Theoretical Analysis And Applications Within Cointegrating Smooth Transition Models

In the history of Economic time-series analysis, it is discovered that utilising linear regression model is important, econometrists have developed a theoretical framework for statistical inference on linear regression models. While research on economic phenomenon goes further, linear regression model appears to have more deviations when applied to describing centain economic and financial phenomenon, or even leads to a conclusion that goes against to common sense or theory foundamentals. For better simulation and explanation of the real economic phenomenon, it is essential to establish nonlinear regression models. Besides, modeling, estimating and testing methods developed based on the assumption of stationary time series data, become unable to solve the issues raised by nonstationarity of real world time series data. Insisting on using the traditional estimation and test methods without considering the nonstationarity(if exists) of data would probably lead to biased estimation or even spurious regression.This paper attemps to establish a model allowing both smooth regime switching and nonstationarity based on Granger and Terasvirta's propose of smooth transition regression model in 1993 and conitegration theory proposed by Granger in 1978. This could be quite valuable for dealing with empirical economical, especially macroecnomical problems, which usally accure because of nonstationarity of variables and smooth (instead of sudden) regime switching as there exists lags in response to sudden shocks.For empirical study, this paper chooses several popular topics in China's economy in recent years, including equity in education, inequality in public service, and the urban-rural income gap, and considers the effects of urban-rural education gap on urban-rural income gap, the effects of the inequality of public service on urban-rural income gap, respectively. In the urban-rural education gap model, the methodology of this paper goes as follows:first, roughly determine the possible explanatory varibles besides the core explanatory variable (urban-rural income gap) according to economic theory and literatures, the variables in this paper are fiscal investment to agriculture, level of urbanization, level of opening, level of government intervention, level of marketization, level of financial development, etc.; second, determine the explanatory variables via statistical significance test on coefficients and Granger Causality tests; third comes the regime-switching function, we need determine the positioning parameter d (or namely the lag order of the threshold variable) according to F statistics, AIC, and R2, then use the Bootstrap based LM test to test linearity on nonlinearity (or namely the test on the existence of regime-switching function) and determine the detailed form of the regime-switching function (this paper mainly discusses two typical forms of regime-switching functions, Logistic and Exponential, and the result shows that the regime-switching function in this education gap model is Logistic type); finally, use NLS (nonlinear least squares) to estimate the parameters, and apply Moonte Carlo based sampling method to the cointegration test on the previous determined model, if the cointegration relationship exists, then use iteration method to get a consistent estimation. This paper also establishes a dynamic panel model, the estimation of which is based on GMM, the result is compared with the cointegrated smooth transition regression model. For the inequality of public service model, we did the same thing, and the result shows that the regime-swtching function in this public service model also takes the form of Logistic. On the whole, the empirical study reveals that, in China, the longrun effect of urban-rural education gap on urban-rural income gap is positive, while the effect of inequality of public service on urban-rural income gap has two different expressions in the two different regimes devided by financial development level.