# Re: st: switching regression and endogenous variables in mlogit

 From Mary Alexinskaya To statalist@hsphsun2.harvard.edu, yatawarr@lerner.udel.edu Subject Re: st: switching regression and endogenous variables in mlogit Date Fri, 15 Apr 2005 10:52:07 -0700 (PDT)

```Dear Ravi and Robert,

I am slightly concerned with the solution proposed by
Robert, because the proceedure that he suggests seems
to be valid only for linear regressions, while Ravi
has a dummy endogenous variable.

While being unaware of the fully correct approach to
tackling this problem, I have a question for Ravi: how
many levels of tariff do you have? Can this variable
be treated as continuous, or, can it be transformed
into a dummy variable (such as "high" and "low" level
of taxes)?

I ask this question because Stata offers easy
solutions for these two cases. In case you have a
continuous explanatory variable, you can explore a
command such as cdsimeq. Or, you can adopt
Rivers-Vuong approach to determine whether your
variable is indeed endogenous and then address the
problem respectively (the approach is proposed in
"Limited Information Estimators and Endogeneity Tests
for Simultaneous Probit Models", Rivers, Vuong,
Journal of Econometrics 39, 1988, pp347-366, and also
explained in Wooldridge, ch.15.3.6).

In case you can have a binary dependent variable, you
can go for biprobit command in Stata (as explained in
Greene 2001, ch.19, this command, which does a
simultaneous estimation, in case of two binary
dependent variables is a valid proceedure).

Please let me know if you do find a real solution for
mlogit with dummy endogenous variable.

Best wishes!
Maria

--- Robert Duval <rduval@gmail.com> wrote:

> Ravi,
>
> The way you formulated your model seems to as a
> restricted (or
> simplified) version of the switching regression
> model (i,e, the one i
> mentioned in my previous email). In your version,
> the coefficients for
> x1-x3 are restricted to be the same under both
> regimes (i.e.
> stabilization programs or not). Some people call
> this in the
> litetature an endogenous dummy variable problem.
>
> The inconsistency that arises from this endogeneity
> can be solved by:
>
> 1) Estimating "x4 = x1 x2 x5 +error", and using the
> predicted "x4 hat"
> out of this estimation, in the second-stage
> equation of interest "Tariff level = x1 x2 x3 'x4
> hat' +e". You would
> have to be careful in adjusting the standard errors
> in the second
> stage because the x4 is a predicted variable with
> its own intrinsic
> variability (this is called generated regressor
> literature).
>
> 2) You can also use the residuals obtained from
> estimating "x4 = x1 x2
> x5 +error",
> denoted by 'v hat' and add them as a regressor in
> interest, i.e.
>
> "Tariff level = x1 x2 x3 x4 'v hat' + e"
>
> Notice that in here the the x4 variable doesn't need
> to be modified.
> apply.
>
> If you are willing to assume normality in the second
> equation, then
> these routines should be quite easy to implement
> using probit.
>
> I think that the treatment effects type of models
> should also give you
> the answer you're looking for. Although, I have
> never used their
> commands in STATA, the set-up of your problem seems
> to me the same as
> the one those models are trying to estimating.
>
> check either the
> Maddala (1983) textbook on LIMited Dependent
> variables, or the Vella
> (1998) "Estimating Models with Sample selection
> bias: A survey" in the
> Journal of Human Resources , or the Wooldrige
>
> Best
> Robert
>
> On 4/15/05, Yatawara, Ravi
> <yatawarr@lerner.udel.edu> wrote:
> > To expand on my investigation ....
> > I consider the effect on tariffs of adopting a
> stabilization plan. The
> > endogeneity  issue arises in that the  decision to
> > stabilization program is  a choice variable,
> correlated with
> > unobservables (relegated to the error term ) that
> affect tariff levels.
> > Each data point is a country  year.
> >
> > So I have 2 equations
> > 1) Tariff level = x1 x2 x3 x4 ( where x4=dummy if
> stabilization occurred
> > that year) + error
> > 2) Stabilization ( 0 or 1) = x1 x2 x5 +error
> >
> > Appreciate any help.  I also tried a treatment
> effects model.
> > Best,
> > Ravi
> > -----Original Message-----
> > From: owner-statalist@hsphsun2.harvard.edu
> > [mailto:owner-statalist@hsphsun2.harvard.edu] On
> Behalf Of Robert Duval
> > Sent: Friday, April 15, 2005 1:43 AM
> > To: statalist@hsphsun2.harvard.edu
> > Subject: Re: st: switching regression and
> endogenous variables in mlogit
> >
> > Does 'movestay' helps solving your question 1? In
> general, in the
> > traditional switching regression model (a la
> > the covariance between the errors in the two
> outcome equations is not
> > identified. Maybe if you explain more in detail
> what are you trying to
> > estimate it would help...
> >
> > best
> > robert
> >
> > On 4/15/05, Yatawara, Ravi
> <yatawarr@lerner.udel.edu> wrote:
> > > Folks,
> > >
> > > I have two questions,
> > > 1) does anyone have a program for doing
> switching regressions?  The
> > > switchr in stata is not what I need since my
> errors in the two
> > equations
> > > are NOT
> > > independent, and identically distributed.
> > >
> > > 2) Is there a way to tackle a potentially
> endogenous variable in a
> > > multinomial logit estimation equation?
> > >
> > > Thanks
> > > Ravi
> > >
> > > *
> > > *   For searches and help try:
> > > *
> http://www.stata.com/support/faqs/res/findit.html
> > > *   http://www.stata.com/support/statalist/faq
> > > *   http://www.ats.ucla.edu/stat/stata/
> > >
> >
> > *
> > *   For searches and help try:
> > *
> http://www.stata.com/support/faqs/res/findit.html
> > *   http://www.stata.com/support/statalist/faq
> > *   http://www.ats.ucla.edu/stat/stata/
> >
> > *
> > *   For searches and help try:
> > *
> http://www.stata.com/support/faqs/res/findit.html
> > *   http://www.stata.com/support/statalist/faq
> > *   http://www.ats.ucla.edu/stat/stata/
> >
>
> *
> *   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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