st: estimating the components of a total

[Jeph Herrin <stata@spandrel.net>]

This is not really a Stata question, but a modelling question, though 
hopefully there is a Stata command that will provide a solution.

I have a dataset which contains reported totals and subtotals from 
approximately 5k respondents. For example, 5k firms are asked about 
their revenues from various sources, which are then summed to create 
total revenues. (Specifically, it is an electronic form which forces 
respondents to provide subtotals that equal their total). However, some 
respondents only report their totals, and for these I am trying to 
estimate the subtotals.

A basic approach would be to simply calculate the ratio for each sub 
category (eg, sales revenue/total revenue) for existing data and use 
this to estimate the missing values. However, because I have a lot more 
information on the respondents - for instance, number of employees, 
assets, etc - I think I can model the subtotal more accurately using 
these variables. The problem is, the subtotals estimated this way do not 
sum to the total.

Concretely, let's say there are three variables -x1-,-x2-,-x3-, and that 
their total t = x1 + x2 + x3. What I'd like is something like 
multivariable regression


 mv x1 x2 x3 = indvar1 + indvar2 + indvar3

with the constraint that

 x1+x2+x3 = t

Does this problem have a name and/or a standard solution?

thanks,
Jeph
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