Re: re. re. st: query on sureg

[Kit Baum <baum@bc.edu>]

Dear Badri

A demand system where you have the expenditure shares  spent on each  
good as the dep.var., with those shares adding to 1 for each  
individual, has two sets of adding-up constraints: the sum of  
coefficients on each good's price must be zero, and the sum of  
coefficients on total expenditures (=income) must be unity. Those  
constraints together imply that the residuals _for each individual_  
will sum to exactly zero, which implies that the residual vectors  
from each equation, when arrayed in a matrix, must yield a singular  
matrix. Due to finite precision arithmetic, not every matrix that  
should be singular shows up as such in a computer program. The  
constraints above NEED NOT be imposed; they will be imposed by the  
structure of the data. (One reason for finite arithmetic to fail in  
this context is that you have stored the expenditure shares in  
floats, rather than doubles, so they only approximately sum to unity  
for each individual).

There are many good discussions of demand system estimation in  
econometrics texts. With regard to  the set of constraints you are  
trying to impose (e.g. the symmetry restrictions implied by Young's  
theorem) I suggest you consult one of those texts.

Kit Baum, Boston College Economics
http://ideas.repec.org/e/pba1.html


On Dec 14, 2005, at 10:09 AM, Badri Narayanan Gopalakrishnan wrote:


> Dear Dr.Kit Baum,
> This is with reference to the forwarded reply of yours to my query  
> on sureg.
> Actually, I had earlier committed this mistake of using sureg for all
> equations without imposing any restrictions on the coefficients, which
> yielded the error that you mentioned.
> However, when I use all equations, while including the constraints
> that would take care of the implicit linear additivity of the
> dependent variable, I thought it should work. As expected by me, it
> did not give the error "singular covariance matrix"!
> But now, it's giving a different error: redundant or inconsistent  
> constraints!
> Thus, I think that the current problem is not because of singular
> covariance matrix.
> In fact, to clarify this doubt, I tried reducing the number of
> constraints while keeping all the equations, and got some results
> without error. However, this will not serve my purpose, as I need all
> constraints to be imposed. Actual number of constraints is 182 and the
> number permissible (n/k) is 177! Hence, I reduced a few constraints to
> be within the limits, but even this did not work.
>
> Could you pelase fugure out what's wrong here?
>
>
> Badri writes:
>
> I'm trying to estimate Almost Ideal Demand Systems using sureg. For
> this I impose a few constraints to be in consistent with the theory.
> Despite all my efforts to ensure that there is no redundancy, stata
> shows: redundant or inconsistent constraints! If it's just redundant,
> I can re-check the constraints and eliminate it. But I've already done
> that. So, is this because my dataset does'nt probably obey these
> constraints, making them inconsistent? In this case, how can I proceed
> further? Is there any other way of tackling this problem, by testing
> for consistency and redundancy of constraints?
>
> Any demand system is a textbook example of a set of linear equations
> which will yield a singular covariance matrix of the errors due to
> adding-up conditions. If you have N goods in your demand system, are
> you trying to estimate all N equations? That will not work in sureg,
> since the "Zellner step" requires that the covariance matrix of errors
> have full rank.
>
> See Greene's econometrics text for more detail on this issue.
> http://pages.stern.nyu.edu/~wgreene/Text/econometricanalysis.htm
>
>
> Kit Baum, Boston College Economics
> http://ideas.repec.org/e/pba1.html
>
> --
> With Warm Regards,
> Badri Narayanan G.,
> Indira Gandhi Institute of Development Research,
> Gen. Vaidya Marg, Goregaon (East),
> Mumbai-400065
*
*   For searches and help try:
*   http://www.stata.com/support/faqs/res/findit.html
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/