13 - Power comparisons of the discontinuous trend unit root tests

Summary

Introduction

Perron (1989) developed unit root tests which allow for a break in the deterministic trend. The Perron test is asymptotically similar. Related tests have also been suggested by Schmidt and Phillips (1992), Oya and Toda (1998), Bhargava (1986, 1996), and Kiviet and Phillips (1992). In this chapter, we extend the Perron unit root tests to allow for multiple breaks in the trend and investigate both their asymptotic and finite sample properties.

Zivot and Andrews (1992) have studied the unit root test when the location of a break point is unknown. They used the t ratio associated with the lagged dependent variable to find the break point. However, the null distribution requires no break in the trend function. Vogelsang and Perron (1998) used the t ratio of the discontinuous trend variable to find the break point. Hatanaka and Yamada (1997) used the residual variance to find the break point, and extended the Zivot–Andrews test so that the null hypothesis allows a discontinuous trend. Break points resulting from these tests may conflict with common knowledge, since researchers have rough ideas on when the break actually happened. The Perron test may be applied by setting a wide break interval that possibly covers a break point through the use of shock dummy variables.

In Section 2 we propose a unified framework for the unit root tests that allow for multiple breaks in both the intercepts and trend coefficients as in the Perron C model, for multiple breaks in intercepts only as in the Perron A model, and for joined trend lines as in the Perron B model.