Does Capital Punishment Deter Murder?

A brief look at the evidence



by John Lamperti

Professor of Mathematics, emeritus

Dartmouth College

Hanover, NH

March, 2010  





In light of the massive amount of evidence before us, I see no alternative but to conclude that capital punishment cannot be justified on the basis of its deterrent effect.


Justice Marshall, U.S. Supreme Court, Furman v. Georgia, 1972


Contrary to the views of some social theorists, I am convinced that the death penalty can be an effective deterrent against specific crimes.


                           Richard M. Nixon (March 10, 1973)



Ethical, philosophical and religious values are central to the continuing controversy over capital punishment. Nevertheless, factual evidence can and should inform policymaking. The evidence for capital punishment as a uniquely effective deterrent to murder is especially important, since deterrence is the only major pragmatic argument on the pro-death penalty side.[1] The purpose of this paper is to survey and evaluate the evidence for deterrence.


We must define the question correctly. We are not asking whether the threat of punishment, in general, deters crime, nor whether there should be heavy penalties for murder. The issue at stake is this: Does capital punishment, in a form that could be practiced in the United States, provide a better deterrent to murder than long imprisonment? In particular, is it likely that expanding the death penalty in New Hampshire would lead to fewer murders or eliminating it to more? If not, capital punishment offers no practical benefits to weigh against its social costs.[2]


 A small (but still substantial and growing) portion of the vast literature on crime and prevention deals with factual evidence about deterrence. This evidence is statistical and the problems of interpretation are difficult. Nevertheless, there is a broad consensus about the answer to our question. We will begin the survey after some general remarks about statistical reasoning.


Kinds of statistical evidence[3]


Statistical analysis is essential for interpreting complex data and making decisions in the face of uncertainty. It's useful to recall two notable cases where statistics helped form social policies.


In 1954 the Public Health Service organized "the biggest public health experiment ever," a field test of the Salk polio vaccine. The goal was to determine whether the new vaccine could substantially reduce the incidence of paralytic polio. Several difficulties had to be overcome. The occurrence of polio varied from year to year and place to place in a seemingly random manner. Moreover, even without any preventive measures the incidence of the disease was low, on the order of 50 cases per 100,000 susceptible children. This meant that large chance variations in the number of cases were to be expected in the study population, and these variations might either mask a positive effect from the vaccine or produce the illusion of an effect where none existed.


To overcome these problems a carefully designed experiment was performed, involving nearly a million children. A "control group" received placebo injections instead of the real vaccine; the rest, of course, were inoculated with the Salk vaccine. The children in the control group were chosen at random from all those who volunteered and qualified for the experiment, and neither they, their parents, nor the doctors who examined them knew which children had received the actual vaccine. This process insured that there were no systematic differences between those receiving the vaccine and the placebo. The incidence of paralytic polio in the control group turned out to be nearly three times greater than that for the vaccinated children, and because of the experimental design a clear conclusion emerged: It was virtually impossible that such an outcome could have happened unless the treatment had a positive effect. Thus the Salk vaccine, though not perfect, was judged a definite success.


A second example is the problem of cigarette smoking and health, especially the effect of smoking on the occurrence of lung cancer. A relationship was first suspected during the 1920s and 30s when physicians in the U.S. and England observed that nearly all their lung cancer patients were heavy smokers.  A 1955 study compared smoking rates and lung cancer deaths (lagged 20 years) for 11 countries, and found a high positive correlation (0.7): higher lung cancer rates went with more smoking. (This sort of correlation can be misleading however, since it is individuals, not countries, who smoke and get cancer.)  Other studies compared groups of smokers with control groups of non-smokers, chosen to be as similar as possible to the smokers in other respects. These investigations made it clear that there is a strong association between heavy smoking and lung cancer, but they do not prove that smoking causes the cancer.


The point is worth stressing, for similar problems arise in investigating capital punishment. While smokers have a much higher incidence of lung cancer than do people who have never smoked, this does not by itself prove that smoking causes cancer. It might happen that some third factor (or a combination of factors) causes the cancer, and that this factor is also associated with smoking. If that were true, then even though smokers would run higher risks of lung cancer than non-smokers there would be no gain from quitting; smoking would only indicate, but not cause, cancer proneness.


