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Econometric Estimates of Deterrence of
the Death Penalty: Facts or Ideology
April 2011 Discussion Paper no. 2011-15
School of Economics and Political Science, University of St. Gallen
Department of Economics
Editor: Martina Flockerzi
University of St. Gallen
School of Economics and Political Science
Department of Economics
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Econometric Estimates of Deterrence of the Death Penalty:
Facts or Ideology1 Gebhard Kirchgässner2 Author’s address: Prof. Dr. Gebhard Kirchgässner SIAW-HSG Bodanstrasse 8 Phone +41 71 224 23 40 Fax +41 71 224 22 98 Email firstname.lastname@example.org Website www.siaw.unisg.ch Revised Version, April 2011. A previous version has been presented at the Workshop on “Beyond the Economics of Crime”, University of Heidelberg, March 20, 2009. I thank Berit Gerritzen for research assistance. – Forthcoming in: Kyklos 64 (2011).
University of St. Gallen, Swiss Institute for International Economics and Applied Economic Research, Leopoldina and CESifo.
Abstract In 2007, the Wall Street Journal published an article claiming that each execution saves more than 70 lives. This example is used to show how easy it is, using simple or advanced econometric techniques, to produce results that do or do not support the deterrence hypothesis. Moreover, we also point to some puzzles which have not been satisfactorily solved so far. We then present a critical survey of the papers published in the last ten years.
It is shown how simple changes can produce quite different results using the same data.
Finally, we draw some conclusions about the usefulness of statistical arguments in policy debates, but also on the moral questions involved in this particular debate.
Keywords Death Penalty, Deterrence, Econometric Evidence, Ideology.
JEL Classification K14; K42 1 Introduction  On November 2, 2007, R.D. ADLER and M. SUMMERS published an article in the Wall Street Journal with the title “Capital Punishment Works”.1) With reference to the diagram in Figure 1 below, they state that over the period considered, from 1979 to 2004, “each execution seems to be associated with 71 fewer murders in the year the execution took place”, and that this association was significant at the 0.05 percent level. Acknowledging that there might be a problem of causality because some murders took place in the years of observation before the executions, they lagged the executions’ variable and got an even stronger result: “Each execution was associated with 74 fewer murders the following year”, statistically significant even at the 0.03 percent level. Their defence of the death penalty ended in the following (rhetorical) question: “Do we save this particular life at the cost of the lives of dozens of future murder victims?”
Figure 1: Executions and homicides, U.S.A., 1979 – 2004
 Aside from this figure, the two authors do not provide any information about how they derive these results. As will be shown below, these are results of OLS regressions that are insufficient according to any standard of conventional econometric techniques. This is the more astonishing as, during recent years, there has been a rather intense debate on this issue, and questions of the appropriate econometric methodology played a major part in this debate.2) Neither of these two authors participated in it. Moreover, the second author, M. SUMhttp://online.wsj.com/article_email/SB119397079767680173-lMyQjAxMDE3OTAzMjkwNzIwWj.html (10/03/09).
2. See, for example, H. DEZHBAKHSH, P. RUBIN and J.M. SHEPHERD (2003), J.J. DONOHUE and J. WOLFERS (2005, 2009), L. KATZ, S.D. LEVITT and E. SHUSTOROVICH (2003), H.N. MOCAN and R.K. GITTINGS (2003), J.M. SHEPHERD (2004, 2005), P.R. ZIMMERMANN (2004, 2006, 2009), as well as the discussion in Economists' Voice, issue 3/5 (April 2006) between J.J. DONOHUE and J. WOLFERS (2006, 2006a) and P.H.
RUBIN (2006, 2006a).
–2– is said to be a professor of quantitative methods.3) But without taking any methodologiMERS, cal problems into account and neglecting all that has been written before, publishing such a paper in the Wall Street Journal might be a better way to get a large audience and corresponding response from the general public than having scientific scruples.
 The ‘economic’ discussion about the possible deterrent effect of the death penalty started with the seminal paper by I. EHRLICH (1975), which itself was a response to a famous book by T. SELLIN (1959). Both used quite different statistical approaches.4) And while T. SELLIN (1959) did not find a significant effect, I. EHRLICH (1975), using a time series of annual data from 1933 to 1967, found a “pure deterrent effect” and concluded that “on average the tradeoff between the execution of an offender and the lives of potential victims it might have saved was of the order of magnitude of 1 for 8” (p. 398) for this observation period.
 This paper was the starting point for a huge debate in the late seventies and eighties. S.
