Null by Design: Statistical Dilution in Immigration-Crime Research

Recent research documents that many research designs in the social sciences are underpowered: they can only detect extremely large -- often implausible -- effects. I show that this problem is structural in the workhorse approach to studying the immigration-crime link: regressing changes in aggregate crime rates on exogenous shifts in local immigrant shares. Because immigrants typically comprise only a small fraction of the population, even large crime-rate differences between immigrants and natives are mechanically diluted. As a result, null findings from such designs are predetermined and reveal little to no information about immigrant-native crime differentials. I derive a closed-form expression for the minimum detectable gap -- the smallest immigrant-native crime difference these regressions can identify. Using Monte Carlo simulations calibrated to real-world immigration and crime data, I then demonstrate that conventional designs only achieve adequate statistical power with implausibly large crime differentials and extreme immigration shocks.