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Re: st: RE: Multiple endogenous regressors: weak instrument robust test statistic for individual coefficients (xtivreg2)?
From
Matthias Flückiger <[email protected]>
To
[email protected]
Subject
Re: st: RE: Multiple endogenous regressors: weak instrument robust test statistic for individual coefficients (xtivreg2)?
Date
Tue, 14 Jan 2014 14:19:36 +0100
Hi Mark.
Thanks for your reply. Indeed, I may have phrased my answer badly. As
I understand it, the Anderson-Rubin test provided by the xtivreg2
command is the joint test
H0: x1=0 & x2=0
However, what I am looking for is a weak instrument robust individual
parameter test, i.e.:
H0: x1=0
Do you have any idea how to obtain such a test statistic?
Thanks,
Matthias
2014/1/14 Schaffer, Mark E <[email protected]>:
> Matthias,
>
>> -----Original Message-----
>> From: [email protected] [mailto:owner-
>> [email protected]] On Behalf Of Matthias Flückiger
>> Sent: 13 January 2014 20:25
>> To: [email protected]
>> Subject: st: Multiple endogenous regressors: weak instrument robust test
>> statistic for individual coefficients (xtivreg2)?
>>
>> Dear all,
>>
>> I am estimating a IV-2SLS model with 2 endogenous regressors (x1, x2) and 2
>> excluded instruments (z1, z2) using the xtivreg2 command. Is there any way
>> to obtain a weak instrument robust test satistic for the individual (a subset
>> of) endogenous parameters? I.e., a Anderson-Rubin test statistic for x1 and
>> x2, respectively.
>
> Unless I misunderstand what you are looking for, it's in the xtivreg2 output you provided:
>
> Weak-instrument-robust inference
> Tests of joint significance of endogenous regressors B1 in main equation
> Ho: B1=0 and orthogonality conditions are valid
> Anderson-Rubin Wald test F(2,108)= 2.20 P-val=0.1161
> Anderson-Rubin Wald test Chi-sq(2)= 4.44 P-val=0.1086
> Stock-Wright LM S statistic Chi-sq(2)= 3.74 P-val=0.1540
>
> --Mark
>
>>
>> Any help would be greatly appreciated.
>>
>> Matthias
>>
>>
>> The command and the corresponding output are:
>>
>> xtivreg2 y ( x1 x2 = z1 z2) , cluster(id ) fe first
>>
>> FIXED EFFECTS ESTIMATION
>> ------------------------
>> Number of groups = 109 Obs per group: min = 2
>>
>> avg = 5.8
>> max = 6
>>
>> First-stage regressions
>> -----------------------
>>
>> First-stage regression of x1:
>>
>> FIXED EFFECTS ESTIMATION
>> ------------------------
>> Number of groups = 109 Obs per group: min = 2
>> avg = 5.8
>> max = 6
>>
>> OLS estimation
>> --------------
>>
>> Estimates efficient for homoskedasticity only Statistics robust to
>> heteroskedasticity and clustering on id
>>
>> Number of clusters (id) = 109 Number of obs = 636
>> F( 2, 108) = 4.33
>> Prob > F = 0.0155
>> Total (centered) SS = 56.34311291 Centered R2 = 0.0290
>> Total (uncentered) SS = 56.34311291 Uncentered R2 = 0.0290
>> Residual SS = 54.70817761 Root MSE = .3228
>>
>> ------------------------------------------------------------------------------
>> | Robust
>> x1 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
>> -------------+----------------------------------------------------------
>> -------------+------
>> z1 | .3654952 .1258542 2.90 0.004 .1160303 .6149601
>> z2 | .1336675 .1063186 1.26 0.211 -.0770744 .3444094
>> ------------------------------------------------------------------------------
>> Included instruments: z1 z2
>> ------------------------------------------------------------------------------
>> F test of excluded instruments:
>> F( 2, 108) = 4.33
>> Prob > F = 0.0155
>> Angrist-Pischke multivariate F test of excluded instruments:
>> F( 1, 108) = 8.64
>> Prob > F = 0.0040
>>
>> First-stage regression of x2:
>>
>> FIXED EFFECTS ESTIMATION
>> ------------------------
>> Number of groups = 109 Obs per group: min = 2
>> avg = 5.8
>> max = 6
>>
>> OLS estimation
>> --------------
>>
>> Estimates efficient for homoskedasticity only Statistics robust to
>> heteroskedasticity and clustering on id
>>
>> Number of clusters (id) = 109 Number of obs = 636
>> F( 2, 108) = 2.27
>> Prob > F = 0.1083
>> Total (centered) SS = 40.33333333 Centered R2 = 0.0079
