Research On Estimation And Application Of MESS Panel Data Model

As the further research of spatial autoregression model(SAR),spatial econometrics has been widely used in empirical research.As an alternative to the spatial autoregressive model(SAR),the matrix exponential space specification(MESS)model changes the spatial effect attenuation process in the SAR model into an exponential decay process.The good properties of the matrix exponent make it does not contain any Jacobian in the process of solving the model,and there is no need to impose special restrictions on the spatial correlation coefficients.The advantages of theoretical modeling,calculation and interpretation have made the MESS models widely concerned.With the availability of panel data increases,a systematic study of the MESS panel data model is an urgent problem to be solved.This paper extends the MESS theory to panel data,proposes a series of MESS panel data models,studies the estimation problems of these models,and applies theoretical research to the real data analysis.In theoretical research,this paper first studies MESS panel data model with fixed effects.Based on the quasi-maximum likelihood estimation(QMLE),the problem of model setting,parameters identify,estimation and incidental problem of MESS panel data model only with individual fixed effect(IF-MESSPD)and with two-ways fixed effects(TF-MESSPD)are studied in detail.Large sample properties of estimations from the direct approach and the transformation approach are systematically discussed.For IF-MESSPD,under the direct approach,when n tends to infinity and T is fixed,the incidental problem will cause the estimation of the variance to be inconsistent.Only when both n and T tend to infinity,all estimations are consistent and have good large sample properties.By contrast,as long as n tends to infinity,all parameter estimations from the transformation approach are consistent and have good large sample properties.For TF-MESSPD,all parameter estimations from the direct approach are consistent only when both n and T tend to infinity.When the speed of n tends to infinity faster than that of T,the asymptotic distribution of all estimations are properly centered to zero.This paper also gives the deviation correction method under direct estimation method.Next,the paper proposes the general random effect MESS panel data model(GRE-MESSPD).Under a series of regularity assumptions,the QML estimates of GRE-MESSPD model are consistent and asymptotically obey the normal distribution.For the estimation of the above models,this paper also designs Monte Carlo simulation to study the finite sample properties of the estimation results.The results shows that the QML estimates of the above models have good small sample properties.Finally,Hausman-type test statistic is constructed for the MESS panel data models with fixed effects and random effects.The results shows that the statistics can effectively identify the category of individual effects.In the empirical research,this paper applies the theoretical part of the research to the impact of the financial indicators of listed companies in China on the stock return rate.First of all,this paper extends the theoretical model of spatial asset pricing to the analysis framework of MESS panel data models.Then the financial indicators are selected,and the spatial weights matrices are constructed by the spatial correlation mechanism of stock returns.The Moran test shows that the stock returns of China have significant spatial correlation.Next,an empirical model is constructed through analysis,and the parameters is estimated by using the method provided in the theoretical part.Finally,the estimation results are compared with the estimation results of the SAR models,and the spatial effect decomposition method is used to decompose the spatial effects of stock returns.Empirical research proves that the theoretical model of this paper has good applicability.