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From |
"Danny Cohen-Zada" <[email protected]> |

To |
<[email protected]> |

Subject |
Re: st: Critical values for stock and yogo test when the clusteroption is used |

Date |
Wed, 27 Feb 2008 19:13:26 +0200 |

Dear Professor Schaffer,

I am grateful to you for your quick reply. I read your paper (especially where it is related to my question - page 24) and i am alittle bit confused. I would be grateful if you can tell me if i am right. In your paper you write "If the user specifies the robust cluster options in ivreg2, the reproted weak instruments test statistics is a Wald F-statistic based on the Kleibergen-Paap rk statistic. Then you continue "In our view, however, the use of the rk wald statistic, as the robust analog of the cragg-donald statistics, is a sensible choice and clearly superior to the use of the latter in the presence of .. clustering".

If i understand this well i do not have to worry that my instrument is weak and maybe i wasn't clear enough in my previous mail. In order to be sure that i am right i will present my output (I only do not know why i specified the cluster option and still obtain the cragg-donald statistic and not the Kleibergen-Paap rk statistic as i see in the outputs of your paper).

Can i come to conclustion base on the output below? If yes, should i compare 158 to 16.38 or should i compare 5.26 to 16.38.

This is the output:

ivreg2 entitled gender fatheduc motheduc siblings tipuah index girlsprop olevatik fath_n_america_europe fath_asia_africa fath_otherloc moth_n_america_europe

moth_asia_africa school_dummy nstud12 nstud12squr ( pupils= ex_cs) if schl_iy==1 , first robust cluster( schlkita)First-stage regressions

-----------------------

First-stage regression of pupils:

OLS estimation

--------------

Statistics robust to heteroskedasticity and clustering on schlkita

Number of clusters (schlkita) = 160 Number of obs = 3477

F( 17, 159) = 20.91

Prob > F = 0.0000

Total (centered) SS = 164186.2675 Centered R2 = 0.4071

Total (uncentered) SS = 3496104 Uncentered R2 = 0.9722

Residual SS = 97338.94342 Root MSE = 5.305

------------------------------------------------------------------------------

| Robust

pupils | Coef. Std. Err. t P>|t| [95% Conf. Interval]

-------------+----------------------------------------------------------------

gender | .1145447 .1273215 0.90 0.370 -.1369148 .3660043

fatheduc | .1756328 .0469734 3.74 0.000 .0828605 .2684051

motheduc | .1615434 .0685023 2.36 0.020 .0262517 .2968351

siblings | .1086323 .1211446 0.90 0.371 -.1306278 .3478923

tipuah | -.2036365 .1995934 -1.02 0.309 -.5978327 .1905598

index | .7451653 .6627006 1.12 0.263 -.5636659 2.053997

girlsprop | 2.874038 1.229628 2.34 0.021 .445527 5.302549

olevatik | -.1522312 .3756952 -0.41 0.686 -.8942278 .5897653

fath_n_ame~e | .0048261 .2376222 0.02 0.984 -.4644768 .4741289

fath_asia_~a | -.4640889 .2690778 -1.72 0.087 -.9955164 .0673387

fath_other~c | .558478 1.373149 0.41 0.685 -2.153487 3.270443

moth_n_ame~e | -.3222788 .250198 -1.29 0.200 -.8164188 .1718613

moth_asia_~a | -.0316187 .3215067 -0.10 0.922 -.6665932 .6033559

school_dummy | -.2655496 1.621763 -0.16 0.870 -3.468526 2.937427

nstud12 | .0284393 .0381495 0.75 0.457 -.0469059 .1037845

nstud12squr | -.0000321 .0000744 -0.43 0.667 -.0001791 .000115

ex_cs | .4494619 .1959078 2.29 0.023 .0625446 .8363791

_cons | 7.021915 4.437086 1.58 0.116 -1.741313 15.78514

------------------------------------------------------------------------------

Included instruments: gender fatheduc motheduc siblings tipuah index girlsprop

olevatik fath_n_america_europe fath_asia_africa

fath_otherloc moth_n_america_europe moth_asia_africa

school_dummy nstud12 nstud12squr ex_cs

------------------------------------------------------------------------------

Partial R-squared of excluded instruments: 0.0437

Test of excluded instruments:

F( 1, 159) = 5.26

Prob > F = 0.0231

Summary results for first-stage regressions

-------------------------------------------

Variable | Shea Partial R2 | Partial R2 | F( 1, 159) P-value

pupils | 0.0437 | 0.0437 | 5.26 0.0231

NB: first-stage F-stat cluster-robust

Underidentification tests:

Chi-sq(1) P-value

Anderson canon. corr. likelihood ratio stat. 155.36 0.0000

Cragg-Donald N*minEval stat. 158.88 0.0000

Ho: matrix of reduced form coefficients has rank=K-1 (underidentified)

