A Note on Estimating Proportions by Linear Regressions.

Alvin A. Cook

Expert InsightsPublished 1971

Demonstration that in linear regression models containing two or more equations in which the dependent variable is a proportion and the observed proportions sum to one across the equations, the estimated probabilities or proportions across all cells sum to one if the parameter estimates are BLUE (best linear unbiased estimator). If the parameter estimates are not BLUE, then Zellner's technique of seemingly unrelated least squares can be used to ensure that the estimated proportions sum to one by constructing the parameter estimates. The results can be generalized to any system of equations that (1) contains the same exogenous variables in each equation and (2) specifies an exact linear constraint on the dependent variables across the equations for each observation. 7 pp.

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Cook, Alvin A., A Note on Estimating Proportions by Linear Regressions. Santa Monica, CA: RAND Corporation, 1971. https://www.rand.org/pubs/papers/P4712.html.
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