Essays on Panel Cointegration
Abstract: This thesis develops new techniques for analyzing cointegrated relationships in panel data. The first chapter is introductory while the remaining six contain the main contributions. The second chapter is concerned with the estimation of a cointegrated panel relation with endogenous regressors, in which case the least squares estimator is biased unless it is conditioned on the lags and leads of the differences of the regressors. The problem is how to choose the appropriate number of lags and leads. This issue is illuminated by examining the performance of several information criteria that facilitate a data dependent choice. The Monte Carlo evidence suggests that the criterion with the best performance also leads to the best performing estimator. Although cointegration is usually considered to be the most natural choice of null hypothesis, most existing panel tests are based on the null hypothesis of no cointegration. The third chapter therefore develops a new test with cointegration as the null. Asymptotic properties of the test are derived and verified in small samples via Monte Carlo simulations, and implementation is illustrated through an application of the test to international R&D spillovers. Relationships that span extensive periods of time are prone to structural breaks. Yet, there is presently no test that is general enough to allow for such breaks. The fourth chapter takes a step in this general direction by proposing a test that allows for multiple structural breaks in the cointegration relation. Asymptotic distribution of the test is derived and critical values are provided to permit accurate testing even in small samples, which is verified using Monte Carlo simulations. An application of the test to the Feldstein-Horioka puzzle is also provided. Empirical evidence suggests that the Fisher hypothesis does not hold, which seems at odds with many theoretical models. The fifth chapter argues that these results can be attributed to the low power of conventional time series tests and that the use of panel data can generate more powerful tests. For this purpose, two panel cointegration tests are developed that allow for cross-sectional dependence, and are shown to be more powerful than existing tests. The empirical results suggest that, based on the new tests, the Fisher hypothesis cannot be rejected. In the sixth chapter, four new error correction based tests for the null hypothesis of no cointegration are proposed. These tests are less restrictive than most existing tests and are therefore more widely applicable, which implies that they are also expected to be more powerful. This is illustrated via simulations. The empirical application shows evidence of cointegration between health care expenditures and GDP. The seventh chapter develops two panel cointegration tests that allow for very general forms of serial correlation structures without the need for any kind of adjustment. This makes them very simple in comparison to existing tests, which do not share this invariance property. Asymptotic distributions are derived and Monte Carlo evidence suggests that the new tests compare favorably with several other popular tests.
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