To settle the question, something more was needed--either evidence for that hypothetical third factor on one hand, in which case smoking would not be the culprit, or clarity about the causal mechanism on the other. In the smoking/lung cancer case no "third factor" has been found, and additional evidence of a genuine link has indeed developed.  For example, there was a dose/response relationship–the more an individual smoked, the greater the chance of lung cancer. Animal studies showed that exposure to cigarette smoke definitely did cause lung cancer in dogs.  Considering this and other work, in 1963 a scientific commission reported to the U.S. Surgeon General the conclusion that heavy smoking can cause lung cancer. That conclusion is now almost universally accepted.


Finally, here is an imaginary (and somewhat facetious) example where a strong association definitely does not equal causation.  Suppose someone studied all the elementary school children in New Hampshire and compared their reading test scores to their shoe sizes.  It’s certain that they would find a very strong positive correlation—children who wear larger shoes have better scores.  Does that mean that parents could help their kids read better by getting them bigger shoes? Hardly! In this case there is an obvious “third factor”: the children’s’ ages.  Fifth and sixth graders are older and usually read better than first and second graders, and they generally also have bigger feet. The association is certainly real, but buying your daughter larger shoes will not make her a better reader.


Capital punishment in the United States


The question of the death penalty and deterrence of homicide has something in common with the smoking/lung cancer problem. Both deal with rare phenomena subject to random fluctuations, and neither can be studied by a controlled experiment like the Salk vaccine trial. In the case of smoking and cancer, initial observations revealed a strong positive association between the two variables, and subsequent research had to determine whether this association was due to a causal relationship. In the capital punishment problem the data are far less clear, and a first look suggests that executions are associated with higher rates of murder rather than lower as deterrence would indicate.  Can any cause-and-effect relation be established in this case?


For decades, murder has been more common in states with capital punishment than in those where it is not used. Data from 1973 to 1984 showed that murder rates in the states without the death penalty were consistently lower and averaged only 63% of the corresponding rates in the states retaining it.[4]  The gap has persisted since that time, and in 2008 the average murder rate in states with capital punishment was 5.2 (per 100,000 people) while in non-death penalty states it was 3.3.[5] No deterrence can be seen here--but it might exist and yet be masked by other factors. Many things affect homicide rates; the problem is to separate the impact, if any, of capital punishment from that of all the other variables, known and unknown.  How can this be done?

An early approach consisted of comparing homicide rates in states with and without capital punishment, choosing groups of neighboring states as nearly alike as possible in other respects. Such comparisons were made by Thorsten Sellin for the years from 1920 to 1958. [6] This method is a far cry from the controlled experiment performed to test the Salk vaccine, since "other things being equal" is never exactly true when comparing units as large and varied as states. Still, if deterrence plays a significant role its effect should show up as lower homicide rates in the death penalty states when compared to similar, neighboring abolition states. Here are Sellin's conclusions:


The data examined reveal that


1. The level of the homicide death rates varies in different groups of states. It is lowest in the New England areas and in the northern states of the Middle West and lies somewhat higher in Michigan, Indiana and Ohio.


2. Within each group of states having similar social and economic conditions and populations, it is impossible to distinguish the abolition state from the others.


3. The trends of the homicide death rates of comparable states with or without the death penalty are similar.


The inevitable conclusion is that executions have no discernible effect on homicide death rates which, as we have seen, are regarded as adequate indicators of capital murder rates.


Another method is to follow the murder rate in a fixed state or jurisdiction and see what happened when capital punishment was abolished, and, in some cases, when it was reintroduced. Sellin and others did studies of this kind too. These investigations again failed to reveal any additional deterrent effect due to capital punishment.[7] Both types of study have been updated by other researchers and the changing practice of executions since 1967 (first a ten year moratorium, then their resumption) has been taken into account. The conclusions--no indications of deterrence--remain the same.[8]


These studies should reveal a general, long-lasting deterrent effect of the death penalty if it exists. Other investigators looked for short-term or special kinds of deterrence. In 1935 Robert Dann published an analysis of homicides in Philadelphia during 60 days before and 60 days after five highly publicized executions. Dann argued that the deterrent effect of the executions should result in lower homicide rates during the post-execution periods. The result was the opposite; rates were higher than usual. Some 20 years later Leonard Savitz did a similar study, although in his work the critical days were the ones when death sentences were pronounced after well-publicized trials. Savitz found no significant difference in homicides for the before and after periods.[9] Similar studies of short-term deterrence were carried out in Chicago and California, and again no deterrent effect was found.


