME) +
γ02CUSTODY + γ21(CUSTODY * TIME)] + [ζ01 + ζ1iTIME + εij]
where EXECUTION is the deterrence measure in MG, and CUSTODY represents
the incarceration parameter. The cross-level interactions of each predictor with
TIME identify whether the effects of TIME differ by levels of the theoretical
predictors—i.e., whether EXECUTION or DETERRENCE variables are, in fact,
associated with a decrease in homicide rates. This is the critical test. The models
are specified with the same time-varying covariates as in MG, Table 2. Estimates
are population-averaged, and an autogressive (AR[1]) covariance structure is
assumed.
Table 2 shows the results of models that apply mixed effects regressions to
the MG data. The models included two expressions of time: a linear measure and a
second order polynomial (time and time2). The latter expression of time reflects
the actual pattern of change in homicide rates over time during the study interval:
rising through 1993 followed by a relatively steep decline through the end of the
study period.271 To illustrate the importance of such assumptions on how we
assess deterrence, I compare the results of a model using only a linear measure of
time with a model using this second order polynomial change. Although all the
variables in the MG analysis were included in these models, Table 2 shows only
the results for two predictors: deterrence (EXECUTION) and incarceration
(CUSTODY). Incarceration is shown because it is an important counterfactual to
the claim of deterrence.272 Both the main effects for each predictor and the
interactions of time with each predictor are shown. The models also include
random intercepts, a technique that controls for differences between the states in
their initial starting points at the outset of the time series in 1977.273 As in Table 1,
the regression estimate (coefficient) is shown together with the standard error and
270
Panel data often are troubled by correlated error terms over time in the relationships
between the dependent variables and the predictors. To adjust for this problem, the models are
estimated using AR(1) covariance structures. See, e.g., GREENE, supra note 157; SINGER & WILLETT,
supra note 269.
271
See, e.g., Richard Rosenfeld, Patterns in Adult Homicide: 1980–1995, in THE CRIME DROP
IN AMERICA 130 (Alfred Blumstein & Joel Wallman eds., 2005).
272
Katz et al., Prison Conditions, supra note 75.
273
See SINGER & WILLETT, supra note 269 (discussing the use and interpretation of random
intercepts).

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the statistical significance (probability) for that parameter. To further assess the
relative contributions of deterrence and incarceration to changes in homicide rates,
Table 2 shows the ratio of the coefficients for the two measures, including the
coefficients for their interactions with time.
The left half of Table 2 shows that when we estimate the effects of deterrence
using a linear time parameter, deterrence is not statistically significant (p=.677) but
incarceration is (p=.016). The ratio of the interactions of TIME * EXECUTION to
TIME * CUSTODY is 7.13, suggesting a strong difference in the relative
contributions of the two variables to homicide rates. The right half of Table 2
repeats this analysis but with a second order polynomial term to model the effects
of the predictors over time. The non-linear term better reflects the actual
distribution of homicide over time. The results are the same. The important
parameter is the line for the interaction of TIME2 * EXECUTION and TIME2 *
CUSTODY. The effects for deterrence are not statistically significant (p=.853),
but the effects of incarceration are (p=.030). The ratio of incarceration to
executions for this model is 10.37, again suggesting that the contributions of
incarceration to declining homicide rates are far greater than the contributions of
execution.
The story told by Table 2 is that an alternate functional form, one designed
explicitly to account for serial correlation (autoregression) in homicide rates within
states over time, produces estimates of deterrence that are not significant. We are
unable to reproduce the estimates of deterrence once we correct for this centrally
important feature in homicide trends and patterns. The regression coefficients in
the model on the left side of Table 2 are similar in size and range to the estimates
obtained using the fixed effects regression models in Table 1, but the standard
errors are far higher and the results not statistically significant. There is greater
range in the estimates of deterrence in the models using the polynomial term on the
right side of Table 2. In this model, we find significant effects only for the custody
variables while execution remains not significant.
C. Instability and Robustness
These analyses were designed neither to contradict the results shown by MG,
nor were they intended as a critique of MG. Rather, these results illustrate the
sensitivity and volatility of estimates of the deterrent effects of capital punishment
on homicide.274 The analyses do show the uncertainty and lack of robustness for
this one study of the effects of capital punishment on murder. Simple adjustments
in measurement, coding, and in the functional form of the regressions all introduce
not consistency in the findings of deterrence, but consistency only in the volatility
of the critical finding. Moreover, any effects on the murder rate are small, and
274

Donohue and Wolfers have also shown the uncertainty of estimates of the deterrent effects
of capital punishment in other studies in the new deterrence literature. See Donohue & Wolfers, Uses
and Abuses, supra note 25.

