Integrated modified least squares estimation and (fixed-b) inference for systems of cointegrating multivariate polynomial regressions

We consider integrated modified least squares estimation for systems of cointegrating multivariate polynomial regressions, i. e., systems of regressions that include deterministic variables, integrated processes and products of these variables as regressors. The errors are allowed to be correlated across equations, over time and with the regressors. Since, under restrictions on the parameters or in case of nonidentical regressors across equations, integrated modified OLS and GLS estimation do not, in general, coincide, we discuss in detail restricted integrated generalized least squares estimators and inference based upon them. Furthermore, we develop asymptotically pivotal fixed-b inference, available only in case of full design and for specific hypotheses.