Abstract
Bai (2009) proposes recursive estimation for panel data models with interactive effects. We study the behaviours of this recursive estimator. The recursive formula is established that shows the behaviours of recursive estimators depend on the initial estimator, the population structure and the iterative steps. Under some general scenarios, we find that the recursive estimator becomes consistent after the first iteration from any initials. We also obtain the optimal number of iterative steps under some prescribed conditions. The central limit theorem of the recursive estimator is established when the initial estimator is OLS. Various simulations are conducted to support our theoretical findings.
Highlights
Recent econometric literature has shown a great deal of interest on panel data regression models with factor structures, especially when both the cross section dimension (N ) and the length of time periods (T ) are large
Bai (2009) advocates to treat both the individual-specific and time-specific effects as unknown constants and proposes the least-squares based recursive approach that involves the use of principal components analysis (PCA) for estimating the factor structure
The first main contribution is that we provide a unified framework accommodating the theory and practice in Bai (2009) by deriving asymptotic properties of the recursive estimator βN(mT) for a fixed number of iterations when N and T tend to infinity jointly
Summary
Recent econometric literature has shown a great deal of interest on panel data regression models with factor structures, especially when both the cross section dimension (N ) and the length of time periods (T ) are large. Bai (2009) advocates to treat both the individual-specific and time-specific effects as unknown constants and proposes the least-squares based recursive approach that involves the use of principal components analysis (PCA) for estimating the factor structure. The second main contribution of this paper is that we establish the asymptotic orders of recursive estimators which reveal how consistency is related to the number of iterations for a particular data generating process. These asymptotics can be used as guidelines for determining checkable stopping rules based on user-specific numerical accuracy (e.g., Dominitz and Sherman, 2005). All proofs and technical details are documented in the appendix
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