Cointegrating Smooth Transition Regressions

Abstract

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+

Functional cointegration: definition and nonparametric estimation

“…Our work also falls within the bounds of the very recent literature on nonlinear cointegration tackled from a purely nonparametric point of view [Karlsten, Myklebust and Tjostheim (2007), Wang and Phillips (2009), Kasparis and Phillips (2009) amongst others]. Note that the idea of a nonlinear long run equilibrium relationship (attractor) was also put forward in the early work of Granger and Hallman (1989), Breitung (2001), Saikkonen and Choi (2004) amongst others.…”

Fiscal policy and TFP in the OECD: measuring direct and indirect effects

“…6 In a pure time series context there is already quite some literature on non-linear cointegration analysis, i.e. asymptotic theory for non-linear regression with integrated processes was developed by, among others, Park and Phillips (2001) and extended to a fairly general non-linear model by Saikkonen and Choi (2004) One additional complication is that the model is not identified as λ it and F ca2 t are not identified separately, only their product is. For instance, multiplying λ it by a constant a while dividing F ca2 t by the same constant, which implies that λ i0 , λ 0 and λ are multiplied by the constant a, leaves the model in equation (16) unchanged as F ca2 t /a (aλ it ) = F ca2 t λ it or equivalently aλ i0 +z it aλ aλ 0 +z t aλ = λ i0 +z it λ λ 0 +z t λ .…”

Bayesian inference in a time varying cointegration model

“…These relations are slowly changing. Further details and motivation can be found in any of the classical econometric papers on time-varying cointegration such as Martins and Bierens (2005) or Saikkonen and Choi (2004).…”