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 e it is serially correlated, –Endogenous regressor: OLS is inconsistent. –Lags of x it 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 e it are serially uncorrelated,

Lagged Dependent Variable Fixed Effects Model –Lags of y it can not be used for instrumental variables. The only choices are x it and lags of x it which depends on the exogeniety assumption of the model. –Under strong exogeneity assumption E(e it |X i )=0

Lagged Dependent Variable Fixed Effects Model: IV

Lagged Dependent Variable Random Effects Model –Even if  it are serially uncorrelated,

Lagged Dependent Variable Random Effects Model –Lags of y it can not be used for instrumental variables. The only choices are x it and lags of x it which depends on the exogeniety assumption of the model. –Under strong exogeneity assumption E(e it |X i )=0

Lagged Dependent Variable Random Effects Model: IV

Lagged Dependent Variable First Difference Model –Assuming e it are serially uncorrelated,

Lagged Dependent Variable First Difference Model –Anderson-Hsiao (1981) Estimator Using y it-2 as an instrument for  y it-1 –Arellano-Bond (1991) Estimator Using y it-2, y it-3, y it-4, …as instruments for  y it-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 y it : LWAGE = log of wage –Explanatory Variables x it : Time-Variant Variables x1 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 x2 i : –ED = years of education  endogenous FEM = 1 if female BLK = 1 if individual is black