截面和面板數(shù)據(jù)分析課件5(復(fù)旦大學(xué)陸銘張晏)(文件)
【正文】 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。 industry。 highearn。 different period ? Data: , which is similar to that used by Sander (1994), es from the National Opinion Research Center’s General Social Survey for the even years from 1972 to 1984 ? Interpretations ? base year: 1972 ? education: .128(4)=.512. ? turning point of age ? heteroskedasticity of error term over time? BP test。 ? To study the importance of lags in behavior or the result of decision making Pooling Independent Cross Sections across Time ? Increase the sample size ? Dummy Variables ? the population may have different distributions in different time periods ? different intercept and slopes ? Year dummy: including dummy variables for all but one year, where the earliest year in the sample is usually chosen as the base year. ? The pattern of coef. on the year dummies ? The change of the coef. of the key variable over time ? policy analysis Example Has the pattern of women’s fertility Changed? ? Factors on Women’s Fertility over Time? ? age。 Panel Data ? Independently Pooled Cross Section ? they consist of independently sampled observations. ? 與單一隨機(jī)樣本的差別：在不同時(shí)點(diǎn)對(duì)總體抽樣可能導(dǎo)致觀測(cè)點(diǎn)不是同分布的（ not identically distributed.） ? Different intercept and slopes ? Policy analysis ? Panel Data ? The same units ? we cannot assume that the observations of longitudinal data are independently distributed across time. ? Special models and methods ? Differencing (remove timeconstant, unobser
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