Ha: matrix has rank>=K (identified)

NB: underidentification statistics not robust

Anderson-Rubin test of joint significance of

endogenous regressors B1 in main equation, Ho:B1=0

F(1,159)= 5.90 P-val=0.0162

Chi-sq(1)= 5.97 P-val=0.0145

NB: Anderson-Rubin stat cluster-robust

Number of clusters N_clust = 160

Number of observations N = 3477

Number of regressors K = 18

Number of instruments L = 18

Number of excluded instruments L2 = 1

IV (2SLS) estimation

--------------------

Statistics robust to heteroskedasticity and clustering on schlkita

Number of clusters (schlkita) = 160 Number of obs = 3477

F( 17, 159) = 4.64

Prob > F = 0.0000

Total (centered) SS = 535.3396606 Centered R2 = -0.2609

Total (uncentered) SS = 2816 Uncentered R2 = 0.7603

Residual SS = 675.0333424 Root MSE = .4406

------------------------------------------------------------------------------

| Robust

entitled | Coef. Std. Err. z P>|z| [95% Conf. Interval]

-------------+----------------------------------------------------------------

pupils | -.0364681 .0175529 -2.08 0.038 -.0708711 -.0020652

gender | .0492141 .0163051 3.02 0.003 .0172566 .0811716

fatheduc | .0141794 .0044121 3.21 0.001 .0055319 .0228269

motheduc | .0150479 .0057364 2.62 0.009 .0038048 .026291

siblings | .0088987 .0082991 1.07 0.284 -.0073673 .0251646

tipuah | -.0272665 .0116795 -2.33 0.020 -.050158 -.0043751

index | .0514334 .0409498 1.26 0.209 -.0288267 .1316935

girlsprop | .1473534 .061805 2.38 0.017 .0262178 .268489

olevatik | -.0408316 .0310203 -1.32 0.188 -.1016302 .019967

fath_n_ame~e | -.0009037 .0204988 -0.04 0.965 -.0410805 .0392731

fath_asia_~a | -.0435657 .0256591 -1.70 0.090 -.0938566 .0067252

fath_other~c | -.1169402 .146099 -0.80 0.423 -.4032889 .1694085

moth_n_ame~e | -.0277134 .0206725 -1.34 0.180 -.0682307 .0128039

moth_asia_~a | -.0140052 .0275814 -0.51 0.612 -.0680638 .0400534

school_dummy | .1578893 .0780717 2.02 0.043 .0048717 .310907

nstud12 | .0047183 .0020431 2.31 0.021 .0007138 .0087228

nstud12squr | -7.48e-06 3.84e-06 -1.95 0.052 -.000015 5.02e-08

_cons | .8993509 .3155496 2.85 0.004 .2808851 1.517817

------------------------------------------------------------------------------

Anderson canon. cor. LR statistic (identification/IV relevance test): 155.358

Chi-sq(1) P-val = 0.0000

Test statistic(s) not robust

------------------------------------------------------------------------------

Cragg-Donald F statistic (weak identification test): 158.058

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

Test statistic(s) not robust

Source: Stock-Yogo (2005). Reproduced by permission.

------------------------------------------------------------------------------

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

(equation exactly identified)

------------------------------------------------------------------------------

Instrumented: pupils

Included instruments: gender fatheduc motheduc siblings tipuah index girlsprop

olevatik fath_n_america_europe fath_asia_africa

fath_otherloc moth_n_america_europe moth_asia_africa

school_dummy nstud12 nstud12squr

Excluded instruments: ex_cs

Dr. Danny Cohen-Zada

Department of Economics

Ben-Gurion University of the Negev

P.O.Box 653

Beer-Sheva 84105

Israel

Tel: +972-8-6472301

Fax: +972-8-6472941

http://www.econ.bgu.ac.il/facultym/danoran/main.htm

----- Original Message ----- From: "Schaffer, Mark E" <[email protected]>

To: <[email protected]>

Sent: Wednesday, February 27, 2008 5:18 PM

Subject: RE: st: Critical values for stock and yogo test when the clusteroption is used

Danny,`-----Original Message----- From: [email protected] [mailto:[email protected]] On Behalf Of Danny Cohen-Zada Sent: Wednesday, February 27, 2008 2:58 PM To: [email protected] Subject: Re: st: Critical values for stock and yogo test when the clusteroption is used Dear Professor Austin and other statalist subscribers I only want to add that in the email today I clarified something that wasn't clear enough in the private mail yesterday. The points is that the results much differ if I use the clustered f-statistic instead of the regular one. The regular f-statistic is 158 which is extremely above the regular critical value (the critical values are between 5.53-16.38). This indicate that the instrument is extremely strong. However, if i compare the clustered f-statistic (5.26) to the regular critical values I may come to an opposite conclusion that my instrument is quite weak (it is only close to the 25% maximal iv size). Should i worry about the strength of my instrument?`

