  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.
