Unit roots and structural breaks in panels: Does the model specification matter?

Abstract

Although the impacts of structural instability on testing for unit root have been studied extensively for univariate time series, such impacts on panel data unit root tests are still relatively unknown. A major issue is the choice of model in accommodating different types of break (instability) prior to testing for unit root. Specifically, researchers must specify a potential break in the intercept, the trend or both before testing for unit root. Model misspecification has been known to have a great impact on the test performance in the univariate case, especially when the selected model fails to accommodate a break in the trend. However, the impact of model misspecification on testing for unit root is still unknown for panel data. This paper has two objectives: (i) it proposes a new test for unit root in the presence of structural instability for panel data. The test allows the intercepts, the trend coefficients or both to change at different date for different individuals. Under some mild assumptions, the test statistics is shown to be asymptotically normal which greatly facilitates valid inferences. (ii) Using the proposed test, this paper provides a systematic study on the impact of structural instability on testing for unit root using Monte Carlo Simulation. Specifically, the impact of model misspecification on the size and the power of the proposed test is discussed in details. Although the test performs reasonably well when the models are correctly specified, Monte Carlo results show that failure to accommodate a break in the trend coefficients can seriously distort the size and the power of the proposed test. In fact, the power of the test decreases when individuals experience a break in the trend coefficients even when the model is correctly specified. This is consistent with the results for univariate time series.