Testing for Common Factors in Large Factor Models

Abstract

We consider large factor models with unobserved factors. We formalize the notion of common factors between different groups of variables and propose to use it as a general approach to study the structure of factors, i.e., which factors drive which variables. The spanning hypothesis, which states that factors driving one group are spanned by those driving another group, can be studied as a special case under our framework. We develop a statistical procedure for testing the number of common factors. Our inference procedure is built upon recent results on high-dimensional bootstrap and is shown to be valid under the asymptotic framework of large n and large T. In Monte Carlo simulations, our procedure performs well in finite samples. As an empirical application, we construct confidence sets for the number of common factors between the macroeconomy and the financial markets.

Keywords: large factor models, inference in high dimensions