Consistent variable selection in large panels when factors are observable

In this paper we develop an econometric method for consistent variable selection in the context of a linear factor model with observable factors for panels of large dimensions. The subset of factors that best fit the data is sequentially determined. Firstly, a partial R2 rule is used to show the existence of an optimal ordering of the candidate variables. Secondly, We show that for a given order of the regressors, the number of factors can be consistently estimated using the Bayes information criterion. The Akaike will asymptotically lead to overfitting of the model. The theory is established under approximate factor structure which allows for limited cross-section and serial dependence in the idiosyncratic term. Simulations show that the proposed two-step selection technique has good finite sample properties. The likelihood of selecting the correct specification increases with the number of cross-sections both asymptotically and in small samples. Moreover, the proposed variable selection method is computationally attractive. For K potential candidate factors, the search requires only 2K regressions compared to 2K for an exhaustive search.