14,816 research outputs found
Inference on Counterfactual Distributions
Counterfactual distributions are important ingredients for policy analysis
and decomposition analysis in empirical economics. In this article we develop
modeling 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 a part of developing the main results, we introduce distribution
regression as a comprehensive and flexible tool for modeling and estimating the
\textit{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.Comment: 55 pages, 1 table, 3 figures, supplementary appendix with additional
results available from the authors' web site
A nonparametric model-based estimator for the cumulative distribution function of a right censored variable in a finite population
In survey analysis, the estimation of the cumulative distribution function
(cdf) is of great interest: it allows for instance to derive quantiles
estimators or other non linear parameters derived from the cdf. We consider the
case where the response variable is a right censored duration variable. In this
framework, the classical estimator of the cdf is the Kaplan-Meier estimator. As
an alternative, we propose a nonparametric model-based estimator of the cdf in
a finite population. The new estimator uses auxiliary information brought by a
continuous covariate and is based on nonparametric median regression adapted to
the censored case. The bias and variance of the prediction error of the
estimator are estimated by a bootstrap procedure adapted to censoring. The new
estimator is compared by model-based simulations to the Kaplan-Meier estimator
computed with the sampled individuals: a significant gain in precision is
brought by the new method whatever the size of the sample and the censoring
rate. Welfare duration data are used to illustrate the new methodology.Comment: 18 pages, 5 figure
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