# «School of Economics and Political Science, University of St. Gallen Department of Economics Editor: Martina Flockerzi University of St. Gallen School ...»

[32] Similar, but even more astonishing results are presented by R.B. EKELUND et al. (2006), for the period from 1995 to 1999. While the existence of the death penalty raises the murder rate, executions and, in particular electrocutions diminish it. J.J. DONOHUE and J. WOLFERS (2009, p. 271f.) comment this result by noticing that the sheer effect of the existence of the death penalty is rather large and the estimated effect even of the executions by electrocution is – 15 – so small, that many more murderers would have had to be executed than even in Texas in the years considered in order to render the total effect negative, i.e. to get a deterrent effect of the death penalty. A second result of R.B. EKELUND et al. (2006) is that multiple murders are not deterred at all: all coefficients, not only those of the existence of death penalty, but also those of the executions have the ‘wrong’ negative sign, and 15 out of the 16 estimated coefficients are highly significant. While this is compatible with a strong brutalisation effect, the authors explain their results by the fact that there is no deterrence currently for murders after the first one, and, referring to the torture practices of the Middle Ages, they demand that one should think of establishing forms of marginal deterrence in the application of capital punishment.

[33] While these studies (at least implicitly) assume that, aside from what is reflected by the state fixed effects, the effects of capital punishment are identical in all states, J. SHEPHERD (2005) finds different results for different states. She strongly believes in the deterrence effect, but she also takes brutalisation into account. And she also looks for an explanation for the often contradictory results that have been produced. Employing the same data of 3054 counties over the time period from 1977 to 1996 as in H. DEZHBAKHSH, P. RUBIN and J.M. SHEPHERD (2003), she is able to perform separate panel estimates for the different states. According to these results, in six states executions have a deterrent effect, where the number of saved lives per execution runs from 6 in Nevada to 61 in South Carolina. In contrast to this, 13 states show a brutalisation effect, from 3 additional murders in Oklahoma to 175 in Utah and Oregon. In the remaining eight states implementing the death penalty, there is no significant effect. She gets similar results using monthly state-level data from 1977 to 1999; there are six states with a deterrent effect and eight states with a brutalisation effect, while the remaining 13 states do not show any significant effect. Using state-level annual data the number of states with a significant effect is even smaller; there are five states with a significant deterrence and another five states with a significant brutalisation effect.

[34] The solution she suggests for this puzzle is a threshold effect: brutalisation as well as deterrence are effective. Deterrence is, however, nonlinear; a certain number of executions is necessary for it to become relevant, because the marginal deterrence effect increases with the number of executions. If there are only rather few executions in a state, the brutalization effect dominates, if there are some more, both effects cancel each other, and if there were more than about 9 executions in the observation period, deterrence dominates. Actually, she shows that those states with a significant deterrence effect had, at the 90 percent confidence level, significantly more executions than the remaining states implementing the death penalty.

[35] Another differentiation was undertaken by M. FRAKES and M. HARDING (2009). They ask for the effect of extending the death penalty eligibility to murders of youth victims and find a significant deterrent effect. They find a similar, but much less significant effect for the eligibility of multiple victim murders, and insignificant, but numerically large effects with the ‘wrong’ sign for narcotic related murders and those with victims over 70 years of age. They do not, however, find a general deterrent effect of capital punishment. Thus, their results are rather mixed.

[36] Aside from the critique in J.J. DONOHUE and J. WOLFERS (2005) and the papers by J.

FAGAN and his co-authors, there are also other papers which do not find a significant deter 16 – rence effect. Using state-level data, L. KATZ, S.D. LEVITT and E. SHUSTOROVICH (2003) estimate a linear model of the murder rate between 1950 and 1990. They present 22 t-statistics for their deterrence variable with a mean of -0.20 and a standard deviation of 1.42. A similar

**result is presented by J.R. LOTT and J. WHITLEY (2007). Using state-level data from the period from 1976 to 1998 and applying Poisson and Negative Binomial regressions, their intention is to show that legalised abortion increased crime. A by-product of their attempt is, however, the result that the execution rate does not have a significant impact on the murder rate:**

the 5 corresponding t-statistics have a mean of -0.05 and a standard deviation of 0.24. Finally, T. KOVANDZIC, L.M. VIERAITIS and D.P. BOOTS (2009), using state level data from 1977 to 2006 and employing fourteen different statistical models and seven different indicators of the deterrence effect, present altogether 98 estimated coefficients out of which only four are statistically different from zero at the 5 percent level. The average t-statistic of their models is

-0.558 with a standard deviation of 0.999.29).4

[37] Figure 6 shows the distributions of the t-statistics of the three groups. The results differ widely, and it is rather difficult to draw firm conclusions. Taking all results together, the only – admittedly weak – indication for the existence of a deterrence effect of death penalty is the fact that the mean of the reported t-statistics is negative even in those papers coming to the conclusion that executions are non-deterring.30) The only papers with positive means are by J.

SHEPHERD (2005) and, despite that they believe in the deterrence effect, by R.B. EKELUND et

29. R. HJALMARSSON (2009) who uses daily time-series data for 1999 to 2004 for three Texas cities, Houston, Dallas and San Antonio, does not find a ‘local effect’ of executions on homicides.

