Efficient Estimation by Fully Modified GLS with an Application to the Environmental Kuznets Curve
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This paper develops the asymptotic theory of a Fully Modified Generalized Least Squares (FMGLS) estimator for multivariate cointegrating polynomial regressions. Such regressions allow for deterministic trends, stochastic trends and integer powers of stochastic trends to enter the cointegrating relations. Our fully modified estimator incorporates: (1) the direct estimation of the inverse autocovariance matrix of the multidimensional errors, and (2) second order bias corrections. The resulting estimator has the intuitive interpretation of applying a weighted least squares objective function to filtered data series. Moreover, the required second order bias corrections are convenient byproducts of our approach and lead to standard asymptotic inference. The FMGLS framework also provides two new KPSS tests for the null of cointegration. A comprehensive simulation study shows good performance of the FMGLS estimator and the related tests. As a practical illustration, we test the Environmental Kuznets Curve (EKC) hypothesis for six early industrialized countries. The more efficient and more powerful FMGLS approach raises important questions concerning the standard model specification for EKC analysis.
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