Estimation of Change Points in Stationary and Nonstationary Regressors and Error Term

Testing and estimation of change points have been widely studied in econometrics. The focus of this chapter is to test and estimate for possible changes in the slope parameter of panel regression models. In Sec. 3.1, we discuss the spurious break in time-series. It is known that there is a tendency to spuriously estimate a break point in the middle of the sample when the errors follow an I(1) process, even though a break point does not actually exist, e.g., Bai (1998). In Sec. 3.2, we discuss estimation of a change point when it does not exist. Baltagi, Kao, and Liu (2017) consider the spurious break in a panel data regression model where the error terms are either stationary or nonstationary. Here the spurious break may still exist even with large panels. As a solution, an FD estimator is proposed. In Sec. 3.3, we discuss spurious break when a change point exists. The results in Bai (1997) for the time-series, Feng, Kao, and Lazarova (2009) for a homogeneous panel data model, and Baltagi, Feng, and Kao (2016) for a heterogeneous panel data model are discussed and compared. In Sec. 3.4, we further discuss a few extensions. We discuss change point estimation in a trend model, a model with a stationary or nonstationary regressor and/or error term, and a model with common factors. Sec. 3.5 compares OLS and FGLS-based Wald-tests in Emerson and Kao (2001) and Baltagi, Kao, and Liu (2019). Sec. 3.6 concludes.