Identifying observed factors in approximate factor models: estimation and hypothesis testing

摘要

Despite their popularities in recent years, factor models have long been criticized for the lackof identification. Even when a large number of variables are available, the factors can only beconsistently estimated up to a rotation. In this paper, we try to identify the underlying factors byassociating them to a set of observed variables, and thus give interpretations to the orthogonalfactors estimated by the method of Principal Components. We first propose a estimation procedureto select a set of observed variables, and then test the hypothesis that true factors are exactlinear combinations of the selected variables. Our estimation method is shown to able to correctly identity the true observed factor even in the presence of mild measurement errors, and our test statistics are shown to be more general than those of Bai and Ng (2006). The applicability of our methods in finite samples and the advantages of our tests are confirmed by simulations. Ourmethods are also applied to the returns of portfolios to identify the underlying risk factors.