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This paper extends the threshold cointegration model developed by Gonzalo, J., and J. Y. Pitarakis. 2006. “Threshold Effects in Cointegrating Relationships.”  Oxford Bulletin of Economics &amp; Statistics  68: 813–33 and Chen, H. 2015. “Robust Estimation and Inference for Threshold Models with Integrated Regressors.”  Econometric Theory  31 (4): 778–810 to allow for a time-varying threshold, which is a function of candidate variables that affect the separation of regimes. We derive the asymptotic distribution of the proposed least-square estimator of the threshold, and study the convergence rate of the threshold estimator. We also suggest test statistics for threshold effect and threshold constancy. Monte Carlo simulations point out that the convergence rate of the threshold estimator is consistent with the asymptotic theory, and the proposed tests have good size and power properties. The empirical usefulness of the proposed model is illustrated by an application to the US data to investigate the Fisher hypothesis.

Time-varying threshold cointegration with an application to the Fisher hypothesis