Econometric Analysis of Panel Data

1
Econometric Analysis of Panel Data

• Lagged Dependent Variables
• Pooled (Constant Effects) Model
• Fixed Effects Model
• Random Effects Model
• First Difference Model
• Arellano-Bond Estimator

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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

3
Lagged Dependent Variable

• Pooled (Constant Effect) Model IV

4
Lagged Dependent Variable

• Fixed Effects Model
• Even if eit are serially uncorrelated,

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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(eitXi)0

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Lagged Dependent Variable

• Fixed Effects Model IV

7
Lagged Dependent Variable

• Random Effects Model
• Even if eit are serially uncorrelated,

8
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(eitXi)0

9
Lagged Dependent Variable

• Random Effects Model IV

10
Lagged Dependent Variable

• First Difference Model
• Assuming eit are serially uncorrelated,

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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

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Lagged Dependent Variable

• First Difference Model
• IV for Anderson-Hsiao Estimator

13
Lagged Dependent Variable

• First Difference Model
• IV for Arellano-Bond Estimator

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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-Invariant Variables x2i
• ED years of education ? endogenous FEM 1 if
  femaleBLK 1 if individual is black