Econometric Analysis of Panel Data

1
Econometric Analysis of Panel Data

• Random Regressors
• Pooled (Constant Effects) Model
• Instrumental Variables
• Fixed Effects Model
• Random Effects Model
• Hausman-Taylor Estimator

2
Random Regressors

• Pooled (Constant Effects) Model
• Other classical assumptions remained.
• OLS is biased Instrumental variables estimation
  should be used.
• IV estimator is consistent.

3
Constant Effects Model

• Instrumental Variables Estimation

4
Constant Effects Model

• Instrumental Variables Estimation
• Instrumental Variables Zi
• Included Instruments X1i
• Zi Wi

5
Constant Effects Model

• Instrumental Variables Estimation

6
Constant Effects Model

• Instrumental Variables Estimation
• HAC Variance-Covariance Matrix

7
Constant Effects Model

• Hypothesis Testing of Instrumental Variables
• Test for Endogeneity
• Test for Overidentification
• Test for Weak Instruments

8
Random Regressors

• Fixed Effects Model
• Other classical assumptions remained.
• Can not estimate the parameters of time-invariant
  regressors, even if they are correlated with
  model error.
• The random regressors x2 has to be time-varying.

9
Fixed Effects Model

• The Model
• Instrumental Variables
• Zi Xi (Zi must be time variant)

10
Fixed Effects Model

• Within Estimator
• Panel-Robust Variance-Covariance Matrix

11
Example Returns to Schooling

• Cornwell and Rupert Model (1988)
• Data (575 individuals over 7 ears)
• Dependent Variable yit
• LWAGE log of wage
• Explanatory Variables xit
• Time-Variant Variables x1it
• EXP work experience (EXP2) ? exogenous WKS
  weeks worked ? endogenous OCC occupation, 1 if
  blue collar ? IVIND 1 if manufacturing
  industry ? IV SOUTH 1 if resides in south ? IV
  SMSA 1 if resides in a city (SMSA) ? IV MS
  1 if married ? IV UNION 1 if wage set by union
  contract ? IV
• Time-Invariant Variables x2i
• ED years of education ? endogenous FEM 1 if
  femaleBLK 1 if individual is black

12
Random Regressors

• Random Effects Model
• Other classical assumptions remained.
• Mundlak approach may be used when
• Instrumental variables must be used if

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Random Effects Model

• The Model

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Random Effects Model

• (Partial) Within Estimator
• Panel-Robust Variance-Covariance Matrix

15
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 (EXP2) ? exogenous WKS
  weeks worked ? endogenous OCC occupation, 1 if
  blue collar ? IVIND 1 if manufacturing
  industry ? IV SOUTH 1 if resides in south ? IV
  SMSA 1 if resides in a city (SMSA) ? IV MS
  1 if married ? IV UNION 1 if wage set by union
  contract ? IV
• Time-Invariant Variables x2i
• ED years of education ? endogenous FEM 1 if
  female ? IV BLK 1 if individual is black ? IV

16
Hausman-Taylor Estimator

• The Model
• Time-variant Variables x1it, x2it
• Time-invariant Variablesx3i, x4i
• Fixed effects model can not estimate b3 and b4
  Random effects model has random regressors x2
  and x4 correlated with u.

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Hausman-Taylor Estimator

• Fixed Effects Model

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Hausman-Taylor Estimator

• Fixed Effects Model
• Within Residuals

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Hausman-Taylor Estimator

• Random Effects Model

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Hausman-Taylor Estimator

• Instrumental Variables
• Hausman-Taylor (1981)
• Amemiya-Macurdy (1986)

21
Hausman-Taylor Estimator

• Instrumental Variable Estimation

22
Example Returns to Schooling

• Cornwell and Rupert Model (1988)
• Data (575 individuals over 7 ears)
• Dependent Variable yit
• LWAGE log of wage
• Explanatory Variables xit
• Time-Variant Variables x1it
• EXP work experience ? endogenous (EXP2)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 ?
  endogenous UNION 1 if wage set by union
  contract ? endogenous
• Time-Invariant Variables x2i
• ED years of education ? endogenous FEM 1 if
  femaleBLK 1 if individual is black