Abstract
Bai (2009) proposes a recursive least-squares estimation method for large panel data models with unobservable interactive fixed effects, but the impact of recursion on the asymptotic properties of the least-squares estimators is not taken into account. In this paper, we extend Bai (2009) by investigating the recursive estimator asymptotically. In general, the asymptotic properties we establish for the recursive estimators largely complement the theory and practice of the recursive least-squares procedure suggested by Bai (2009). In particular, we show that consistency of the recursive estimator depends on three key points, consistency of the initial OLS estimator, the number of recursive steps and the endogeneity arising due to the dependence between regressors and interactive effects. Compared to the theoretical estimator in Bai (2009), such endogeneity affects the convergence rate of recursive least-squares estimators. Finite sample results are provided to illustrate our findings in detail.
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
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
