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


From   "Danny Cohen-Zada" <danoran@bgu.ac.il>
To   <statalist@hsphsun2.harvard.edu>
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" <M.E.Schaffer@hw.ac.uk>
To: <statalist@hsphsun2.harvard.edu>
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: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of
Danny Cohen-Zada
Sent: Wednesday, February 27, 2008 2:58 PM
To: statalist@hsphsun2.harvard.edu
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/cert


After 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" <austinnichols@gmail.com>
To: <statalist@hsphsun2.harvard.edu>
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
<danoran@bgu.ac.il>
> 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
>>
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