Estimation and inference for causal functions with multi-way clustered data

原文摘要

We propose methods for estimation and uniform inference for a broad class of causal functions, such as conditional average treatment effects and continuous treatment effects, under multi-way clustering. The causal function is identified as the conditional expectation of a Neyman-orthogonal signal that depends on high-dimensional nuisance parameters. We introduce a two-step procedure: the first step uses machine learning to estimate the nuisance parameters, and the second step projects the estimated Neyman-orthogonal signal onto a dictionary of basis functions whose dimension grows with the sample size. We consider both full-sample and multi-way cross-fitting approaches to this procedure and derive a functional limit theory for the resulting estimators. For uniform inference, we develop a novel resampling method, the multi-way cluster-robust sieve score bootstrap, which extends the sieve score bootstrap of Chen and Christensen (2018) to settings with multi-way clustering. Extensive simulations demonstrate that the proposed methods exhibit favorable finite-sample performance. We apply our approach to study the causal relationship between mistrust levels in Africa and historical exposure to the slave trade. Accounting for the two-way clustering by ethnicity and region, our inference method rejects the null hypothesis of uniformly zero effects and uncover heterogeneous treatment effects, with particularly strong impacts in regions with high historical trade intensity.

摘要来源：RePEc · 出版社摘要