Testing for Common Latent Factors Across Two Short Panels

This paper develops inference tools for the number of common latent factors across two large cross-sectional panels observed over a short time span (large n, small T). Our approach builds on a general test for determining the dimension of the intersection of two matrix column spaces, where each matrix is estimated with noise. The proposed test statistics are based on canonical correlations, and their asymptotic distributions are derived via perturbation methods. An empirical application to large cross-sections of monthly US stock returns and corporate bond returns finds that, on average, five latent factors influence both asset classes over an 18-month period. Our results suggest that a plausible candidate for a common factor is a stock portfolio with weights sorted on book leverage. Overall, the common factors between the two asset classes behave more like stock characteristic portfolios than bond characteristic portfolios, both in terms of pricing performance and time series dynamics.