A projection based approach for interactive fixed effects panel data models

TL;DR

This paper presents a simple sieve-based estimator for panel data models with interactive fixed effects, offering improved inference methods and practical application to economic growth analysis.

Contribution

It introduces a novel, non-iterative estimator based on partial least squares that accounts for smooth factor loadings in panel data models.

Findings

Estimator performs well in simulations with low mean squared error.

Bootstrap inference achieves accurate coverage probabilities.

Method applied successfully to analyze OECD growth determinants.

Abstract

This paper introduces a straightforward sieve-based approach for estimating and conducting inference on regression parameters in panel data models with interactive fixed effects. The method's key assumption is that factor loadings can be decomposed into an unknown smooth function of individual characteristics plus an idiosyncratic error term. Our estimator offers advantages over existing approaches by taking a simple partial least squares form, eliminating the need for iterative procedures or preliminary factor estimation. In deriving the asymptotic properties, we discover that the limiting distribution exhibits a discontinuity that depends on how well our basis functions explain the factor loadings, as measured by the variance of the error factor loadings. This finding reveals that conventional ``plug-in'' methods using the estimated asymptotic covariance can produce excessively conservative coverage probabilities. We demonstrate that uniformly valid non-conservative inference can be achieved through the cross-sectional bootstrap method. Monte Carlo simulations confirm the estimator's strong performance in terms of mean squared error and good coverage results for the bootstrap procedure. We demonstrate the practical relevance of our methodology by analyzing growth rate determinants across OECD countries.