Clustering and Standard Error Bias in Fixed Effects Panel Data Regressions

Abstract

We address several issues concerning standard error bias in pooled time-series cross-section regressions. These include autocorrelation, problems with unit root tests, nonstationarity in levels regressions, and problems with clustered standard errors. We conduct unit root test for crimes and other variables. We use Monte Carlo procedures to illustrate the standard error biases caused by the above issues in pooled studies. We replicate prior research that uses clustered standard errors with difference-in-differences regressions and only a small number of policy changes. Standard error biases in the presence of autocorrelation are substantial when standard errors are not clustered. Importantly, clustering greatly mitigates bias resulting from the use of nonstationary variables in levels regressions, although in some circumstances clustering can fail to correct for standard error biases due to other reasons. The “small number of policy changes” problem can cause extreme standard error bias, but this can be corrected using “placebo laws”. Other biases are caused by weighting regressions, having too few units, and having dissimilar autocorrelation coefficients across units. With clustering, researchers can usually conduct regressions in levels even with nonstationary variables. They should, however, be leery of pitfalls caused by clustering, especially when conducting difference-in-differences analyses.