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# Re: st: suregub

 From Alfonso Sanchez-Penalver <[email protected]> To "[email protected]" <[email protected]> Subject Re: st: suregub Date Wed, 2 Apr 2014 23:38:44 -0400

```Hi Merdith,

The only experience I've had with budget shares is when teaching a PhD econometrics class that I used a paper by Christensen and Greene (1976) for the seemingly unrelated regressions assignment. They estimated a translog cost function together with the factor cost shares functions. The problem is that such a system is by definition singular and cannot be estimated with all equations, so the practice is to drop one of the shares and assume that it's met and thus use the restrictions that such model would have on the linear combination of the coefficients in the whole system to transform the rest of the equations by substituting the expressions derived for the coefficients in the dropped equation from the system restrictions into the rest of the equations. Greene (2012) pp. 307 - 314 explains this in detail for the cases of the Cobb-Douglas and translog cost functions.

References:
Christensen, Laurits R. and William H. Greene, “Economies of Scale in U.S.
Electric Power Generation,” The Journal of Political Economy, August 1976, 4, Part
1, 655–676.

Greene, William H., Econometric Analysis, 7 ed., Upper Saddle River, NJ USA:
Prentice Hall, 2012.

I hope this helps,

Alfonso Sánchez-Peñalver, PhD

> On Apr 2, 2014, at 5:01 PM, Meredith Herd <[email protected]> wrote:
>
> Hi Alfonso, Thanks very much for the response. My study is about budget shares for different hospital departments and what determines/affects those shares. So my 5 dependent variables are budget shares for those departments (i.e. ratios of the amount budgeted for y1 (or y2…y5) over the total hospital budget) so hence why I wanted them to add to 1. Then, my independent variables are those that are hypothesized to affect those shares – these are the same regressors across all 5 equations (although I might try an autoregressive model with one time lag). My equations would be (y1 x1 x2 x3 x4 L1.y1) (y2 x1 x2 x3 x4 L1.y2) (y3 x1 x2 x3 x4 L1.y3) (y4 x1 x2 x3 x4 L1.y4) (y5 x1 x2 x3 x4 L1.y5) but where I may decide eventually to omit the lagged autoregressive independent variable. I am not sure how to constrain this system such that the y’s all sum to 1 so any advice would be greatly appreciated. Thanks once again.  Best, Meredith
>
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