CAMERON (1994, p. 197f.) speaks of two generations of papers, the first one published between 1975 and 1978, i.e. around the time when the moratorium on capital punishment was lifted in the United States, and the second one after 1982, covering the time after the moratorium. The data used were partly time series, and partly cross section data, and all but a few studies, which looked at Canada or the United Kingdom, used U.S. data.5) The results are rather mixed. In particular, they proved the fragility of the results of I. EHRLICH (1975) with respect to the specification of the test equation as well as the time period employed. Thus, while the overall results do not support his conclusion, they also do not give strong support to the opposite hypothesis. All that can be said is that the empirical evidence provided in this research does not lead to any strong conclusion.6)  In recent years, a third generation of papers has been published on this topic.7) The main difference to the first two waves is that now panel data are used, mostly for the U.S. states, but partly also for U.S. counties.8) This allows to distinguish between those states with and those without the death penalty, i.e. it avoids an aggregation bias when using time series data resulting from mixing these two categories, which might bias the estimated coefficients (and t-statistics) downwards. It can also take into account unobserved heterogeneity between the states which is not allowed for when using cross-section data. The use of state (or county) fixed effects to take account of this unobserved heterogeneity might, on the other hand, also create a bias.
3. Actually, he is Professor of Management Science at Pepperdine University, but is also teaching statistics and quantitative methods.
4. For a comparison of the two approaches see, for example, D.C. BALDUS and J.W. COLE (1975).
5. Studies for Canada are, for example, K.L. AVIO (1979) or S. LAYSON (1983), studies for the United Kingdom are K.I. WOLPIN (1978, 1978a).
6. For an overview of these results see, for example, the two surveys by S. CAMERON (1988, 1994).
7. See the literature mentioned in Footnote 2 above and discussed in Section 3 of this paper.
8. In recent years, there are only few studies using cross-section of time series data. See, for example, P.K.
NARAYAN and R. SMYTH (2006) or R. HJALMARSSON (2009).
–3–  The results of this recent debate are, again, rather mixed. The old divide between the faculties which already characterised the earlier debates remains; while most (or perhaps nearly all) (U.S.) economists believe in the validity of the deterrence hypothesis and present corresponding results, most, but not all, scientists from other faculties, in particular law, have serious doubts on its validity and demonstrate the fragility of the results presented by economists.
However, contrary to earlier discussions, the econometric methods used are the same: Today, non-economists are able to use the same advanced statistical techniques equally well as economists. Correspondingly, some of the discussions are about methodological problems, especially on the reliability of the data and the quality of the instruments used in instrumental variables estimations.
 The debate about the deterrence effect is, however, just one of three such debates in the United States, where mainly ideology seems to drive the empirical results. The second one is about gun prevalence and homicides,9) a discussion that is also relevant to Switzerland.10) The third one is whether legalised abortion reduced crime.11) All three debates are highly politicised, and one could get the impression that in all three debates the authors mainly try to find scientific arguments to support their political convictions. This is not illegitimate, but it can easily lead to selective perceptions of the reality.
 One can really gain the impression that the economics of crime and the question whether death penalty deters murders or not is just a romping place for ideologists. However, that prior beliefs might have an impact on the reported results on the deterrent effect of death penalty has already been discussed by W.S. MCMANUS (1985). This does not imply that authors are necessarily shirking; it might simply be the result of selective perceptions: if contradictory results can be derived, authors choose those in the validity of which they are convinced a priori and are looking for strong arguments in order to support these results.
 In the following, we first take the data and methodology used by R.D. ADLER and M.
SUMMERS mentioned above and show how easy it is to produce contradictory results (Section 2). From a methodological point of view, this goes even beyond what I. EHRLICH (1975) did when starting the economic discussion about this topic. However, due to the publication in the Wall Street Journal, the results of these two authors did get a far wider audience in the general public than those of all other authors, and the simplicity of this approach makes it very easy to demonstrate the possibility of manipulations that are equally possible if we would employ more advanced techniques. Moreover, in this section we also point to some puzzles in
9. See, for example, I. AYRES and J.J. DONOHUE (2003, 2003a, 2009, 2009a), P.J. COOK and J. LUDWIG (2006), M. DUGGAN (2001), T. KOVANDZIC, M.E. SCHAFFER and G. KLECK (2008), F. PLASSMANN and J.
WHITLEY (2003), C. MOODY and TH.B. MARVELL (2008, 2009) or L. STOLZENBERG and S.J. D’ALESSIO (2000).
10. In Switzerland, people serving in the army usually have their military guns or handguns at home even after they have definitely finished their military service. However, a considerable proportion of homicides and suicides are performed by using these weapons, and – in international comparison – Switzerland has a relatively high rate of gun suicides and homicides. Nevertheless, in February 2011, a popular initiative to severely restrict having military guns at home failed.
11. See, for example, J.J. DONOHUE and S. LEVITT (2001, 2004, 2008), C.L. FOOT and C.F. GOETZ (2008), T.
JOYCE (2004, 2009, 2009a) and J.R. LOTT and J. WHITLEY (2007).