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depending on the model specification and other plausible empirical decisions, also
could appear to be a counter-deterrent. But I take no more faith in that finding
than I do in deterrence, simply because of the poor conceptual specification of the
factors that produce murders in this study and the others in the new deterrence
literature, and the numerous limitations in measurement and method that were
discussed earlier.
The limitations identified here are not likely to be an artifact of the decisions
of MG: that many of the problems identified and addressed in these analyses are
also plainly evident in other datasets used in the new deterrence literature.275 The
cyclical movements of homicide over the three decades since Furman and Gregg
are simply too large to be influenced by small numbers of executions that are
widely scattered across the states and so heavily concentrated in one state as to
make executions in the others appear to be anomalies. Legal scholars and
legislators makers should take note of this uncertainty before taking what amounts
to a leap of faith rather than an extension of scientific fact.
V. CONCLUSION: A CAUTIONARY TALE
The new deterrence studies claim that each execution prevents anywhere from
three to thirty two murders. This is hardly a new claim: about 30 years ago, similar
claims about the death penalty were made just before executions resumed
following the post-Furman moratorium. One thousand executions later, the claim
has been revived by a small group of researchers touting advances in econometric
techniques and new data sources that resolve technical problems in the earlier
work. Endorsing these claims, Sunstein and Vermeule suggest that this evidence
“morally” requires executions, a conclusion echoed by Becker and Posner. These
arguments too are neither new nor correct.
The new deterrence literature fails to provide a stable foundation of scientific
evidence on which to base law or policy. Nor can this evidence be used to
calibrate the normative implications of new “facts” about lives saved or lost. As in
the debate over Ehrlich’s findings, simple but necessary changes in the functional
form of regression equations, combined with measurement strategies that provide
more complete and accurate data, produce different results that differ from the
current crop of studies, results that are far more equivocal. Even more significant
modifications to these studies, such as using research designs that more closely
approximate quasi-experiments that account for murder trends in states with no
executions, also produce different and equivocal results.276 Conceptual errors and
omissions in specifying the multiple influences on murder rates seriously bias the
estimates of deterrence.
275

For example, Shepherd’s decision to drop cases with missing data on homicide rates in high
murder and high execution states such as Florida. See Shepherd, Murders of Passion, supra note 15,
at 304.
276
See Donohue & Wolfers, Uses and Abuses, supra note 25.

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The wide range of results, and the sensitivity of findings to even the most
minor tweaks, introduces model uncertainty. Each study in the new deterrence
literature, both those that confirm and those that challenge the deterrence claims,
uses a particular model of crime that embodies a choice of data, time period,
control variables, and statistical specifications. Variation in these choices is part of
a vigorous scientific vetting of a theoretical proposition. While model uncertainty
is endemic to this process, the uncertainty here is so wide and so profound as to
raise strong cautions on reaching any conclusion about deterrence, much less
policy. At the end of the day, econometric “pyrotechnics”277 may dazzle, but they
are diversions that fail to advance the debate on capital punishment.
Sunstein and Vermeule embrace these findings, and use the evidence to
animate their calls for a more vigorous use of the death penalty. Sunstein and
Vermeule are willing to tolerate error in the estimates of deterrence, arguing that
doubts about their robustness should not stand in the way of increasing the use of
execution if executions can avoid harm.278 The problem for them is that the
fragility of the new deterrence evidence, a function of the fundamental empirical
and theoretical errors in this body of work, raises concerns greater than simply just
“doubt”: the conclusions in this body of work are wrong, there is no reliable
evidence of deterrence. The only scientifically and ethically acceptable conclusion
from the complete body of existing social science literature on deterrence and the
death penalty is that it impossible to tell whether deterrent effects are strong or
weak, or whether they exist at all.279
Social science sets a high bar for causal inference, demanding caution until
such claims can be replicated under a variety of experimental conditions. Several
such replication efforts, facilitated by generous sharing of data and statistical
programs, suggest that these claims of deterrence are volatile and inconsistent,
sensitive to alternate ways to measure murder rates and decisions on how to
account for anomalies such as missing information and years with no homicides.280
Depending on commonplace methodological adjustments, regression models can
just as easily show that executions increase murder or reduce murder.281 In fact,
this work fails the tests of rigorous replication and robustness analysis that are the
hallmarks of good science. And the analyses here and elsewhere suggest that the
prospect for replications that will produce a range of estimates that can confirm the
core finding of deterrence are not forthcoming.
As a matter of social science, it is important to ask how this debate, in reality
the second round in the debate over deterrence and the death penalty, arrived at

277
278
279
280
281

Id.
Sunstein & Vermeule, supra note 34.
Donohue & Wolfers, The Death Penalty, supra note 147.
Donohue & Wolfers, Uses and Abuses, supra note 25.
Id.

