PanelDataNotes-8

# PanelDataNotes-8 - Econometric Analysis of Panel Data...

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Econometric Analysis of Panel Data William Greene Department of Economics Stern School of Business

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Econometric Analysis of Panel Data 8. Instrumental Variables Estimation
Structure and Regression it it it it it it it y E ,  i,t" = sibling t in family i       E ' true' education measurable only with error       S  measured 'schooling' = E w ,  w=measurement error = + γ + ε = = + it Earnings (structural) equation x β Reduced  it it it it it it it 2 it it it w y (S w )       =  S  + (   w )  for least squares (OLS or GLS)     Cov[S ,(   w )] 0     Consistency relies on this covariance equaling 0.     How = + γ - + ε + γ ε - γ ε - γ = -γσ ≠ it it form x β x β Estimation problem  to estimate   and   (consistently)? γ β

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Agenda Single equation instrumental variable estimation Exogeneity Instrumental Variable (IV) Estimation Two Stage Least Squares (2SLS) Generalized Method of Moments (GMM) Panel data Hausman and Taylor’s formulation Application Arellano/Bond/Bover framework
Exogeneity Structure                    E[ ] =  Regression   [ ]                       E[ ]= Projection   "Regression of   on  "            y  =  X  +  β ε | X g(X)   0 ε y  =  X  + g(X) +  - g(X) β ε =  E[y| X]  +  u, u| X 0    =  X   +  w ε θ y X it it it i1 i2 iT        Exogeneity:   E[ | ] 0 (current period) Strict Exogeneity: E[ | , ,..., ] 0 (all periods) (We assume no correlation a ε = ε = y   =  X( + )  +  w β θ The problem :                  X is not exogenous. x x x x cross individuals.)

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The Effect of Education on LWAGE = β + β + β + β + + 1 2 3 4 ...ε What is ε? ,... + everything el Abil se ity, Motivation Ability, Motivation = f( , , , ,...) LWAGE EDUC EXP EDUC GENDER SMSA SOUTH 2 EXP
What Influences LWAGE? = β + β + β + β + + 1 2 3 4 Ability, Motivation Ability, Motivat ( , ,...) ... ε( ) Increased is associated with increases in ion Ability Ability, Motivati ( , , on LWAGE EDUC X EXP EDUC X 2 EXP β 3 ...) and ε( ) What looks like an effect due to increase in may be an increase in . The estimate of picks up the effect of and the hidden effect of . Ability, Motivation Ability Ability EDUC EDUC

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= β + β + β + β + + 1 2 3 4 ( , , ,. ..) ... ε( ) Increased is asso Abili ciate ty, Motivation Ability, Motivation Ability, Motiva d with increases in ( , , , ti . n . o LWAGE EDU Z Z Z C X EXP EDUC X 2 EXP β 3 .) and not ε( ) An effect due to the effect of an increase on will only be an increase in . The estimate of picks up the effect of only. Ability, Motiv
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## This note was uploaded on 01/05/2012 for the course B 55.9912 taught by Professor Willamgreene during the Fall '11 term at NYU.

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PanelDataNotes-8 - Econometric Analysis of Panel Data...

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