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st: Valid and Relevant Instrument
From
Miguel Àngel García López <[email protected]>
To
[email protected]
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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