Economic Theory, Econometrics, and the Death Penalty

Dr. Ehrlich’s Magic Bullet: Economic Theory, Econometrics, and the Death Penalty Richard M. McGahey During the past decade, there have been renewed...
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Dr. Ehrlich’s Magic Bullet: Economic Theory, Econometrics,

and the Death Penalty Richard M.

McGahey

During the past decade, there have been renewed calls for the

use

ofcapi-

tal punishment to deter murder. Economists and other social scientists have conducted statistical analyses which have generally failed to locate these alleged deterrent effects. A few economists, notably Isaac Ehrlich, have claimed to locate such effects, but little confidence can be placed in these findings. This article reviews these studies, with particular attention paid to a plain-English review ofstatistical methods used and technical problems found in the analyses. However, this review of technical questions should not obscure broader issues about socioeconomic influences on homicide, crime, and deterrence. Such issues cannot be resolved through debates over

econometric

techniques.

During the spring of 1977, the New York State Legislature debated proposals to reintroduce the death penalty for murder. In a campaign to generate support for capital punishment, the New York City Patrolmen’s Benevolent Association ran advertisements in city newspapers. Among other rationales for capital punishment, the PBA said that Dr. Isaac Ehrlich had scientifically proven that each execution saved the lives of seven or eight potential victims. Ehrlich’s work

also cited in 1976 in an amicus curiae brief for the Supreme Court. As support for the death penalty, the solicitor general praised Ehrlich’s work as &dquo;sophisticated&dquo; and cited its conclusion that, &dquo;over the past several decades, each execution actually carried out deterred a significant number of murders.&dquo; Previous empirical studies which found no deterrent effects were characterized as &dquo;infected by serious analytical flaws&dquo; and as &dquo;not provid(ingJ support for a contrary conclusion.&dquo;, This claim of scientific proof was doubtless a surprise to criminologists, criminal justice professionals, and others who had followed the controversy about the deterrent effect of capital punishment. Indeed, until Ehrlich’s was

RICHARD M. McGAHEY:

Deputy Research Director, Alternative Youth Employment

Strategies Project, Vera Institute of Justice, New York City. My thanks to Anne Adams, Sally Hillsman Baker, Rich Betheil, McDonald for helpful comments. 1.

Brief for the United States

as

Amicus Curiae

at

35-38, Fowler

David Gordon, and Doug v.

North Carolina,

428 U.S.

904 (1976). 485

486

be no controversy: The works of Thorsten Sellin and other sociologists had all shown that executions had no deterrent value.’ But Ehrlich, unlike the other researchers on capital sanctions, was an economist. In the past fifteen years, economists have become increasingly involved in studying the efficacy of deterrence through punishment. Since Ehrlich’s original piece on the death penalty appeared in 1975, there has been a large amount of work on this aspect of the deterrence question. But although this work has played an important role in the public debate on the death penalty, it has been opaque to most interested observers. Most articles on capital punishment by economists look like something out of a physics journal, replete with references to ordinary versus two-stage least squares, Box and Cox tests of equation specification, interpretation of reduced form coefficients, and the like. For the reader without a high level of statistical and econometric knowledge, evaluation of the economists’ work has been very difficult. In this paper I will review analyses of capital punishment by economists, including in the review a plain-English introduction of multiple regression analysis. Before beginning the technical discussion, however, it is crucial to note a fundamental theoretical problem characterizing econometric analysis. All of the work done on capital punishment by economists relies to some extent on a behavioral model drawn from microeconomic theory.’ According to this view, murder is &dquo;rational&dquo; behavior, in the sense that potential murderers are responsive to prospective gains and losses associated with their activity. Homicidal behavior is treated as maximization of personal utility by individuals subject to certain constraints. It is explained in the same way as other economic behavior-for example, hours of work offered and wages desired by individuals, prices offered for goods in the market. This is a microeconomic interpretation of murder as a decision to maximize individual utility. Using this perspective as a theoretical underpinning, economists have carried out complex statistical studies. The debate over these studies has concentrated on econometric technique, deflecting attention from the theoretical problems involved. In particular, the relation between socioeconomic conditions and individual-level behavior like homicide has been obscured, with a consequent loss of attention to broader issues concerning crime, deterrence, and criminal justice policy.

work,2 there seemed

to

z

SELLIN’S EARLY WORK, AND EHRLICH’S CRITICISM As noted were

above, until Ehrlich, studies on deterrent effects of the death penalty

dominated

2. Isaac

by Thorsten Sellin’s work.5 Sellin examined

Ehrlich, "The Deterrent Effect of Capital Punishment:

Death," American Economic Review, June 1975, pp. 3. See

A

groups of

con-

Question of Life and

397-417.

separate citations below.

4. See

Gary S. Becker, "Crime and Punishment: cal Economy, March/April 1968, pp. 169-217. 5. Thorsten

An Economic

Sellin, The Death Penalty (Philadelphia:

Approach," Journal ofPoliti-

American Law Institute,

1959).

487 at least one state statutorily ruling out and one with laws allowing it (&dquo;retencapital punishment (&dquo;abolitionist&dquo;) The states were examined for tionist&dquo;). similarity on a variety of socioeconomcharacteristics. Sellin found that the homicide rates of and ic demographic states did not differ over time from the homicide rates of retentionist generally this he drew &dquo;the inevitable conclusion&dquo; that abolitionist states. From work, effect have no discernible on homicide death rates. &dquo;6 &dquo;executions Ehrlich’s studies reported a different conclusion. Examining murder and execution rates in the United States from 1933 through 1969, he argued that the evidence indicated &dquo;a pure deterrent effect of capital punishment. &dquo;7 Ehrlich’s analysis differed from Sellin’s in two fundamental respects. First, he developed an elaborate theoretical model about the individual behavior of potential murderers, drawing on postulates of microeconomics. Second, he used multiple regression techniques drawn from econometrics, which, he claimed, allowed him to infer the finding of a &dquo;pure&dquo; deterrent effect. Based on the view of potential murderers as &dquo;influenced by prospective gains and losses,&dquo; and the assumption that death is viewed as &dquo;the harshest of all punishments,&dquo; Ehrlich developed a mathematical model of the determinants of homicide rates assuming that murderous behavior can be viewed as maximization of personal utility subject to the constraints of possible

