A new Cramer-Von Misses cointegration test with application to environmental Kuznets curve

This article introduces a new Cramer-Von Misses (CVM) cointegration test robust to nonlinearities. We characterize nonlinear cointegration in terms of a nonlinear moving-average filter (high pass filter) of a matrix based on permutation matrices on the discrepancy of empirical distributions. A Cramer-Von Misses (CVM) test statistic is proposed for testing the null hypothesis of two independent random walks against a broad range of cointegrating alternatives with monotonic nonlinearities and level shifts in the cointegration relationship. We derive the asymptotic distribution of this induced-order Cramer-Von Misses (CVM) cointegration test. This new non-parametric test statistic has two important properties: the invariance to monotonic transformations of the series and the robustness for the presence of several parameter shifts or structural changes. We analyse the small sample properties of this test by Monte Carlo simulations and evaluate the power of the test. Finally, this CVM test is applied to the analysis of long run environmental Kuznets curve which relates economic growth and pollution. In particular, we consider a nonlinear cointegration between gross domestic product (GDP) and CO2 emissions. Our new CVM test is able to find evidence of cointegration while classical single equation cointegration tests are not.