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st: Re: suregub
Christopher Baum <email@example.com>
st: Re: suregub
Fri, 4 Apr 2014 21:53:16 +0000
On Apr 3, 2014, at 8:33 AM, Meredith wrote:
> I am using Baum's written command -suregub- on an unbalanced panel dataset to estimate 5 regressions where each of my equations have the same explanatory variables. In addition, I would like to constrain my equations such that the 5 y dependent variables add up to 1.0. I have typed -constraint define 1 [y1] + [y2] + [y3] + [y4] [y5] = 1. But is this the correct syntax?
Stata's constraint syntax cannot be used to constrain data; only parameters. If you want the five dep vars to add up to one, make sure they do in the data.
But the setup you have proposed has a couple of problems. For one thing, when you have an identity on the LHS of an equation system (as we do in a consumer choice problem, with expenditure shares, or a portfolio model, with asset shares), and the same RHS variables (because theory implies that they should be the same), there are multiple constraints already in place. The five vectors of residuals will not be linearly independent, because if you allocate more to category i, you must allocate less elsewhere so the LHS variables still sum to one. This implies that the residual VCE is by construction singular, and a technique like SUR that requires a full rank matrix cannot work in that case. You must drop one of the equations. The coefficients of the dropped equation are linear combinations of those in the estimated equations, as in the consumer choice example, a $1 change in income must cause a $1 change in spending across the categories. Likewise, holding income fixed, the ef!
fetcs of changing one of the prices must sum to zero over the full set of equations, so you can infer the coefficient in the missing equation from those you do estimate (with -lincom-). This means this has nothing to do with Stata's constraints; if you had a balanced panel, there is no way you could apply standard -sureg- to a full set of expenditure share equations. If you had a balanced panel, I would use -sureg- on any 4 of the equations with the -isure- option, as iterating the SUR estimator makes it invariant to the choice of dropped equation (which is otherwise arbitrary).
Professor of Economics and Social Work, Boston College, Chestnut Hill MA, USA
DIW Research Professor, Department of Macroeconomics, DIW Berlin, Berlin, Germany
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