The Research On Panel Linear Fixed Effects Models With Serial Correlation And Cross Sectional Dependence

Information era shows various kinds of panel data constantly. As a result, itoffers the possibility of multi-angle and multi-faceted thinking to scientific research.Meanwile, due to the augmentation of both the cross-sectional and the time dimension,it also brings much more challenges to our analysis. Panel data analysis, especially theLarge Panel (both the time dimension T and the cross section dimension N are large),is playing an increasing role in many kinds of fields, including economic, financial,biomedical and environmental science. Panel data fixed effects models have beenwidely applied to different kinds of areas, because it can not only solve the problem ofendogenous in some degree but also can reflect the heterogeneity among individuals.However, there are strict assumptions about idiosyncratic error in the classicfixed effects model. It demands that the idiosyncratic-errors of different times of thesame individual should be independent, so do the ones of different individuals of thesame time. That is, there is no serial correlation and cross-sectional dependence.Ignore either the serial correlation or the cross-sectional dependence will lead to theinvalidity of the model parameter estimation and the bias of standard errors. On thebasis of summarizing the existing articles, the problems elaborate in this paper can bedivided into two parts, namely, fixed effects model with serial correlation only and themodel with both serial correlation and cross-sectional dependence.To sum up, the main contribution of this paper can be outlined in two aspects asfollows. On the one hand, we generalize the moving blocks empirical likelihoodmethod (Qiu&Wu (2013)) and then apply it into the fixed effects model when thereexists serial correlation in idiosyncratic-errors. New method shows four advantages:1. The new approach assumes that serial correlation is in the form of mixingalesequence, which is an extremely generalized time serial process, thus avoidingmisspecification of serial correlation form largely.2. Large sample theories ensure that the new method allows the panel data timedimension T to tend to infinity. And the simulations show that the new method is alsoadapt to the small T (such as T=6).3. Monte Carlo simulations show that the new method is much more effectivethan that of parameter method of Baltagi&Li (1994) and non-parameter one of Gon alves (2011)4. An empirical analysis on the relationship between PM2.5and conventionalatmospheric pollution indicators is applied to illustrate the high accuracy of newmethod.On the other hand, when comes to the fixed effects model with both correlationand cross-sectional dependence, the paper borrows the moment equations of theprocedure of quadratic inference function(Qu. et al (2000)) and then combines theextended score vector with the moving blocks empirical likelihood method toestimates the model. New method owns four merits:1. The new method only requires that the serial correlation satisfies themixingale sequence and there is no restriction on cross-sectional dependence.Therefore, it takes into account the data characters of both the time-series data andcross section sufficiently, at the same time, it reduces the probability of statisticalinference failure due to the model misspecification.2. Asymptotic properties suggest that the new method is suitable to the panel datathat the time dimension T tends to infinity and cross-sectional dimension N is limited.But simulation results prove that the new method works well for large cross sectiondimension (N=500) too.3. Limited sample simulations show that the new method is much more effectivethan the existing methods that can deal with the fixed effects model companied withserial correlation and cross-sectional dependence, such as Gon alves (2011) andVogelsang (2012).4. An empirical research of the relationship between CO2emissions and theurbanization also suggests the validity of the new method.