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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   Kit Baum <>
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 10:42:03 -0400

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   |
An Introduction to Stata Programming |
   An Introduction to Modern Econometrics Using Stata  |

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
In order words is there a command in STATA that can test for
endogeneity when the sample size is small?

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