  This article discusses tests for nonlinear cointegration in the presence of
variance breaks. We build on cointegration test approaches under
heteroskedasticity (Cavaliere and Taylor, 2006, Journal of Time Series
Analysis) and nonlinearity (Choi and Saikkonen, 2010, Econometric Theory) to
propose a bootstrap test and prove its consistency. A Monte Carlo study shows
the approach to have satisfactory finite-sample properties. We provide an
empirical application to the environmental Kuznets curves (EKC), finding that
the cointegration test provides little evidence for the EKC hypothesis.
Additionally, we examine a nonlinear relation between the US money demand and
the interest rate, finding that our test does not reject the null of a smooth
transition cointegrating relation.
