Estimation Of Several Dynamic Panel Data Models

In recent decades,there has been a growing interest in the study of panel data models,and it has become the most rapidly developing direction in econometrics.Panel data models has been largely applied in economics,such as labor economics,health economics as well as development economics.Panel data involve two dimensions:a cross-sectional dimension N,and a time-series dimension T.The theoretical properties of model estimators would depend on the size of N and T.Earlier studies mainly focused on micro panels with large N and small T,and the asymptotics of estimators was usually discussed in the case of large N.With the improvement of data collection technology,there are more and more panel data with large N and large T.These large-N,large-T panels call for the use of large-N and large-T asymptotics rather than just large-N asymptotics.Moreover,when T is large,there is a need to consider some special issues,such as dynamics,non-stationarity and cross-sectional dependence.In these cases,the estimation methods and the theoretical properties of the estimators need to be reexamined.In this thesis,several kinds of dynamic panel models with time trend,non-stationarity or cross-sectional dependence are considered.Some theoretical results of the estimators are established as N and T tend to infinity,these results are non-trivial and new in the literature,which provide some new findings for dynamic panel data models.The contents of this thesis are as follows:(1)For the general dynamic panel model,we apply forward orthogonal deviations(FOD)or first difference(FD)to eliminate the individual effect,the optimal GMM estimation based on FD is obtained,and this estimator is found to be identical with GMM based on FOD,hence the relationship between FOD and FD is derived as a by-product.Additionally,we investigate how the theoretical properties of GMM estimators depend on N or T via Monte Carlo simulation,it is shown that the GMM estimators are biased of order 1/N for fixed T,while the efficient mainly depends on the size of T.(2)We consider GMM and simple instrumental variable(Ⅳ)type estimation of dynamic panel data models with both individual-specific effects and heterogeneous time trend when both N and T tend to infinity.As the main theoretical contribution,the asymptotic properties of the GMM and Ⅳ estimation of the lag coefficient are established.The results show that the GMM estimations with optimal weighting matrix are consistent and asymptotically normally distributed,but have asymptotic bias of order(?),while the two-stage least square estimation(2SLS)using non-optimal weighting matrix is inconsistent when N and T are of similar magnitude.We also establish the asymptotic unbiasedness of the simple Ⅳ estimation using first-difference lagged dependent variable as instrument,and establish the invalidity of using level lagged dependent variable as instrument for the simple Ⅳ estimation.Additionally,we also consider two types of bias-corrected GMM estimators,which perform better in terms of bias and efficiency.Monte Carlo simulations confirm our findings.(3)For the dynamic panel data models with both time trend and unit root,we consider two simple instrumental variable estimators(Ⅳ)based on FOD and double first difference(2FD)transformation,respectively.In the unit root case,the usual instruments only satisfy orthogonality conditions but fail the relevance condition,as a result,the theoretical properties of estimators would be different from those of the stationary case.The results show that Ⅳ estimator based on FOD is inconsistent as N tends to infinity and T is fixed,but when T→∞ as N→∞,the estimator is(?)consistent and its limit distribution is(?)times a standard Cauchy.However,regardless of whether T is fixed or infinite,Ⅳ based on 2FD is inconsistent and has a constant bias as N→∞.In addition,the bias-corrected versions of the above two estimators are also proposed.The main results are further verified by Monte Carlo simulations.(4)We consider a dynamic panel data model with non-stationary multifactor error structures.There are three key ingredients of the model:dynamics,non-stationarity and cross-sectional dependence.In this case,we apply the common correlated effect(CCE)method to estimate the model parameters and obtain CCE and CCE mean group(CCEMG)estimators,and the asymptotic properties of the CCE and CCEMG estimators are derived as both N and T tend to infinity.We show that both CCE and CCEMG estimators are consistent,and the CCEMG estimator is asymptotically normally distributed under certain conditions.The theoretical findings are further supported for small samples via an extensive Monte Carlo study,and it shows that the CCE estimator is robust to a wide variety of data generation processes.The proposed procedure is also illustrated by an empirical application to analyzing U.S.cigar dataset.