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Econometric Analysis of Panel Data PD8参考
Econometric Analysis of Panel Data Lagged Dependent Variables Pooled (Constant Effects) Model Fixed Effects Model Random Effects Model First Difference Model Arellano-Bond Estimator Lagged Dependent Variable Pooled (Constant Effects) Model If eit is serially correlated, Endogenous regressor: OLS is inconsistent. Lags of xit can be used for IVs under weak exogeneity assumption of the model: Lagged Dependent Variable Fixed Effects Model If eit are serially uncorrelated, Lagged Dependent Variable Fixed Effects Model Lags of yit can not be used for instrumental variables. The only choices are xit and lags of xit which depends on the exogeniety assumption of the model. Under strong exogeneity assumption E(eit|Xi)=0 Lagged Dependent Variable Random Effects Model Even if eit are serially uncorrelated, Lagged Dependent Variable Random Effects Model Lags of yit can not be used for instrumental variables. The only choices are xit and lags of xit which depends on the exogeniety assumption of the model. Under strong exogeneity assumption E(eit|Xi)=0 Lagged Dependent Variable First Difference Model Assuming eit are serially uncorrelated, Lagged Dependent Variable First Difference Model Anderson-Hsiao (1981) Estimator Using yit-2 as an instrument for Dyit-1 Arellano-Bond (1991) Estimator Using yit-2, yit-3, yit-4, …as instruments for Dyit-1 Lagged Dependent Variable First Difference Model IV for Anderson-Hsiao Estimator Lagged Dependent Variable First Difference Model IV for Arellano-Bond Estimator Example: Returns to Schooling Cornwell and Rupert Model (1988) Data (575 individuals over 7 years) Dependent Variable yit: LWAGE = log of wage Explanatory Variables xit: Time-Variant Variables x1it: EXP = work experience WKS = weeks worked ? endogenous OCC = occupation, 1 if blue collar, IND = 1 if manufacturing industrySOUTH = 1 if resides in southSMSA = 1 if resides in a city (SMSA)MS = 1 if married UNION = 1 if wage set by union contract Time-Invari
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