Job market paper

Estimation uncertainty in repeated finite populations

Standard errors need to be adjusted down when the sample is a large fraction of the population of interest (a finite population setup). I consider the empirically relevant case where a finite population coexists with a measurement problem, in that the features of interest are not necessarily observable even if the entire population is sampled. I show that conventional standard errors remain generally conservative in this context and propose Finite Population Corrections (FPCs) that guarantee non-conservative inference when repeated measurements are available. FPCs rely on weak dependence across measurements and are very simple to implement. I apply these methods to two empirical settings where uncertainty has been previously understood in different ways: predicting lethal encounters with police using data on all U.S. police departments, and studying firm misallocation with a census of large Indonesian firms. Finite-population inference leads to confidence intervals that are up to 50% shorter in the former and illustrates the need to account for measurement uncertainty in the latter.

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