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From |
Kit Baum <[email protected]> |

To |
Badri Narayanan Gopalakrishnan <[email protected]> |

Subject |
Re: re. re. st: query on sureg |

Date |
Wed, 14 Dec 2005 10:46:08 -0500 |

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

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**Follow-Ups**:**Re: re. re. st: query on sureg***From:*Badri Narayanan Gopalakrishnan <[email protected]>

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