Nonparametric classes for identification in random coefficients models when regressors have limited variation

TL;DR

This paper investigates the conditions under which the distribution of coefficients in various random coefficients models can be identified when regressors have limited variation, including discrete support and nonlinear transformations.

Contribution

It introduces nonparametric classes for identification in models with restricted regressor support, exploring trade-offs and extending to complex models like panel data and deconvolution.

Findings

Identification is possible under certain support restrictions.

Trade-offs between coefficient distribution restrictions and regressor support.

Extensions to nonlinear, infinite regressors, and panel data models.

Abstract

This paper studies point identification of the distribution of the coefficients in some random coefficients models with exogenous regressors when their support is a proper subset, possibly discrete but countable. We exhibit trade-offs between restrictions on the distribution of the random coefficients and the support of the regressors. We consider linear models including those with nonlinear transforms of a baseline regressor, with an infinite number of regressors and deconvolution, the binary choice model, and panel data models such as single-index panel data models and an extension of the Kotlarski lemma.