Inference with small samples

Abstract

Applied researchers commonly employ inference methods that are asymptotically valid. However, in many cases, the asymptotic theories assumed in these methods do not satisfactorily approximate the scenarios in which they are utilized. Consequently, we may encounter an excess of false-positive results. This research proposal considers the use of alternative inference methods in scenarios where traditional methods relying on asymptotic approximations are not reliable. Specifically, at least three articles related to inference in small samples (in at least one dimension) will be developed: (i) a survey article categorizing different inference methods for scenarios with few treatments. Particularly, clarifying the assumptions they employ and evaluating which methods would be most appropriate in different situations; (ii) another article developing a new inference method for difference-in-differences (DD) estimators for a scenario where there is currently no valid alternative in the literature: when we have few treatments, variation in treatment timing, and heterogeneous treatment effects; (iii) a third article developing alternatives for inference for shift-share models that are valid in small samples under relatively stronger assumptions, yet are also asymptotically valid under weaker assumptions. Additionally, programs for R and/or Stata will be developed to implement inference methods for DD with few treatments. (AU)