截面和面板數(shù)據(jù)分析課件5(復(fù)旦大學(xué)陸銘張晏)-資料下載頁
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【正文】 le. ? If Ti is the number of time periods for crosssectional unit i, we simply use these Ti observations in doing the timedemeaning. ? Any regression package that does fixed effects makes the appropriate adjustment for this loss of degree of freedom. ? If the reason a firm leaves the sample (called attrition) is correlated with the idiosyncratic error— those unobserved factors that change over time and affect profits— then the resulting sample section problem (see Chapter 9) can cause biased estimators. Fortunately, FE means that, with the initial sampling, some units are more likely to drop out of the survey, and this is captured by ai. Random Effects Estimation ? Random Effects Model: If the unobserved effect ai is uncorrelated with each explanatory variable, ? The usual pooled OLS can give consistent estimators of , but as its standard errors ignore the positive serial correlation in the posite error term, they will be incorrect, as will the usual test statistics. ? Solution: use GLS to solve the serial correlation problem Random Effects Estimation: GLS transformation ? GLS transformation to eliminate the serial correlation: ? quasidemeaned data ? Estimation of : ? where a is a consistent estimator of . These estimators can be based on the pooled OLS or fixed effects residuals. ? Random Effects Estimator: The feasible GLS estimator that uses ? in place of RE, FE and PLS ? Pooled OLS: ? Random Effects Estimator: ? Fixed Effects Estimator: ? The transformation in () allows for explanatory variables that are constant over time, and this is one advantage of random effects (RE) over either fixed effects or first differencing. However, we are assuming that education is uncorrelated with unobserved effects, ai, which contains ability and family background. Random Effects or Fixed Effects? ? In reading empirical work, you may find that authors decide between fixed and random effects based on whether the ai (or whatever notation the authors use) are best viewed as parameters to be estimated or as outes of a random variable. ? When we cannot consider the observations to be random draws from a large population— for example, if we have data on states or provinces— it often makes sense to think of the ai as parameters to estimate, in which case we use fixed effects methods. ? Even if we decide to treat the ai as random variables, we must decide whether the ai are uncorrelated with the explanatory variables. But if the ai are correlated with some explanatory variables, the fixed effects method (or first differencing) is needed。 if RE is used, then the estimators are generally inconsistent. Hausman Test: Random Effects or Fixed Effects? ?Comparing the FE and RE estimates can be a test for whether there is correlation between the ai and the xitj, assuming that the diosyncratic errors and explanatory variables are uncorrelated across all time periods. ?Hausman Test: Steps for Panel Data Analysis ?Group Effects Test： ?Hausman Test: Example The Return to Education over Time References ?Jeffrey M. Wooldridge, Introductory Econometrics—— A Modern Approach, Chap 13.
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