erc/metu
INTERNATIONAL CONFERENCE IN ECONOMICS  IV
September 13-16, 2000, Ankara

Bootstrap Based Unit Root Tests Under Structural Change

Mehmet Balcılar (Çukurova University)

Abstract

There is huge and growing literature in econometrics on the tendency of unit root tests to incorrectly reject the null hypothesis of a unit root when the data has undergone structural changes. Unit root tests are shown to have poor power even when there is no structural change. When there are structural changes these tests almost have zero power. In response, unit root tests, such as the Perron and Zivot-Andrews tests, were proposed to take into account the effect of structural changes. Unfortunately, structural change unit roots incorrectly reject the null of a unit root due to large transitory fluctuations. This result further complicates the matters and leaves empirical researchers with an undoubtedly large uncertainty. Recent studies showed that power of unit root tests can be improved under quasi differencing. Elliot, Rothenberg, and Stock (Econometrica, 1995) developed unit root tests that are approximately uniformly most powerful invariant. In this study, we obtain the asymptotic distributions of Dickey-Fuller unit root tests under quasi differencing when data has structural changes. The tests have similar power properties to the tests of Elliot, Rothenberg, and Stock (1995). We then show that the bootstrap is valid for these tests under the null of a unit root. This holds under both known and endogenous break point assumptions. We show that when bootstrap critical values are used the performance of structural change unit root tests significantly improve. Properties of both parametric and nonparametric bootstrap methods are investigated. These include model based bootstrap methods, such as sampling from an autoregression, and nonparametric bootstrap methods, such as the moving blocks bootstrap, sieve bootstrap, and stationary bootstrap. Results of the Monte Carlo study reveal that the model based and sieve bootstraps outperform the others. We also examine several methods of confidence interval construction. These include, conventional asymptotic confidence interval, Stock's local-to-unity asymptotic confidence interval, percentile bootstrap, percentile-t bootstrap, bias corrected confidence interval, bias corrected and accelerated confidence interval, and Hansen's grid bootstrap. Among these grid bootstrap outperformed the others in many cases.

Economic Research Center
Middle East Technical University
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e-mail: metuerc@metu.edu.tr