Cointegrating Polynomial Regressions with Power Law Trends: Environmental Kuznets Curve or Omitted Time Effects?

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.