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Econometric Analysis of Panel Data

Explore the intricacies of instrumental variables in panel data analysis, including fixed effects, random effects, and first difference models. Learn the assumptions required for instrumental variables and the implications for different models. Illustrated with the example of the Cornwell and Rupert Model (1988) on Returns to Schooling. Gain insights into labor market equilibrium modeling and the impact of endogenous variables.

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Econometric Analysis of Panel Data

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  1. Econometric Analysis of Panel Data • Instrumental Variables in Panel Data • Assumptions of Instrumental Variables • Fixed Effects Model • Random Effects Model • First Difference Model

  2. Instrumental Variables in Panel Data • The Model with Random Regressors • Instrumental Variables • Instrumental variables can be obtained through use of exogenous regressors X1 in periods other than the current period, using the exogeneity assumption.

  3. Assumptions of Instrumental Variables • Summation Assumption • Exogenous variables X1 are included in Z. • Z may include excluded exogenous variables (other than X1), although they are difficult to find.

  4. Assumptions of Instrumental Variables • Contemporary Exogeneity Assumption • Any time-invariant exogenous variables in X1 can be used only once as an instrument.

  5. Assumptions of Instrumental Variables • Weak Exogeneity Assumption(Predetermined Instruments Assumption)

  6. Assumptions of Instrumental Variables • Strong Exogeneity Assumption • For dynamic models, at most weak exogeneity of instruments can be assumed. • Time invariant instruments can be used only once.

  7. IV for Fixed Effects Model • Fixed Effects Model • Strong exogeneity of instrumental variables must be assumed for the fixed effects model so that the within estimates are consistent.

  8. IV for Random Effects Model • Random Effects Model • Strong exogeneity of instrumental variables must be assumed for the random effects model so that the GLS parameter estimates are consistent.

  9. IV for First Difference Model First Difference Model

  10. IV for First Difference Model • First Difference Model • No time-invariant variables. • To consistently estimate the first-difference model, we need only the Weak Endogeneity assumption for the instrumental variables.

  11. 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  endogenousOCC = 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  endogenousFEM = 1 if femaleBLK = 1 if individual is black

  12. Example: Returns to Schooling Labor Market Equilibrium Model Labor Demand Equationlwage = exp exp2 wks occ ind south smsa ms union [blk fem ed] Labor Supply Equationwks = lwage union [fem ed] Endogenous or predetermined variable: [ed]

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