On Tue, 9 Dec 2003 [email protected] wrote:
>
>
> 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
>
>
Dealing with zero expenditure shares in demand system analysis is an
ongoing problem, but as far as I know there is no widely used solution.
A few papers that have looked at the issue include Deaton and Irish
(1984), Griffiths and Valenzuela (1998), and Cornick, Cox, and Gould
(1994).
Huang (1999) discusess estimation of the SUR Tobit model using the MCECM
algorithm, though I don't know if anyone has implemented it in Stata.
Hope these few references help. If anyone has Stata code for any of these
models, I'd love to hear about it.
-- Brian
-- [email protected]
References
----------
Cornick, J., Cox, T., and Gould, B. (1994). Fluid milk purchases: A
multivariate tobit analysis. American Journal of Agricultural
Economics, 76, 74-82.
Deaton, A. and Irish, M. (1984). Statistical models for zero
expenditures in household budgets. Journal of Public Economics,
23, 59-80.
Griffiths, W. and Valenzuela, M. (1988). Missing data from
infrequency of purchase: Bayesian estimation of a linear
expenditure system. In Fomby and Hill (Eds.), Advances in
Econometrics (vol. 13): Messy Data--Missing Observations,
Outliers, and Mixed-Frequency Data, Stamford, CT: JAI Press.
Huang, H.-C. (1999). Estimation of the SUR tobit model via the
MCECM algorithm. Economic Letters, 64, 25-30.
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