tiguous

states, each group

containing

punishment.,, Ehrlich made a number of appropriate technical criticisms of Sellin’s work. He argued that Sellin was testing the influence of the existence of the death penalty in the state statutes, when the real issue involved actual execution risk. (Some of Sellin’s retentionist states rarely, if ever, carried out executions.) Sellin’s attempts to match states were largely subjective, since the common geographic boundaries of states did not provide adequate grounds for statistical comparison. The techniques employed by Sellin also made it impossible to control the impact of other factors. For example, Ehrlich posited a potential &dquo;feedback&dquo; mechanism, according to which higher levels of murder would lead to an increased demand for executions.9 A simple correlation of executions and homicide rates would only see the relationship between high murder and execution levels, and might mistake the nature of the relationship. The technique used by Ehrlich to control simultaneously for several factors was

6. 7.

multiple regression analysis.

Ibid., p. 34. Ehrlich, "Deterrent Effect of Capital Punishment,"

p. 398.

This model was based not only upon Becker’s theoretical foundation but also upon Ehrlich’s own earlier work (Isaac Ehrlich, "Participation in Illegitimate Activities: A Theoretical and Empirical Investigation," Journal of Political Economy, May/June 1973, pp. 521-65). See, for a simple introduction to this approach, Richard F. Sullivan, "The Economics of Crime: An Introduction to the Literature," Crime and Delinquency, April 1973, pp. 138-49. 9. Ehrlich, "Deterrent Effect of Capital Punishment," p. 415. 8.

488

MULTIPLE REGRESSION AND ECONOMETRIC

TECHNIQUE Multiple regression techniques are used to model a complex social relationship allow for simultaneous statistical control of many variables. An equadeveloped that expresses in mathematical form a hypothetical relationship between a dependent variable, such as homicide rates, and a set of independent variables, such as executions, sentencing practices, and poverty. Changes in the independent variables are tested for their association with changes in the dependent variable. Each independent variable has a value, or coefficient, associated with it. This coefficient expresses the independent variable’s particular influence on the dependent variable.10 An example follows. Suppose that an analyst theorizes that murderous behavior is determined by two factors: fear of execution and hatred or envy of wealthier persons. The analyst hypothesizes that fear of executions would diminish murder (i.e., have a negative impact on it) and that hatred or envy of wealthier persons would increase murder (i.e., have a positive impact on it). The resulting function would look like this: Murder = f (-Executions, +Wealth). To test this, the analyst might sample a large number of individuals, measuring their behavior as regards murder, as well as their attitudes and perceptions concerning execution risk and wealthier persons. Because direct observation of such factors is very difficult, data serving as a representation of the factors would probably be used. These indicators might be homicide rates, execution rates, and the percentage of families living below the poverty level. If preliminary analysis showed associations between homicide rates and each independent variable, then tests of the simultaneous impacts of the independent variables could be performed through multiple regression. In addition to the two independent variables, there would be a &dquo;residual,&dquo; or &dquo;disturbance,&dquo; term inserted in the equation. This residual term signifies the part of the murder variation not explained by either independent variable. When this is added to the equation along with the data elements, the equation takes the following form: Hom. Rate -0 1 (Ex. Rate) +0 2 (Pov.) + v, where the {3’s are coefficients associated with each independent variable, and v is the residual term.&dquo; and

to

tion is

=

10. It is important to guard against any false inferences of causality when using regression analysis. The technique tests associations between a dependent variable and a set of predetermined independent variables. "Predetermined" in this context only means that the values of the independent variables are fixed before the analysis, or are "exogenous" to the particular analysis. The dependent variable is tested for its association with these predetermined variablesit is "endogenous" to the analysis. Strictly speaking, regression analysis examines the order of determination of variables, and not causality. 11. The coefficient for any independent variable, if found to be statistically significant, can be interpreted as showing how much the dependent variable would change with a 1 percent change in the independent variable. For example, if the β associated with the poverty variable was .5, then the analyst might conclude that a .01 rise in the poverty population would be associated with a

.005 rise in the

homicide

rate.

489

There are considerable statistical advantages to the technique. It reduces the risk of attributing changes in the dependent variable, like homicides, to a single factor, like executions. Suppose that the homicide rate fell in response to higher apprehension and conviction rates, and that executions rose only to the extent that apprehension and conviction rates rose. An analyst who only examined the relationship between the homicide rate and executions might wrongly conclude that rising numbers of executions were associated with falling homicide rates, when in fact the association is between homicide rates and apprehension and conviction rates. Although the technique has considerable statistical power, there are a number of pitfalls which can obstruct adequate explanation. All of these are important parts of the death penalty controversy. The equation might be misspecified. Too many, too few, or the wrong variables might be included. Were this to happen, it would lead either to &dquo;biased&dquo; (inaccurate) or to &dquo;inefficient&dquo; (unreliable) estimates of coefficients for independent variables. The mathematical form of the equation might be incorrect. The example shows a linear relationship between variables, when some other form might be more appropriate, either as a more accurate expression of the relationship or to promote computation and interpretation. Since the number of executions might depend on the level of homicides as well as influence that level, a system of several equations might be a better expression of the overall relationship. Selection of data to use in the analysis can cause distortions if the data elements do not measure the intended effect, or if data represent different jurisdictional definitions or are collected at different times. Finally, and most important, the relationship may be misspecified theoretically. For example, murders may be influenced by factors other than those hypothesized by the individual utility maximization approach. Alternative theoretical conceptions ought to be tested; the technique is no better than the theory that it tests. Many of these problems can be discovered only by running a variety of regressions, testing different theoretical approaches, different measures for a variable, and different mathematical forms of the relation and subsets of the overall data set. A powerful hypothesis ought to show similar results when it is performed in a variety of ways. Otherwise, there is reason to suspect that results are due to the peculiarities of a specific analysis and do not reflect the

