Theory And Applications Of Panel Data Models With Factor Error Structures

Panel data models are been increasingly popular in modern theoretical and applied econometrics. An important advantage of panel data is that researchers can obtain consistent eatimates of important parameters while controlling for unobservable cross-sectional heterogeneity (Ahn, Lee and Schmidt,2013). An example of such heterogeneity is individual effect, which reflects individual’s unobservable features, such as estimating wage-determination equations in labor economics, individual’s innate talents and skills are unobservable, it is extremely difficult, if not possible, to estimate parameters consistently based on cross-sectional data. However, when panel data are available, the effect of education on wage can be estimated consistently, even if the unobservable individual heterogeneity appears. Standard panel data models usually assume that the unobservable individual effect is time-invariant, but indidual-varying error component, implying that in the full sample, the heterogenous feature of every single individual is time-constant, obviously, this assumption is excessively restrictive. Some research shows, labor’s productivity changes over the business cycle, so we can infer that individual’s talent or skill will also change over the business cycle (Ahn, Lee and Schmidt,2001). Therefore, in the process of constructing and applying empirical models, it is not always appropriate to use time-constant individual effects to capture individual’s unobservable feature. There is a huge literature on panel data models with error term consisting of both individual effect and time effect (common factor) additively at the same time, not only trying to capture the individual feature, but also to control the specific time effect, such as the individual-constant macro policy shock. Howerer, although adding time effects to the model may make the model better, and may enhance the scope of its application, just as the defect of individual effect, what the time effect reflects is just that at each period, the effect of the shock of common factor on all individual is the same. To avoid the defect and weakness of traditional models, economists introduce the individual effect and time effect multiplicatively into models, sot factor structures are formed, such that including the additive models as special cases.Comparing to traditional fixed effect model, the introduction of error factor structures not only makes the modeling of heterogeneity in a more flexible way, but also supplies effective way to control cross-sectional dependence pervasive in macroeconomic and financial data. Allowing individual effect, common factor and factor loading to correlate with regressors, makes the setup of endogeneity more diverse, and model specification more conform to economic reality. Factor error structures are the classic styles of factor model, so can be estimated by the method of factor analysis. Following this, based on the current literature, this paper further studies model specification and the method of parameter identification and estimation, and apply the theory to study China’s practical problem.In the aspects of theoretical studies, first of all, due to the fact that what the representative literature considers are all about identification and estimation of traditional two-dimensional models, considering that three or higher dimensional panel data models are widely used in empirical international economics, while theoretical studies are rather rare, this paper studies the consistent estimation method of three-dimensional static and dynamic balanced and unbalanced model separately, and examine the finite sample properties of the estimators based on Monte Carlo simulation experiments.Secondly, considering that individuals may form group structure based on their latent feature, that is, the coefficients of individuals are the same within each group but differ across groups. Ando and Bai (2013,2014) introduce group factor structures into homogeneous and heterogeneous models, but group factor and factor loading are group-specific. In real economy, common factors are not necessarily group-specific, so model specification is flawed. Considering the special construction of the above models, they are not general both in theoretical and applied aspects, this paper considers the situation when factors are common, while factor loadings are group-specific, that is, factor loadings are the same for individuals who belongs to the same group. Based on the idea of iterative estimation, this paper studies the estimation of static and dynamic models with exogenous group factor structures when common factors are observable and unobservable, and following the idea of penalized regression, further studies parameter estimation and group identification of models with endogenous group factor error structures.In addition, this paper generalizes factor error structures from single equation model to panel structural VAR system. Combining the idea of parameter identification and estimation of dynamic pane model and PSVAR, based on iteration method of GMM and principal component analysis, this paper discusses the methods of identification and estimation of model parameters.In the aspects of empirical studies, first of all, applying financial data from listed companies from China’s Shanghai and Shenzhen exchange, this paper constructs a dynamic model with exogenous group factor structures and the common factors are observable. By grouping individual company based on their industry attributes, and on the perspective of micro money demand, this paper studies the effect of monetary policy as common shock on industry. The results show that, traditional industries are more sensitive to monetary policy shock, while the textile, IT, food and beverage, medicine and biological product industries, which belong to the service and high-tech industries are only little sensitive to the shock. Secondly, based on PSVAR models with factor error structures, this paper studies the dynamic interdependence of human capital, trade openness, urbanization and China’s provincial total factor productivity. Results show that, urbanization shock has the greatest cumulative effects on human capital accumulation, while TFP shock has negative cumulative effects. Urbanization as growth polar has greatest cumulative effect on itself, while all endogeneous variables have positive effect on TFP. Social and environmental common factors prone to enhance human capital accumulation, urbanization, and TFP, but at times of financial crisis, the common factors disturb TFP. Comparing to less developend areas, middle and eastern provinces are more sensitive to common factor shocks.