Interactive Effects Panel Data Models with General Factors and Regressors

TL;DR

This paper introduces an iterated principal components estimator for panel data models with unobservable factors and regressors, achieving asymptotic normality, efficiency, and bias reduction without requiring prior knowledge of factor structure or integration order.

Contribution

It proposes a novel estimator that handles general regressors and unobservable factors, eliminating the need for pre-testing or specifying factor number and integration order.

Findings

Estimator is asymptotically normal and oracle efficient.

Under certain conditions, estimator is free of incidental parameters bias.

Strong factor trends can eliminate bias without additional assumptions.

Abstract

This paper considers a model with general regressors and unobservable factors. An estimator based on iterated principal components is proposed, which is shown to be not only asymptotically normal and oracle efficient, but under certain conditions also free of the otherwise so common asymptotic incidental parameters bias. Interestingly, the conditions required to achieve unbiasedness become weaker the stronger the trends in the factors, and if the trending is strong enough unbiasedness comes at no cost at all. In particular, the approach does not require any knowledge of how many factors there are, or whether they are deterministic or stochastic. The order of integration of the factors is also treated as unknown, as is the order of integration of the regressors, which means that there is no need to pre-test for unit roots, or to decide on which deterministic terms to include in the model.