.. est table TwoSLS1 TwoSLS2 GMM het,b(%9.5f) se Variable TwoSLS1 TwoSLS2 GMM_het hi_empunion totchr

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1 3,. Cameron and Trivedi (2010) Microeconometrics Using Stata, Revised Edition, Stata Press 6 Linear instrumentalvariables regression 9 Linear panel-data models: Extensions.. GMM xtabond., GMM(Generalized Method of Moments). GMM TSLS( ), GMM TSLS, TSLS, TwoSLS1.. use mus06data.dta, clear. global x2list totchr age female blhisp linc. ivregress 2sls ldrugexp (hi empunion=ssiratio ) $x2list,vce(robust) ( ). estimates store TwoSLS ( ) z. E {z i (y i x iβ)} = 0 (14) 2. x2list, ivmodel,.. global ivmodel ldrugexp (hi empunion=ssiratio multlc) $x2list. quietly ivregress 2sls $ivmodel,vce(robust). est store TwoSLS2 GMM.. quietly ivregress gmm $ivmodel,wmatrix(robust). est store GMM het 4 GMM 23

2 .. est table TwoSLS1 TwoSLS2 GMM het,b(%9.5f) se Variable TwoSLS1 TwoSLS2 GMM_het hi_empunion totchr age female blhisp linc _cons legend: b/se, TwoSLS1 TwoSLS2 GMM het 10%., TwoSLS2 GMM het,,.. 2, ( ). gmm wmatrix(robust), 2sls vce(robust) ,. (test of overientifying restriction) 6.,,. 2 gmm.. quietly ivregress gmm $ivmodel,wmatrix(robust). estat overid Test of overidentifying restriction: Hansen s J chi2(1) = (p = ) 5 Microeconometrics Using Stata, Revised Edition gmm 6 Hansen Sargan Hansen-Sargan 24

3 5%, ivregress gmm ldrugexp (hi empunion=ssiratio lowincome multlc firmsz) $x2list, >wmatrix(robust) Instrumental variables (GMM) regression Number of obs = 10,089 Wald chi2(6) = R-squared = GMM weight matrix: Robust Root MSE = Robust ldrugexp Coef. Std. Err. z P> z [95% Conf. Interval] hi_empunion totchr age female blhisp linc _cons Instrumented: Instruments: hi_empunion totchr age female blhisp linc ssiratio lowincome multlc firmsz. estat overid Test of overidentifying restriction: Hansen s J chi2(3) = (p = ) 1%,., hi empunion ,. GMM, TSLS,. 3.3 GMM,. Microeconometrics Using Stata, Revised Edition, Stata Press 9 Linear panel-data models: Extensions.,. y it = γ 1 y i,t γ p y i,t p + x itβ + α i + ϵ it, t = p + 1,..., T (15) α i. x it ϵ it., γ 1,, γ p β 7. AR(1) y it = γ 1 y i,t 1 + α i + ϵ it 7 25

4 ,. 1 ϵ i1. y,., 2, γ 1 1., γ 1 0, α i.,,. 15 within 8., within y i,t 1 ȳ i ϵ it ϵ i., within p = 1,. y it = γ 1 y i,t 1 + x itβ + α i + ϵ it ȳ i = γ 1 ȳ i + x iβ + α i + ϵ i, γ, within. y it ȳ i = γ 1 (y i,t 1 ȳ i ) + (x it x i) β+ (ϵ it ϵ i ) 15 ϵ it, y i,t 1 ȳ i ϵ it ϵ i., y i,t 1 ϵ i,t 1., ϵ i, ϵ i,t 1, y i,t 1 ϵ i. (y i,t 1 ȳ i ),,., within,,,. FD within FD(first difference).,. y it = γ 1 y i,t γ p y i,t p + x itβ + ϵ it, t = p + 1,..., T (16) 15. within,., ϵ it., FD, y i,t 1 ϵ it, OLS. y it = γ 1 y i,t 1 + γ 2 y i,t 2 + ϵ it, t = p + 1,..., T, y i,t 1 = y i,t 1 y i,t 2 ϵ it = ϵ it ϵ i,t 1., y i,t 1 ϵ i,t 1,., y i,t 2. (y i,t 2 y i,t 3 ) (ϵ it ϵ i,t 1 ),, y i,t 2 ϵ it 8 within 26

