Multi-level Panel Data Model Estimation Theory And Simulation Studies

Multilevel model is a new statistic model that developed for hierarchical data, in which the regression coefficient is considered as random variable. For example, when data are separated into two levels, the level one variables are used to establish a linear regression model, in which the coefficients are considered as random variables. The random coefficients then form a level 2 regression model using level two variables. By this way, relationships of variables among different levels, as well as the concern of errors between different levels can be studied. Further more, the variations between the levels can be estimated.The panel data is a combination of cross-sectional data and time-series data, and the panel data model is a useful econometric model for panel data. For this reason, the application of panel data on econometric analysis can deal with cross-sectional data and time-series data at the same time. It can control the individual time-independent heterogeneity, as well as the time effects from different objects, in the aim of better recognition and measure on the significant effects of cross-sectional data and time-series data. But this model can't be used to analyze multilevel effect.This paper summarizes the characteristics of multilevel model and the panel data model, and suggests a multilevel panel data model which combine the level effects and time effect, so that it can analyze the hierarchical structural data. Meanwhile, time effects are introduced in the model, considering the differences between the individuals and groups, as well as the explanations on the causes of variation of variances. The covariance structure is analyzed, and the estimation methods using Iterative Generalized Least Squares Estimation (IGLS) and the Restricted Iterative Generalized Least Squares Estimation (RIGLS) are proposed. Finally, the comparisons between multilevel model and panel data model are studied by simulating data.