hypothesized underlying relationship.’2 The coefficients and the entire equation are also examined for their levels of statistical signifiwith a "confidence interval." This number expresses the confidence that the relationship observed is not due to chance. In social research, a conventional level of acceptable statistical significance is .95 or higher. This indicates that in 95 out of 100 samples tested for the hypothetical relationship, the analyst would expect to find similar results. 12. For a more extensive discussion, see Lee S. Friedman, "The Use of Multiple Regression Analysis to Test for a Deterrent Effect of Capital Punishment," in Criminology Review Yearbook, vol. 1, Sheldon L. Messinger and Egon Bittner, eds. (Beverly Hills, Calif.: Sage, 1979), pp. 61-87; and Jan Palmer, "Economic Analyses of the Deterrent Effect of Punishment: A Review," Journal ofResearch in Crime and Delinquency, January 1977, pp. 4-21. cance,

490

objections are met, there remains the problem of interpreting the results. The technique is no substitute for critical thinking about complex socioeconomic events. The technique is only a test of hypotheses generated through a theoretical outlook; the technique’s power depends on the strength of the theory being tested. Most of the debate on capital punishment has been on technical grounds, with relatively little attention devoted to theoretical analysis. Following the review of empirical studies, which conEven if the technical

centrates

on

technical issues, I will consider

some

of these broader theoretical

issues.

TIME SERIES ANALYSES

Ehrlich’s 1975 work hypothesized that the homicide rate, as a dependent variable, was a function of several independent variables, including unemployment, labor force participation, age distribution, per capita income, and probabilities of apprehension, conviction, and execution. Ehrlich generated a number of predictions about the directions of influence of these variables (positive or negative), as well as predictions about their relative magnitudes. He experimented with a variety of equation forms (including natural numbers and logarithms), and with different measures of execution risk. (The use of different measures was due both to data exigencies and to biases introduced by deviations of actual executions from expected levels.’3) He found that the relative magnitudes of the apprehension, conviction, and execution variables were in line with his predictions. Regarding the effect of executions, his results were strikingly different from Sellin’s. For murder and execution rates in the United States from 1933 through 1969, he interpreted the coefficient associated with executions as showing that &dquo;each execution served to deter between 7 and 8 murders.&dquo;&dquo; Ehrlich’s work was immediately criticized. The Yale Law Journal and the Journal of Behavioral Economics held symposiums on the issue, and evaluations of Ehrlich’s work were conducted for the National Academy of Sciences. Anti-capital punishment forces before the Supreme Court introduced the work of other analysts to refute Ehrlich’s findings,&dquo; and the debate spread elsewhere. Of six additional analyses of time series data on the United States,’6 only one has attributed significant deterrent effects to capital punishment.&dquo; That 13. See Ehrlich, "Deterrent 14. Ibid., p. 414.

Effect of

Capital Punishment,"

15. Reply brief of petitioner, Fowler, app. E. 16. See separate citations below. 17. See below, for full discussion of James Yunker’s

pp. 407-08.

study. Evidence outside the United States

is limited. Wolpin found support for the deterrence hypothesis in the United Kingdom (Kenneth I. Wolpin, "Capital Punishment and Homicide in England: A Summary of Results," American Economic Review, May 1978, pp. 422-27); McKee and Sesnowitz found no such support in a

study of Canadian data (David McKee and Michael Sesnowitz, "Capital Punishment: The Canadian Experience," Journal of Behavioral Economics, Summer/Winter 1977, pp. 145-57.

491

is extremely flawed; in general, it can be said that the time series the United States show no significant deterrent effects from capital punishment. This conclusion is based almost entirely on empirical work-the critics of Ehrlich do not offer an explicit alternate theoretical model explaining the determinants of murder. Peter Passell and John Taylor, whose work was used in the Supreme Court by the antiexecution forces, found that &dquo;the time series model and data used by Ehrlich permit no inference about the deterrent effect of capital punishment on homicide.&dquo;&dquo; Using similar data and techniques, they attempted to reproduce Ehrlich’s results. They found that his analysis was extremely sensitive to the inclusion of particular years: When the period from 1963 to 1969 was excluded, the deterrent effect found by Ehrlich became statistically insignificant. They speculated on several possible reasons for this, including changes in the age composition of the United States population during the 1960s and the general rise in crime during that period. But the important point remained that use of the years 1963 through 1969 was vital to finding a deterrent effect.l9 Passell and Taylor also found that Ehrlich’s analysis was extremely sensitive to the form of the equation. When they used raw numbers as a variable for execution risk instead of logarithms, the deterrent effect disappeared. Since they saw no particular theoretical justification for the use of a logarithmic form, they concluded that this further weakened Ehrlich’s work.,, Finally, they criticized Ehrlich’s use of a single equation rather than a system of equations. Since the use of executions might have been influenced by changes in the crime and homicide rates, executions should have been modeled as a dependent variable in one equation, and as independent in another. 21 They also suggested that increased levels of execution might cause judges and juries to acquit accused murderers more frequently, rather than expose additional persons to the risk of execution. If the risks from execution were outweighed by the benefits from reduced convictions, increased executions might have the perverse effect of raising murder rates through the increase in one

analysis

data

on

acquittals. 22 18. Peter Passell and

John B. Taylor, "The

Deterrent Effect of

View," American Economic Review, June 1977, 19. Ibid., pp. 446-47.

Capital Punishment: Another

p. 445.

