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st: Question on Wooldridge's Procedure 18.1

vipul bhatt
Hi Stata Users,

I have a question on Wooldrige's Procedure 18.1 which relates to IV estimation when the endogenous regressor is a binary variable.

Suppose I want to estimate the following equation:

Y = a0 + a1 * X1  + a2* X2 + error

where X1 is an indicator variable and is also endogenous. Assume that we have exactly 1 instrument Z for X1.

X2 is an exogenous variable. The parameter of interest is a1.

Now, for a more efficient estimation it is often suggested to use the following two step estimation method:

Step 1: Estimate a Probit for the binary endogenous regressor on all exogenous variable and the instrument variable to obtain fitted probabilities.

Probit: X1  = f (Z, X2,) + error

Gives us predicted X1 : X1_hat1

Step 2: Use the fitted probabilities from (step 1 above) X1_hat1 and all exogenous regressors as instruments to obtain a more efficient estimate of the binary endogenous regressor. So in this step I  use the standard 2sls procedure:
 
First stage: X1= b0 = b1*X1_hat1 + b2*X2 + error

This gives us the predicted value X1_hat2.

Second Stage: Y = a0 + a1 * X1_hat2  + a2* X2 + error


My question relates to the validity of the instrument  Z. To argue for the validity of  this instrument should I consider Z's statistical significance in  the Probit model of  Step 1?

Or

since step 1 is simply an extra step to obtain fitted probabilities to be used as instruments , we should only look  at the statistical significance of the fitted values (X1_hat1) in the first stage of  2sls estimation in Step 2, i.e. whether or not b1=0 ?

Wooldrige claims that we can ignore the step 1 estimation properties and focus only on step 2.  However he does not offer any explanation for the same. I will really appreciate any comments or suggestions you may have on this issue.

Thanks,

VB


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Re: st: Question on Wooldridge's Procedure 18.1

Austin Nichols
vipul bhatt <[hidden email]> :
None of the above (or below, in this case).  Use the predicted value
from your -probit- as an excluded instrument in -ivreg2- (on SSC) and
read the help file for -ivreg2- for tests of identification and overid
tests.  The part you can ignore is that your excluded instrument is
generated, which is like the zeroth stage (with the first and second
stages being done by -ivreg2- is a single step)--Wooldridge does not
say you can ignore the first stage.  See also
http://www.stata-journal.com/article.html?article=st0136
or slide 55 out of 95 in
http://www.stata.com/meeting/germany09/nichols.pdf
or e.g.
http://www.stata.com/statalist/archive/2007-04/msg00415.html

On Thu, Jan 7, 2010 at 8:52 AM, vipul bhatt <[hidden email]> wrote:
<snip>
My question relates to the validity of the instrument  Z. To argue for
the validity of  this instrument should I consider Z's statistical
significance in  the Probit model of  Step 1?

>
> Or
>
> since step 1 is simply an extra step to obtain fitted probabilities to be used as instruments , we should only look  at the statistical significance of the fitted values (X1_hat1) in the first stage of  2sls estimation in Step 2, i.e. whether or not b1=0 ?
>
> Wooldrige claims that we can ignore the step 1 estimation properties and focus only on step 2.  However he does not offer any explanation for the same. I will really appreciate any comments or suggestions you may have on this issue.
>
> Thanks,
>
> VB

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AW: st: Question on Wooldridge's Procedure 18.1

Martin Weiss-5

<>

" or e.g.
http://www.stata.com/statalist/archive/2007-04/msg00415.html"


Did some characters go missing at some point from the code in this post?
"esto" should probably be "eststo"?




HTH
Martin


-----Ursprüngliche Nachricht-----
Von: [hidden email]
[mailto:[hidden email]] Im Auftrag von Austin Nichols
Gesendet: Donnerstag, 7. Januar 2010 15:33
An: [hidden email]
Betreff: Re: st: Question on Wooldridge's Procedure 18.1

vipul bhatt <[hidden email]> :
None of the above (or below, in this case).  Use the predicted value
from your -probit- as an excluded instrument in -ivreg2- (on SSC) and
read the help file for -ivreg2- for tests of identification and overid
tests.  The part you can ignore is that your excluded instrument is
generated, which is like the zeroth stage (with the first and second
stages being done by -ivreg2- is a single step)--Wooldridge does not
say you can ignore the first stage.  See also
http://www.stata-journal.com/article.html?article=st0136
or slide 55 out of 95 in
http://www.stata.com/meeting/germany09/nichols.pdf
or e.g.
http://www.stata.com/statalist/archive/2007-04/msg00415.html

