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st: estimating the components of a total


From   Jeph Herrin <stata@spandrel.net>
To   statalist@hsphsun2.harvard.edu
Subject   st: estimating the components of a total
Date   Tue, 13 Mar 2012 11:43:22 -0400


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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