Estimation And Testing Studies Of Factor-augmented Panel Regression Models With Missing Data

The factor-enhanced panel regression model is an important extension of the traditional fxed-efects model.It can deal with unobserved heterogeneity,has strong applicability and interpretability,and is widely used in macro and micro economic felds.So far,a lot of scholars have conducted extensive research on such models,ranging from both N and T being large under the full panel to N large but T fxed,to N large with missing data T large panels are thoroughly researched.However,there are still few studies on the fxed-T with missing data.Therefore,this paper studies the estimation and testing of factor-enhanced panel regression models with large N and fxed T with missing data.This paper does two aspects of work on factor-enhanced panel regression models with missing data: the frst work is to propose an estimation method for the panel in the case where N is large and T is fxed,which is suitable for non-randomly missing.The estimation idea is to frst divide the unbalanced panel data into a limited number of subsets,so that the observed time points of the individuals in each subset are the same,so that each subset can as a complete panel data,and then use the cross-sectional mean of the observable variables in each subset to asymptotically eliminate the interaction efect,and fnally obtain a pooled estimate of the slope coeffcient,and also give the asymptotic properties and proof of the estimation.The second work is to propose a joint test statistic for serial correlation and heteroscedasticity in the idiosyncratic errors.Since the proposed estimation method is less effcient when the error term is heteroskedastic or serial correlative,in order to detect the potential serial correlation and heteroscedasticity in the idiosyncratic errors,this paper proposes a test method based on QR decomposition.A joint test statistic is developed that asymptotically follows a chi-square distribution under the null hypothesis.Monte Carlo simulation results show that the estimation method proposed in this paper and the proposed joint test statistic perform well under limited samples.Finally,the estimation method proposed in this paper is applied to a practical example,and the estimation results are basically consistent with the actual experience.