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Inference on counterfactual distributions

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  • Victor Chernozhukov

    ()
    (Institute for Fiscal Studies and MIT)

  • Iván Fernández-Val

    (Institute for Fiscal Studies and Boston University)

  • Blaise Melly

Abstract

Counterfactual distributions are important ingredients for policy analysis and de-composition analysis in empirical economics. In this article we develop modelling 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 part of developing the main results, we introduce distribution regression as a comprehensive and flexible tool for modelling 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. This is a revision of CWP05/12 and CWP09/09

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Bibliographic Info

Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP17/13.

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Date of creation: May 2013
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Handle: RePEc:ifs:cemmap:17/13

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Keywords: Counterfactual distribution; decomposition analysis; policy analysis; quantile regression; distribution regression; duration/transformation regression; Hadamard differentiability of the counterfactual operator; weighted bootstrap; unconditional quantile and distribution effects;

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