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Re: st: switching regression and endogenous variables in mlogit


From   Robert Duval <rduval@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: switching regression and endogenous variables in mlogit
Date   Fri, 15 Apr 2005 13:04:28 -0400

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 estimation of your main
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 adjustment in the
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 your equation of
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.
The previous comments of adjusting the se's still 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.

If you want to read more about this I suggest you 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 graduate textbook.

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 the adopt a
> 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 Maddala and Nelson,1975)
> 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
> >
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