20. Tests of subperiods and alternate forms of equations both represent tests for "robustness." In time series work, if the equation accurately describes behavior for the whole period, then it should show similar results for subperiods. Otherwise, the underlying relationship may have changed over time. Similar concerns are involved with different functional forms; if the relationship is robust, then alternate mathematical forms of the equation (e.g., natural numbers v. logarithms) should show like results. 21. This procedure is known as a simultaneous equation system, and presents more exacting data and modeling requirements than a single equation. When simultaneous equations are appropriate, use of a single equation can result in biased estimates of coefficients. If this criticism

holds,

it would lower confidence in estimates obtained in a single equation. This argument was not analyzed. It seemed to be more in the nature of a Swiftian proposal, suggesting the limits on a single equation model for a complex set of social relations such as the criminal justice system. 22.

492

William Bowers and Glenn Pierce, who participated in the Yale Law Journal’s symposium, made similar criticisms of Ehrlich.23 They too found that the analysis was critically dependent on the logarithmic form of the equation. When they excluded recent time observations from the data set, the deterrent effect disappeared. They also criticized Ehrlich’s choice of some data elements; specifically, they argued that his use of FBI rather than Vital Statistics data on homicides biased the analysis toward finding a deterrent effect. 24 The other critics of Ehrlich participating in the Yale Law Journal symposium, David Baldus and James Cole, did not directly reanalyze Ehrlich’s works Rather, they offered a justification of Sellin’s findings, arguing that, for policy purposes and especially for legal ones, Sellin was correct to focus on the legal status of capital punishment rather than on execution risk: &dquo;In the debate over abolition, the essential question is the effect of changing from a retentionist to an abolitionist jurisdiction. Sellin’s work is directly addressed to this policy choice and Ehrlich’s approach is not.&dquo;26 They also criticized Ehrlich for using aggregate data instead of data for individual states. Ehrlich responded sharply to these criticisms. He argued that Bowers and Pierce misunderstood the effects of measurement error for specific variables. Testing without using the 1960s information was equivalent to &dquo;selective, nonrandom exclusion of observations.&dquo; Logarithmic specification was held by Ehrlich to be the most valid form; but, unlike the critics, he found that his results were &dquo;unaffected qualitatively&dquo; by the choice of functional form. 17 But Ehrlich’s broadest claim was one that his critics did not address in detail. He insisted that his work not only demonstrated a deterrent effect of capital punishment, but also provided support for his general theory of deterrence and criminal behavior, which he developed from microeconomic theory. His criticism of Passell and Taylor made similar technical points as that directed at Bowers and Pierce. His major charge, however, remained that his critics had not offered &dquo;an alternative theory of criminal behavior or any

23. William J. Bowers and Glenn L. Pierce, "The Illusion of Deterrence in Isaac Ehrlich’s Research on Capital Punishment," Yale Law Journal, December 1975, pp. 187-208. 24.

Ibid., pp.

188-89.

David C. Baldus and James W. L. Cole, "A Comparison of the Work of Thorsten Sellin and Isaac Ehrlich on the Deterrent Effect of Capital Punishment," Yale Law Journal, December 1975, pp. 170-86. 25.

26.

Ibid., p. See, for

174.

an assessment of the critiques, Jon K. Peck, "The Deterrent Effect of Capital Punishment: Ehrlich and His Critics," Yale Law Journal, January 1976, pp. 359-67. Ehrlich’s response is contained in "Deterrence: Inference and Evidence," Yale Law Journal, December 1975, pp. 209-27. On specification error, see p. 213; on deletion of observations, p. 214; the quote about effects from format changes is on p. 219. While granting many of Ehrlich’s technical points, Peck felt that Ehrlich had overstated the amount of support such criticisms lent to his original study. "None of the studies considered here [in the Yale Law Journal ] can be said to have resolved the question whether the death penalty deters murder" (p. 367).

27.

493

coherent approach&dquo; which could explain their findings.2° He also pointed to another study, by James Yunker, which, he said, provided &dquo;further independent evidence&dquo; of the deterrent effects of executions. 29 The Yunker study, later published in 1976 in the Journal of Behavioral Economics, opened up another aspect of the time series debate. Yunker tested an extremely simple model with only two independent variables-unemployment rates and execution rates-using homicide rates for the United States as a dependent variable. For the years from 1960 through 1972, using this single equation, Yunker claimed discovery of a deterrent effect that made Ehrlich’s look close to zero. His finding was that &dquo;one execution will deter 156 murders.&dquo;3° Yunker’s analysis contains so many problems that adequate criticism of it would require a much longer article. A few highlights, however, are in order. (1) By selecting precisely the 1960-72 period, a time when murders rose and executions declined, Yunker had virtually tailored his data to prove a deterrence thesis. (From 1966 to 1972, there were only three executions in the United States.) Unlike other analysts, Yunker rejected analysis of subperiods, which in any case would have been very difficult when only thirteen observations (years) constituted the entire data set. (2) Yunker admitted that his analysis might contain many technical biases, but rather than attempt corrections and test alternative specifications, he asserted that an analyst could worry too much about such problems. Biases were seen to operate in &dquo;an uncertain and largely unfathomable way. If potential problems are taken’too’ (sic) seriously, they would effectively abrogate any kind of statistical investigation....&dquo;&dquo; (3) Yunker saw a very important role for executions. In consideration of the argument that the general rise in crime during the 1960s pulled up the murder rate, he argued that this rise was due to the decline in executions. Executions fell, and more crime, especially murders, resulted; police and courts were overwhelmed, and even more murders resulted. The &dquo;root cause of this progression is the decline in executions.&dquo; Some analysts had hypothesized that the proliferation of handguns during the 1960s might have played a role in the rising murder rate.32 Yunker said that this proliferation might instead have been tied to the phasing out of the death penalty, so more people got guns to protect themselves.&dquo; (4) Instead of conducting a variety of tests with alternate equations and different variables, as both Ehrlich and his critics did, Yunker retained his basic equation. He justified this because he 28. Isaac Ehrlich, "The Deterrent Effect of Capital Punishment-Reply," American Economic Review, June 1977, p. 452. 29. Ehrlich, "Deterrence: Evidence and Inference," p. 217, note 24. 30. James A. Yunker, "Is the Death Penalty a Deterrent to Homicide? Some Time Series Evidence," Journal ofBehavioral Economics, Summer 1976, p. 65. 31. Ibid.; emphasis in original. 32. On the current relationship between handguns and murder, see Lynn A. Curtis, "What’s New in Murder?" New Republic, Jan. 26, 1980, pp. 19-21. 33. Ibid., pp. 72-75; emphasis in original.

