By estimating separate equations you are not imposing the adding up
constraint. Let me descrbe two applications that estimate share equations.
The context is estimating shares of consupmtion across consumer products
for households and price elasticities.
One approach is to use the almost ideal demand system of Deaton and
Muelbauer (1980). In this case, share equations are estimated
simultaneously using the same set of regressors. The adding up
restrictions and other restrictions implied by economic theory are imposed.
The equations are estimated by maximum likelihood. See Poi (2002) in Stata
Journal 2(4) for some Stata code.
Another approach is the logit approach. You can model the share using the
conditional logit model. In this case, shares are function of alternative
specific characteristics. See Nevo (2000) "A Practitioner's Guide to
Estimation of Random Coefficients Logit Models of Demand" for more on
extensions of this model.
Either way, you would have to write up some code to estimate the share
equations correctly.
Regards,
--Alex Cavallo
Lexecon
(312) 322-0208 voice
(312) 322-0218 fax
On Tue, 9 Dec 2003, Mark Hanly wrote:
> Hi John,
>
> Thank you for your reply.
>
> My feeling is that we cannot apply OLS in this case because we are
looking
> at the share of total distance a person travels on a particular day by,
for
> example, car. Many people not travel by car at all on a particular day so
> their dependent variable will be zero, whereas many others will travel
> exclusively by car on that day so their share of total distance travelled
> that day that is done by car is one. (And the same will be true for the
> other mode shares - transit and walking.)
>
> The general advice seems to be that we would have to model this using a
> tobit model with 2 cluster points (at zero and one) if we model each
> equation separately because OLS, it is said, will give a poor fit and
could
> introduce bias.
>
> Because the independent variables are the same for each dependent
variable,
> I would think that the error terms of each of the separate equations
would
> be related somehow. Or, at least, this should be checked for/accounted
for
> using some kind of SUR and the results compared with the three separate
> estimations.
>
> However, I am open to all advice on this.
>
> Regards,
> Mark
>
> At 10:21 09/12/2003 -0500, you wrote:
> >Hi,
> >
> >If the independent variables are the same, the OLS and SURE estimators
are
> >equivalent. So, there is no gain in applying this estimator.
> >
> >John Kane
> >Dept. of Economics
> >SUNY-Oswego
>
> Mark Hanly
> Research Fellow
>
> ESRC Transport Studies Unit
> University College London
> London WC1E 6BT
> tel +44 (0)20 7679 1584
> fax +44 (0)20 7679 1567
>
> www.cts.ucl.ac.uk
> www.cts.ucl.ac.uk/seminars
>
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