5 ., FD p 2. Anderson and Hsiao (1981) ϵ it y i,t 2 y i,t 1., x it,., Arellano and Bond (1991),, ϵ it,. Arellano and Bond. 3.4 Arellano-Bond : AR(2).,. 16 AR,,. GMM, Arellano-Bond. y it = α + γ 1 y i,t 1 + γ 2 y i,t 2 + ϵ it, t = 4, 5, 6, 7 7.,, 4. t y y y ( 1) y ( 2) ϵ ϵ 1 y i1 ϵ i1 2 y i2 y i2 y i1 ϵ i2 ϵ i2 ϵ i1 3 y i3 y i3 y i2 y i2 y i1 ϵ i3 ϵ i3 ϵ i2 4 y i4 y i4 y i3 y i3 y i2 y i2 y i1 ϵ i4 ϵ i4 ϵ i3 5 y i5 y i5 y i4 y i4 y i3 y i3 y i2 ϵ i5 ϵ i5 ϵ i4 6 y i6 y i6 y i5 y i5 y i4 y i4 y i3 ϵ i6 ϵ i6 ϵ i5 7 y i7 y i7 y i6 y i6 y i5 y i5 y i4 ϵ i7 ϵ i7 ϵ i6, t = 4 ϵ i4 y i1 y i2, t = 5 ϵ i5 y i1, y i2, y i3, t = 6 4, t = 7 5., = 14,,

6 mus08psidextract.dta, AR(2)... use mus08psidextract.dta, clear. xtabond lwage,lags(2) vce(robust) Arellano-Bond dynamic panel-data estimation Number of obs = 2,380 Group variable: id Number of groups = 595 Time variable: t Obs per group: min = 4 avg = 4 max = 4 Number of instruments = 15 Wald chi2(2) = One-step results (Std. Err. adjusted for clustering on id) Robust lwage Coef. Std. Err. z P> z [95% Conf. Interval] lwage L L _cons Instruments for differenced equation GMM-type: L(2/.).lwage Instruments for level equation Standard: _cons 4,165,, ( ) = 2, 380. lwage L1. L2. y i,t 1 y i,t 2., FD. L(2/.), t y i,t 2, y i,t 3,..., y i,1., = 0.84,. GMM 1, (S.E ) 2. 28

7 . xtabond lwage,lags(2) twostep vce(robust) Arellano-Bond dynamic panel-data estimation Number of obs = 2,380 Group variable: id Number of groups = 595 Time variable: t Obs per group: min = 4 avg = 4 max = 4 Number of instruments = 15 Wald chi2(2) = Two-step results (Std. Err. adjusted for clustering on id) WC-Robust lwage Coef. Std. Err. z P> z [95% Conf. Interval] lwage L L _cons Instruments for differenced equation GMM-type: L(2/.).lwage Instruments for level equation Standard: _cons 1 2, S.E. 2. T, Arellano-Bond,,. maxldep()., t y i,t 2.. xtabond lwage,lags(2) vce(robust) maxldep(1) Arellano-Bond dynamic panel-data estimation Number of obs = 2,380 Group variable: id Number of groups = 595 Time variable: t Obs per group: min = 4 avg = 4 max = 4 Number of instruments = 5 Wald chi2(2) = One-step results (Std. Err. adjusted for clustering on id) Robust lwage Coef. Std. Err. z P> z [95% Conf. Interval] lwage L L _cons Instruments for differenced equation GMM-type: L(2/2).lwage 29

8 Instruments for level equation Standard: _cons t = 4 7 y i2, y i3, y i4, y i5 5.,, 6., maxldep(2), S.E., xtabond xtabond Arellano-Bond.,,, fem( ),blk( ),ed( ). occ( 1), south( 1), smsa( 1),ind( 1)... xtabond lwage occ south smsa ind,lags(2) maxldep(3) pre(wks,lag(1,2)) > endogenous(ms,lag(0,2)) endogenous(union,lag(0,2)) twostep vce(robust) > artests(3) Arellano-Bond dynamic panel-data estimation Number of obs = 2,380 Group variable: id Number of groups = 595 Time variable: t Obs per group: min = 4 avg = 4 max = 4 Number of instruments = 40 Wald chi2(10) = Two-step results (Std. Err. adjusted for clustering on id) WC-Robust lwage Coef. Std. Err. z P> z [95% Conf. Interval] lwage L L wks L ms union occ south smsa ind _cons Instruments for differenced equation GMM-type: L(2/4).lwage L(1/2).L.wks L(2/3).ms L(2/3).union Standard: D.occ D.south D.smsa D.ind Instruments for level equation Standard: _cons 30

