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st: Valid and Relevant Instrument


From   Miguel Àngel García López <MiquelAngel.Garcia@uab.cat>
To   statalist@hsphsun2.harvard.edu
Subject   st: Valid and Relevant Instrument
Date   Thu, 09 Feb 2012 11:05:26 +0100

Hi!

Im new with IV and I want to know if my instrument is relevant/valid.
Its coefficient is significant in the First Stage regression and its Partial Rsquared is high (0.1251).

However, the weak-instrument-robust inference are: 
Anderson-Rubin Wald test     F(1,561)= 0.30      P-val=0.5828
Anderson-Rubin Wald test     Chi-sq(1)=0.31      P-val=0.5803
Stock-Wright LM S statistic  Chi-sq(1)=0.31      P-val=0.5796

Thank you for your help!

Miquel

. ivreg2 ldenb9106 (d_via_02ramp9110  =  id_01roma_cat) d_fer_02stations ldenb1991 dist_603 dist_sub tri if dummyarea==3, robust first

First-stage regressions
-----------------------

. ivreg2 ldenb9106 (d_via_02ramp9110  =  id_01roma_cat) d_fer_02stations ldenb1991	dist_603	dist_sub	tri	if	dummyarea==3,	robust	first

First-stage regressions


First-stage regression of d_via_02ramp9110:

OLS estimation


Estimates efficient for homoskedasticity only
Statistics robust to heteroskedasticity

Number of obs =      568
F(  6,   561) =    24.57
Prob > F      =   0.0000
Total (centered) SS     =  2869.458742                Centered R2   =   0.2873
Total (uncentered) SS   =  3506.945701                Uncentered R2 =   0.4169
Residual SS             =  2045.049655                Root MSE      =    1.909


Robust
d_via_02~110       Coef.   Std. Err.      t    P>t     [95% Conf. Interval]

d_fer_02st~s    .3118674   .1299838     2.40   0.017      .056553    .5671817
ldenb1991   -.3513644   .1666977    -2.11   0.035    -.6787923   -.0239365
dist_603   -.0616819   .0108497    -5.69   0.000    -.0829929   -.0403709
dist_sub    .1955812   .0501961     3.90   0.000      .096986    .2941764
tri   -.0057209   .0053618    -1.07   0.286    -.0162526    .0048107
id_01roma~at   -.2700282   .0465692    -5.80   0.000    -.3614994   -.1785569
_cons    2.087004   1.035305     2.02   0.044     .0534567    4.120551

Included instruments: d_fer_02stations ldenb1991 dist_603 dist_sub tri
id_01roma_cat

Partial R-squared of excluded instruments:   0.1251
Test of excluded instruments:
F(  1,   561) =    33.62
Prob > F      =   0.0000



Summary results for first-stage regressions


Variable     Shea Partial R2    Partial R2      F(  1,   561)    P-value
d_via_02ramp     0.1251           0.1251             33.62       0.0000

NB: first-stage F-stat heteroskedasticity-robust

Underidentification tests
Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified)
Ha: matrix has rank=K1 (identified)
Kleibergen-Paap rk LM statistic             Chi-sq(1)=24.12    P-val=0.0000
Kleibergen-Paap rk Wald statistic           Chi-sq(1)=34.04    P-val=0.0000

Weak identification test
Ho: equation is weakly identified
Kleibergen-Paap Wald rk F statistic                33.62
See main output for Cragg-Donald weak id test critical values

Weak-instrument-robust inference
Tests of joint significance of endogenous regressors B1 in main equation
Ho: B1=0 and overidentifying restrictions are valid
Anderson-Rubin Wald test     F(1,561)= 0.30      P-val=0.5828
Anderson-Rubin Wald test     Chi-sq(1)=0.31      P-val=0.5803
Stock-Wright LM S statistic  Chi-sq(1)=0.31      P-val=0.5796

NB: Underidentification, weak identification and weak-identification-robust
test statistics heteroskedasticity-robust

Number of observations               N  =        568
Number of regressors                 K  =          7
Number of instruments                L  =          7
Number of excluded instruments       L1 =          1

IV (2SLS) estimation


Estimates efficient for homoskedasticity only
Statistics robust to heteroskedasticity

Number of obs =      568
F(  6,   561) =    42.16
Prob > F      =   0.0000
Total (centered) SS     =  43.31054213                Centered R2   =   0.4612
Total (uncentered) SS   =   43.4473615                Uncentered R2 =   0.4629
Residual SS             =  23.33470216                Root MSE      =    .2027


Robust
ldenb9106       Coef.   Std. Err.      z    P>z     [95% Conf. Interval]

d_via_02~110   -.0067545   .0122787    -0.55   0.582    -.0308204    .0173113
d_fer_02st~s   -.0172749   .0229106    -0.75   0.451    -.0621788     .027629
ldenb1991   -.2398206    .021196   -11.31   0.000    -.2813641   -.1982772
dist_603   -.0017096   .0017323    -0.99   0.324    -.0051048    .0016857
dist_sub    .0020486   .0072484     0.28   0.777     -.012158    .0162552
tri    .0016679   .0008998     1.85   0.064    -.0000957    .0034315
_cons    1.364544   .1356612    10.06   0.000     1.098653    1.630435

Underidentification test (Kleibergen-Paap rk LM statistic):             24.121
Chi-sq(1) P-val =    0.0000

Weak identification test (Kleibergen-Paap rk Wald F statistic):         33.622
Stock-Yogo weak ID test critical values: 10% maximal IV size             16.38
15% maximal IV size              8.96
20% maximal IV size              6.66
25% maximal IV size              5.53
Source: Stock-Yogo (2005).  Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.

Hansen J statistic (overidentification test of all instruments):         0.000
(equation exactly identified)

Instrumented:         d_via_02ramp9110
Included instruments: d_fer_02stations ldenb1991 dist_603 dist_sub tri
Excluded instruments: id_01roma_cat


. 

Miquel

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