Theory And Application Of Threshold Panel Data Model

From the perspective of model setting,panel data model can capture individual differences in dynamic data adjustment through intercept items,thus reduce errors from data aggregation.From the perspective of data characteristics,panel data has two dimensions:time series and cross-section,and takes both advantages of cross-sectional data and that of time-series data.As a result,panel data model has been widely used in econometric analysis,and become one of the most important branches of econometrics research.However,traditional panel data model assumes a linear relationship among the economic variables;thus,the conclusion is likely to be wrong if the traditional panel data model is used to analyze the relationship between economic variables with nonlinear characteristics.Threshold panel data model,which combines the panel data with nonlinearity to study the nonlinear problems in real economy,overcomes this shortcoming and expands the traditional panel data model.Therefore,threshold panel data model has become one of the most forward research fields in modern econometrics.According to the methodology,we divide the threshold panel data models into three groups:static threshold panel data model,ordinary dynamic threshold panel data model(dynamic items without threshold effects),and dynamic threshold panel data model with threshold effects in dynamic items.For static threshold panel model and dynamic threshold panel model,the cases of endogenous threshold variables and exogenous threshold variables are discussed separately.The structure of this paper is accordingly arranged.The followings are the main content and innovations of this paper.For the static threshold panel model,Hansen(1999)proposes a concentrated least squares estimation method and lots of scholars do empirical research based on this.In this paper,we extend the hypothesis of exogenous threshold variables,and consider the endogenous threshold variable.In particular,we discuss three different specifications in the model:first,both the threshold panel data model and the threshold variable equation do not contain individual effect(ETM-PTR);second,the threshold panel data model contains individual effects,while the threshold variable equation does not contain individual effects(FE1-ETM-PTR);third,both the threshold panel data model and the threshold variable equation contain individual effects(FE2-ETM-PTR).Also,we introduce the corresponding estimation methods.For empirical study,this paper studies the threshold relationship between inflation rate and relative price variability(RPV)in China.The results show that the impact of inflation rate on the relative price variability changed twice with the gradual increase in inflation,that is,there are two threshold effects.Thus,a relatively clear innovation in application is formed.For the ordinary dynamic threshold panel data model,foreign scholars have done a lot of empirical research based on the two-stage estimation method proposed by Caner and Hansen(2004).However,this estimation method is for the threshold regression model with endogenous variables,and whether it is adapted for ordinary dynamic threshold panel data model is neither supported by theoretical proof nor supported by simulation experiments.As an innovation,we extends the two-stage estimation method proposed by Caner and Hansen(2004),and proposes the two-stage estimation method of ordinary dynamic panel data model with threshold effect.The simulation results show very good finite sample properties,for both threshold parameter and autoregressive coefficient.In addition,the two-stage estimation method proposed in this paper is applicable under both the large threshold effect and the small threshold effect.Finally,based on the ordinary dynamic threshold panel data model,this paper studies the effect of economic growth on public health expenditure in China.For the dynamic threshold panel data model with threshold effects in dynamic items,this paper considers both exogenous threshold variables and endogenous threshold variables.For the former,we introduce four estimation methods which can get consistent estimators:FD-GMM estimation,SYS-GMM estimation,FD-2SLS estimation and maximum likelihood estimation.For the latter,we introduce the FD-GMM estimation method,obtain the consistent estimators of the threshold parameter and the slope coefficient,and give the asymptotic distributions of the estimators.Based on the FD-GMM estimator and the FD-2SLS estimator,we introduce the method of testing for exogeneity under the framework of the dynamic threshold panel data model.In addition,comparing the four estimation methods under exogenous threshold variables,we found that for FD-2SLS estimation,the finite sample property of the threshold parameter estimation is very good,while that of the slope coefficient is poor;for FD-GMM and SYS-GMM estimation,the finite sample performance of the two are relatively close,and both are not very good.For maximum likelihood estimation,the finite sample performance of both threshold parameters and slope coefficients are good.The corporate capital structure is the research hotspot in the corporate finance field,especially the adjustment speed of the corporate capital structure to target capital structure,as an important indicator of measuring the capital structure decision making.However,it is difficult to find the factors affecting the adjustment speed of capital structure,since the adjustment speed of corporate capital structure is measured by the coefficient of dynamic items in the regression model.Dynamic threshold panel data model with threshold effects in dynamic items can capture the changes of the enterprise capital structure adjustment speed and its influencing factors,given that it describes the variation of dynamic items and slope coefficient by threshold effect.Based on dynamic threshold panel data model with threshold effects in dynamic items,this paper studies the nonlinear adjustment of capital structure of listed firms in China,selecting corporate investment,firm size,financing constraints,growth opportunities and free cash flow as threshold variables.This is not only an advanced research in the field of enterprise capital structure,but also a good reflection of the application value of dynamic threshold panel data model with threshold effects in dyanmic items.