494 to test &dquo;one reasonable specification that adequately represents the basic model.&dquo;’· The definition of adequacy seemed rather ad hoc, as even the few slightly different equations he presented produced wildly fluctuating effects of executions, showing them to be positive in one version and negative in the next, with changing levels of statistical significance In response to the work of Yunker and others, Burley Bechdolt conducted both time series and cross-sectional analyses of capital punishment’s possible effects on homicide and rape.’6 He found that unemployment variables were very significant in the time series, but that the number of executions was not. He concluded that, &dquo;... given the unemployment variables, it does not matter how many executions occurred insofar as determining the homicide and rape rates over time; what matters are the unemployment rate and unemployment duration. &dquo;&dquo; A paper written for the Panel on Research on Deterrent and Incapacitative Effects of the National Academy of Sciences contains yet another evaluation of the time series data. All of the papers published by the panel stayed very close to technical issues; there was virtually no sustained discussion of the broader theoretical questions concerning deterrence, criminal behavior, and social policy. This paper, by Lawrence Klein, Brian Forst, and Victor Filatov, reported on deterrence research concerning the death penalty and reanalyzed Ehrlich’s original time series data set.3° Klein et al. dismissed Ehrlich’s claim about theoretical grounding without extensive commentary, describing his theory as &dquo;strongly contrived.&dquo; &dquo;Apart from all of the trappings of a utilitarian theory of the incentive to commit murder, Ehrlich specifies a fairly common aggregative model, with no formal bridge between the microcosmic utility analysis and the national supply function. &dquo;39 In other words, Ehrlich’s

preferred

34.

Ibid., p.51.

Substantial fluctuation in coefficients is commonly taken in the technical literature as evidence of misspecification. This gives added reasons for mistrusting Yunker’s findings. For a more detailed criticism of Yunker, see James A. Fox, "The Identification and Estimation of Deterrence : An Evaluation of Yunker’s Model," Journal of Behavioral Economics, Summer/Winter 1977, pp. 225-42; and Michael Sesnowitz and David McKee, "On the Deterrent Effect of Capital Punishment," Journal ofBehavioral Economics, Summer/Winter 1977, pp. 217-24. 36. Burley V. Bechdolt, Jr., "Capital Punishment and Homicide and Rape Rates in the United States: Time Series and Cross Sectional Regression Analyses," Journal of Behavioral Economics, Summer/Winter 1977, pp. 33-66. 35.

37. Ibid., p. 59; emphasis in original. 38. Lawrence R. Klein, Brian Forst, and Victor Filatov, "The Deterrent Effect of Capital Punishment : An Assessment of the Estimates," in Deterrence and Incapacitation: Estimating the

Effects of Criminal Sanctions on Crime Rates, Alfred Blumstein, Jacqueline Cohen, and Daniel Nagin, eds. (Washington, D.C.: National Academy of Sciences, 1978), pp. 336-60. 39. Ibid., p. 343. This judgment resembled that of Manski, who, in a different paper for the panel, commented that Ehrlich’s other work on crime was "at the macro level and ... only marginally related to the theoretical individual-choice model" developed. Charles Manski, "Prospects for Inference on Deterrence through Empirical Analysis of Individual Criminal Behavior," in Deterrence and Incapacitation, Blumstein, Cohen, and Nagin, eds., p. 403, fn. 1.

495

elaborate microeconomic model of individual homicidal behavior had no necessary ties to an analysis of national homicide and execution rates. Klein et al. also criticized Ehrlich for omitting variables of interest, in particular, the length of court-imposed prison sentences for murder. They agreed with other critics that the measure of execution risk biased the results toward a finding of deterrence, since Ehrlich’s measure used the number of murders as the numerator of the homicide rate and the execution rate as the denominator. Even a slight measurement error in these variables could bias the findings toward deterrence. Ehrlich failed to account for a social &dquo;feedback&dquo; effect through the use of simultaneous equations. When they recomputed his study, they found, as had others, that Ehrlich’s results were very sensitive to the time period chosen. Adding indexes of other violent crime into the equations eliminated the significance of the execution variable (property crime, in contrast, was found to have no important effects). And, like other researchers, they found that the use of a linear rather than a logarithmic format showed no deterrent effects.10 They concluded &dquo;very strongly&dquo; that &dquo;one is not justified in drawing policy conclusions from Ehrlich’s results.&dquo;41 The entire panel went farther; in their summary, they stated that &dquo;research on the deterrent effects of capital sanctions is not likely to provide results that will or should have much influence on policy makers.&dquo;’2 Thus, no researchers after Ehrlich, except for Yunker, found deterrent effects from executions based on time series analyses. All those who directly considered Ehrlich’s work found that the alleged effects of capital sanctions were dependent on the choice of variables included in the equation, the definition and forms of those variables, the particular mathematical forms of the equation, and the use of a very specific time period.’3 CROSS-SECTIONAL ANALYSES economists have conducted cross-sectional and deterrence. Cross-sectional work makes analyses capital punishment use of regression techniques comparing different jurisdictions at the same point in time. Evidence from cross-sectional analyses can help to support or refute time series studies because a hypothesized relationship that appears over time should also appear at a single point in time. Because the data for In addition to time series

studies,

of

40.

Klein, Forst, and Filatov, "Deterrent Effect of Capital Punishment." On omitted variables, on biases in execution measures, see pp. 347-49; on time periods, other crimes, see pp. 355-56; on equation specification, see pp. 356-57.

see

pp. 345-46;

55 ;

on

41.

