Panel Data面板数据.docxVIP

Panel DataPanel data set contains repeated observations for the same unit yit and xit for units i = 1,2,...,N and periods t = 1,2,...,T. ?Also called longitudinal data. Advantage of panel data: Compare with time series or cross-sectional data sets are that Panel data allow consistent estimation in the presence of (time invariant) omitted variables. This solves a common identification problem in econometrics. They allow identification of certain parameters or questions, without the need to make restrictive assumptions. E.g. panel data make it possible to analyse changes on an individual level. Examples:Wages and characteristics of individuals.Investments and earnings of firms.?Aggregate prices and Exchange rates for countries Two different settings: ?? NT: The cross-sectional dimensión dominates. ? T N: The time series dimension dominates. OLS for Panel Data for i = 1,2,...,N and t = 1,2,...,T.The error term varies between individuals and time captures all unobservable factors that affect yit..To estimate OLS we need It is unrealistic to assume that the error term from different periods are uncorrelated, given that we repeatedly observe the same individuals.OLS is likely to be inefficient relative to an estimator that exploits the correlation over time A panel Data model assumes that:Remarks:The condition for pooled OLS to be consistent is E (uit | xit ) = 0. The unobserved characteristics are uncorrelated with xit. Even if E(uit | xit ) = 0, the error term still has a specific structure . A GLS estimator is more efficient than OLS: Random effects model. In many cases the problem is that is correlated with xit .?Pooled OLS and the random effects estimators are inconsistent. The solution is to transform the model to eliminate : Fixed effects model. Efficiency of the parameters:Because panel data sets are typically larger than cross-sectional or time series data sets, and explanatory variables vary over two dimensions (individuals and time) rather than one, panel