>> Total (uncentered) SS = 40.33333333 Uncentered R2 = 0.0079
>> Residual SS = 40.01470425 Root MSE = .2761
>>
>> ------------------------------------------------------------------------------
>> | Robust
>> x2 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
>> -------------+----------------------------------------------------------
>> -------------+------
>> z1 | .0293852 .1057135 0.28 0.782 -.1801572 .2389276
>> z2 | -.2039007 .0972056 -2.10 0.038 -.396579 -.0112223
>> ------------------------------------------------------------------------------
>> Included instruments: z1 z2
>> ------------------------------------------------------------------------------
>> F test of excluded instruments:
>> F( 2, 108) = 2.27
>> Prob > F = 0.1083
>> Angrist-Pischke multivariate F test of excluded instruments:
>> F( 1, 108) = 3.49
>> Prob > F = 0.0645
>>
>>
>>
>> Summary results for first-stage regressions
>> -------------------------------------------
>>
>> (Underid) (Weak id)
>> Variable | F( 2, 108) P-val | AP Chi-sq( 1) P-val | AP F( 1, 108)
>> x1 | 4.33 0.0155 | 8.73 0.0031 | 8.64
>> x2 | 2.27 0.1083 | 3.53 0.0604 | 3.49
>>
>> NB: first-stage test statistics cluster-robust
>>
>> Stock-Yogo weak ID test critical values for single endogenous regressor:
>> 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.
>>
>> Underidentification test
>> 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)=3.16 P-val=0.0755
>>
>> Weak identification test
>> Ho: equation is weakly identified
>> Cragg-Donald Wald F statistic 1.75
>> Kleibergen-Paap Wald rk F statistic 1.55
>>
>> Stock-Yogo weak ID test critical values for K1=2 and L1=2:
>> 10% maximal IV size 7.03
>> 15% maximal IV size 4.58
>> 20% maximal IV size 3.95
>> 25% maximal IV size 3.63
>> Source: Stock-Yogo (2005). Reproduced by permission.
>> NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.
>>
>> Weak-instrument-robust inference
>> Tests of joint significance of endogenous regressors B1 in main equation
>> Ho: B1=0 and orthogonality conditions are valid
>> Anderson-Rubin Wald test F(2,108)= 2.20 P-val=0.1161
>> Anderson-Rubin Wald test Chi-sq(2)= 4.44 P-val=0.1086
>> Stock-Wright LM S statistic Chi-sq(2)= 3.74 P-val=0.1540
>>
>> NB: Underidentification, weak identification and weak-identification-robust
>> test statistics cluster-robust
>>
>> Number of clusters N_clust = 109
>> Number of observations N = 636
>> Number of regressors K = 2
>> Number of endogenous regressors K1 = 2
>> Number of instruments L = 2
>> Number of excluded instruments L1 = 2
>>
>> IV (2SLS) estimation
>> --------------------
>>
>> Estimates efficient for homoskedasticity only Statistics robust to
>> heteroskedasticity and clustering on id
>>
>> Number of clusters (id) = 109 Number of obs = 636
>> F( 2, 108) = 1.38
>> Prob > F = 0.2549
>> Total (centered) SS = 40.33333333 Centered R2 = -0.6194
>> Total (uncentered) SS = 40.33333333 Uncentered R2 = -0.6194
>> Residual SS = 65.31571726 Root MSE = .352
>>
>> ------------------------------------------------------------------------------
>> | Robust
>> y | Coef. Std. Err. z P>|z| [95% Conf. Interval]
>> -------------+----------------------------------------------------------
>> -------------+------
>> x1 | -.5789745 .3461093 -1.67 0.094 -1.257336 .0993872
>> x2 | -.3621129 .6874695 -0.53 0.598 -1.709528 .9853026
>> ------------------------------------------------------------------------------
>> Underidentification test (Kleibergen-Paap rk LM statistic): 3.158
>> Chi-sq(1) P-val = 0.0755
>> ------------------------------------------------------------------------------
>> Weak identification test (Cragg-Donald Wald F statistic): 1.755
>> (Kleibergen-Paap rk Wald F statistic): 1.553
>> Stock-Yogo weak ID test critical values: 10% maximal IV size 7.03
>> 15% maximal IV size 4.58
>> 20% maximal IV size 3.95
>> 25% maximal IV size 3.63
>> 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: x1 x2
>> Excluded instruments: z1 z2
>> *
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>> * http://www.ats.ucla.edu/stat/stata/
>
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