Nonparametric Estimation of the Marginal Effect in Fixed-Effect Panel Data Models: An Application on the Environmental Kuznets Curve∗

This paper considers nonparametric estimation of panel data models using local linear least squares when fixed effects present. The local marginal effect is of the main interest. A withingroup type nonparametric estimator is developed, where the fixed effects are eliminated by subtracting individual specific locally weighted time average (i.e., using the local within transformation). It is shown that the local-within-transformation-based estimator satisfies the standard properties of the local linear estimator. In comparison, the nonparametric estimators based on the conventional within transformation or first difference result in biased estimators, where the bias does not degenerate even with large samples. The new estimation is applied to examine the nonlinear relationship between the U.S. income and nitrogen-oxide level (i.e., the environmental Kuznets curve) using U.S. state-level panel data.