A projection-based approach for interactive fixed effects panel data models

This article introduces a straightforward sieve-based approach for estimation and inference of 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. 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. As a consequence, 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. An application to cross-country growth rates shows that higher consumption and government spending are associated with lower growth. Contrary to existing methods, we find that within OECD countries investment fosters growth, whereas a higher investment price level reduces it.