It is sometimes suggested that capital punishment provides added protection for police and prison guards, and a number of states that have abolished capital punishment for “ordinary” murder retain it for the killing of police or prison staff. This sort of deterrence has been investigated several times, and no evidence was found that absence of capital punishment makes police or prison work more dangerous.[10] One survey did, however, confirm that police in death penalty states believe it contributes to their safety. Interestingly, the same survey showed police in the abolition states believing by almost the same margin that absence of capital punishment did not add to the hazards of their jobs.


Since the mid 1970s investigators have used more sophisticated statistical methods both to analyze new data and to reexamine older findings in new ways. With some exceptions (see the next section) the results are consistent with the earlier findings. Bailey and Peterson, for example, conclude that "Deterrence and capital punishment studies have yielded a fairly consistent pattern of non- deterrence." Although they find agreement that "the overall (general) homicide rate is not responsive to capital punishment," they do call for further research into particular types of crimes.[11]


Regression models: Ehrlich and others


By the mid 1970s, informed opinion agreed that existing data showed no increased deterrence due to the death penalty. A study by economist Isaac Ehrlich broke that pattern. Ehrlich considered U.S murder and execution statistics for the period 1933-1969 together with measures of social factors such as unemployment and per capita income, and then tried to establish a mathematical model predicting the murder rate from all the other variables, national execution rates among them. His model produced a negative coefficient for the execution variable (i.e., more executions are associated with fewer homicides), which he asserted was statistically significant.  Ehrlich concluded that "In light of these observations, one cannot reject the hypothesis that punishment, in general, and execution, in particular, exert a unique deterrent effect on potential murderers."[12]


This study was important for methodological reasons, since it was apparently the first time multiple regression was used to investigate deterrence. (This innovation made it hard for non-mathematicians to understand and evaluate the paper.)  Moreover, the fact that Ehrlich was the first researcher to claim positive evidence for added deterrence due to capital punishment guaranteed that his work would receive attention.


Ehrlich's data were soon studied by other investigators and his results reconsidered. Peter Passell and John Taylor focused on Ehrlich's observed negative relation between executions and homicide rates, and asked what happens when the time period chosen for the model is changed. They also experimented with varying his assumptions as to the model's functional form. In both cases they found that some broad aspects of the model were unchanged, but the indication of a special deterrent effect from executions disappeared completely. Passell and Taylor concluded that whatever the other virtues of Ehrlich's work, no valid inference about deterrence could be drawn from it.[13] Another research team, William Bowers and Glen Pierce, found much the same thing.[14] Others have experimented with their own regression models for both time-series and cross-sectional (interstate) studies. The results are mixed, but most of the researchers failed to find any evidence for deterrence.


I have had some personal experience with this issue. Students in a statistics class I taught at Dartmouth experimented with Ehrlich's model and data during our study of regression analysis. We confirmed Passell and Taylor's finding that the indication of deterrence was extremely unstable when small changes were made in Ehrlich's assumptions. My own conclusion is that regression on nationally aggregated data can never yield reliable evidence on deterrence, pro or con. The signal, if any, is hopelessly buried in the noise.


In the final section of his paper, Ehrlich interpreted the negative correlation he found as suggesting a "tradeoff between executions and murders," and he estimated that over the period 1935-1969, "an additional execution per year ... may have resulted, on average, in 7 or 8 fewer murders." This dramatic statement was only slightly softened by his qualification that "the expected trade-offs ... mainly serve a methodological purpose."


