Testing for Nonlinear Cointegration under Heteroskedasticity

TL;DR

This paper develops a bootstrap testing method for nonlinear cointegration that accounts for heteroskedasticity and variance breaks, with applications to environmental and monetary economics.

Contribution

It introduces a new bootstrap test for nonlinear cointegration under heteroskedasticity and proves its consistency, extending previous methods to more complex data scenarios.

Findings

The test has good finite-sample properties in simulations.

No strong evidence for cointegration in environmental Kuznets curves.

No rejection of nonlinear cointegration between US money demand and interest rate.

Abstract

This article discusses Shin (1994, Econometric Theory)-type 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, serial correlation, and endogeneity (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 in a variety of scenarios. 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