Detection And Estimation Of Common Breaks In Fixed Effect Of Panel Data

Panel data is widely used in economics and statistics,and in panel data,common breaks are frequent occurrences.For example,The financial crisis has had a major global impact.The finance policy and oil price shock may affect every country's output and income.And the credit crunch and debt crisis may affect every company's stock returns.Also,an emergence of a new technology,a discovery of a new medicine have their own consequences on people or other entities.Therefore,detection and estimation of the break point seems very important.For a single time series,it is difficult to identify the break point,for panel data,it is much easier to estimate the break point with a number of series.Because there are more information to cover the true break point with cross section dimension and time dimension in panel data.Thus the extended research and empirical analysis have very important theoretical significance and empirical value.In this paper,we extend the the common breaks in means for panel data to common breaks in fixed effect model.Estimation of break point in fixed effect is not consistent under least squares estimation,so the model should be transformed to the mean-differencing model first.Then we use least squares estimation to estimate the break point and the asymptotic theory and limiting distribution are obtained.In proving the consistence,the asymptotic theory is taken as the number of series goes to infinity with the number of observations either fixed or going to infinity as well,which overcomes a number of limitations associated with univariate series.We also carry out the Monte carlo simulation and empirical research to verify the theory.Eventually,we compare two methods of OLS and multiple regression analysis to estimate common break point.The theoretical proof indicateS that the total sum of squared residuals under the two methods are essentially the same.And we also use these two methods to carry out the empirical research via Matlab on the 18 cities' GDP data of Henan Province,verifying the correctness of the theoretical proof.