Estimating Semiparametric and Nonparametric Fixed Effects Panel Data Models with mgcv

Abstract

This paper provides a practical guide to estimating semiparametric and nonparametric fixed-effects panel data models using the mgcv package in R. The focus is implementation: handling fixed effects with unit indicators, first differencing, or penalized unit effects; specifying smooth terms; and conducting cluster-robust inference. Monte Carlo experiments compare \code{mgcv::bam} estimators with linear and fixed-series spline estimators. Simulations suggest that penalized splines adapt to unknown smoothness and estimate functions accurately in the designs studied here. A penalty-adjusted cluster-robust covariance estimator yields tests with near-nominal size for finite-dimensional parameters, and confidence bands provide accurate coverage for centered unknown functions.