Estimation and Inference for Cointegrated Systems of Multi-Factor Production Functions: Modelling the Joint Behavior of GDP and Emissions

This paper develops integrated modified ordinary and generalized least squares estimation for systems of cointegrating multivariate polynomial regressions, i. e., systems of equations that include deterministic variables, integrated processes and (cross-)products of non-negative integer powers of these variables as regressors. The stationary errors are allowed to be correlated across equations, over time and with the regressors. The necessity to consider integrated modified generalized least squares estimation arises in the case of estimation under restrictions, which in general implies that ordinary and generalized least squares estimators cease to be identical. We discuss in detail hypothesis testing for the unrestricted and restricted estimators. Furthermore, we develop asymptotically pivotal fixed-b inference, shown to be available only in special cases. A brief illustration to modelling output and emissions as a Cobb-Douglas-Translog cointegrated production system with TFP, capital and labor as inputs indicates the potential usefulness of the developed methods for climate econometrics.