The idea that one execution might prevent 7 or 8 murders is easily grasped and remembered. This is unfortunate, because no such conclusion is justified by Ehrlich's research. We have seen that the negative correlation between murders and executions in his model disappears when minor changes are made in certain assumptions. But even if the model were much more accurate and stable, the "trade-off" idea would still be invalid. It requires the doubtful assumption that all other factors could remain constant while the execution rate alone was increased. Worse yet, it confounds association and causation.


Ehrlich himself surely understood this; that is presumably what he meant when he spoke of a “methodological purpose."  But he did not stress or explain the need for caution, and predictably some of his readers did not get the point. They were, in effect, ready to buy their children larger shoes to improve their reading scores; that is, to step up executions in order to prevent homicides. But the hope of saving seven, or any number, of lives by one additional execution cannot be defended by Ehrlich's work. The earlier conclusion, that U.S. murder statistics give no evidence for an additional deterrent effect of capital punishment, still held.


Ehrlich’s work, like that of his critics, became possible in the 1970s because of access to high-speed computing.  Since then much easier access to computing, as well as widespread access to substantial data sets, have encouraged others to undertake econometric-style investigations of capital punishment and deterrence.  So far in the 21st century about 10 substantial studies have been published.  Their findings have been mixed, with some claiming evidence of execution/murder “trade-offs” similar to or larger than Ehrlich’s 7 or 8, while others found no such evidence or even an effect in the opposite direction (so-called “brutalization” hypothesis). A summary of these studies, together with a major new investigation, can be found in a very recent article by three University of Texas researchers. Their results “provide no empirical support for the argument that the existence or application of the death penalty deters prospective offenders from committing homicide.”[15]  


Deterrence--or the opposite?


If capital punishment really has any effect on homicide rates, that effect must be small. Worse, it might go the wrong way! There are cases where the death penalty has been a cause of homicide rather than a preventive.


How could capital punishment be a cause of murder? In a medical paper, Dr. Louis West has described what he calls "attempting suicide by homicide."[16] In these bizarre cases a person actually kills in order to court death by execution. Here is one of them:


Recently an Oklahoma truck driver had parked to have lunch in a Texas roadside cafe. A total stranger--a farmer from nearby--walked through the door and blew him in half with a shotgun. When the police finally disarmed the man and asked why he had done it, he replied, "I was just tired of living."


Others have also documented examples of killing to invite execution; for example, Clinton Duffy, the former warden of San Quentin prison, described several cases in his 1963 book 88 Men and 2 Women. In these instances the death penalty was a cause of homicide rather than a preventive.[17]


Another possibility is the so-called "brutalization hypothesis," which suggests that capital punishment can encourage homicide by seeming to legitimize killing of enemies. Studies from London and New York State have found an increase in homicides after highly publicized executions, rather than the decrease consistent with deterrence.[18] How valid these findings are and how generally they might apply is not clear.


On the other hand, there is also anecdotal evidence that some homicides may have been deterred by the death penalty. For example, in 1971 the Los Angeles Police Department reported that half of a group of suspects under arrest for robbery stated that they had decided not to carry or not use weapons in their "work" to avoid any risk of a killing which could lead to their own execution. These statements to police can hardly be taken at face value, but some such cases are probably genuine.


When we acknowledge that there must be instances when capital punishment helps deter a murder, we must also recognize that at other times it can encourage what it is meant to prevent. Since neither effect can be measured directly we must turn back to the statistical studies, which seek to determine the net effect. Their evidence does not prove that the death penalty is no added deterrent to murder, nor could it. It does show, I believe, that any special deterrent effect is small in magnitude, and it might go in either direction. That is still probably all that can be said.


Further discussion


How do advocates of capital punishment reply to all this? Some rely uncritically on investigations such as Ehrlich's or those of his successors that claim to find evidence that deterrence is real.  Others state opinions like those of Professor Ernest van den Haag of New York University. In an article "On deterrence and the death penalty''[19] van den Haag offered neither new data nor new analysis to support his belief that capital punishment has a special deterrent value. Instead he gave psychological and "common sense" arguments on its behalf, together with a general criticism of the findings of "Professor Sellin et al." He feels that the statistics are not good enough, that "the similar areas are not similar enough, the periods are not long enough;....'' After more such criticism van den Haag concludes: "I doubt that the presence or absence of a deterrent effect of the death penalty is likely to be demonstrable by statistical means. It is on our uncertainty that the case for deterrence must rest."


