Econometric Analysis of Panel Data Instrumental Variables in
Econometric Analysis of Panel Data • Instrumental Variables in Panel Data – Assumptions of Instrumental Variables – Fixed Effects Model – Random Effects Model – First Difference Model
Instrumental Variables in Panel Data • The Model with Random Regressors • Instrumental Variables – Instrumental variables can be obtained through use of exogenous regressors X 1 in periods other than the current period, using the exogeneity assumption.
Assumptions of Instrumental Variables • Summation Assumption – Exogenous variables X 1 are included in Z. – Z may include excluded exogenous variables (other than X 1), although they are difficult to find.
Assumptions of Instrumental Variables • Contemporary Exogeneity Assumption – Any time-invariant exogenous variables in X 1 can be used only once as an instrument.
Assumptions of Instrumental Variables • Weak Exogeneity Assumption (Predetermined Instruments Assumption)
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.
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.
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.
IV for First Difference Model • First Difference Model
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.
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 x 1 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 x 2 i: – ED = years of education endogenous FEM = 1 if female BLK = 1 if individual is black
Example: Returns to Schooling • Labor Market Equilibrium Model – Labor Demand Equation lwage = exp 2 wks occ ind south smsa ms union [blk fem ed] – Labor Supply Equation wks = lwage union [fem ed] – Endogenous or predetermined variable: [ed]
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