Re: st: SUREG for Almost Ideal Demand System

["Brian P. Poi" <brian@poiholdings.com>]

On 07/01/2011 08:37 PM, Michael Musyoka wrote:

> Thanks a lot Poi for the assistance. Indeed I have managed it directly with the
> coefficients from Sureg. But once I extract the coefficients into a matrix, I am
>
> not getting the se and variance covariance matrix. Is there a way to combine
> nlcom with matrix of coefficients? this will make it possible to do the own and
> cross elasticities by stating i=j or i>j and vice versa at once....
> For example...say Matrix E...Expenditure coefficient in Sureg....then
>
> matrix list E
> matrix c=J(13,1,1)
> matrix Expel=J(13,1,0)
> matrix n=J(13,1,0)
> forval i=1/13 {
> forval j=1/1  {
> mat Expel[`i',`j']=c[`i',`j']+(scd[`i',`j']*E[`i',`j'])/sw[`i',`j']
> nlcom (shares:c[`i',`j']+(0.33450538*E[`i',`j'])/.14810108)
> }
> }

I may have been unclear when I stated that -nlcom- could estimate 
multiple functions at once.  What I meant by that was that if you want 
to obtain the variance-covariance matrix of multiple estimates, you 
specify all of the functions in the same call to -nlcom-.  No looping is 
required.

For example, say you've just replicated example 4 from the Reference 
manual entry for -nlsur-, so that the active estimation results in Stata 
contain a 4-equation demand system.  Now, let's obtain the vector of 
income elasticities and the corresponding covariance matrix.  For the 
basic AIDS model, the income elasticity for the i'th good is eta_i = 1 + 
beta_i / w_i.  To implement this formula, we need to pick the set of 
expenditure shares at which we want the elasticities.  For simplicity, 
we will use the means.  In Stata,


// Get the means of the	w's
summ w1, meanonly
scalar w1_mean = r(mean)
summ w2, meanonly
scalar w2_mean = r(mean)
summ w3, meanonly
scalar w3_mean = r(mean)
summ w4, meanonly
scalar w4_mean = r(mean)

nlcom   (1 + _b[/b1]/w1_mean)                           ///
        (1 + _b[/b2]/w2_mean)                           ///
        (1 + _b[/b3]/w3_mean)                           ///
        (1 + (-_b[/b1] - _b[/b2] - _b[/b3])/w4_mean)


mat eta = r(b)
mat etaV = r(V)

// Let's verify Engel aggregation to check our results
mat ws = (w1_mean, w2_mean, w3_mean, w4_mean)
mat result = eta*ws'
mat list result

// Here	is the complete	covariance matrix:
mat list etaV


Instead of thinking in terms of a matrix of price elasticities, think in 
terms of a vector where we stack the columns one on top of another.  If 
the price elasticity matrix is 4x4, then think in terms of a 16x1 vector 
of functions; otherwise, conceptualizing what the covariance matrix of 
what is already a matrix gets tricky.  In this case your call to -nlcom- 
would include a total of 16 functions, one for each elasticity of good i 
with respect to price j.

I hope this helps.


   -- Brian Poi
   -- brian@poiholdings.com
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