9 , occ, endogenous() ms union., lag(0,2), 0., ms union 1., L1.., 2., ms ms t 1 ms t 2., pre(wks,lag(1,2)) wks 9. endogenous().,, 5%. ϵ it., AR(2), 2 ϵ it ϵ i,t k (k 2)., COV ( ϵ it, ϵ i,t 1 ) = COV (ϵ it ϵ i,t 1, ϵ i,t 1 ϵ i,t 2 ) = COV (ϵ i,t 1, ϵ i,t 1 ) 0,, k 2. COV ( ϵ it, ϵ i,t k ) = COV (ϵ it ϵ i,t 1, ϵ i,t k ϵ i,t k 1 ) = 0. artests(). artests(3)., artests(2),, 3.. estat abond Arellano-Bond test for zero autocorrelation in first-differenced errors Order z Prob > z H0: no autocorrelation. 2,.,. estat sargan, vce(robust),,. 9 31

10 . xtabond lwage occ south smsa ind,lags(2) maxldep(3) pre(wks,lag(1,2)) > endogenous(ms,lag(0,2)) endogenous(union,lag(0,2)) twostep artests(3). estat sargan. estat sargan Sargan test of overidentifying restrictions H0: overidentifying restrictions are valid chi2(29) = Prob > chi2 = %. 3.6 xtdpdsys Arellano-Bond E (y is ϵ it ) = 0 (s t 2), FD y i,t 2, y i,t 3,.... Arellano and Bover (1995) Blundell and Bond (1998)., E (y i,y 1 ϵ it ) = 0, Stata xtdpdsys xtdpdsys lwage occ south smsa ind,lags(2) maxldep(3) pre(wks,lag(1,2)) >endogenous(ms,lag(0,2)) endogenous(union,lag(0,2)) twostep vce(robust) >artests(3) 10 ado xtabond2 xtabond 32

11 System dynamic panel-data estimation Number of obs = 2,975 Group variable: id Number of groups = 595 Time variable: t Obs per group: min = 5 avg = 5 max = 5 Number of instruments = 60 Wald chi2(10) = Two-step results WC-Robust lwage Coef. Std. Err. z P> z [95% Conf. Interval] lwage L L wks L ms union occ south smsa ind _cons Instruments for differenced equation GMM-type: L(2/4).lwage L(1/2).L.wks L(2/3).ms L(2/3).union Standard: D.occ D.south D.smsa D.ind Instruments for level equation GMM-type: LD.lwage LD.wks LD.ms LD.union Standard: _cons ,., 10-60%. xtabond, estat abond,, vce(robust), estat sargan. 3.7 xtdpd ϵ it., estat abond?. ϵ it xtdpd Stata,.. xtdpd L(0/2).lwage L(0/1).wks occ south smsa ind ms union, >div(occ south smsa ind) dgmmiv(lwage,lagrange(2 4)) >dgmmiv(ms union,lagrange(2 3)) dgmmiv(l.wks,lagrange(1 2)) >lgmmiv(lwage wks ms union) twostep vce(robust) artests(3) 33

12 Dynamic panel-data estimation Number of obs = 2,975 Group variable: id Number of groups = 595 Time variable: t Obs per group: min = 5 avg = 5 max = 5 Number of instruments = 60 Wald chi2(10) = Two-step results (Std. Err. adjusted for clustering on id) WC-Robust lwage Coef. Std. Err. z P> z [95% Conf. Interval] lwage L L wks L occ south smsa ind ms union _cons Instruments for differenced equation GMM-type: L(2/4).lwage L(2/3).ms L(2/3).union L(1/2).L.wks Standard: D.occ D.south D.smsa D.ind Instruments for level equation GMM-type: LD.lwage LD.wks LD.ms LD.union Standard: _cons 15 ϵ it MA(1),, ϵ it = η it + δη i,t 1. η it i.i.id.. GMM GMM. GMM TSLS,. ( ),, GMM,.. 34

13 ,... Y i = β 0 + β 1 X 1i + + β k X ki + β k+1 W 1i + + β k+r W ri + u i, i = 1,..., n, Y i β 0, β 1,..., β k+r X 1i,..., X ki k, u i. W 1i...., W ri r u i. u i,. Z 1i..., Z mi m. (m > k),. m < k, ( ), m = k.,,,

% 10%, 35%( 1029 ) p (a) 1 p 95% (b) 1 Std. Err. (c) p 40% 5% (d) p 1: STATA (1). prtesti One-sample test of pr

1 1. 2014 6 2014 6 10 10% 10%, 35%( 1029 ) p (a) 1 p 95% (b) 1 Std. Err. (c) p 40% 5% (d) p 1: STATA (1). prtesti 1029 0.35 0.40 One-sample test of proportion x: Number of obs = 1029 Variable Mean Std.