Statistical Inference on Partially Linear Panel Model under Unobserved Linearity

TL;DR

This paper introduces a new statistical method using a modified spline basis for identifying linear components in partially linear panel data models with fixed effects, ensuring consistent estimation and effective inference.

Contribution

It proposes a novel procedure for linearity detection in panel models that is both theoretically justified and practically convenient, including a path-based algorithm that avoids tuning parameter selection.

Findings

Consistently estimates the regression function

Accurately detects linear components in panel data

Demonstrates effectiveness through simulations and real data applications

Abstract

A new statistical procedure, based on a modified spline basis, is proposed to identify the linear components in the panel data model with fixed effects. Under some mild assumptions, the proposed procedure is shown to consistently estimate the underlying regression function, correctly select the linear components, and effectively conduct the statistical inference. When compared to existing methods for detection of linearity in the panel model, our approach is demonstrated to be theoretically justified as well as practically convenient. We provide a computational algorithm that implements the proposed procedure along with a path-based solution method for linearity detection, which avoids the burden of selecting the tuning parameter for the penalty term. Monte Carlo simulations are conducted to examine the finite sample performance of our proposed procedure with detailed findings that confirm our theoretical results in the paper. Applications to Aggregate Production and Environmental Kuznets Curve data also illustrate the necessity for detecting linearity in the partially linear panel model.