30. The mean of these t-statistics is -0.780 with a standard deviation of 5.710. The mean of the t-statistics in those studies claiming a significant deterrence effects is -2.879 with a standard deviation of 2.703. See also the summary of the t-statistics in Table A1 of the Appendix.

– 17 – al. (2006). If the true value would be zero, we should more often observe a (non-significant) positive mean, in particular in those studies denying a deterrent effect.

[38] Despite the fact that the econometric techniques employed in these studies are much more advanced than those in the first two waves, serious methodological problems remain.

First of all, there are still serious data problems. The results are heavily dependent on measures of the deterrence variable as, for example, the rather different results employing the H.N.

MOCAN and R.K. GITTINGS (2003) data show. Moreover, as J. FAGAN, F.E. ZIMRING and A.

GELLER (2006) show, the correct specification of the dependent variable is also a major problem. The functional form of the equation does not, on the other hand, seem to be a major problem: those studies that employ log-linear instead of linear specifications do not produce consistently different results.

[39] There are, however, other serious econometric problems that have only been considered in some of the studies and at least were not always solved convincingly. One of the major problems is simultaneity. Potential offenders might choose from a portfolio of different criminal acts. Thus, a system of equations containing a separate equation for every punishable act would be appropriate. If only one equation, i.e. the one for murder rates, is estimated, the usual cure is to employ instrumental variable estimates. However, as several studies show, the question which variables are well suited for being an instrument is highly debatable, and the results are largely dependent on the instruments used.

[40] Another major problem in this respect is the possible instantaneous and/or feedback relation between murders and executions; executions might not only have an effect on murder rates but murder rates also on executions. In the time domain, this might not be considered as being an important problem because, if they have any impact, murder rates should have a positive effect on executions. Thus, not taking this into account might downward bias the estimated coefficients of the deterrence variables and their t-statistics. The considerable increase of the estimated parameters in the model of P.R. ZIMMERMANN (2006) by switching from OLS to TSLS might point in this direction.

[41] There is, however, another problem in this respect. All panel studies use state (or county) fixed effects. Thus, different average levels of murder rates between the states are not explained but represented by dummy variables. Thus, all that can be explained by these regressions are reactions over time. The more interesting question as to whether states with the death penalty have in the long-run higher or lower murder rates than those that do not execute cannot be answered by these models. Given the fact mentioned above that those states without the death penalty have consistently lower murder rates than those with, this is a serious problem. Because even if an increase of executions deters murderers in the short-run, there might be a long-run brutalisation effect that is not reflected in the models. Thus, we have again a serious simultaneity problem: states might have less need for the death penalty if their murder rate is lower, but fewer executions might also lead to less brutalisation.

[42] Attempts in this direction have been done by investigating the effect of the moratorium or its lifting in 1976, respectively. Several studies take this into account, partly by introducing dummy variables for the existence of a death penalty statute and partly by considering the re 18 – introduction of the death penalty in different states as natural experiments. However, the results of those studies are also far from being univocal. H. DEZHBAKHSH and J.M. SHEPHERD (2006) find that the abolition of the death penalty was associated with an increase while its reintroduction led to a (smaller) decrease of homicides, but J.J. DONOHUE and J. WOLFERS (2005) using a difference-in-difference approach do not find any evidence in this respect.

Moreover, DEZHBAKHSH and J.M. SHEPHERD (2006) find a significant positive effect of the moratorium on murder rates in their state-panel date regression results, while the results of J.

FAGAN, F.E. ZIMRING and A. GELLER (2006) mentioned above do not point in this direction.

Finally, J.K. COCHRANE and M.B. CHAMLIN (2000) investigate the effects of re-introducing capital punishment in California in 1992. Using an ARIMA-approach they find “a significant decline in the level of non-stranger felony-murders and a significant increase of argumentbased murders of strangers in the period following the [first] execution” (p. 685) on April 21 and, therefore, a deterrence as well as a brutalisation effect. But while the brutalisation effect remained permanent and was even increasing over time, the deterrent effect declined over time and appeared, therefore, “to be contingent on an additional, perhaps continuous application” (p. 701) of the death penalty. Nevertheless, the net effect of executions on homicide was zero.31)

**4 Concluding Remarks**

[43] A critical and cautious examination of these results leads to the conviction that we cannot draw any strong conclusions. While there is some evidence that a deterrent effect might exist, it is too fragile to be certain. Furthermore, the possible quantitative effect usually measured by the number of homicides prevented by each execution is so uncertain that it is difficult to conclude anything that would be relevant for policy purposes.32) Of course, defenders of the death penalty as G.S. BECKER (2006) or R.A. POSNER (2006) will still insist that the econometric evidence is strong enough to justify the belief in a considerable deterrence effect, even if they admit that the evidence is far from being perfect.33) Those who consider the death

31. A similar study is performed by W.C. BAILEY (1998) (with reference to J.K. COCHRANE, M.B. CHAMLIN and M. SETH (1994)) to investigate the effects of the re-introduction of capital punishment in Oklahoma in