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Powerful and Serial Correlation Robust Tests of the Economic Convergence Hypothesis

In this paper, a likelihood ratio approach is taken to derive a test of the economic convergence hypothesis in the context of the linear deterministic trend model. The test is designed to directly address the nonstandard nature of the hypothesis, and is a systematic improvement over existing methods for testing convergence in the same context. The test is first derived under the assumption of Gaussian errors with known serial correlation. However, the normality assumption is then relaxed, and the results are naturally extended to the case of covariance stationary errors with unknown serial correlation. The test statistic is a continuous function of individual t-statistics on the intercept and slope parameters of the linear deterministic trend model, and therefore, standard heteroskedasticity and autocorrelation consistent estimators of the long-run variance can be directly implemented. Building upon the likelihood ratio framework, concrete and specific tests are recommended to be used in practice. The recommended tests do not require the knowledge of the form of serial correlation in the data, and they are robust to highly persistent serial correlation, including the case of a unit root in the errors. The recommended tests utilize the nonparametric kernel variance estimators, which are analyzed using the fixed bandwidth (fixed-b) asymptotic framework recently proposed by Kiefer and Vogelsang (2003). The fixed-b framework makes possible the choice of kernel and bandwidth that deliver tests with maximal asymptotic power within a specific class of tests. It is shown that when the Daniell kernel variance estimator is implemented with specific bandwidth choices, the recommended tests have asymptotic power close that of the known variance case, as well as good finite sample size and power properties. Finally, the newly developed tests are used to investigate economic convergence among eight regions of the United States (as defined by the Bureau of Economic Analysis) in the post-World-War-II period. Empirical evidence is found for convergence in three of the eight regions.