Constrained Principal Components Estimation of Large Approximate Factor Models

Principal components (PC) are fundamentally feasible for the estimation of large factor models because consistency can be achieved for any path of the panel dimensions. The PC method is however inefficient under cross-sectional dependence with unknown structure. The approximate factor model of Chamberlain and Rothschild [1983] imposes a bound on the amount of dependence in the error term. This article proposes a constrained principal components (Cn-PC) estimator that incorporates this restriction as external information in the PC analysis of the data. This estimator is computationally tractable. It doesn't require estimating large covariance matrices, and is obtained as PC of a regularized form of the data covariance matrix. The paper develops a convergence rate for the factor estimates and establishes asymptotic normality. In a Monte Carlo study, we find that the Cn-PC estimators have good small sample properties in terms of estimation and forecasting performances when compared to the regular PC and to the generalized PC method (Choi [2012]).