Inference on two component mixtures under tail restrictions

TL;DR

This paper demonstrates that two-component mixture models can be nonparametrically identified using tail restrictions and exclusion constraints, leading to simple estimators and tests with good finite-sample properties.

Contribution

It introduces a novel identification strategy for two-component mixtures using tail restrictions and exclusion, along with practical estimators and a testing procedure.

Findings

Identified mixture components nonparametrically using tail restrictions.

Developed simple closed-form estimators for components and mixing proportions.

Validated estimators through simulation showing strong finite-sample performance.

Abstract

Many econometric models can be analyzed as finite mixtures. We focus on two-component mixtures and we show that they are nonparametrically point identified by a combination of an exclusion restriction and tail restrictions. Our identification analysis suggests simple closed-form estimators of the component distributions and mixing proportions, as well as a specification test. We derive their asymptotic properties using results on tail empirical processes and we present a simulation study that documents their finite-sample performance.