2010): “Analyzing the Random Coefficient Model Nonparametrically”. Econometric Theory

Linearity in a causal relationship between a dependent variable and a set of regressors is a common assumption throughout economics. In this paper we consider the case when the coefficients in this relationship are random and distributed independently from the regressors. Our aim is to identify and estimate the distribution of the coefficients non-parametrically. We propose a kernel based estimator for the joint probability density of the coefficients. Although this estimator shares certain features with standard nonpara-metric kernel density estimators, it also differs in some important characteristics which are due to the very different setup we are considering. Most importantly, the kernel is nonstandard, and derives from the theory of Radon transforms. Consequently, we call our estimator the Radon Transform Estimator (RTE). We establish the large sample behavior of this estimator, in particular rate optimality and asymptotic distribution. In addition, we extend the basic model to cover extensions including endogenous regressors and addi-tional controls. Finally, we analyze the properties of the estimator in finite samples by a simulation study, as well as an application to consumer demand using British household data