Police, Crime and the Problem of Weak Instruments: Revisiting the “More Police, Less Crime” Thesis

Objectives. A key question in the general deterrence literature has been the extent to which the police reduce crime. Definitive answers to this statement, however, are difficult to come by because while more police may reduce crime, higher crime rates may also increase police levels, by triggering the hiring of more police. One way to help overcome this problem is through the use of instrumental variables (IV). Levitt, for example, has employed instrumental variables regression procedures, using mayoral and gubernatorial election cycles and firefighter hiring as instruments for police strength, to address the potential endogeneity of police levels in structural equations of crime due to simultaneity bias. Methods. We assess the validity and reliability of the instruments used by Levitt for police hiring using recently-developed specification tests for instruments. We apply these tests to both Levitt’s original panel dataset of 59 US cities covering the period 1970–1992 and an extended version of the panel with data through 2008. Results. Results indicate that election cycles and firefighter hiring are “weak instruments”—weak predictors of police growth that, if used as instruments in an IV estimation, are prone to result in an unreliable estimate of the impact of police levels on crime. Conclusions. Levitt’s preferred instruments for police levels—mayoral and gubernatorial election cycles and firefighter hiring—are weak instruments by current econometric standards and thus cannot be used to address the potential endogeneity of police in crime equations.