# [no subject]

```Maarten,

> -----Original Message-----
> From: [email protected]
> [mailto:[email protected]] On Behalf Of
> Maarten A Allers
> Sent: Friday, January 18, 2008 9:21 AM
> To: [email protected]
> Subject: Re: st: Endogenous right hand side variable
>
> Dear All,
>
> The message I just sent (Endogenous right hand side variable)
> was cut in two (the second part appearing under the heading
> [no subject]). Please forgive me for trying again.
>
> Reading this thread puzzles me. Rodrigo's suggestion appears
> to be different from Mark's, although it seems to be meant as
> a clarification.
> Rodrigo's solution is described in Wooldridge (2002, p. 574,
> http://www.stata.com/bookstore/cspd.html).
> I have a slightly different model:
>
> y1 = a*x1 + b*y3 +e1
> y2 = c*x2 + e2
> y3 = max(0 , y2)
> where y2 is potentially endogenous, and only observed when
> y2>0. y1, y3,
> x1 and x2 are always observed.
>
> My model differs from Rodrigo's (and Wooldridge's) model
> because y1 is always observed, whereas, in Rodrigo's model,
> both y1 and y2 are unobserved when y2<0. My model seems more
> in line with Kathleen's original question.
>
> I think I should:
> 1) estimate y2 by -tobit-
> 2) use fitted values of y2 to generate y3hat=max(0,y2hat)
> 3) use y3hat to estimate y1.
>
> The problem is to obtain correct standard errors. Am I right
> to assume Mark's suggestion will help me here? That is, use
> y3hat as an instrument in step 3) as in
>
> ivreg y1 (y3 = y3hat) x1
>
> I would very much appreciate your advise, and, if possible, a
> reference.

You need to argue that the procedure satisfies the requirements for
consistency of IV, namely that

y3hat is correlated with y3  (easy)

y3hat is uncorrelated with e1 (needs a bit of thought)

Your y3hat is defined as max(0,y2hat) where y2hat=chat*x2.

The slightly tricky bit - but I think you're OK - is that you say y2 is
potentially endogenous and observed only if it's strictly positive.  Say
for some i, e2_i is a big negative shock, so that even though c*x2_i>0,
y2_i is < 0.  You observe y3_i=0, and if y2 is endogenous because e1 and
e2 are correlated (say positively), the fact that y3_i will be at its
minimum will be associated with e1_i being also being a big negative
shock.  But you are using y2hat has your instrument, with an exogenous
cut-off of 0.  The fact that y3_i is a censored observation (because
e2_i is << 0) doesn't make y3hat_i a "predicted censored" observation
(because chat*x2_i>0). That is, your censoring for y3hat is driven by x2
and the (presumably consistently estimated) chat, and not by e2_i.

Sooo... I think you're OK.

Would be very interested to hear what others think about this?

BTW [self-advertising warning] you might want to use -ivreg2- instead of
-ivreg-.  More diagnostics and options.

HTH.

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

>
> Regards - Maarten
>
>
>
> RE: st: Re: Endogenous right hand side variable From
> "McCullough, Kathleen" <[email protected]> To
> <[email protected]> Subject RE: st: Re:
> Endogenous right hand side variable Date Tue, 6 Jun 2006
> 19:02:52 -0400
>
> Thank you to all who have helped with this. I will try the
> suggestion from Mark that relates to the Wooldridge text.
>
> The censored endogenous variable follows a distribution that
> seems consistent with a tobit specification. If we were
> merely modeling the determinates of the use of this factor, I
> would use a Heckman model to control for selection bias, but
> in this case we are interested in this variables relation to
> another factor, so that approach will not with our research question.
>
> Thank you all!
> Kathleen
>
>
> From: [email protected] on behalf of Austin Nichols
> Sent: Tue 6/6/2006 2:23 PM
> To: [email protected]
> Subject: Re: st: Re: Endogenous right hand side variable
>
>
>
> Rodrigo -
> I assume Mark is referring to page 574 in
> http://www.stata.com/bookstore/cspd.html
>
> if (y1, y2) observed when y3>0,
> run a tobit of y3 on Z,
> save the residuals vhat, and
> then
> . ivreg2 y1 (y2 = vhat Z)
>
> though it is not clear to me from the original post that any
> tobit is required. (A variable with a lot of zeros could mean
> a number of very different things.)
>
> On 6/6/06, Rodrigo A. Alfaro <[email protected]> wrote:
> > > Mark,
> > >
> > > I don't understand this point "Finally, estimate using IV with the
> predicted
> > > values of the endogenous regressor as the single excluded
> instrument." did
> > > you mean IV regression using the predicted values as
> instruments of
> > > the original endogenous?
> > >
> > > Rodrigo.
> > >
> > > ----- Original Message -----
> > > From: "Schaffer, Mark E" <[email protected]>
> > > To: <[email protected]>
> > > Sent: Tuesday, June 06, 2006 12:54 PM
> > > Subject: RE: st: Re: Endogenous right hand side variable
> > >
> > >
> > > Kathleen, Rodrigo et al.,
> > >
> > > An alternative to Rodrigo's proposal of full system
> estimation is to
> > > use a trick that Wooldridge describes in his 2002 book.
