Inference on Counterfactual Distributions
Abstract
We develop inference procedures for counterfactual analysis based on regression methods. We analyze the effect of either changing the distribution of covariates, or changing the conditional distribution of the outcome given covariates, on the entire marginal distribution of the outcome. For both of these 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 counterfactual effects, including the effects on the entire marginal distribution function, quantile function, and 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. Results on distribution regression as a tool for modeling the entire conditional distribution, encompassing duration/transformation regression, and representing an alternative to quantile regression, are also of independent interest.Keywords
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