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this point. Like the cold fusion scandal in the 1980s,282 when bold scientific claims
were greeted with widespread enthusiasm by the public that fueled a sharp
mobilization of academic and political institutions, there was a quick and
passionate embrace of the new deterrence claims by a small community of legal
scholars and death penalty advocates. As the new evidence leeched into the
mainstream media and eventually into political discourse and appellate arguments,
the evidence was reified as scientifically rigorous. And as with the cold fusion
episode, these claims seem to be unable to withstand scientific vetting.
There are several distinctions between cold fusion and the current deterrence
debate. Cold fusion was the work of two scientists. The new deterrence is the
work of several researchers, nearly all economists, using core elements of identical
data sets on executions, death sentences, and murders, and submitting their papers
to peer reviewed journals in economics and non-peer reviewed law reviews. One
can only speculate about what happens between submission of an empirical article
to a good journal and an editorial decision. But Walter McManus showed that it is
not unreasonable to assume that a reviewer’s priors influence her posteriors.283
When McManus introduced the priors of researchers into a representative
regression model of murders and executions, he showed that “significant conflicts
remain over the estimated deterrent effect of an additional execution, even after the
researchers have confronted the same data. The conflicting interpretations of the
data evidence are serious.”284 Model uncertainty would be large in a condition

282
For a thorough account of the cold fusion episode, see Michele Landis Dauber, The Big
Muddy, 57 STAN. L. REV. 1899 (2005). When Stanley Pons and Martin Fleischmann announced at a
press conference in March 1989 that they had achieved cold fusion, their news was wildly embraced
by the public and the media as a scientific breakthrough that promised to transform the nation’s
protracted and contentious debate over energy policy. (Cold fusion is defined by Wikipedia as “a
sustained nuclear fusion in a beaker of water at room temperature that would produce vast quantities
of energy at little cost and with few environmental risks.” For a general description of cold fusion,
see Cold Fusion on Wikipedia, at http://en.wikipedia.org/wiki/Cold_Fusion). But the scientific
community greeted the news with skepticism and caution. The discovery came not through a process
of vetting via scientific publication and replication, but instead was presented to the scientific
community via the news media. Although they invited peer review and replication, they pre-empted
scientific testing by claiming that other scientists had already “repeated his experiments with
success”. FRANK CLOSE, TOO HOT TO HANDLE: THE RACE FOR COLD FUSION 335 (1991). The claim
that other scientists had vetted the Pons and Fleischmann finding was untrue. Although some
scientists reached similar conclusions, others were skeptical and suspected several methodological
flaws. It took some time, since these other researchers were starting from scratch, but eventually,
physicists rejected the cold fusion claims as soon as mistakes were uncovered and published.
According to John Huizenga, one physicist said of their research, “If you got a paper like that from an
undergraduate, you would give it an F.” JOHN HUIZENGA, COLD FUSION: THE SCIENTIFIC FIASCO OF
THE CENTURY 24 (1992). Sadly, as evidence mounted that the results could not be replicated, Pons
and Fleishmann refused to admit that there were problems in the initial research that undermined their
claims.
283
McManus, supra note 6.
284
Id. at 423.

