Econometric Analysis of Panel Data Lagged Dependent Variables
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 • Pooled (Constant Effect) Model: IV
Lagged Dependent Variable • Fixed Effects Model – Even 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 • Fixed Effects Model: IV
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 • Random Effects Model: IV
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 x 1 it: – EXP = work experience WKS = weeks worked endogenous OCC = occupation, 1 if blue collar, IND = 1 if manufacturing industry SOUTH = 1 if resides in south SMSA = 1 if resides in a city (SMSA) MS = 1 if married UNION = 1 if wage set by union contract • Time-Invariant Variables x 2 i: – ED = years of education endogenous FEM = 1 if female BLK = 1 if individual is black
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