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st: confidence interval for the prediction (yhat) in the case of weak instruments.

From   "Danny Cohen-Zada" <>
To   <>
Subject   st: confidence interval for the prediction (yhat) in the case of weak instruments.
Date   Sun, 9 Mar 2008 17:47:55 +0200

Suppose that i estimate the effect of x1 on y, where z is used as an instrument for x1. Suppose also that z is found to be a weak instrument for x1. Using the AR test i find that x1 has a negative significant effect on y. Now, i want to graph the predicted proabilility (of y=1) as a function of x1 (when all other variables are at their mean). I want to include in the graph also the confidence interval of the predicted probability. for this purpose i use the command prgen. In the case, where z is a weak instrument for x1, can i trust this graph. If not, do you have an idea how to depict the correct ci for the predicted probability.



----- Original Message ----- From: "Schaffer, Mark E" <>
To: <>
Sent: Friday, March 07, 2008 5:36 PM
Subject: st: RE: AR confidence interval that take clustering into account


-----Original Message-----
[] On Behalf Of
Danny Cohen-Zada
Sent: Friday, March 07, 2008 3:07 PM
Subject: st: AR confidence interval that take clustering into account


I learned from you and from professor schaffer that i can
obtain the AR test with ivreg2 (taking clustering into account)

I have a model with one endogenous variable and one
instrument and I have to cluster the standard errors. Could
you please tell me how  i can  create AR confidence intervals
that take the clustering into account?
It's pretty easy but a bit laborious.  Just do a grid search.  That is,

1.  Pick a possible value for the coefficient beta on your endogenous
variable X.  Call it beta_tilda.

2.  Create a new dependent variable, Y_tilda = Y-beta_tilda*X, where Y
is your original dependent variable.

3.  Regress Y_tilda on all the exogenous regressors and excluded

4.  Test the joint significance of your excluded instruments using an F

The grid search means repeating (1)-(4) above across possible values of
beta_tilda until you find out where the rejection area starts and ends,
i.e., the two values of beta_tilda where the F stat has a p-value of
about 5%.

The problem you may run into is that AR confidence intervals can be
empty or disjoint (!).  I don't recall if disjoint AR CIs are possible
with an exactly-identified equation but empty AR CIs certainly are.  If
you get this in your case, it suggests problems, e.g., your excluded
instrument may be invalid.  (Think about it - if your excluded
instrument is correlated with the error term, then even if your
beta_tilda is the true beta, you'll get a significant F stat on the
excluded instrument because it's not exogenous in the AR regression.)

Hope this helps.


Prof. Mark E. Schaffer
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

Thank you very much

----- Original Message -----
From: "Austin Nichols" <>
To: <>
Sent: Thursday, February 28, 2008 4:00 PM
Subject: Re: st: conditional likelihood ratio test when the
cluster option is used in ivreg (weak instrument).

> Danny--
> The answer is no, you cannot "trust this result" from a
command that
> does not allow cluster-robust estimation when you must use
> standard errors in the IV (ivreg2) estimation.  If clustering is
> important, and you have said that it is, and you have a weak
> instruments problem, you must either improve the quality of your
> instruments by adding/finding more excluded instruments, in
which case
> you probably want the LIML/CUE options on -ivreg2- (and
overID tests),
> or you can use a method of inference robust to the presence of weak
> instruments that allows clustering, namely Anderson-Rubin
> regions.  I discussed this in some detail at NASUG5, and
some of the
> material appears in the slides at
> and some in
Stata Journal
> 7(4).  On Anderson-Rubin tests/conf regions, see the Dufour and
> Taamouti ref linked from
> (though I prefer constructing the confidence region rather than the
> projection onto individual axes that they advocate--the
latter can be
> deceptive if, say, there are two variables measuring a similar
> quantity and you can reject that both coefs are simultaneously zero
> because the conf ellipse does not include the origin, but the
> projections might both overlap zero).  Tests are easier than
> confidence regions for this approach, obviously.
> On Thu, Feb 28, 2008 at 8:09 AM, Danny Cohen-Zada
> wrote:
>> I will try to edit my question to be clearer.
>>  Suppose that i estimate the following iv model with the
cluster option.
>>  ivreg2 y1 x1 x2 (y2 =  z1 ), ffirst cluster (x3)
>>  I tested that my instrument is weak (using the clustered
>> f-statistic) and  found that my instrument is weak.
>>  Then i run the conditional likelihood ratio test
>>  condivreg y1 x1 x2 (y2= z1)
>>  This command does not have the cluster option.
>>  Supose that i find that the p-value of this test is 0.000 . Can i
>> trust this  result even when i use clustered standard errors in my
>> ivreg estimation.
>>  Thanks
>>  Danny
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