Varying Random Coefficient Models

TL;DR

This paper introduces a new estimation method for varying random coefficient models that captures nonlinear unobserved heterogeneity, providing theoretical inference, bootstrap confidence bands, and practical application to housing demand elasticity.

Contribution

It develops a novel estimator for VRC density using weighted sieve minimum distance with Hermite functions, advancing inference in nonlinear heterogeneity models.

Findings

Estimator performs well in finite samples.

Provides convergence rates and limit theory for density estimation.

Successfully applied to analyze income elasticity heterogeneity.

Abstract

This paper provides a new methodology to analyze unobserved heterogeneity when observed characteristics are modeled nonlinearly. The proposed model builds on varying random coefficients (VRC) that are determined by nonlinear functions of observed regressors and additively separable unobservables. This paper proposes a novel estimator of the VRC density based on weighted sieve minimum distance. The main example of sieve bases are Hermite functions which yield a numerically stable estimation procedure. This paper shows inference results that go beyond what has been shown in ordinary RC models. We provide in each case rates of convergence and also establish pointwise limit theory of linear functionals, where a prominent example is the density of potential outcomes. In addition, a multiplier bootstrap procedure is proposed to construct uniform confidence bands. A Monte Carlo study examines finite sample properties of the estimator and shows that it performs well even when the regressors associated to RC are far from being heavy tailed. Finally, the methodology is applied to analyze heterogeneity in income elasticity of demand for housing.