Re: st: Dynamic quadratic almost ideal demand system

[Jorge Eduardo Pérez Pérez <jorge_perez@brown.edu>]

Poi's quaids code bases the inclusion on demographics on this paper

Ray, R.  1983.  Measuring the costs of children: An alternative
approach.  Journal of Public Economics 22: 89-102.

which you can look up, From a quick look at that paper, the covariates
here enter in the coefficient of the log price index and in the price
index itself. That is in contrast to allowing them to modify a(p),
which allows them to enter linearly in the share equation.

In general, modifying a(p) linearly in the share equation is
demographic translating. Modifying b(p) is demographic scaling. You
seem to be doing both, but Poi's approach only does scaling. That may
explain the difference of results.

I suppose Poi's -quaids- exact formulas can be found in his 2012 Stata
Journal article, to which sadly I don't have access to right now. But
looking at the internals of his code, we can see what is being done.

This is found in _quaids__utils.mata, a part of Poi's -quaids- routine

-----

if (ndemo > 0) {
cofp = J(rows(lnp), 1, 0)
for(i=1; i<=rows(lnp); ++i) {
cofp[i] = lnp[i,.]*(eta'*demo[i,.]')
}
cofp = exp(cofp)
mbar = 1 :+ demo*rho'
}
else {
cofp = J(rows(lnp), 1, 1)
mbar = J(rows(lnp), 1, 1)
}
if (quadratics == "") {
// The b(p) term
bofp = exp(lnp*beta')
}
else {
bofp = J(rows(lnp), 1, 1)
}
for(i=1; i<=neqn; ++i) {
shr[.,i] = alpha[i] :+ lnp*gamma[i,.]'
if (ndemo > 0) {
shr[., i] = shr[., i] +
(J(rows(lnp), 1, beta[i]) + demo*eta[.,i]):*
(lnexp - lnpindex - ln(mbar))
}
else {
shr[., i] = shr[., i] + beta[i]*(lnexp - lnpindex)

}
if (quadratics == "") {
shr[., i] = shr[., i] + lambda[i]:/(bofp:*cofp):*(
(lnexp - lnpindex - ln(mbar)):^2)
}
}

-----

As can be seen, Poi's method allows b(p) to be scaled by a function
c(p), which in turn depends on interactions of log prices and
demographics. The total expenditure is also scaled by a mbar function,
which is equal to 1 + a linear function in demographics.

Hope this helps,









--------------------------------------------
Jorge Eduardo Pérez Pérez
Graduate Student
Department of Economics
Brown University


On Wed, Feb 26, 2014 at 1:46 PM, Nigussie Tefera
<nigussie.tefera@gmail.com> wrote:
> Dear statlist,
>
> I am trying to estimate dynamic quadratic almost ideal demand system
> using Poi's 2012 nlsur _quaids approach.  Poi's 2012 approach, available
> with stata 13 version, can handle the linear and quadratic demand system
> with an extension for demographic variables. However, I need to extend
> the model for dynamic quaids as I am dealing with panel data analysis.
> Moreover, I need to control for expenditure endogeneity as well as zero
> consumption expenditure problem. The approaches for dealing with zero
> consumption expenditure varies but I prefer running multivariate probit
> estimation at first stage (to determine the probability of consuming
> that food items/groups and also to control any correlation among food
> items) and predicting the standard normal density function (PDF) and the
> standard normal cumulative distribution function (CDF) which could be
> augmented in the demand specification following Pan et al., 2008; Zheng
> and Henneberry, 2010 approaches. Predicting CDF and PDF is easy but
> augmenting in the demand system is a bit challenging as the Poi's 2012
> approach does not allow us to do so.
>
> Moreover, I have tried to write stata code based on Poi's 2008 nlsur
> code (available on the website) but I came up with different regression
> results as compared to the results with Poi's 2012 quaids. One causes of
> the difference could be the way that demographic variable entered in the
> model.  In order to do so I am modifying the alpha(i) both in the share
> equations as well as total price aggregate equation (a(p)) not in
> (b(p)). But I am not sure whether poi's quaids are doing the same or
> not. Any suggestion would be very grateful.
>
> Best
>
> Nigussie
>
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