Modal regression for fixed effects panel data

Most research on panel data focuses on mean or quantile regression, while there is not much research about regression methods based on the mode. In this paper, we propose a new model named fixed effects modal regression for panel data in which we model how the conditional mode of the response variable depends on the covariates and employ a kernel-based objective function to simplify the computation. The proposed modal regression can complement the mean and quantile regressions and provide better central tendency measure and prediction performance when the data are skewed. We present a linear dummy modal regression method and a pseudo-demodeing two-step method to estimate the proposed modal regression. The computations can be easily implemented using a modified modal–expectation–maximization algorithm. We investigate the asymptotic properties of the modal estimators under some mild regularity conditions when the number of individuals, N, and the number of time periods, T, go to infinity. The optimal bandwidths with order (NT)-1/7\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(NT)^{-1/7}$$\end{document} are obtained by minimizing the asymptotic weighted mean squared errors. Monte Carlo simulations and two real data analyses of a public capital productivity study and a carbon dioxide emissions study are presented to demonstrate the finite sample performance of the newly proposed modal regression.