When a researcher estimates a regression function with state level data, why are there standard errors that differ from zero? Clearly the researcher has information on the entire population of states. Nevertheless researchers typically report conventional robust standard errors, formally justified by viewing the sample as a random sample from a large population. In this paper we investigate the justification for positive standard errors in cases where the researcher estimates regression functions with data from the entire population. We take the perspective that the regression function is intended to capture causal effects, and that standard errors can be justified using a generalization of randomization inference. We show that these randomization-based standard errors in some cases agree with the conventional robust standard errors, and in other cases are smaller than the
conventional ones.

Joint with Alberto Abadie, Susan Athey and Jeffrey Wooldridge.