Testing Slope Homogeneity In Panel Data Models With Spatial Error Term

Over the past few years,spatial panel data model has been widely used in empirical research.Allowing cross-sectional dependence in error term,the spatial error model is favored.However,conventional panel spatial error model imposes a strong constraint on the homogeneity of each section coefficient.On the empirical level,policy implementers may pay more attention to heterogeneity effects.Then based on homogeneity spatial error model,the coefficient estimates for the model are only average effects.At the theoretical level,misidentification of the types of cross-section coefficients may result in inconsistent and/or less valid estimators,which in turn affect statistical inference and hypothesis testing.Therefore,before applying the traditional spatial error model,it is essential to test slope homogeneity of the coefficients of each section.On the other hand,the current theoretical research on the homogeneity test in the panel data models mainly focuses on the three directions based on the disturbance with autocorrelation,heteroscedasticity and strong cross sectional dependence caused by the factor interaction term.Under the framework of the weak cross-sectional dependence generated by the spatial autoregressive structure in error term,this paper attempts to test the homogeneity of the section coefficients,which can further enrich the theoretical research about slope homogeneity test in panel data models..Firstly,this paper introduces the random coefficients into the traditional panel data models and establishes the spatial error model with slope heterogeneity.Then we construct the corresponding null hypothesis and alternative hypothesis and establish a LM test statistic to detect the slope homogeneity in sections.Under the assumption of independent and identical normal distribution,we prove the LM test statistic is asymptotically distributed as chi-square distribution with the degree of freedom as the number of explanatory variables.Analysis shows that the LM test statistic has a certain local test power.Secondly,we relax the hypothesis of normality and construct the first robust test statistic called LM1_robust by adjusting the variance covariance matrix of the score vector.And considering the potential model misspecification,we also establish the second robust test statistic called LM2_robust based on the quasi-maximum likelihood estimation theory(White,1982).The last two robust test statistics are both expected to be distributed as chi-square distribution and we only give some simple derivations.Monte Carlo simulation results show that,firstly in the data generation process of the spatial error model,all the other three LM-type test statistics: BEA statistic(Breitung at al.,2016),JL statistic(Juhl and Lugovskyy,2014)and SC statistic(Su and Chen,2013)performe poor in finite sample properties,while the size and power performance of the LM test statistic in this paper are better.Second,in the normal case,whether N>T or T>N,the finite sample properties of the LM test statistic of this paper perform well,and the stronger spatial correlation in the disturbance term will increase power.Third,in the non-normal situation,the second robust test statistic LM2_robust has very small size distortions in short panel and long panel,while both the LM and LM1_robust have significant size distortions in short panel.And size distortion of the two test statistics will be greatly reduced in long panel.Moreover,the stronger spatial correlation in the error term significantly improves the size performance of the three test statistices in the short panel.In the normal case or the nonnormal situation,it is difficult to distinguish the power of the three test statistics of LM,LM1_robust and LM2_robust in N>T or T>N.But the power of all the three test statistics rise much faster with T than with N.Finally,in the case of heteroscedasticity,whether N>T or T>N,the size performance of the second robust test statistic LM2_robust always outweigh the other two test statistics and shows very close to the nominal size.Meanwhile,stronger spatial correlation in error term will significantly reduce the size distortion of the LM and LM1_robust test statistic.