Panel cointegrating polynomial regressions: group-mean fully modified OLS estimation and inference

We develop group-mean fully modified OLS (FM-OLS) estimation and inference for panels of cointegrating polynomial regressions, i.e., regressions that include an integrated process and its powers as explanatory variables. The stationary errors are allowed to be serially correlated, the integrated regressors – allowed to contain drifts – to be endogenous and, as usual in the panel literature, we include individual-specific fixed effects and also allow for individual-specific time trends. We consider a fixed cross-section dimension and asymptotics in the time dimension only. Within this setting, we develop cross-section dependence robust inference for the group-mean estimator. In both the simulations and an illustrative application estimating environmental Kuznets curves (EKCs) for carbon dioxide emissions we compare our group-mean FM-OLS approach with a recently proposed pooled FM-OLS approach of de Jong and Wagner.