> The method
> > > takes advantage of the fact that simple IV gives
> consistent estimates.
> > >
> > > In a first step, estimate the Tobit-type relationship between the
> > > endogenous regressor and the full set of exogenous variables,
> > > including the excluded instruments.
> > >
> > > Then, get the predicted values from this Tobit.
> > >
> > > Finally, estimate using IV with the predicted values of the
> > > endogenous regressor as the single excluded instrument.
> > >
> > > No ex post adjustment of the var-cov matrix is necessary,
> since the
> > > last step is simple IV and therefore gets you consistent
> estimates
> > > of the var-cov matrix as well as the parameters.
> > >
> > > Very convenient, more efficient than IV on the original equation
> > > (which is also consistent, btw), but not as efficient as a full
> > > system estimation.
> > >
> > > Cheers,
> > > Mark
> > >
> >> > > -----Original Message-----
> >> > > From: [email protected]
> >> > > [mailto:[email protected]] On Behalf Of
> >> > > Rodrigo A. Alfaro
> >> > > Sent: 06 June 2006 17:44
> >> > > To: [email protected]
> >> > > Subject: Re: st: Re: Endogenous right hand side variable
> >> > >
> >> > > Deepankar,
> >> > >
> >> > > I think that Kathleen wants to use tobit because this
> "endogenous
> >> > > right-hand side variable that is zero for over half of the
> >> > > observations" let's say censored, not because the variable is
> >> > > discrete. Also, I think that -heckman- is not the solution (I
> >> > > mean using the command)... in that procedure there is only one
> >> > > endogenous variable, in the problem we have 2. A
> two-stage here
> >> > > involves do the tobit, makes the predictions, put into
> the linear
> >> > > equation and estimate that.
> >> > > It seems easy to do it, the problem is to adjust the
> standard errors.
> >> > >
> >> > > Rodrigo.
> >> > >
> >> > >
> >> > > ----- Original Message -----
> >> > > From: "Deepankar Basu" <[email protected]>
> >> > > To: <[email protected]>
> >> > > Sent: Tuesday, June 06, 2006 12:08 PM
> >> > > Subject: Re: st: Re: Endogenous right hand side variable
> >> > >
> >> > >
> >> > > Kathleen,
> >> > >
> >> > > Some quick thoughts on your questions.
> >> > >
> >> > > 1. Why do you want the endogenous variable to be
> estimated with a
> >> > > tobit regression? The variable in question does not
> seem to be a
> >> > > discrete random variable. If it has a mixture
> distribution, you
> >> > > might want to do a joint likelihood estimation as Rodrigo
> >> > > suggests.
> >> > >
> >> > > 2. If you want a two-stage procedure with a tobit in the first
> >> > > stage and an OLS in the second, you could look at Heckman-type
> >> > > selection
> models.
> >> > >
> >> > > Deepankar
> >> > >
> >> > > On Tue, 2006-06-06 at 11:44 -0400, Rodrigo A. Alfaro wrote:
> >>> > > > Dear Kathleen,
> >>> > > >
> >>> > > > I don't know if there is procedure in Stata for this model.
> >> > > The model
> >>> > > > sounds
> >>> > > > interesting, maybe there is some code in Gauss, Matlab or R.
> >>> > > >
> >>> > > > An alternative solution if to estimate the entire
> problem in a
> joint
> >>> > > > framework. You could write down the likelihood for this
> >> > > problem and solve
> >>> > > > it
> >>> > > > using -ml- procedures in Stata. The book of Gould "MLE with
> >> > > Stata" could
> >>> > > > help you in this matter.
> >>> > > >
> >>> > > > Rodrigo.
> >>> > > >
> >>> > > > ----- Original Message -----
> >>> > > > From: "McCullough, Kathleen" <[email protected]>
> >>> > > > To: <[email protected]>
> >>> > > > Sent: Tuesday, June 06, 2006 9:20 AM
> >>> > > > Subject: st: Endogenous right hand side variable
> >>> > > >
> >>> > > >
> >>> > > > I seem to be having some trouble posting today, so I am
> >> > > going to send this
> >>> > > > message again. I am sorry if it is a duplicate.
> >>> > > >
> >>> > > > I am estimating a model with a endogenous right-hand side
> >> > > variable that is
> >>> > > > zero for over half of the observations. Otherwise it is a
> >> > > continuous
> >>> > > > variable. The dependent variable is continuous. Is there a
> specific
> >>> > > > procedure to help control for this situation? I was
> >> > > concerned that using
> >>> > > > IVREG2 might not be effective as you cannot specify that
> >> > > the endogenous
> >>> > > > variable should be estimated with a tobit model. It does
> >> > > not appear that
> >>> > > > there is a canned procedure with a first stage tobit and
> >> > > second stage OLS
> >>> > > > model.
> >>> > > >
> >>> > > > I appreciate any suggestions that you might have.
> >>> > > >
> >>> > > > Regards,
> >>> > > > Kathleen

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