Cointegrating Smooth Transition Regressions

This paper studies the smooth transition regression model where regressors are I(1) and errors are I(0). The regressors and errors are assumed to be dependent both serially and contemporaneously. Using the triangular array asymptotics, the nonlinear least squares estimator is shown to be consistent, and its asymptotic distribution is derived. It is found that the asymptotic distribution involves a bias under the regressor-error dependence, which implies that the nonlinear least squares estimator is inefficient and unsuitable for use in hypothesis testing. Thus, this paper proposes a Gauss–Newton type estimator that uses the nonlinear least squares estimator as an initial estimator and is based on regressions augmented by leads and lags. Using leads and lags enables the Gauss–Newton estimator to eliminate the bias and have a mixture normal distribution in the limit, which makes it more efficient than the nonlinear least squares estimator and suitable for use in hypothesis testing. Simulation results indicate that the results obtained from the triangular array asymptotics provide reasonable approximations for the finite-sample properties of the estimators and t-tests when sample sizes are moderately large. The cointegrating smooth transition regression model is applied to the Korean and Indonesian data from the Asian currency crisis of 1997. The estimation results partially support the interest Laffer curve hypothesis. But overall the effects of interest rate on spot exchange rate are shown to be quite negligible in both nations.This paper was partly written while the first author was visiting the Institute of Statistics and Econometrics at Humboldt University, Berlin. This author acknowledges financial support from the Alexander von Humboldt Foundation under a Humboldt Research Award and from the Yrjö Jahnsson Foundation. The second author wrote this paper while visiting the Cowles Foundation for Research in Economics, Yale University. This author thanks the faculty and staff of the Cowles Foundation, especially Don Andrews, John Geanakoplos, David Pearce, Peter Phillips, and Nora Wiedenbach, for their support and hospitality. The second author was financially supported for the research in this paper by Kookmin University. The authors thank Don Andrews, Helmut Lütkepohl, Peter Phillips, Bruce Hansen, and two referees for their valuable comments on this paper. Part of the data studied in this paper was provided by Chi-Young Song, whom we thank.