Nonparametric Regression with Common Shocks

Abstract

This paper considers a nonparametric regression model for cross-sectional data in the presence of common shocks. Common shocks are allowed to be very general in nature; they do not need to be finite dimensional with a known (small) number of factors. I investigate the properties of the Nadaraya-Watson kernel estimator and determine how general the common shocks can be while still obtaining meaningful kernel estimates. Restrictions on the common shocks are necessary because kernel estimators typically manipulate conditional densities, and conditional densities do not necessarily exist in the present case. By appealing to disintegration theory, I provide sufficient conditions for the existence of such conditional densities and show that the estimator converges in probability to the Kolmogorov conditional expectation given the sigma-field generated by the common shocks. I also establish the rate of convergence and the asymptotic distribution of the kernel estimator.

Linear IV regression estimators for structural dynamic discrete choice models

“…Souza-Rodrigues (2016) establishes the asymptotic properties of the kernel regression estimator for crosssectional data in the presence of common shocks.…”

Efficient Estimation for the Derivative of Nonparametric Function by Optimally Combining Quantile Information

“…As we all know, lots of estimation methods, including the kernel regression method, the spline smoothing method,the orthogonal series approximation method and the local polynomial method, have been investigated for estimating the nonparametric regression function m(t). The relevant works can be referred but not limited to [1][2][3][4][5]. However, we need to estimate m (t), that is, the derivative of m(t), in many situations.…”