Specifying the Relationship Between Crime and Prisons

There is no scholarly consensus as to the proper functional form of the crime equation, particularly with regard to one critical, explanatory variable—prison population. The critical questions are whether crime and prison rates must be differenced, whether they are cointegrated, and whether they are simultaneously determined—whether crime and prison cause one another. To determine the proper specification, different researchers have applied unit-root, cointegration, and Granger tests to very similar data sets and obtained very different results. This has led to very different specifications and predictably different implications for public policy. These differences are more likely to be due to the methods used, rather than to real differences among the data sets. When the best available methods are used to identify the proper specification for a panel of U.S. states, results are fairly clear. Crime rates and prison populations are close to unit-root; crime and prison are not cointegrated; crime clearly affects subsequent prison populations. Thus the best specification of the crime equation must rely on differenced data and instrumental variables. Alternative specifications run a substantial risk of spurious results.