In this paper, we develop new threshold cointegration tests with SETAR and MTAR adjustment allowing for the presence of structural breaks in the equilibrium equation. We propose a simple procedure to simultaneously estimate the previously unknown breakpoint and test the null hypothesis of no cointegration. Thereby, we extend the well-known residual-based cointegration test with regime shift introduced by (Gregory, A. W., and B. E. Hansen. 1996a. “Residual-based Tests for Cointegration in Models with Regime Shifts.” Journal of Econometrics 70: 99–126) to include forms of nonlinear adjustment. We derive the asymptotic distribution of the test statistics and demonstrate the finite-sample performance of the tests in a series of Monte Carlo experiments. We find a substantial decrease of power of the conventional threshold cointegration tests caused by a shift in the slope coefficient of the equilibrium equation. The proposed tests perform superior in these situations. An application to the “rockets and feathers” hypothesis of price adjustment in the US gasoline market provides empirical support for this methodology.
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