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Deterrence and the Death Penalty (2012) / Chapter Skim
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5 Time-Series Studies
Pages 75-100

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From page 75...
... • Second, time-series studies generally examine the association be tween execution events and homicides; panel studies generally mea sure the association of homicide rates with ratios that are intended to measure the probability of execution.
From page 76...
... Perhaps the most important difference among time-series studies is the number of execution events ex amined. Some time-series research focuses on the effect of a single execution event, and other studies combine data on many execu tion events and analyze their temporal association with homicide rates in a single statistical model.
From page 77...
... The problem of generalizing from the findings of even a convincing event study is indicative of still another fundamental committee concern with all the time-series studies. The researchers who carry out such studies never clearly specify why potential murderers respond to execution events.
From page 78...
... Over the period, this correlation is –0.68. However, there are innumerable obvious objec tions to interpreting this negative association as deterrence because many factors that influence the homicide rate were also changing over this time period.
From page 79...
... . As a consequence the time-series studies analyze the association between deviations from statistical trend lines that summarizes the execution time series and the homicide rate time series As an illustration, consider again Figures 5-1 and 5-2.
From page 80...
... reports that, even in deviation form, the execution and publicity time series were highly correlated. A more fundamental concern is that execution event studies do not clearly specify why potential murderers respond to execution events.
From page 81...
... If time-series analysis finds that homicide rates are responsive to such deviations, the question is why? One possibility is that potential murderers interpret a deviation as new information about the intensity of the application of capital punishment -- that is, that the deviation signals a change in the part of the sanction regime that relates to the application of capital punishment.
From page 82...
... Hence, the committee has no basis for assessing whether the findings of time-series studies reflect a real effect of executions on homicides or are artifacts of models that incorrectly specify how deviations cause potential murderers to update their forecasts of the future course of executions. VECTOR AUTOREGRESSIONS Evidence Under Existing Criminal Sanction Regimes One methodology used in time-series studies of deterrence is known as vector autoregressions (VARs)
From page 83...
... In studies of the deterrent effect of capital punishment, systems such as (5-1) have focused on the coefficients b1, b2,…, which relate lagged levels of execution rates to the time t homicide rate.
From page 84...
... The absence of Granger causality does not imply that a counterfactual change in executions because of a change in the sanction regime facing potential murderers would fail to generate changes in homicides at later dates. Despite the fact that Granger causality is only a statistical concept, findings on the statistical question of whether executions Granger-cause homicides have been used to make substantive claims about the deterrent effect of capital punishment.
From page 85...
... Neither asks what conclusions about deterrence can be drawn when one does not assume a particular time-series specification or when one allows for different deterrent effects in different time periods. Neither the time-series specification nor the appropriate data range are known a priori to a researcher.
From page 86...
... Put simply, the rational-criminal model places no restrictions on the presence or absence of Granger causality from executions to homicides. The reason the model does not imply such time-series restrictions on the relationship between executions and homicides is not a function of its specific rationality assumptions; rather, the central point is that the rationalcriminal model supposes that individual beliefs about sanctions risks derive from their perception of the criminal sanction regime in which they live, not from the occurrence of executions per se.
From page 87...
... It follows that an empirical finding of no Granger causality does not necessarily imply the absence of a deterrence effect to capital punishment. Furthermore, if the candidate explanations for criminal behavior are either that criminals are not subject to deterrent effects or that potential murderers obey a rational model of criminal behavior, then Granger causality from executions to homicides does not necessarily provide support for the deterrence explanation.
From page 88...
... Under the rational-criminal model, one can potentially connect execution events to behavior if one discards the specific assumption of rational expectations and instead supposes that people use data on the occurrence of executions to update their subjective beliefs about the sanction regime in which they live. Suggestions of such updating appear in the some studies, but the committee is unaware of any formal model of beliefs and behavior that make tests of Granger causality that have interpretable implications for deterrence.
From page 89...
... A distinct question concerns the capacity of atheoretical time-series methods in general and Granger causality tests in particular to provide information on the deterrent effect of capital punishment under alternative sanction regimes from those that have existed and currently exist in the United States. As described elsewhere in this report, the historical capital punishment regime is one in which executions are very infrequent in comparison with the numbers of homicides.
From page 90...
... He found a statistically significant difference between homicide rates in the week prior to an execution and the week after an execution. A more detailed analysis found that this reduction was subsequently reversed, so that homicides were displaced in time rather than reduced.
From page 91...
... In that situation, the data would tend to show lower homicide rates in the week after executions than in the week before simply because the week after occurs later than the week before. Without a full specification of the properties of the total homicide process, one cannot understand the effects of individual executions.
From page 92...
... TIME-SERIES REGRESSIONS Another strand of the literature estimates time-series regressions that relate homicide rates or levels to executions and other covariates. Although VARs are also time-series regressions, the work discussed in this section differs in several respects from the work discussed above.
From page 93...
... Other regressions, in which statistical significance fails, are not accounted for in the author's strong conclusions. As noted in Chapter 4, a finding that an estimate is statistically insignificant does not imply that the true deterrent effect is zero or even that it is small.
From page 94...
... The various studies that use this methodology assert that all such factors are incorporated in the coefficient b, but there is no reason to believe that this is true. Because CAPM is predicated on investors' optimally investing in financial instruments in the context of competitive markets for these products, for Cloninger's specification to be sensible he would have to demonstrate that potential murderers engage in an analogous optimization problem that is aggregated to produce state-level homicide rates.
From page 95...
... study is to see whether differences in the Singapore and Hong Kong homicide rates can be explained by execution rates in Singapore, none having occurred in Hong Kong over the time frame of the analysis. Letting hS,t denote the Singapore homicide rate in year t and hHK,t the Hong Kong homicide rate in year t, the paper examines whether hS,t – hHK,t, once trends are accounted for, is associated with either the execution rate for Singapore or the execution level in Singapore.
From page 96...
... A distinct reason that this study is not informative about the deterrent effect of capital punishment is that the key assumption underlying the analysis -- that any systematic or predictable component of the homicide rate difference, hHK,t – hS,t, can only be due to capital punishment -- is not credible. The paper's own regressions lead inevitably to this conclusion.
From page 97...
... CONCLUSIONS The committee analysis of the different strategies for using time series to uncover deterrent effects for capital punishment has consistently found the inferential claims to be flawed, whether the study in question does or does not find evidence of a deterrence effect. A common theme in our critiques of individual studies is that the underlying "decision theory" of potential murderers is consistently un- or underspecified, so that the implications of the time-series relationships between executions and homicide rates is unclear.
From page 98...
... Yet because of the state's high fraction of executions nationally, Texas data are frequently used for studies. Texas might have experienced changes in the execution sanction regime, which would be useful for identifying deterrent effects, but this perspective has not been systematically explored, despite some occasional references to regime shifts in Texas.9 In this respect, we think that the focus on Texas in the time-series literature may be misguided.
From page 99...
... It is thus immaterial whether the studies purport to find evidence in favor or against deterrence. They do not rise to the level of credible evidence on the deterrent effect of capital punishment as a determinant of aggregate homicide rates and are not useful in evaluating capital punishment as a public policy.
From page 100...
... . The deterrent effect of capital punishment: New evidence on an old controversy.


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