Using Electoral Cycles in Police Hiring to Estimate the Effect of Police on Crime: Comment

In an in uential paper in the June 1997 American Economic Review, Steven Levitt argues that there is an electoral cycle in police hiring, with faster hiring in election years and slower hiring in other years. He then uses elections as an instrument for police hiring to estimate the causal effect of police on crime. This comment points out that a weighting error in Levitt’s estimation procedure led to incorrect inferences for the key results of the paper. Levitt presents a series of regression models explaining changes in crime rates in different cities over time, including ordinary least squares (OLS) and two-stage least squares (2SLS) speciŽ cations. He draws two main conclusions. First, police substantially reduce violent crime, but have a smaller effect on property crime. Second, 2SLS estimates are consistently more negative than OLS estimates. Levitt’s 2SLS results for violent crime are driven by a large, apparently precise estimate of the effect of police on murder. This is surprising since among the seven categories of crime considered, murder exhibits the greatest year-toyear variability. It turns out that the precision of the murder estimate is due to a weighting error. The weighting procedure was designed to give relatively more weight to crimes with lower year-to-year variability. However, an error in Levitt’s computer program accomplished exactly the opposite, giving highly variable crimes the most weight in the estimation, and severely biasing all standard errors. To demonstrate the substantive implications of this error, I present replication estimates that use the correct (and intended) weighting scheme. When weights are employed correctly, the data support neither of Levitt’s main conclusions. First, correctly weighted 2SLS estimates show no signiŽ cant effect of police on any of the crime categories under consideration. Pooled 2SLS estimates for violent crime (the estimates that Levitt emphasized in his discussion and that are cited in the literature) are half the published magnitude and statistically indistinguishable from zero. Pooled 2SLS property crime estimates, while more precise when correctly weighted than when not, are also indistinct from zero. Second, 2SLS estimates are sometimes more negative and sometimes more positive than the OLS estimates, and the two are never statistically distinguishable when correctly weighted. The weighting error arose in the attempt to gain efŽ ciency. Since covariates and instruments are the same for all crime categories, estimation separately for each crime category is best, barring coefŽ cient restrictions across crime categories (Arnold Zellner, 1962 p. 351). If the estimation were performed separately for each crime category, then no weighting would be necessary. However, Levitt imposes coefŽ cient restrictions across crime categories throughout , necessitating joint estimation. Analyzed separately, the largest 2SLS t ratio is 1.4. When analyzed jointly and weighted correctly, the largest 2SLS t ratio is 1.5. Analyzed jointly and weighted incorrectly, the largest 2SLS t ratio increases to 3.4. In the spirit of replication, I attempted recollection of each series used in Levitt. For the most part, the data replication effort was successful. The primary correction I report is to