Quantile Mixture Models: Estimation and Inference

• In Event: Innovations in Causal Inference: Quantile Mixtures, Empirical Bayes Aggregation, and Synthetic Controls

Abstract

Nonparametric density mixture models are popular in Statistics and Econometrics but suffer from computational and inferential hurdles. This paper introduces nonparametric quantile mixture models as a convenient counterpart, discusses several applications, and proposes a computationally efficient sieve estimator based on a generalized method of L-moments. We develop a full inferential theory for our proposed estimator. In doing so, we make several contributions to statistical theory that allow us to extend a numerical bootstrap method to high-dimensional settings. We show that, as a direct byproduct of our theory, we can provide an inference method for the distributional synthetic controls of Gunsilius (2023), a novel approach to counterfactual analysis for which formal inference methods were not yet available. As an empirical application of the latter, we apply our proposed approach to inference in assessing the effects of a large-scale environmental disaster, the Brumadinho barrage rupture, on the local wage distribution. Our results uncover a range of effects across percentiles, which we argue are consistent displacement effects, whereby median-earning jobs are replaced by low-paying contracts. Finally, we also consider applications of our method in financial management and the equity premium puzzle.

Author

• Luis A. F. Alvarez, University of São Paulo
  Presenting Author