Empirical Process Methods in Econometrics

This paper provides an introduction to the use of empirical process methods in econometrics. These methods can be used to establish the large sample properties of econometric estimators and test statistics. In the first part of the paper, key terminology and results are introduced and discussed heuristically. Applications in the econometrics literature are briefly reviewed. A select set of three classes of applications is discussed in more detail. The second part of the paper shows how one can verify a key property called stochastic equicontinuity. The paper takes several stochastic equicontinuity results from the probability literature, which rely on entropy conditions of one sort or another, and provides primitive sufficient conditions under which the entropy conditions hold. This yields stochastic equicontinuity results that are readily applicable in a variety of contexts. Examples are provided.