Understanding Crime Trends Workshop Report (2008) / Chapter Skim
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7 On the Use of Aggregate Crime Regressions in Policy Evaluation--Steven N. Durlauf, Salvador Navarro, and David A. Rivers
7 On the Use of Aggregate Crime Regressions in Policy Evaluation--Steven N. Durlauf, Salvador Navarro, and David A. Rivers
Pages 211-242
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Rivers Despite recent efforts to employ microeconomic data and natural experiments, aggregate crime regressions continue to play a significant role in criminological analyses. One use of these regressions is predictive, as illustrated by the papers in this volume that employ aggregate crime trends regressions -- Baumer (Chapter 5)
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We then apply our general arguments to areas in the empirical criminology literature: the convergence of crime rates, capital punishment, and shall-issue concealed weapons laws. The next section discusses whether the limitations that exist in using crime regressions mean that they should be replaced by quasi-experimental methods, and a final section concludes the chapter.
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Their behavior is forward looking, and it is also assumed to be consistent over time. In particular they try as best they can to anticipate the consequences of their actions." To see how crime choice may be formally described, we follow the standard binary choice model of economics.
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(4) This conditional probability structure captures the microfoundations of the economic model we wish to study.
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from choice-based foundations illustrates how standard aggregate crime regressions require a number of statistical assumptions if they are to be interpreted as aggregations of individual behavior. The assumption of a uniform density for the individual specific heterogeneity is of concern; in order to ensure that the probabilities of each choice are bounded between 0 and 1, the support of the uniform density may need to be agent-specific. Unfortunately, other random utility speci See Aldrich and Nelson (1984, Chapter 1)
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i ,t l ,t i ,t l ,t l ,t ) the various payoff components but will not produce a closed form solution for the aggregate crime rate.
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MODEL UNCERTAINTY Our derivation of aggregate crime rates from microfoundations assumed that the researcher had strong prior information about the individual decision process. Put differently, our derivation of an aggregate crime regression
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These categories are meant to identify general types of model uncertainty that are common in social science analyses. At the same time, our decomposition of model uncertainty is not unique; one can well imagine alternative divisions.
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Specifically, Black and Nagin (1998) found that the use of quadratic time trends in place of state-specific linear time trends eliminates the evidence of a link between liberalization of concealed weapons laws and crime rates found in Lott and Mustard (1997)
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Exchangeability, roughly speaking, captures the idea that observations, such as state-specific crime rates, may be treated as draws from a common statistical process. One example of sensitivity of empirical claims to assumptions about parameter heterogeneity is again found in the controversy between Black and Nagin and Mustard and Lott.
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. An application to a crime context, the deterrent effect of capital punishment, is Cohen-Cole et al.
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For example, Horowitz argues that in order to use cross-county data to evaluate the average effect of shall-issue laws, if there are differences between the states, so that the crime rate in a county is determined by some set of factors X, then in order to identify the effect of the laws "one must use a set that consists of just the right variables and, in general, no extra ones." But as shown in Heckman and Navarro (2004) , this is true only for a particular set of empirical strategies known as matching, of which linear regression is a special case.
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POLICY-RELEVANT CALCULATIONS Basic Ideas In this section, we explicitly consider the relationship between statistical models and policy evaluation from a decision-theoretic perspective. The fact that statistical significance levels do not equate to policy statements is well known (see Goldberger, 1991, for a nice discussion)
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report. Model Averaging and Policy Evaluation When model uncertainty is present, the optimal policy calculation equation (13)
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Unlike the case of the social scientist, the model has no intrinsic interest to a policy maker; it is simply an additional source of uncertainty in the effects of a policy. Beyond Model Averaging Once model uncertainty is involved in policy evaluation, new considerations can arise.
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APPLICATIONS TO CRIMINOLOGY ISSUES In this section, we apply some of our general arguments to current controversies in criminology. Convergence in Crime Rates A first example in which more careful attention is needed to the determinants of aggregate crime regressions involves efforts to evaluate convergence among aggregate crime rates.
