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This paper develops the asymptotic theory of a Fully Modified GeneralizedLeast Squares estimator for multivariate cointegrating polynomial regressions.Such regressions allow for deterministic trends, stochastic trends and integerpowers of stochastic trends to enter the cointegrating relations. Our fullymodified estimator incorporates: (1) the direct estimation of the inverseautocovariance matrix of the multidimensional errors, and (2) second order biascorrections. The resulting estimator has the intuitive interpretation ofapplying a weighted least squares objective function to filtered data series.Moreover, the required second order bias corrections are convenient byproductsof our approach and lead to standard asymptotic inference. We also studyseveral multivariate KPSS-type of tests for the null of cointegration. Acomprehensive simulation study shows good performance of the FM-GLS estimatorand the related tests. As a practical illustration, we reinvestigate theEnvironmental Kuznets Curve (EKC) hypothesis for six early industrializedcountries as in Wagner et al. (2020).

Efficient Estimation by Fully Modified GLS with an Application to the Environmental Kuznets Curve