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Re: st: STATA command for Testing for endogeneity when the sample size is small. Is there a small sample correction?


From   Stephen Armah <armah.stephen@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: STATA command for Testing for endogeneity when the sample size is small. Is there a small sample correction?
Date   Sat, 28 Mar 2009 11:31:26 -0500

Dear Kit,
Thanks for your helpful answer.

On 3/28/09, Kit Baum <baum@bc.edu> wrote:
> <>
> Although the justification for many things with regard to instrumental
> variables estimators is only asymptotic, I don't see why the Durbin-Wu-
> Hausman test implemented by Baum/Schaffer/Stillman's -ivreg2- option -
> endog()- would be problematic in a sample of size 186. That does not
> sound particularly small to me, but the ability of the test to
> distinguish between OLS and IV may be fairly weak with that amount of
> data.
>
> I have simulated the performance of -endog()- for different sample
> sizes, random subsets of the griliches76 dataset used in -help ivreg2-
> in which I have added random noise to the variable considered
> endogenous. Here is the average p-value for the Durbin-Wu-Hausman
> endogeneity test, derived from 1000 replications at each sample size
> (en):
>
>        en |      mean
> ---------+----------
>        50 |   .398134
>       100 |  .3549545
>       150 |  .3360662
>       200 |  .3105404
>       250 |  .2703655
>       300 |  .2614716
>       350 |  .2356522
>       400 |  .1967296
>       450 |  .1733359
>       500 |  .1310702
>       550 |  .1082535
>       600 |  .0737662
>       650 |  .0503589
>       700 |  .0329359
>       750 |  .0164609
> ---------+----------
>
> It is apparent that a test that can comfortably reject the null that
> OLS is appropriate at a sample size of 600+ has little power to do so
> for sample sizes of 150-200. However, I am not aware of any
> modification to the test that would enable it to be more powerful in
> smaller samples.
>
>
> Kit Baum   |   Boston College Economics & DIW Berlin   |
> http://ideas.repec.org/e/pba1.html
>                                An Introduction to Stata Programming
> |   http://www.stata-press.com/books/isp.html
>     An Introduction to Modern Econometrics Using Stata  |
> http://www.stata-press.com/books/imeus.html
>
>
>
> On Mar 28, 2009, at 02:33 , Stephen wrote:
>
>> I am trying to test for endogeneity but I think I  the command that I
>> am using to test for endogeneity in STATA is not very powerful when
>> the sample size is small.
>> I have a panel of 31 countries and 6 four-year periods.
>>
>>
>> I am usinging: ivreg2 y x1 x2 (x3 = z1...zn), endog(x3)
>> where y is the dependent variable, the xi are the independent
>> variables so that x3 is endogenous, x1 and x2 are exogenous and the zi
>> are instruments.
>>
>> Does anyone know of a test of endogeneity in STATA witha small sample
>> correction?
>> In order words is there a command in STATA that can test for
>> endogeneity when the sample size is small?
>
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