🤖 AI Summary
This study addresses efficient estimation and robust inference for semiparametric and nonparametric models with fixed effects in panel data. The authors propose a unified framework based on penalized splines, handling fixed effects via unit indicators, first-differencing, or penalized unit-specific effects, and leverage mgcv::bam for scalable fitting. A novel penalty-adjusted cluster-robust covariance estimator is developed, which remains valid under unknown smoothness and substantially improves the accuracy of finite-dimensional parameter tests and the coverage performance of function-wise confidence bands. Monte Carlo simulations demonstrate that the proposed method excels in function estimation, maintains correct test size, and achieves reliable interval coverage across various scenarios.
📝 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.