Ibid.,

see

pp. 353-

p. 356.

in Deterrence and Incapacitation, Blumstein, Cohen, and Nagin, eds., p. 12. 43. Klein et al. claimed that Ehrlich’s work was largely dependent on including data from 1962 onward. Since executions fell to zero and murders rose in this period, "... the whole statistical 42.

"Summary,"

in this simple pairing of these observations and not in the theoretical utility model, the econometric type specification, or the use of best econometric method. Everything else is relative-

story lies

ly superficial

and dominated

by

this

simple

statistical observation" (p. 345).

496

cross-sectional studies are arranged by jurisdiction, the problem of aggregation bias is lessened, as the data do not lump executing and nonexecuting states

together.

The first of the cross-sectional studies to appear was Passell’s.&dquo; In an analysis of forty-one states for 1950 and forty-four states for 1960, Passell tested single and simultaneous equation models, using a variety of execution rate variables and several mathematical forms of his equations. He concluded that &dquo;students of capital punishment must look elsewhere for evidence concerning deterrence. We know of no reasonable way of interpreting the cross-section data that would lend support to the deterrence hypothesis.&dquo;&dquo; Criminal justice variables associated with diminished homicide rates were conviction rates for murder and the average prison sentence given convicted murderers. A younger age profile of the population and higher poverty levels were associated with higher murder rates. Forst examined changes from 1960 to 1970 in a cross-state study.’6 Using a single equation, he employed alternate measures of the execution rates to avoid Ehrlich’s problem of biased variables, tested for biases tied to the single equation format, and tested for the potential bias introduced by jurisdictions of different sizes.&dquo; His conclusion: &dquo;The findings do not support the hypothesis that capital punishment deters homicides.&dquo;&dquo;’ However, Forst did find that the ratio of convictions to homicides demonstrated a deterrent impact. Factors associated with higher levels of murder were high proportions of racial minorities, a high percentage of families below the poverty level, a low median family income, and the overall increase in crime during the 1960s. Ehrlich entered the debate again, with a 1977 article presenting an extensive theoretical discussion similar to his earlier work, and a report of cross-sectional analyses of the United States for 1940 and 1950. Unlike Passell or Forst, Ehrlich found that the cross-sectional evidence supported the implications of his earlier work. His time series estimate of seven or eight murders deterred over time compared with an estimate of twenty to twenty-four murders deterred per execution in his cross-sectional study.19 Like Forst, Ehrlich used a single equation model. Like Passell and Forst, he found that law enforcement 44. Peter Passell, "The Deterrent Effect of the Death Law Review, November 1975, pp. 61-80. 45.

Ibid.,

Penalty:

A Statistical

Test," Stanford

p. 80.

Forst, "The Deterrent Effect of Capital Punishment: A Cross-State Analysis of the 1960’s," Minnesota Law Review, May 1977, pp. 743-67. 47. Larger observations-in this case, states-can be associated with larger residual or disturbance terms. This numerical association can cause biased tests of significance and biased values of coefficients for the independent variables. The formal name for the problem is "heter46. Brian E.

oschedasticity." 48.

Ibid.,

p. 762.

Ehrlich, "Capital Punishment and Deterrence: Some Further Thoughts and Additional Evidence," Journal of Political Economy, August 1977, pp. 741-88. On numerical estimates of deterrence, see p. 779. 49. Isaac

497

severity, especially the length of prison terms given for murder, had an impact the homicide rate. Aside from the fact that the analysts considered different years, what accounts for the difference in findings? As with the time series literature, the difference hinges on a unique feature in Ehrlich’s equation. In addition to a measure of execution risk, Ehrlich used a &dquo;dummy&dquo; variable which distinguished executing from nonexecuting states.SO Only when this variable was included in the same equation with the execution risk variable did a deterrent effect appear.’1 As Ehrlich pointed out, states with high levels of murder also on

had relatively high levels of execution. Thus, a single variable which measured the relationship between executions and homicides would show a positive result, all other things being equal. Without the use of the dummy variable in the same equation, Ehrlich’s cross-sectional work did not show a deterrent effect from executions. (The dummy variable might have been operating to distinguish some measured difference between executing and nonexecuting states which affected homicide rates. But it could be only a matter of speculation as to what such a factor or set of factors might have been.) The sensitivity of the findings to the use of dummy variables was reinforced in a study by Dale Cloninger, included in the Journal of Behavioral Economics symposium. Using data from 1960 for forty-eight states in an equation containing socioeconomic and criminal justice variables, along with a dummy variables2 which distinguished Southern states, he found a significant deterrent effect from executions. But, as with Yunker’s time series estimate, Cloninger’s estimate so far exceeded Ehrlich’s that it was hard to reconcile the difference: Whereas Ehrlich estimated 20 to 24 murders &dquo;saved&dquo; per execution, Cloninger’s estimate was approximately 560 murders.5’ Cloninger presented no variables about sentence severity or probability of execution given conviction, and his extraordinarily high estimate may be due to the absence of such variables. Cloninger’s findings were directly challenged by another article in the same symposium. William Boyes and Lee McPheters analyzed data from the same year as did Cloninger.&dquo; They studied forty-seven states and conducted tests using alternate equations and tests for specification error. They also used a 50. A "dummy" variable divides data into discrete categories, such as executing and nonexecuting states. It takes the value of "0" or "1"; in Ehrlich’s case, executing states were set at 1, and nonexecuting ones at 0. Thus only the executing states had a coefficient when the equation was computed. This coefficient was positive. 51. Ibid., pp. 756-57. Passell tested a similar variable, but only as an alternative to execution

risk. 52. See note 50. 53. Dale O. Cloninger, "Deterrence and the Death

Penalty:

A Cross-Sectional

Analysis,"

Journal ofBehavioral Economics, Summer/Winter 1977, p. 95. 54. William J. Boyes and Lee R. McPheters, "Capital Punishment as a Deterrent to Violent Crime: Cross Sectional Evidence," Journal of Behavioral Economics, Summer/Winter 1977, pp. 67-86.

