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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 15:41:50 +0100
Hi Mark,
thank you very much for the information and the link.
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: 14 January 2014 13:20
>> To: [email protected]
>> Subject: Re: st: RE: Multiple endogenous regressors: weak instrument robust
>> test statistic for individual coefficients (xtivreg2)?
>>
>> 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?
>
> This is an interesting question, and one where the theory is still being worked out. My understanding is that it depends, among other things, on the assumptions you make about whether the other endogenous regressor is weakly or strongly identified.
>
> Anna Mikusheva has a nice little review paper that discusses this (see Section 6):
>
> Anna Mikusheva
> Survey on statistical inferences in weakly-identified instrumental variable models
> Applied Econometrics / ПРИКЛАДНАЯ ЭКОНОМЕТРИКА
> Theory and methodology / Теория и методология
> 29 (1) 2013
> http://pe.cemi.rssi.ru/pe_2013_1_117-131.pdf
>
> In any case, I'm not aware of any Stata packages that will do these procedures for you, so you're probably in "roll your own" territory.
>
> HTH,
> Mark
>
>> 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
>> >> *
>> >> * For searches and help try:
>> >> * http://www.stata.com/help.cgi?search
>> >> * http://www.stata.com/support/faqs/resources/statalist-faq/
>> >> * http://www.ats.ucla.edu/stat/stata/
>> >
>> >
>> > -----
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>> >
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>>
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>
>
> -----
> Sunday Times Scottish University of the Year 2011-2013
> Top in the UK for student experience
> Fourth university in the UK and top in Scotland (National Student Survey 2012)
>
>
> We invite research leaders and ambitious early career researchers to
> join us in leading and driving research in key inter-disciplinary themes.
> Please see www.hw.ac.uk/researchleaders for further information and how
> to apply.
>
> Heriot-Watt University is a Scottish charity
> registered under charity number SC000278.
>
>
> *
> * For searches and help try:
> * http://www.stata.com/help.cgi?search
> * http://www.stata.com/support/faqs/resources/statalist-faq/
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*
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