Inference on Counterfactual Distributions
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Chernozhukov_Inference on.pdf
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Author(s)
Chernozhukov, Victor V.
Melly, Blaise
Fernandez-Val, Ivan
Date Issued
November 2013
Journal
Econometrica
Publisher
The Econometric Society
Citation
Chernozhukov, Victor, Ivan Fernandez-Val and Blaise Melly. “Inference on Counterfactual Distributions.” Econometrica 81, no. 6 (2013): 2205–2268.
Version
Author's final manuscript
Abstract
Counterfactual distributions are important ingredients for policy analysis and decomposition analysis in empirical economics. In this article, we develop modeling and inference tools for counterfactual distributions based on regression methods. The counterfactual scenarios that we consider consist of ceteris paribus changes in either the distribution of covariates related to the outcome of interest or the conditional distribution of the outcome given covariates. For either of these scenarios, we derive joint functional central limit theorems and bootstrap validity results for regression-based estimators of the status quo and counterfactual outcome distributions. These results allow us to construct simultaneous confidence sets for function-valued effects of the counterfactual changes, including the effects on the entire distribution and quantile functions of the outcome as well as on related functionals. These confidence sets can be used to test functional hypotheses such as no-effect, positive effect, or stochastic dominance. Our theory applies to general counterfactual changes and covers the main regression methods including classical, quantile, duration, and distribution regressions. We illustrate the results with an empirical application to wage decompositions using data for the United States.
As a part of developing the main results, we introduce distribution regression as a comprehensive and flexible tool for modeling and estimating the entire conditional distribution. We show that distribution regression encompasses the Cox duration regression and represents a useful alternative to quantile regression. We establish functional central limit theorems and bootstrap validity results for the empirical distribution regression process and various related functionals.
MIT Department
Massachusetts Institute of Technology. Department of Economics
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DOI of Published Version
https://doi.org/10.3982/ecta10582
