Sieve estimation of state-varying factor models

In this paper, we propose a sieve approach to estimate state-varying factor models, where the factor loadings vary over specific state variables. Our methodology consists of a two-step estimation procedure for the parameters of interest. In the first step, we achieve preliminary consistent estimates of the factors and factor loadings via nuclear norm regularization (NNR). In the second step, we perform post-NNR iterative least squares estimations for the factors and factor loadings. We establish the asymptotic properties of these estimators. Based on the estimation theory, we propose a test for the null hypothesis of constant factor loadings and examine the asymptotic properties of the test statistic. Monte Carlo simulations demonstrate the favorable performance of the proposed estimation procedure and testing method in finite samples. An application to a U.S. macroeconomic dataset suggests potential state-dependency within the U.S. economy.