ANALYZING THE RANDOM COEFFICIENT MODEL NONPARAMETRICALLY
提出一种基于Radon变换的核估计器，用于非参数估计随机系数模型中系数的联合概率密度，并证明其大样本性质，通过模拟和英国家庭数据应用验证。
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 nonparametrically. We propose a kernel-based estimator for the joint probability density of the coefficients. Although this estimator shares certain features with standard nonparametric kernel density estimators, it also differs in some important characteristics that 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 additional 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.