Inference on Counterfactual Distributions

70 Pages Posted: 26 Aug 2008 Last revised: 8 Apr 2009

See all articles by Victor Chernozhukov

Victor Chernozhukov

Massachusetts Institute of Technology (MIT) - Department of Economics; New Economic School

Iván Fernández‐Val

Boston University - Department of Economics

Blaise Melly

Brown University - Department of Economics

Date Written: April 4, 2009

Abstract

In this paper we develop procedures for performing inference in regression models about how potential policy interventions affect the entire marginal distribution of an outcome of interest. These policy interventions consist of either changes in the distribution of covariates related to the outcome holding the conditional distribution of the outcome given covariates fixed, or changes in the conditional distribution of the outcome given covariates holding the marginal distribution of the covariates fixed. Under either of these assumptions, we obtain uniformly consistent estimates and functional central limit theorems for the counterfactual and status quo marginal distributions of the outcome as well as other function-valued effects of the policy, including, for example, the effects of the policy on the marginal distribution function, quantile function, and other related functionals. We construct simultaneous confidence sets for these functions; these sets take into account the sampling variation in the estimation of the relationship between the outcome and covariates. Our procedures rely on, and our theory covers, all main regression approaches for modeling and estimating conditional distributions, focusing especially on classical, quantile, duration, and distribution regressions. Our procedures are general and accommodate both simple unitary changes in the values of a given covariate as well as changes in the distribution of the covariates or the conditional distribution of the outcome given covariates of general form. We apply the procedures to examine the effects of labor market institutions on the U.S. wage distribution.

Keywords: Policy effects, counterfactual distribution, quantile regression, duration regression, distribution regression

JEL Classification: C14, C21, C41, J31, J71

Suggested Citation

Chernozhukov, Victor and Fernandez-Val, Ivan and Melly, Blaise, Inference on Counterfactual Distributions (April 4, 2009). MIT Department of Economics Working Paper No. 08-16, Available at SSRN: https://ssrn.com/abstract=1235529 or http://dx.doi.org/10.2139/ssrn.1235529

Victor Chernozhukov (Contact Author)

Massachusetts Institute of Technology (MIT) - Department of Economics ( email )

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HOME PAGE: http://www.mit.edu/~vchern/

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Ivan Fernandez-Val

Boston University - Department of Economics ( email )

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HOME PAGE: http://people.mit.edu/ivanf

Blaise Melly

Brown University - Department of Economics ( email )

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Providence, RI 02912
United States

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