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Varying random coefficient models

Christoph Breunig

Journal of Econometrics, 2021, vol. 221, issue 2, 381-408

Abstract: This paper analyzes 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.

Keywords: Random coefficients; Varying coefficients; Sieve minimum distance; Hermite functions; Rate of convergence; Bootstrap uniform confidence bands (search for similar items in EconPapers)
JEL-codes: C14 C21 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1016/j.jeconom.2020.04.049

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Journal of Econometrics is currently edited by T. Amemiya, A. R. Gallant, J. F. Geweke, C. Hsiao and P. M. Robinson

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