Weighted Block Empirical Likelihood Inference For Panel Data Model

With the advent of the big data era,panel data from biomedical,macro and micro economic,financial and other fields is no longer limited to small sample size(both the time dimension T and the cross section dimension N are small).Moreover,the intricate relationship between information sources also prevents the independence of panel data from being guaranteed.On the one hand,the existence of serial correlation and cross-sectional dependence invalidates the classical estimation methods such as least squares method,empirical likelihood method,etc.On the other hand,large panel data bringschallenge to some existing methods in computation.In order to deal with panel data model with complex dependent structure effectively and robustly,based on Nordman's(2009)idea,this paper introduces a weight function into block empirical likelihood method,and proposes a Weighted Block Empirical Likelihood(WBEL)method combined with the generalized estimation equation.In this paper,the improved BEL is presented for the innovation with correlation and innovation with corss-sectional dependence.In addition,we make use of expended score vector from Qu et al.(2000)to deal with corss-sectional dependece.In simulation,we compare the improved BEL with the Moving Block Empirical Likelihood method(MBEL)proposed by Qiu & Wu(2015).The result shows that the improved BEL can be applied to large N panel data as well as MBEL.At the same time,accuracy of the estimation by improved BEL is improved steadily no matter how much T is.The main contributions of this paper can be summarized from the following three points:1.For time series,we compare three commonly methods to select the optimal bandwidth in Block Empirical Likelihood: Progressive Block Empirical Likelihood,Automatic Block-Length Selection and Cross-Validation.According to the result from Monte Carlo simulation,the reasonable selection way for bandwidth is obtained and extended to panel data in the following content.2.For panel data with serial correlation,we propose Weighted Block Empirical Likelihood to deal with the corresponding models basing on General Estimationg Equations.The proposed method not only reduces the correlation between data-blocks by weighting data,but also preserves the correlation structure in every data-block well.In addition,theoretical and simulation results show that the proposed method can be applied to all kinds of time dimensions.Especially when T is samll,the effect is better than MELE.3.For panel data with serial correlation and cross-sectional dependence,we combine the extended score vector with WBEL to solve generalized linear model.On the one hand,WBEL of base matrix is used to reduce the amount of computation in large N similar to GEE,on the other hand,the assumption about structure of cross-sectional dependence is avoided.