Consistent estimation of panel data models with multifactor structures under short time dimension situations.
thesisposted on 28.02.2017 by Peng, Bin
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The thesis investigates three panel data models. For each model, we tend to use a multifactor struc-ture to capture the cross-sectional dependence and the correlation between regressors and errors. We focus on providing results which are available to the large N and small T cases (say T<10). There is no doubt that our set-ups violate the basic requirements of the ordinary least squares (OLS), nonlinear least squares (NLS) and two stage least squares (TSLS) estimators. Therefore, we provide alternative consistent estimators in each corresponding chapter and investigate their as-ymptotic properties. Since we never take a large T average, the complexities of the joint large N and T limits are bypassed and the assumptions on the time dimension are relaxed. In Chapter 3, we focus on the cases with homogeneous and heterogeneous slopes. Relevant mo-ments conditions and three corresponding estimators are given. Also, we show that three estimators have nice asymptotic properties for both homogeneous and heterogeneous slopes models. Since they all can be expressed in closed form, it is very easy to apply these estimators to the real data sets. Furthermore, we show that tests on the interest parameters can be constructed using standard t- and F- procedures. Then we follow Su and Jin (2012) and propose a single index panel data model in Chapter 4. Even though our model is less general than the nonparametric version in Su and Jin (2012), we believe it is a nice compromise between applicability and generality. In this chapter, some corresponding identification issues are addressed and a new estimation procedure is presented by using sieve estimation. To explain the new procedure clearly, we use NLS estimator as a benchmark. The numerical results show that our semiparametric estimator is close enough to the NLS estimator while we do not have too much information on the interest function. Finally, in Chapter 5, we introduce the multifactor structures to the structural equation panel data model. As we see, the existence of the multifactor structure causes the inconsistent estimation for the tradi-tional limited information maximum likelihood (LIML) and two stage least squares (TSLS) meth-ods. However, under proper transformation, we still can employ LIML and TSLS estimators to gain the consistent estimation and show that these two estimators are asymptotically identical. For the LIML estimator, we express the asymptotic results in an easy representation. The Monte Carlo studies are presented in each chapter to back up our theoretical results.