  The environmental Kuznets curve predicts an inverted U-shaped relationship
between environmental pollution and economic growth. Current analyses
frequently employ models which restrict nonlinearities in the data to be
explained by the economic growth variable only. We propose a Generalized
Cointegrating Polynomial Regression (GCPR) to allow for an alternative source
of nonlinearity. More specifically, the GCPR is a seemingly unrelated
regression with (1) integer powers of deterministic and stochastic trends for
the individual units, and (2) a common flexible global trend. We estimate this
GCPR by nonlinear least squares and derive its asymptotic distribution.
Endogeneity of the regressors will introduce nuisance parameters into the
limiting distribution but a simulation-based approach nevertheless enables us
to conduct valid inference. A multivariate subsampling KPSS test is proposed to
verify the correct specification of the cointegrating relation. Our simulation
study shows good performance of the simulated inference approach and
subsampling KPSS test. We illustrate the GCPR approach using data for Austria,
Belgium, Finland, the Netherlands, Switzerland, and the UK. A single global
trend accurately captures all nonlinearities leading to a linear cointegrating
relation between GDP and CO2 for all countries. This suggests that the
environmental improvement of the last years is due to economic factors
different from GDP.