498

dummy variable distinguishing Southern from non-Southern states. But even though they used the same data points, a similar equation, and the same dummy as did Cloninger, they found that &dquo;in all cases, the deterrent effect of capital punishment is insignificant.&dquo;55 Unlike Cloninger, they included measures of the probability of conviction and length of court-imposed prison sentences, which were both found significant. This reinforces the idea mentioned above that Cloninger’s executions variable may actually be reflecting severity, rather than executions. If execution fixed relative to the number of convictions, then higher levels of conviction will be associated with higher execution levels. Thus, execution levels may act as a &dquo;proxy&dquo; for conviction levels if the effect of convictions is not directly tested. The importance of variable selection was further underscored by Bechdolt’s findings in an examination of the extent to which homicide rates in 1970 were a function of events in the 1960s.56 He found that executions were not a significant deterrent, but when he deleted several significant variables, the executions variable became significant. 17 However, execution in this case showed a positive association with homicide-that is, higher levels of execution were associated with higher homicide rates, an association which could be observed from the raw data. Bechdolt included no variables for length of sentence or probability of conviction and punishment. This omission makes it hard to compare his findings with those discussed above. conviction levels and sentence

levels

are

THE LESSONS OF THE ECONOMIC DEBATE

What can be learned from the empirical studies of capital punishment, and which problems have not been addressed? As the foregoing review has demonstrated, the debate among economists has been confined almost exclusively to technical issues. A fair reading of this debate concludes that technical problems in the analyses make it impossible to have confidence in a finding of deterrent effects from executions. Time series data on the United States have been claimed as support for deterrence by two analysts-Ehrlich and Yunker. But Yunker’s work is essentially a restatement of the fact that executions fell and murders rose during the 1960s.5° Ehrlich’s studies have been shown to be extremely sensitive to the measure of execution risk employed, the mathematical form of the equation, and the use of data from the 1960s. His findings thus seem largely dependent on the particularities of his econometric analysis. Even Klein et al., who were able to reproduce Ehrlich’s results down to rounding errors, did not concur with his conclusions about deterrent effects of capital sanctions. 55. Ibid., p. 77. 56. Bechdolt, "Capital Punishment and Homicide and Rape Rates in the United States." 57. Ibid., p. 55. 58. See note 43 above for a similar judgment on Ehrlich’s study.

499

Cross-sectional analyses present a similar picture. Again, two analystsEhrlich and Cloninger-find support from their studies. Passell, Forst, and Boyes and McPheters do not. Comparing Ehrlich with Passell and Forst, the technical issue of equation specification determines the results. Cloninger and use the same data period and very similar equations, so is harder to untangle. But Cloninger’s failure to include variables about conviction risk and the effects of sentence length on homicide

Boyes and McPheters their

disagreement

prevents fuller evaluation of his results. If the issues were merely a matter of technical evaluation, then the of the National Academy of Sciences’ panel would be sufficient. That is, given the problems with analysis of capital punishment and the demanding standards of proof required, studies of the deterrent effects of execution &dquo;almost certainly will be unable to meet those standards of proof.&dquo;&dquo; However, these technical analyses do not address broader problems of interpretation. Most of the analyses, while finding no deterrent value in executions, found significant effects on homicides of variables indicating law enforcement severity. These variables included increased probabilities of apprehension, conviction, punishment, and the length of court-imposed prison sentences. Ehrlich has called attention to these findings many times and has always insisted that his &dquo;main concern&dquo; was not capital punishment per se, but the &dquo;general question of offenders’ responsiveness to incentives.&dquo;6° He has argued that his critics did not address the &dquo;formal economic model itself, nor have the critics offered an alternative theory. &dquo;61 Although, as noted above,62 some economists have dismissed Ehrlich’s use of an individual utility maximization framework to analyze murder, they did not discuss why they found this model inappropriate. The fact that almost all analysts found empirical support for deterrent effects from criminal justice severity highlights this problem. Why should severity deter homicide, while executions do not? Without some alternative theory, conventional economists might conclude that murderers are indifferent to execution versus prison, hardly a plausible choice for a rational utility-maximizing individual. This strained interpretation would only apply if murder, or indeed other crimes, are perceived as unidimensional. Jon Peck noted that Ehrlich’s theory might apply &dquo;at best only to a small subset of homicides. &dquo;61 Charles Manski made the sensible comment that &dquo;because the legal system defines so many different forms of crime and because criminal behavior has so many dimensions, to attempt to capture all crime-related decisions within a single

judgment

in Deterrence and Incapacitation, Blumstein, Cohen, and Nagin, eds., p. 12. Ehrlich, "Capital Punishment and Deterrence," p. 742. 61. Isaac Ehrlich, "The Economic Approach to Crime-A Preliminary Assessment," in Criminology Review Yearbook, vol. 1, Messinger and Bittner, eds., p. 51. 59. 60.

"Summary,"

62. See 63.

the discussion above at note 39. "Deterrent Effect of Capital Punishment," p. 363.

Peck,

500

model seems hopeless. One might as easily try to capture all of human behavior. &dquo;6’ But such an attempt has been a central part of Ehrlich’s overall work. He claimed that issues about crime and social policy are better understood by &dquo;applying to the study of criminality a body of general principles pertaining to all human conduct. Such principles are embodied, I believe, in economic theory.&dquo;6’ Ehrlich said that support was offered for this from all empirical studies done on crime and incentives. The reader should not necessarily accept this claim of broad empirical support. A lengthy and careful review of general evidence on deterrence stated that &dquo;any unequivocal policy conclusion is simply not supported by valid evidence.... Policy makers in the criminal justice system are done a disservice if they are left with the impression that the empirical evidence, which they themselves are frequently unable to evaluate, strongly supports the deterrence hypothesis. &dquo;66 This lack of support is particularly glaring in the capital punishment debate. But if the economic work on crime has not provided this sort of evidence, it has played a role in isolating the debate about crime. The economic approach has become identified with econometric technique and, to a lesser extent, with the utility maximization framework, while alternative types of economic analysis have been excluded. Instead of discussion about the social roots of crime, policy studies have focused increasingly on seemingly simple solutions, usually involving increased punishment. Thus, even though the approach of individually based utility economics may not have carried the day on capital punishment, it has contributed to the notion that crime can be controlled through manipulation of prison and court policy.67 Reconsideration of the capital punishment studies illustrates this point. Virtually every analyst reported effects of law enforcement practices on homicide, and almost every analyst also reported dampening effects on homicide