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such as this.285 The priors of the researchers, in other words, overwhelm the data,
and the data simply are not strong enough to lead researchers to a consensus or
convergent conclusion. It is not hard to see, given McManus’ demonstration, how
like-minded researchers would reach similar conclusions.
But understanding the priors of researchers can not explain how reviewers and
journal editors would overlook the same flaws that are apparent to many others
who have critiqued this body of work. One assumes that reviewers and editors
have a wider distribution of priors, but whether the priors of reviewers and editors
enter into peer review decisions is unknowable for the moment. I suspect a
different dynamic: a set of papers about murder were reviewed as part of an
interior conversation among economists who have little or no familiarity with the
dynamics of murder, murderers, and criminal legal institutions. Other opinions
seem to be unwelcome in this literature.286 Editors and reviewers alike seem
impervious to the kind of intellectual humility that would sustain a result at
dissonance with the dominant paradigm of price theory. When discussing the
study of deterrence as carried out by economists, Coase287 notes in Economics and
Contiguous Disciplines that:
Punishment, for example, can be regarded as the price of crime. An
economist will not debate whether increased punishment will reduce
crime; he will merely try to answer the question, by how much? The
economist’s analysis may fail to touch some of the problems found in the
other social systems. . . .288
Indeed, potentially the most disturbing concerns in this interlude reside not
just in the willingness (or preference) of good journals to publish stylized
econometrics over substantive social science theory. Rather, these decisions also
are rooted in the striking absence of either critical commentary or substantive
contributions by scholars from other disciplines since the initial publication of
these articles over the past decade.289 In fact, these other disciplines are
marginalized or dismissed in the current debate. Nor do editors or reviewers
285

Leamer, supra note 6.
Sorensen et al., supra note 129, at 569 (showing that Cloninger and Marchessi fail to cite
one article on the deterrent effects of the death penalty authored by a sociologist). My own reading
of these articles shows similar omissions in several articles. Shepherd breezily dismisses the
contributions of sociologists to the empirical literature on the death penalty as insubstantial and
perhaps ideologically motivated. See Shepherd, Murders of Passion, supra note 15; Shepherd,
Deterrence Versus Brutalization, supra note 46.
287
Ronald H. Coase, Economics and Contiguous Disciplines, 7 J. LEGAL STUD. 201 (1978).
288
Id. at 210.
289
In fact, concern with declining critical commentary has also been raised by others. For an
empirical illustration of the problem in major economic journals, see, for example, Philip R.P. Coelho
et al., Decline in Critical Commentary, 1963–2004, 2 ECON. J. WATCH 355 (2005), available at
http://www.econjournalwatch.org/pdf/CoelhoetalEconomicsInPracticeAugust2005.pdf.
286

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challenge this self-referential group with concerted attempts to test more rigorously
for the immediate impact of a change in threatened punishment with more detailed
crime data and a better causal theory. Unfortunately for anyone interested in the
deterrent impact of harsher sentences, several of the built-in safeguards for selfcorrection within the social sciences have clearly failed in this instance. Whether
the explanation resides in orthodox beliefs, lack of critical skepticism, or whatever
else may be responsible, the failure to maintain scientific and intellectual rigor is
particularly disturbing. Indeed, any study which is not adequately challenged by
one’s scholarly peers can only hinder rather than help the credibility of scholarly
contributions to either side of the deterrence debate.
As a regulatory matter, embracing the new deterrence findings ignores risks
of error that would have serious consequences. As a normative matter, the
implications are dangerous. Research at Columbia Law School on reversals in
capital sentences from 1973–1995 showed that the number of serious errors
leading to reversal in capital sentences increased sharply with higher rates of death
sentences per murder.290 More than two death sentences in three during this time
were reversed, and at resentencing, approximately five percent were exonerated.291
Even the harshest critics of the Columbia studies acknowledge that the lower
bound on error rates is four in ten.292 Making more people eligible for execution
increases the risks of horrific errors of wrongful conviction that are far more likely
in states that execute “many people.” The clamor to make policy if not law under
these conditions of uncertainty is expensive and dangerous.
In this episode, a group of scholars combine some sophisticated empirical
strategies to compare the use of the death penalty with a sample of state murder
rates. They introduce a set of theoretically tangential controls, and reach a
conclusion of deterrence that fails to replicate when more complete data are
applied, when unsustainable coding decisions are corrected, and when the
functional form is modified to account for the rigid structure of the data. The
appeal of this simple story of deterrence is obvious. Sadly, though, “it is easier to
muddy the waters than it is to calm them,”293 especially in the midst of recent
erosion in popular support for the death penalty that followed the moratorium on
executions in Illinois,294 the exoneration of the 100th person from death row,295 and

