Estimation uncertainty in repeated finite populations
Selected for the REStud North America Tour 2025
Abstract
Often, datasets cover much of the population under study — think of censuses of firms or workers, or state-level panels. Yet, standard practice remains to treat the sample as drawn from a hypothetical superpopulation, and classical finite-population adjustments are of limited use since they rule out unobserved heterogeneity. In this paper, I study settings where interest is in population averages over a latent characteristic, and the data only provides noisy, repeated measurements. I show that conventional standard errors are generally too large, and propose Finite Population Corrections (FPCs) that guarantee non-conservative inference. FPCs are very simple to implement via covariance restrictions. I apply these to (i) predicting lethal police encounters using data from all U.S. police departments and (ii) studying labor misallocation from a census of Indonesian firms. FPCs yield standard errors that properly combine uncertainty from measurement and from sampling — and lead to confidence intervals that are up to 50% shorter in these applications.