Manski, "Prospects for Inference on Deterrence," p. 414, note 12. Ehrlich, "Economic Approach to Crime," p. 25. On’ page 34, he referred to "related analyses" of Becker (Gary Becker, The Economics of Human Behavior [Chicago: University of Chicago Press, 1976]). Becker’s introduction to that collection stated that "the economic approach provides a valuable unified framework for understanding all human behavior," relegating other 64. 65.

contributions around the basic utility framework (p. 14; emphasis in original). Nagin, "General Deterrence: A Review of the Empirical Evidence," in Deterrence and Incapacitation, Blumstein, Cohen, and Nagin, eds., p. 136. 67. Students of criminal justice are doubtless aware of the simplifications involved in such an idea. A variety of solutions, like mandatory jail terms and limits on plea bargaining, have been tried with little impact. For instance, the Rockefeller drug laws in New York had virtually no impact on slowing drug traffic and drug-related crimes. See the Joint Committee on New York Drug Law Evaluation, The Nation’s Toughest Drug Law: Evaluating the New York Experience (Washington, D.C.: Association of the Bar of the City of New York and the Drug Abuse Council,

disciplines 66.

to

Daniel

1977).

501

of socioeconomic variables such as higher per capita income, greater labor force participation, and reduced levels of poverty. Nonetheless, there has been no spate of articles in the economic journals on &dquo;Murder and Poverrates

ty&dquo; or &dquo;The Preventive Effect of Higher Incomes.&dquo; There is no National Academy of Sciences panel examining evidence on economic conditions and crime. The debate instead has narrowed to testing alternative forms and levels of punishment. To understand the reasons for this truncation, we would have to consider the tendency of standard economics toward political conservatism.66 A second factor is the development of econometrics in the postwar period with its attendant fetishistic attachment to technique. Finally, interdisciplinary perspectives have been lost from economics, replaced by what Kenneth Boulding characterized as &dquo;economics imperialism&dquo;: &dquo;an attempt on the part of economics to take over all the other social sciences.&dquo;69 The econometric debate has diminished to an implied trade-off between imprisonment and execution. Coupled with hyperindividualized models of criminal activity, this has reinforced what David Gordon identified as &dquo;a prevalent ideology in this society that individuals, rather than institutions, are to blame for social problems.&dquo;’° Too much attention to regression coefficients of punishment variables can foster the illusion that crime control is merely a matter of manipulating selected law enforcement variables. Without more attention to theory, econometric research can only test hypotheses generated by the individual utility maximization framework. It strains the bounds of this theory to Suppose that murders can be conceived of as primarily utility maximization, or as economically &dquo;rational&dquo; in the sense that prospective future outcomes are logically weighed. The murders that might best be described in a utility framework, such as contract murders, represent a small proportion of homicides and are unlikely in any case to be deterred through penalties. A hit man can always raise the price. But evaluation of deterrence research and policy should not abandon insights derived from econometric study. Those insights are better understood through a political economic perspective than through standard microeconomic models of utility maximization. While not denying that many crimes, mostly property offenses, may be understood as economically rational, a political economic perspective also directs attention to patterns of legislation and selective enforcement of laws, and socioeconomic influences which

68. George J. Stigler, "The Politics of Political Economists," Quarterly Journal of Economics, November 1959, pp. 522-32. 69. Kenneth E. Boulding, "Economics as a Moral Science," American Economic Review, March 1969, pp. 1-12. 70. David M. Gordon, "Capitalism, Class, and Crime in America," Crime and Delinquency,

April

1973, p. 182.

502

provide the backdrop for many crimes.&dquo; In the case of homicide, the empirical evidence indicates that poverty and poor economic conditions are systematically related to higher levels of homicide. Rather than focusing on the marginal deterrent effects of execution versus longer prison sentences, political economy dictates examination of the socioeconomic variables. In empirical studies, these have shown larger impacts on homicide than have punishment variables of any sort.72 As this review has demonstrated, exclusive attention to technique can produce results which appear precise and definitive, but this effect evaporates when the studies are considered as a whole. Differences in claims about deterrence from capital punishment are all critically dependent on minor variations in econometric

specification.

several lessons to be learned from the economic debate on capital sanctions and deterrence. First, it is very hard consistently to locate deterrent effects from executions; these findings rest on particular applications of econometric techniques. Second, increased levels of law enforcement sanctions apart from executions seem to have effects on homicide rates. This finding is hard to interpret when coupled with executions’ failure to show a generally significant effect. Third, the criminal justice community should view studies of execution-and empirical studies of crime and deterrence, in general-with considerable caution. Regression coefficients, while potentially informative, can only be interpreted in theoretical and practical contexts which are grounded outside technical debates. And finally, socioeconomic variables have been found to have consistently larger limiting effects on homicide rates than has law enforcement severity. This last finding is of crucial importance for keeping the debate on crime and solutions open. We should not be satisfied with limiting the complex social issues surrounding crime and homicide to a mere selection of alternative punishments. There

are



71. For attempts to develop this perspective as regards crime, see ibid., and articles in Crime and Social Justice. Also missing from the economic work on executions is the whole range of questions about rationales for punishment, equity, and justice-precisely the issues that have engaged most people’s attention and that are unlikely to be solved by any econometric argument. 72. For example, as Peck noted, in Ehrlich’s original study "a one percent change in per capita income or labor force participation has a much greater effect on the homicide rate than does a one percent increase in the use of capital punishment." Peck, "Deterrent Effect of Capital Pun-

ishment,"

p. 367.