290

See LIEBMAN ET AL., A BROKEN SYSTEM, PART II, supra note 88.
LIEBMAN ET AL., A BROKEN SYSTEM, PART I, supra note 231.
292
Joseph L. Hoffman, Violence and the Truth, 76 IND. L.J. 939, 946 (2001).
293
Dauber, supra note 282.
294
See Rob Warden, Illinois Death Penalty Reform: How it Happened, What it Promises, 95 J.
CRIM. L. & CRIMINOLOGY 381, 406 (2005). See generally DAVID L. PROTESS & ROBERT WARDEN, A
PROMISE OF JUSTICE (1998) (documenting the media reactions to the exonerations of the four death
row inmates).
295
Samuel R. Gross et al., Exonerations in the United States, 1989 Through 2003, 95 J. CRIM.
L. & CRIMINOLOGY 523, 527 (2005).
291

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the revelations of widespread reversals and errors in capital sentences.296
Complexity and uncertainty, though, are what the data say. Until this research
survives the rigors of replication and thorough testing of alternative hypotheses,
this research provides no basis for decisions to take many more lives.
This cohort of studies and researchers, like Ehrlich before them, has created
unjustified confidence in the minds of legislators, death penalty advocates, and a
small group of legal scholars about the capacity of death sentences and executions
to deter murder. They raise their concerns to a high moral ground, and brush off
evidentiary doubts as unreasonable cautions that place potential beneficiaries at
risk of severe harm. Although rebukes like this and others may put the brakes on
the rush to once again embrace deterrence as the cure for murder, interludes such
as this one also remind us to invoke the tough, neutral social science standards and
commonsense causal reasoning before taking a path that can do far more harm than
good.

APPENDIX A. PARTIAL LIST OF STUDIES PUBLISHED AFTER 1990
ON DETERRENT EFFECTS OF THE DEATH PENALTY

Harold J Brumm & Dale O. Cloninger, Perceived Risk of Punishment and the
Commission of Homicides: A Covariance Structure Analysis, 31 J. ECON.
BEHAV. & ORG. 1 (1996).
Dale O. Cloninger, Capital Punishment and Deterrence: A Portfolio Approach, 24
APP. ECON. 645 (1992)
Cloninger, Dale O.& Roberto Marchesini, Execution and Deterrence: A QuasiControlled Group Experiment, 35 APPLIED ECON.569 (2001).
Dale

O. Cloninger & Roberto Marchesini, Executions, Moratoriums,
Commutations, and Deterrence: The Case of Illinois (June 2005),
available at http://econwpa.wustl.edu:8089/eps/le/papers/0507/0507002.
pdf.

Hashem Dezhbakhsh et al., Does Capital Punishment Have a Deterrent Effect?
New Evidence from Postmoratorium Panel Data, 5 AM. L. & ECON. REV.
344 (2003).
Hashem Dezhbakhsh & Joanna M. Shepherd, The Deterrent Effect of Capital
Punishment: Evidence from a “Judicial Experiment,” 44 ECON. INQUIRY
512 (2006)
296

See LIEBMAN ET AL., A BROKEN SYSTEM, PART I, supra note 231; LIEBMAN
BROKEN SYSTEM, PART II, supra note 88.

ET AL.,

A

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Lawrence Katz et al., Prison Conditions, Capital Punishment, and Deterrence, 5
AM. L. & ECON. REV. 318 (2003).
Zhiqiang Liu, Capital Punishment and the Deterrence Hypothesis: Some New
Insights and Empirical Evidence, 30 E. ECON. J. 237 (2004)
H. Naci Mocan & R. Kaj Gittings, Getting Off Death Row: Commuted Sentences
and the Deterrent Effect of Capital Punishment, 46 J.L. & ECON. 453
(2003).
Joanna M. Shepherd, Deterrence Versus Brutalization: Capital Punishment’s
Differing Impacts Among States, 104 MICH. L. REV. 203 (2005).
Joanna M. Shepherd, Murders of Passion, Execution Delays, and the Deterrence of
Capital Punishment, 33 J. LEGAL STUD. 283 (2004).
Jon Sorenson et al., Capital Punishment and Deterrence: Examining the Effect of
Executions on Murder in Texas, 45 CRIME & DELINQ. 481 (1999).
Paul R. Zimmerman, Estimates of the Deterrent Effect of Alternative Execution
Methods in the United States: 1978–2000, 65 AM. J. ECON. & SOC. 909
(2006).
Paul R. Zimmerman, Executions, Deterrence, and the Incidence of Murder, 7 J.
APPLIED ECON. 163 (2004).
James A. Yunker, A New Statistical Analysis of Capital Punishment Incorporating
U.S. Postmoratorium Data, 82 SOC. SCI. Q. 297 (2002).