Inference in Differences-in-Differences: How Much Should We Trust in Independent Clusters?

We analyze the conditions in which ignoring spatial correlation is problematic for inference in differences-in-differences (DID) models. Assuming that the spatial correlation structure follows a linear factor model, we show that inference ignoring such correlation remains reliable when either (i) the second moment of the difference between the pre- and post-treatment averages of common factors is low, or (ii) the distribution of factor loadings has the same expected values for treated and control groups, and do not exhibit significant spatial correlation. We present simulation results with real datasets that corroborate these conclusions. Our results provide important guidelines on how to minimize inference problems due to spatial correlation in DID applications.