Null by Design: Statistical Dilution in Immigration-Crime Research

Recent research documents that many research designs in the social sciences are underpowered: they can detect only 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. While this design may identify changes in native criminal behavior, I demonstrate that it is largely uninformative regarding the difference in crime propensities between immigrants and natives. Because immigrants typically comprise a small fraction of the population, even large group-level differences are mechanically diluted. I formalize the minimum detectable gap - the smallest immigrant-native crime difference these regressions can reliably distinguish from zero given standard design parameters. Using Monte Carlo simulations calibrated to real-world immigration and crime data, I demonstrate that conventional designs only achieve adequate statistical power with implausibly large crime differentials and extreme immigration shocks.