Nonparametric Estimation
and Testing of Fixed Effects Panel Data Models.
Abstract
In this paper we consider the problem of estimating nonparametric panel
data models with so-called fixed effects, i.e., random effects that are
correlated with the predictors in an unspecified manner. We derive the
rate of convergence and asymptotic distribution of an iterative
nonparametric kernel estimator. We further propose a test statistic for
testing the null hypothesis of random effects against fixed effects in a
nonparametric panel data regression model. We also extend the estimation
method to the case of a semiparametric partially linear fixed effects
model. Simulations are used to support the asymptotic development. We
apply the methods to estimate the relationship between caloric intake
and income using data obtained from the China Health and Nutrition
Survey. With this data, a standard analysis ignoring the possibility of
fixed effects suggests the implausible finding that at low levels of
income, increases in income are not related to increases in caloric
intake: the fixed effect approach gives estimates that are in accord
with economic theory.
