Inference on Counterfactual Distributions

Details Inference on Counterfactual Distributions Inference on Counterfactual Distributions

2009-04-06

arxiv.org/abs/0904.0951v2

Statistics

Methodology

50 pages, 1 table, 5 figures, supplementary appendix with numerical example comparing quantile and distribution regression and

Scientific paper

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.

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