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Econometric Analysis of Panel Data Random Regressors –Pooled (Constant Effects) Model Instrumental Variables –Fixed Effects Model –Random Effects Model –Hausman-Taylor Estimator

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

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Constant Effects Model Instrumental Variables Estimation

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Constant Effects Model Instrumental Variables Estimation –Instrumental Variables: Z i –Included Instruments: X1 i –# Z i ≥ # W i

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Constant Effects Model Instrumental Variables Estimation

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Constant Effects Model Instrumental Variables Estimation HAC Variance-Covariance Matrix

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Constant Effects Model Hypothesis Testing of Instrumental Variables –Test for Endogeneity –Test for Overidentification –Test for Weak Instruments

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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.

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Fixed Effects Model The Model Instrumental Variables –#Z i ≥ #X i (Z i must be time variant)

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Fixed Effects Model Within Estimator –Panel-Robust Variance-Covariance Matrix

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Example: Returns to Schooling Cornwell and Rupert Model (1988) Data (575 individuals over 7 ears) –Dependent Variable y it : LWAGE = log of wage –Explanatory Variables x it : Time-Variant Variables x1 it : –EXP = work experience (+EXP 2 ) exogenous WKS = weeks worked endogenous OCC = occupation, 1 if blue collar IV IND = 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 x2 i : –ED = years of education endogenous FEM = 1 if female BLK = 1 if individual is black

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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

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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 (+EXP 2 ) exogenous WKS = weeks worked endogenous OCC = occupation, 1 if blue collar IV IND = 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 x2 i : –ED = years of education endogenous FEM = 1 if female IV BLK = 1 if individual is black IV

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Hausman-Taylor Estimator The Model –Time-variant Variables: x1 it, x2 it –Time-invariant Variables:x3 i, x4 i –Fixed effects model can not estimate 3 and 4; 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)

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Hausman-Taylor Estimator Instrumental Variable Estimation

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Example: Returns to Schooling Cornwell and Rupert Model (1988) Data (575 individuals over 7 ears) –Dependent Variable y it : LWAGE = log of wage –Explanatory Variables x it : Time-Variant Variables x1 it : –EXP = work experience endogenous (+EXP 2 ) 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 endogenous UNION = 1 if wage set by union contract endogenous Time-Invariant Variables x2 i : –ED = years of education endogenous FEM = 1 if female BLK = 1 if individual is black

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1. 2 3 5 There are at least three generally recognized sources of endogeneity. (1) Model misspecification or Omitted Variables. (2) Measurement Error.

1. 2 3 5 There are at least three generally recognized sources of endogeneity. (1) Model misspecification or Omitted Variables. (2) Measurement Error.

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