Nonlinear Multivariate Cointegrating Regression And Its Application To Consumption Expenditure

People always regard the level of consumption as one of the main determinants of global well-being and it has an important influence on the country's economic productivity,business cycles and economic policies.Therefore,it is indispensable to study consumption expenditure in China.Since Granger first proposed the concept of cointegration,cointegration theory has become an important theory for studying national consumption expenditure.But most of literatures are limited to model with univariate regressor.This is clearly restrictive from a view of practice.For example,the Carbon Kuznets Curve(CKC)relates the per capita C02 emission of a country to its per capita GDP.But with the same per capita GDP.different countrys' energy structure affect per capita C02 emission greatly.Therefore,the nonlinear multivariate cointegration is still an open problem.Because the nonlinear model is restricted by "curse of dimensionality":the nonlinear multivariate cointegration regression model is still an open question.At present,there are two commonly used meth-ods to avoid "curse of dimensionality":the semi-parametric additive model and the single index model.Since this topic tends to consider the semi-parametric estimation of multivariable semi-parametric additive(or nonadditive)model mod-els with nonstationary time series,it is necessary to elaborate and apply basic cointegration theory and these two methods.Finally,as an application of cointegration theory,this study considers the impact of per capita.dispensable income and real interest rates on per capita consumption expenditure from 2013 to 2017 in China.The model chosen is a semi-parametric model,where the coefficient of per capita disposable income is the only non-paramctric term.Many studies show that the model is more likely to be nonlinear.Therefore,it is necessary to analyze the stability of the required variables before applying the model,and analyze the co-integration relationship.The methods used are ADF test and EG two-step method.It can be concluded that the log value of the consumption expenditure and disposable income can satisfy the first order integration and the co-integration relationship and the real interest rate is the stable sequence.Since the model is additive,the orthogonal sequence approximation method and kernel estimation method can be used to estimate the nonparamtric items preliminarily.Then based on the hypothetical test,reasonable assumptions H0 was ma.de,i.w.take the assumption that the nonparametric term is k-order polynomial and the accuracy of the specific statistic is analyzed by using the bootstrap method.The test results show that,under the significance level of 0.1,the null hypothesis is accepted when k=1,3.It implies that the nonparametric term is more likely to be one or three polynomials of real interest rate.In addition,by using ADF test,The residual of k= 1 is stable,but k = 3 not.It implies that the non-parameter term more like 1-order polynomial,which is particularly similar to the results obtained by the orthogonal sequence approximation method and kernel estimation method.Therefore,in the last five years,the dependence of per capita consumption expenditure on per capita disposable income and real interest rate in China tend to favor the situation of H0 when k=1.The innovation of this paper:1.This topic to consider in the empirical analysis of the semiparametric model does not contain zero mean condition,and the original methods,witch require the zero mean condition,orthogonal sequence approximation and nuclear estimate method,are also suitable for this kind of model.At the same time,the way of generating bootstrap sample is adjusted.2.The implementation of Matlab for using orthogonal sequence approxima-tion,kernel estimation method and Bootstrap testing process is provided.3.Methods for the study on the per capita consumption expenditure is inte-grated,i.e.the semi-parameter estimation methods for a kind of multivariable models and the specification testing based on bootstrap method are combined,which gives a more reliable model assumptions,in addition a suitable bootstrap method can also be applied according to the data dependency relationship(block bootstrap,sieve bootstrap)to match the specification testing.