Common Factors in Nonstationary Panel Data with a Deterministic Trend – Estimation and Distribution Theory

Abstract

The paper studies large-dimension factor models with nonstationary factors and allows for deterministic trends and factors integrated of order higher then one. We follow the model specification of Bai (2004) and derive the convergence rates and the limiting distributions of estimated factors, factors loadings and common components. We discuss in detail a model with a linear time trend. We illustrate the theory with an empirical example that studies the fluctuations of the real activity of U.S. economy. We show that these fluctuations can be explained by two nonstationary factors and a small number of stationary factors. We test the economic interpretation of nonstationary factors.