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Inference on counterfactual distributions

Authors: Victor Chernozhukov , Ivan Fernandez-Val and Blaise Melly
Date: 13 February 2012
Type: cemmap Working Paper, CWP05/12
DOI: 10.1920/wp.cem.2012.0512


We develop inference procedures for policy analysis based on regression methods. We consider policy interventions that correspond to either changes in the distribution of covariates, or changes in the conditional distribution of the outcome given covariates, or both. Under either of these policy scenarios, we derive functional central limit theorems for regression-based estimators of the status quo and counterfactual marginal distributions. This result allows us to construct simultaneous confidence sets for function-valued policy effects, including the effects on the marginal distribution function, quantile function, and other related functionals. We use these confidence sets to test functional hypotheses such as no-effect, positive effect, or stochastic dominance. Our theory applies to general policy interventions and covers the main regression methods including classical, quantile, duration, and distribution regressions. We illustrate the results with an empirical application on wage decompositions using data for the United States. Of independent interest is the use of distribution regression as a tool for modeling the entire conditional distribution, encompassing duration/transformation regression, and representing an alternative to quantile regression.

This is a revision of CWP09/09.

Download full version
New version:
Victor Chernozhukov, Ivan Fernandez-Val and Blaise Melly May 2013, Inference on counterfactual distributions, cemmap Working Paper, Institute for Fiscal Studies
Previous version:
Victor Chernozhukov, Ivan Fernandez-Val and Blaise Melly May 2009, Inference on counterfactual distributions, cemmap Working Paper, The IFS

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