The short answer is "yes", you should worry, and your intution below is right. The problem starts out just like the usual problem of using non-robust SEs for inference. If the disturbance is heteroskedastic or clustered, the usual SEs are wrong, and usually [sic] you'll get SEs that are "too small" and test stats that are "too big". The same features of the data that give you these test stats that are "too big" will give you a first-stage F-stat that is also "too big", and so the Stock-Yogo critical values will be wrong. Where it gets complicated is that the S-Y critical values for weak identification come from Monte Carlos. My understanding is that if you want the "right" critical values for cases where the standard S-Y iid assumption is loosened, you have to specify how it's loosened, i.e., in your case, what kind of clustering you've got. That said, using a cluster-robust first-stage F stat with the S-Y critical values is not bad and in the absence of anything better is probably the best you can do. It's also worth noting that the first-stage F-stat can also be used as a test for *under*identification a la Anderson. (See the paper by myself, Kit Baum and Steve Stillman in the latest issue of the SJ, vol. 7 no. 4 2007.) This is a test with an asymptotic justification and uses standard critical values, and the robust first-stage F stat with this standard critical values is fine. Since underidentification is a lower hurdle than weak identification, if you can't reject the null that your equation is underidentified, you can pretty safely also fail to reject the null that it's weakly identified. Hope this helps. Cheers, Mark Prof. Mark E. Schaffer Director Centre for Economic Reform and Transformation Department of Economics School of Management & Languages Heriot-Watt University Edinburgh EH14 4AS UK 44-131-451-3494 direct 44-131-451-3296 fax http://www.sml.hw.ac.uk/certAfter all, i guess that as the clustered f-statistic is much lower than the regular one, the clustered critical value should also be lower? That is, don't we require to much when we compare the clustered f-statistic to the regular critical values. Best, Danny ----- Original Message ----- From: "Austin Nichols" <[email protected]> To: <[email protected]> Sent: Wednesday, February 27, 2008 3:36 PM Subject: Re: st: Critical values for stock and yogo test when the clusteroption is used > All-- > My reply (Tue, Feb 26, 2008 at 4:42 PM) to this interlocutor's private > email yesterday was: > *************** > Until someone redoes Stock and Yogo with various kinds of clustering, > you are stuck comparing your value to their table. One reason no one > has done that is that different kinds of clustering might produce > different answers, so the critical values might be more > problem-specific, and you might have to run your own simulations for > your own case, using observed intra-cluster correlations in the data. > *************** > If anyone has a different answer, I'd be interested to hear it. Note > that the ref for Stock and Yogo is in the help for -ivreg2- on SSC and > in http://www.stata.com/meeting/5nasug/wiv.pdf. > > On Wed, Feb 27, 2008 at 7:33 AM, Danny Cohen-Zada <[email protected]> > wrote: >> I would be thankful to anybody that can give me an advice concerning >> the critical values in the stock and yogo test. >> >> >> I estimate the following IV model with the cluster option >> >> ivreg2 y1 x1 x2 (y2 = z1 ), ffirst cluster (x3) >> >> (In my model I have only one endogenous regressor and one excluded >> instrument). >> >> I know that the Stock and Yogo statistic assume conditional >> homoskedasticity and independence. Since I use the cluster option I >> can not use the reported stock and yogo statistic (f statistic on >> the exluded instrument) and the reported critical values. >> >> I know that I can use the command ffirst to obtain the corrected f >> statistic on the excluded instrument. It differ substantially from >> the unclustered f statistic (regular = 158, clustered=5.26, the >> regular critical values are in the range 5.53-16.38). However, I >> still have a problem because I do not know what the corrected >> critical values are (I guess that I can not use the regular critical >> values). If i used the regular f-statistic and the regular critical >> values i find that my instruments are very very strong. This picture >> is changed if i compare the corrected f-statisticto the regular >> critical values. >> >> I would be thankful to anybody who knows how I can check that my >> instruments are not weak in a regression where the cluster option is >> used. >> Specifically, >> to which value should I compare the corrected f-statistic on the >> excluded instrument obtained by the command ffirst. >> >> >> Best, >> >> Danny >> > * > * For searches and help try: > * http://www.stata.com/support/faqs/res/findit.html > * http://www.stata.com/support/statalist/faq > * http://www.ats.ucla.edu/stat/stata/ > * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/* * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

* * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**RE: st: Critical values for stock and yogo test when the clusteroption is used***From:*"Schaffer, Mark E" <[email protected]>

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