Assessing the Relative Power of Structural Break Tests Using a Framework Based on the Approximate Bahadur Slope

We compare the asymptotic relative efficiency of the Exp, Mean, and Sup functionals of the Wald, LM and LR tests for structural change analyzed by Andrews (1993) and Andrews and Ploberger (1994). We derive the approximate Bahadur slopes of these tests using large deviations techniques. These show that tests based on the Mean functional are inferior to those based on the Sup and Exp when using the same base statistic. Also, for a given functional, the Wald-based test dominates the LR-based test, which dominates the LM-based one. We show that the Sup and Mean type tests satisfy Wieand’s (1976) condition so that their slopes yield the limiting (as the size tends to zero) asymptotic relative Pitman efficiency. Using this measure of efficiency, the Mean type tests are also inferior to the Sup. We also compare tests based on the Wald and LM statistics modified with a HAC estimator. In this case, the inferiority of the LM-based tests is especially pronounced. The relevance of our theoretical results in finite samples is assessed via simulations. Our results are in contrast to those of Andrews and Ploberger (1994) based on a local asymptotic framework and our analysis thereby reveals its potential weaknesses in the context of structural change problems.