Cointegrating polynomial regressions with power law trends

The common practice in cointegrating polynomial regressions (CPRs) often confines nonlinearities in the variable of interest to stochastic trends, thereby overlooking the possibility that they may be caused by deterministic components. As an extension, we propose univariate and multivariate CPRs that incorporate power law deterministic trends. Conventional fully modified estimation is demonstrated to be inadequate for valid asymptotic inference. As a solution, we employ simulation-based methods. Building on this concept, we also introduce a simulation-based procedure to combine subsampling KPSS tests. This approach significantly improves empirical power compared to the existing Bonferroni procedure. Applying our framework to the environmental Kuznets curve, we find reduced evidence that recent environmental improvement can be attributed solely to economic growth.