Selecting the Correct Number of Factors in Approximate Factor Models: The Large Panel Case with Group-Bridge Estimators

This paper proposes a Group Bridge estimator to select the correct number of factors in approximate factor models. It contributes to both shrinkage estimation and factor model literature. We extend the conventional Bridge estimator from a single equation to a large panel context. The proposed estimator can consistently estimate the factor loadings of relevant factors and shrink the loadings of irrelevant factors to zero with probability approaching one. Hence, it provides a consistent estimate for the number of factors. We also propose an algorithm for the new estimator and Monte Carlo experiments show that our algorithm converges reasonably fast and that our estimator has very good performance in small samples. An empirical example based on a commonly used US macroeconomic data set is provided in the paper as well.