Threshold Cointegration And Applications To Chinese Economy

In macroeconomy, most of time series data are unit root process; therefore the theory of cointegration has undergone considerable development and various econometric and statistical methods have been developed for the analysis of cointegrated time series and many of them are now routinely applied in empirical studies. Under the standard cointegration frame, cointegration vector characterizes the long-run equilibrium relationship, and the ECM characterizes the short-run variety and adjustment effect, so the cointegration vector and ECM are supplement each other. Granger gained Nobel Prize of economics in 2003 for the contribution to cointegration. But standard cointegration theory imposes at least three strong restrictions on the underlying economic behavior:(1)the long-run equilibrium is unque;(2)the adjustment toward the equilibrium is symmetric; (3)the equilibrium correction is a constant proportion of the previous equilibrium error. Those indicate that the cointegration relationship and adjustment effect of standard cointegration are linear, which is according to economic theory and actual economic status quo, need not be the case. Once ignoring nonlinear of actual, your results maybe wrong when you instead of nonlinear model with linear model. Threshold cointegration expends standard cointegration with nonlinear aiming to the shortcomings of standard cointegration. The goal of threshold cointegration is to study the nonlinearity and nonstationarity in economics; therefore, threshold cointegration became a central part of modern time series econometrics.The basic idea of threshold cointegration is using the TR (or STR) model to characterize the long-run equilibrium and adjustment effect in cointegration frame. But threshold cointegration is an advanced econometrics theory developed recently, there are much problems needing to solution. Base on the need of actual economic status quo, this paper expands and ameliorate the disadvantages of existing threshold cointegration. So the threshold cointegration developed in this paper can better describe actual economic. The contributions of this paper in theory are those: (1) Kapetanios, Shin (2004) use exponential function describe nonlinear adjustment effect in ECM. In this paper, we describe nonlinear adjustment effect in ECM with unknown transition function (exponential function or logistic function), and develop test procedures and test statistic to test transition function. The Monte Carlo simulation result shows its small-sample wonderful performances. (2) Under the condition of threshold cointegration vector is unknown, Hansen,Seo(2002) characterizes nonlinear adjustment effect with two-regime TR model in ECM, therefore the adjustment effect change sharply, which is too restrictive and not fit of many actual economic phenomena. This paper develops an ECM,in which the threshold cointegration vector and smooth transition function are unknown, to characterize nonlinear adjustment effect, therefore adjustment is continuous. Furthermore, we propose test procedures and estimation method to test and estimatethreshold cointegration vector and adjustment effect of the ECM. The simulation result shows that estimated parameters are consistent and test statistic have good small sample performances. (3) Choi, Saikkonen(2004) follow the common practice in threshold cointegration and permit both serial and contemporaneous correlations between the regressions and the error term of the model. In order to allow for this feature, they estimate the model with DNLS and propose LM statistic to test linearity. Once the test results show that the model is nonlinear (threshold cointegration), Choi,Saikkonen(2005) propose DNLS to estimate cointegration vector and employ KPSS statistic, calculating with subsamples of the DNLS residuals, to test threshold cointegration. This paper extend Choi, Saikkonen's(2004,2005) test and estimating methods with fully modify OLS. The mathematics proofs and simulation show that the test statistics developed by this paper have same limiting distribution with Choi, Saikkonen(2005)and fully modify OLS is better than DNLLS under small-sample. (4) We extend threshold cointegration to panel data and use TR model to characterize panel cointegration vector. We base on Westerlund,Edgerton's(2005) idea to develop panel threshold cointegration test statistic and derive the limiting distribution of our statistic, and found the limiting distribution is normal distribution and doesn't depend on nuisance parameters. Furthermore, the Monte Carlo simulation result shows panel threshold cointegration statistic small-sample wonderful performances.As the examples of empirical study, firstly three cases which are Taylor Rule in China's monetary policy, the regime switch of Phillips Curve and the factors that affect on the farmer's expending on health care are investigated respectively in the paper. The analysis of Taylor Rule is based on threshold cointegration defined on adjustment effect of ECM, while the study of Phillips Curve is based on threshold cointegration defined on cointegration vector, and the farmer's expending on health care is based on panel data cointegration. Lastly, this paper studies the effect of the urban-rural income disparity to actual economic growth with regime switch panel data cointegration and threshold cointegration in China. We firstly define and calculate the Theil index ,which measure the urban rural income disparity , based on the dual structure in urban and rural economy, and then specify a panel cointegration model and threshold cointegration model with respect to the Chinese situation of rural-urban income disparity and economic restructure transforming. The estimated results indicate that there is nonlinear cointegartion relationship witch depending on the level of the rural-urban income disparity and the economic stage. Such result implies that the effect of rural-urban income disparity to economic growth is positive at the beginning of Chinese reform; however, the effect is negative at present. Estimated PVECM indicates that the long-run effects of the disparity depress the economic growth and stimulate the disparity in short run.