  This paper develops an inferential theory for state-varying factor models of
large dimensions. Unlike constant factor models, loadings are general functions
of some recurrent state process. We develop an estimator for the latent factors
and state-varying loadings under a large cross-section and time dimension. Our
estimator combines nonparametric methods with principal component analysis. We
derive the rate of convergence and limiting normal distribution for the
factors, loadings and common components. In addition, we develop a statistical
test for a change in the factor structure in different states. We apply the
estimator to U.S. Treasury yields and S&P500 stock returns. The systematic
factor structure in treasury yields differs in times of booms and recessions as
well as in periods of high market volatility. State-varying factors based on
the VIX capture significantly more variation and pricing information in
individual stocks than constant factor models.