On Thu, Jan 7, 2010 at 8:52 AM, vipul bhatt <[hidden email]> wrote:
<snip>
My question relates to the validity of the instrument  Z. To argue for
the validity of  this instrument should I consider Z's statistical
significance in  the Probit model of  Step 1?
>
> Or
>
> since step 1 is simply an extra step to obtain fitted probabilities to be
used as instruments , we should only look  at the statistical significance
of the fitted values (X1_hat1) in the first stage of  2sls estimation in
Step 2, i.e. whether or not b1=0 ?
>
> Wooldrige claims that we can ignore the step 1 estimation properties and
focus only on step 2.  However he does not offer any explanation for the
same. I will really appreciate any comments or suggestions you may have on
this issue.
>
> Thanks,
>
> VB

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Re: st: Question on Wooldridge's Procedure 18.1

vipul bhatt
In reply to this post by Austin Nichols
Hi,

Thank you for these useful links. When I said Wooldrige mentions that we can ignore step 1 estimation I was actually referring to zeroth stage where I do probit of binary endogenous regressor on my instrument Z. Can we ignore insignificance of Z in this zeroth stage and simply focus on the validity of the predicted probablities (as these are my 'generated instrument') using output of ivreg2?

Thank you,
VB

--- On Thu, 7/1/10, Austin Nichols <[hidden email]> wrote:

> From: Austin Nichols <[hidden email]>
> Subject: Re: st: Question on Wooldridge's Procedure 18.1
> To: [hidden email]
> Date: Thursday, 7 January, 2010, 8:03 PM
> vipul bhatt <[hidden email]>
> :
> None of the above (or below, in this case).  Use the
> predicted value
> from your -probit- as an excluded instrument in -ivreg2-
> (on SSC) and
> read the help file for -ivreg2- for tests of identification
> and overid
> tests.  The part you can ignore is that your excluded
> instrument is
> generated, which is like the zeroth stage (with the first
> and second
> stages being done by -ivreg2- is a single step)--Wooldridge
> does not
> say you can ignore the first stage.  See also
> http://www.stata-journal.com/article.html?article=st0136
> or slide 55 out of 95 in
> http://www.stata.com/meeting/germany09/nichols.pdf
> or e.g.
> http://www.stata.com/statalist/archive/2007-04/msg00415.html
>
> On Thu, Jan 7, 2010 at 8:52 AM, vipul bhatt <[hidden email]>
> wrote:
> <snip>
> My question relates to the validity of the instrument  Z.
> To argue for
> the validity of  this instrument should I consider Z's
> statistical
> significance in  the Probit model of  Step 1?
> >
> > Or
> >
> > since step 1 is simply an extra step to obtain fitted
> probabilities to be used as instruments , we should only
> look  at the statistical significance of the fitted values
> (X1_hat1) in the first stage of  2sls estimation in Step 2,
> i.e. whether or not b1=0 ?
> >
> > Wooldrige claims that we can ignore the step 1
> estimation properties and focus only on step 2.  However he
> does not offer any explanation for the same. I will really
> appreciate any comments or suggestions you may have on this
> issue.
> >
> > Thanks,
> >
> > VB
>
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> *   For searches and help try:
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> *   http://www.stata.com/support/statalist/faq
> *   http://www.ats.ucla.edu/stat/stata/
>


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Re: st: Question on Wooldridge's Procedure 18.1

Austin Nichols
In reply to this post by Austin Nichols
martin--
That older post uses the earlier (now obsolete) forms of the
user-written commands.  Of course, nothing is lost if you simply
ignore those commands:

sysuse auto, clear
treatreg pri wei, treat(for=mpg) r
ivreg pri wei (for=mpg), r
probit for wei mpg
predict ghat
ivreg pri wei (for=ghat), r
reg for wei ghat, r
predict vhat, resid
reg pri wei for vhat, r

or rewrite:

est clear
sysuse auto, clear
treatreg pri wei, treat(for=mpg) r
est sto treat
ivreg pri wei (for=mpg), r
est sto ivreg
probit for wei mpg
predict ghat
ivreg pri wei (for=ghat), r
est sto pr18_1
reg for wei ghat, r
predict vhat, resid
reg pri wei for vhat, r
est sto pr18_1cf
est table *, t eq(1)


