Common breaks in time trends for large panel data with a factor structure

Abstract

In this paper, I analyse issues related to the estimation of a common break in a large panel of time series data. Each series in the panel consists of a linear time trend and a random error. The linear time trend is subject to a break that occurs at the same date for all series. The error term is cross-sectionally correlated through a factor structure. The break date is estimated jointly with the common factors. In particular, two break date estimators are analysed: the first is obtained as an iterative solution while the second is obtained as a global solution. The asymptotic properties of these estimators are analysed under both global and local asymptotic frameworks. These two estimators are shown to be asymptotically equivalent and to achieve a faster rate of convergence than the simple break date estimator that does not take common factors into account. The limiting distributions of the proposed break date estimators are provided so that asymptotically valid confidence intervals can be formed. Monte Carlo simulation results are provided to support the theoretical results.