Inference on Directionally Differentiable Functions

• 成果类型: Article
• 署名作者: Fang, Zheng; Santos, Andres
• 署名单位: Texas A&M University System; Texas A&M University College Station; University of California System; University of California Los Angeles
• 刊物名称: REVIEW OF ECONOMIC STUDIES
• ISSN/ISSBN: 0034-6527
• DOI: 10.1093/restud/rdy049
• 发表日期: 2019
• 页码: 377-412
• 关键词: wage inequality; bootstrap; parameters; BOUNDARY; demand; models; set

摘要

This article studies an asymptotic framework for conducting inference on parameters of the form f(.0), where f is a known directionally differentiable function and.0 is estimated by <^>.n. In these settings, the asymptotic distribution of the plug- in estimator f( <^>.n) can be derived employing existing extensions to the Delta method. We show, however, that ( full) differentiability of f is a necessary and sufficient condition for bootstrap consistency whenever the limiting distribution of <^>.n is Gaussian. An alternative resampling scheme is proposed that remains consistent when the bootstrap fails, and is shown to provide local size control under restrictions on the directional derivative of f. These results enable us to reduce potentially challenging statistical problems to simple analytical calculations- a feature we illustrate by developing a test of whether an identified parameter belongs to a convex set. We highlight the empirical relevance of our results by conducting inference on the qualitative features of trends in ( residual) wage inequality in the U. S.