That remarkable statement makes a weak case indeed. It is true that statistical evidence cannot prove that any effect is precisely zero. If, for example, the Salk vaccine had no impact whatever, this could not have been proved by the trial described earlier. The experimental results would have indicated, with a high degree of confidence, that any benefit from the vaccine must lie below a certain level. As the amount of data increased that level would become smaller, and zero effect would be the natural conclusion.  It would be perverse to then decide to use the vaccine anyhow because the tests did not exclude the possibility that there could be some benefit, however small.  Such a decision would be even more unreasonable if the vaccine was very costly or had dangerous side effects. This, in effect, is just what van den Haag advocates in relation to capital punishment. As negative evidence accumulates, it becomes more and more implausible to base one's "case for deterrence" on the smaller and smaller region of uncertainty that remains.




We have surveyed a great deal of material; there is a lot more not mentioned here. None of it has the clarity of a well-designed statistical experiment, nor could it. And yet despite that uncertainty, I believe Justice Marshall was right, and Richard Nixon wrong, in the judgments quoted at the start of this paper. Marshall's view is today supported by an overwhelming majority among America's leading criminologists, who believe that capital punishment does not contribute to lower rates of homicide.[20]


There is a strong international trend against capital punishment. In recent years Great Britain (1973), Canada (1976), France (1981), Australia (1985), Italy (1994) and Spain (1995), among others, have eliminated capital punishment for murder after extensive study and debate. Russia adopted a moratorium in 1996 and has not executed anyone since. South Africa abolished capital punishment in 1995 after its transition to democracy. In 1998 the European Union Council reasserted the “opposition of the European Union to the death penalty in all cases and in all circumstances.”  Executions have also become less frequent in many nations where the death penalty remains on the books, and in 2009 no executions were carried out anywhere in the Western Hemisphere—except in the United States.[21]


The trend toward abolition has not been observed to cause increases in homicide. In Canada, for example, around three murders were committed per every 100,000 people before the death penalty was abolished in 1976, while after that the rate consistently went down reaching 1.85 homicides per 100,000 people in 2003.[22]  Other nations such as Great Britain have experienced increases in murder--but even greater increases in other violent crimes that were never subject to death sentences. Some years ago this passage from a United Nations study summed it up: "It is generally agreed that the data which now exist show no correlation between the existence of capital punishment and lower rates of capital crime."[23] The conclusion still holds.


Many of those who defend the deterrent value of the death penalty rely on strong intuitive feelings that capital punishment should be uniquely effective. When the available evidence doesn't support that conclusion, they argue that the evidence is imperfect. It is. But if there were a substantial net deterrent effect from capital punishment under modern U.S. conditions, the studies we have surveyed should clearly reveal it. They do not.




If executions protected innocent lives through deterrence, that would weigh in the balance against capital punishment's heavy social costs. But despite years of trying, this benefit has not been proven to exist; the only certain effects of capital punishment are its liabilities. The death penalty in New Hampshire serves no social purpose, and its abolition would be a practical and a moral step forward.


Supreme Court Justice Blackmun, a Nixon appointee, ruled in the Furman case that capital punishment is not per se unconstitutional. That does not mean it is a good policy. An excerpt from Blackmun's Furman opinion can well conclude this paper:


I yield to no one in the depth of my distaste, antipathy, and, indeed, abhorrence, for the death penalty.... That distaste is buttressed by a belief that capital punishment serves no useful purpose that can be demonstrated.




[1] It is often suggested that executing convicted murderers can at least save money. This common belief is wrong; executions are far more expensive than life imprisonment. See Mark Costanzo and Lawrence White, "An overview of the death penalty and capital trials: history, current status, legal procedures, and cost," Journal of Social Issues 50, no. 2 (summer 1994), pp, 1-18. More up to date research, summarized and cited in testimony before the NH Commission, has reinforced that conclusion. 