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If one considers the determinants of female crime rates, there is no reason to believe that the changes between 1960 and 1975 are simply another draw from the same process generating the changes between 1975 and 1990. Similarly, LaFree's evaluation of convergence between industrializing poor nations and industrialized rich ones assumes that intracountry homicide rate changes are generated by a second-order stationary process.
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O'Brien is relatively circumspect in interpreting his results, but even his speculations on how to explain the finding of no convergence in homicide with convergence in other crimes are not justifiable, since without a theory as to why unconditional convergence is to be expected, there are so many ways to differentiate the experiences of men and women that it is not clear whether there is a fact to be explained. As for LaFree, if there are factors outside the modernization process that determine crime rates -- and obvious candidates include socioeconomic factors, such as levels of unemployment and inequality, demography, and differences in national criminal justice systems -- then the absence of unconditional convergence does not speak to the empirical relevance of modernization or any other theory considered in isolation.
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Microfoundations From the perspective of our first argument, that aggregate models should flow from aggregation of individual behavioral equations, the Dezhbakhsh, Rubin, and Shepherd specification can be shown to be flawed. Specifically, the way in which probabilities are used does not correspond to the probabilities that arise in the appropriate decision problem.
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The decision to commit a homicide, under the economic model of crime, depends on the entire range of penalties and their associated probabilities. Changes in the rates at which murderers are sentenced to life imprisonment without parole, for example, are not accounted for by Dezhbakhsh, Rubin, and Shepherd or, as far as we know, any other capital punishment deter
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, then it is no longer clear what it means to say that a Dezhbakhsh, Rubin, and Shepherd-type regression provides evidence on the effects of capital punishment. Does an increase in long prison sentences because of death sentences followed by reversals correspond to what is understood to be the deterrent effect of capital punishment?
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argue that evidence of a deterrent effect can produce a moral case for capital punishment, in that the decision of a government to fail to implement a life-saving policy is equivalent to the decision to implement a policy that costs lives. Sunstein and Vermeule (2005)
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Rather, our claim is that the policy implications of the uncertainty associated with deterrence effects cannot be assessed outside of the policy maker's preferences. Right-to-Carry Laws and Crime: Firearms and Violence Revisited Our third example is the controversy over the effects of shall-issue concealed weapons laws in the National Academies report Firearms and Violence (National Research Council, 2005)
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The disagreement between Wilson and the rest of the National Academies committee reflects the absence in the report of an explicit evaluation of how model uncertainty interacts with evidence of shall-issue laws. While the assertion that it is impossible to statistically identify the correct specification of a statistical model is true at some level of generality (although the report is frankly unclear on what is meant by this)
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One answer to our advocacy of model averaging as a tool to address model uncertainty of the type facing the National Academies committee is that a given body of empirical studies captures only a small fraction of the universe of potential models (and indeed might represent a measure 0 set)
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And we do not know, given our priors, how the relative goodness of fit of the different models analyzed in the National Academies report would translate into different posterior model probabilities. Our discussion of the assumptions that underlie the interpretation of aggregate crime regressions may all be interpreted as examples for H orowitz's arguments about the limitations of regression analysis of crime.
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Overall, we do not see good reasons to regard natural experiments as superior to regressions with observational data in terms of their relative utility as means of understanding crime.10 It is straightforward to construct examples in which one methodology can provide insights that the other does not. Each has a contribution to make in criminological research.
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. Econometric evaluation of social programs, part III: Distributional treatment effects, dynamic treatment effects, dynamic discrete choice, and general equilibrium policy evaluation.
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. Model uncertainty and policy evaluation: Some theory and empirics.
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. The effect of prison population size on crime rates: Evidence from prison overcrowding litigation.
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. Is capital punishment morally required?
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