On Thu, Jan 7, 2010 at 9:40 AM, Martin Weiss <[hidden email]> wrote:

>
> <>
>
> " or e.g.
> http://www.stata.com/statalist/archive/2007-04/msg00415.html"
>
>
> Did some characters go missing at some point from the code in this post?
> "esto" should probably be "eststo"?
>
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*   http://www.stata.com/help.cgi?search
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Re: st: Question on Wooldridge's Procedure 18.1

Austin Nichols
In reply to this post by vipul bhatt
vipul bhatt <[hidden email]>:

No, you cannot--this is point of the sentence
"Note that the weak instrument diagnostics
will fail miserably using these
approaches."
in http://www.stata.com/meeting/germany09/nichols.pdf

Your weak instrument diagnostics should come from straight IV, not
procedure 18.1--note that procedure 18.1 would go through if Z was
pure noise, and the predicted value of your endogenous variable could
be very highly correlated with the endogenous variable, leading you to
think you had very strong instruments.  This is also a problem using
predictions as excluded instruments in other settings (e.g.
http://www.nber.org/papers/w11279 which uses predicted income as an
instrument for income), and then reporting the diagnostics as if the
predictions are actual measured data.

On Thu, Jan 7, 2010 at 10:13 AM, vipul bhatt <[hidden email]> wrote:
> Hi,
>
> Thank you for these useful links. When I said Wooldrige mentions that we can ignore step 1 estimation I was actually referring to zeroth stage where I do probit of binary endogenous regressor on my instrument Z. Can we ignore insignificance of Z in this zeroth stage and simply focus on the validity of the predicted probablities (as these are my 'generated instrument') using output of ivreg2?
>
> Thank you,
> VB
>

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Re: st: Question on Wooldridge's Procedure 18.1

vipul bhatt
Hi,
Thank you for this clarification.

VB

--- On Thu, 7/1/10, Austin Nichols <[hidden email]> wrote:

> From: Austin Nichols <[hidden email]>
> Subject: Re: st: Question on Wooldridge's Procedure 18.1
> To: [hidden email]
> Date: Thursday, 7 January, 2010, 8:52 PM
> vipul bhatt <[hidden email]>:
>
> No, you cannot--this is point of the sentence
> "Note that the weak instrument diagnostics
> will fail miserably using these
> approaches."
> in http://www.stata.com/meeting/germany09/nichols.pdf
>
> Your weak instrument diagnostics should come from straight
> IV, not
> procedure 18.1--note that procedure 18.1 would go through
> if Z was
> pure noise, and the predicted value of your endogenous
> variable could
> be very highly correlated with the endogenous variable,
> leading you to
> think you had very strong instruments.  This is also a
> problem using
> predictions as excluded instruments in other settings
> (e.g.
> http://www.nber.org/papers/w11279 which uses predicted
> income as an
> instrument for income), and then reporting the diagnostics
> as if the
> predictions are actual measured data.
>
> On Thu, Jan 7, 2010 at 10:13 AM, vipul bhatt <[hidden email]>
> wrote:
> > Hi,
> >
> > Thank you for these useful links. When I said
> Wooldrige mentions that we can ignore step 1 estimation I
> was actually referring to zeroth stage where I do probit of
> binary endogenous regressor on my instrument Z. Can we
> ignore insignificance of Z in this zeroth stage and simply
> focus on the validity of the predicted probablities (as
> these are my 'generated instrument') using output of
> ivreg2?
> >
> > Thank you,
> > VB
> >
>
> *
> *   For searches and help try:
> *   http://www.stata.com/help.cgi?search
> *   http://www.stata.com/support/statalist/faq
> *   http://www.ats.ucla.edu/stat/stata/
>


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Re: st: Question on Wooldridge's Procedure 18.1

B.Gibbons
This post has NOT been accepted by the mailing list yet.
In reply to this post by Austin Nichols
Hi Austin, I'm currently using the 18.1 method in a project and have seen your warnings about using tests of instrument strength through the 18.1 method.

My 1st question is whether those warnings are solely because of the potential that the non-linearity in the probit may be correlated with the binary endogenous variable - and falsely show good instrument strength.

2nd - what if there is both strong correlation between the non-linearity in the probit AND strong instruments in the model: is there reason to worry about this non-linearity as having a potential bias, especially since you can't test the exclusion restriction for that?

Thanks for any comments, Brent
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