In this paper , we suggest and analyze a new class of specification tests for random coefficient models. These tests allow to assess the validity of central structural features of the model , in particular linearity in coefficients , generalizations of this notion like a known nonlinear functional relationship, or degeneracy of the distribution of a random coefficient, i. e. , whether a coefficient is fixed or random, including whether an associated variable can be omitted altogether. Our tests are nonparametric in nature, and use sieve estimators of the characteristic function. We provide formal power analysis against global as well as against local alternatives. Moreover, we perform a Monte Carlo simulation study , and apply the tests to analyze the degree of nonlinearity in a heterogeneous random coefficients demand model. While we find some evidence against the popular QUAIDS specification with random coefficients, it is not strong enough to reject the specification at the conventional significance level .
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 .
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In this paper , we suggest and analyze a new class of specification tests for random coefficient models. These tests allow to assess the validity of central structural features of the model , in particular linearity in coefficients , generalizations of this notion like a known nonlinear functional relationship, or degeneracy of the distribution of
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,
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random coefficient, i. e. , whether a coefficient is fixed or random, including whether an associated variable can be omitted altogether. Our tests are nonparametric in nature, and use sieve estimators of the characteristic function. We provide formal power analysis against global as well as against local alternatives. Moreover, we perform a Monte Carlo simulation study , and apply the tests to analyze the degree of nonlinearity in a heterogeneous random coefficients demand model. While we find some evidence against the popular QUAIDS specification with random coefficients, it is not strong enough to reject the specification at the conventional significance level
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