Econometrica: Nov 2013, Volume 81, Issue 6

Inference on Counterfactual Distributions

https://doi.org/10.3982/ECTA10582
p. 2205-2268

Victor Chernozhukov, Iván Fernández‐Val, Blaise Melly

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.

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Supplemental Material

Supplement to "Inference on Counterfactual Distributions"

This zip file contains the data and programs for the empirical application.  A brief guide to the content of the folder is given in the README.PDF file.

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Supplement to "Inference on Counterfactual Distributions"

This supplement material contains the proof of he validity of bootstrap confidence bands for counterfactual functionals, a numerical comparison of quantile and distribution regression estimators, additional empirical results, and details about the variance decomposition of the composition effect.

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