[2] The greatest cost is that innocent people have been executed, and that others surely will be in the future. For a review of cases in which people were wrongly sentenced to die, see chapter 25 in Hugo Adam Bedau (ed.),The Death Penalty in America: Current Controversies (Oxford, 1997). See also Charles Black, Capital Punishment: The Inevitability of Caprice and Mistake (Norton, 1974). In recent years the case of Troy Davis, who has spent many years on death row in Georgia for a crime he probably did not commit, has attracted considerable attention. See also “Trial by Fire,” The New Yorker, Sept. 7 2009, for a detailed account of the trial and execution of an almost surely innocent man in Texas.


3 This section borrows heavily from an excellent book: Statistics, Third Edition, by David Freedman, Robert Pisani and     Roger Purves, New York: Norton, 1998.


[4] Data from Ruth Peterson and William Bailey, "Murder and capital punishment in the evolving context of the post-Furman era," Social Forces, March 1988, pp. 774-807. The exception to this pattern is the District of Columbia, which has no death penalty and very high homicide rates. (Of course D.C. is not a state, and special circumstances apply.)


[5] Data from the Death Penalty Information Center web site at


[6] Thorsten Sellin, The Death Penalty (1959). Excerpts from this book and many other sources were reprinted (along with some new material) in a useful anthology The Death Penalty in America, edited by Hugo A. Bedau (1964).  Sellin was a leading criminologist and a pioneer in death-penalty studies until his death in 1994.


[7] This work and that described below is summarized in William Bailey and Ruth Peterson, "Murder,capital punishment, and deterrence: a review of the literature," chapter 9 in Bedau (1997), note 2.


[8]  See Peterson and Bailey, op. cit. in note 4.


[9] Savitz's article was reprinted in Bedau's 1964 anthology cited in note 6.


[10] A recent investigation is Bailey and Peterson, "Murder, capital punishment, and deterrence: a review of the evidence and an examination of police killings," Journal of Social Issues, summer

1994, pp. 53-74.


[11] Bailey and Peterson, op. cit.


[12]  "The deterrent effect of capital punishment: A question of life or death," American Economic

Review June 1975, pp. 397-417.


[13] "The deterrence controversy: a reconsideration of the time series evidence," in Capital

Punishment in the United States, H. Bedau and C. Pierce, editors, 1976.


[14] "The illusion of deterrence in Issac Ehrlich's research on capital punishment," Yale Law Journal, Dec. 1975, pp. 187-208


[15]   Tomislav Kovanzik, Lynne Vieraitis, and Denise Boots, “Does the death penalty save lives?  New evidence from state panel data, 1977 to 2006,” Criminology and Public Policy, Vol.  8 (2009, Issue 4.


[16]  "Medicine and Capital Punishment," in To Abolish the Death Penalty, Hearings before the U.S. House Judiciary Committee, March and July, 1968, p. 124. Dr. West chaired the Department of Psychiatry, Neurology and Behavioral Sciences at the University of Oklahoma School of Medicine.


[17] Further examples are described by M. W. Espy Jr. in "Capital punishment and deterrence: what the statistics cannot show," Crime & Delinquency, Oct. 1980, pp. 537-544.


[18] William Bowers and Glenn Pierce, "Deterrence or brutalization: what is the effect of executions?" Crime and Delinquency, Oct. 1980, pp. 453-484.


[19]  Journal of Criminal Law, Criminology and Police Science 60 (1969), p.141.


[20] Michael Radelet and Ronald Akers, "Deterrence and the death penalty: the views of the experts," Journal of Criminal Law & Criminology 87, no.1 (1996), pp. 1-16.  Radelet with another collaborator, Traci Lacock, recently replicated this survey of leading criminologists and again found an overwhelming consensus that executions do not lower homicide rates.  (The same Journal, vol. 99, 2009.)


[21]  In addition to the United States, nations carrying out sizable numbers of death sentences in 2009 include China (the number of executions is a “state secret” but it is known to be more than the rest of the world combined), Iran, Iraq, Saudi Arabia, Yemen, Sudan, Viet Nam and Seria, in decreasing order.  The United States was in fifth position with 52.


[22] See “Canada online” at


[23]  Capital Punishment, a United Nations study, 1968.


Go Back