A Note on Estimating Proportions by Linear Regression

The estimation of the parameters of a linear regression model in which the dependent variable is a fraction or proportion frequently occurs in statistical analyses. An example of such an analysis has been performed by McCall in studying the movements of people into andor out of various income classes over time. In the note the author shows that the estimated proportions sum to one and no constraint is needed on the proportions if the parameter estimates are BLUE. If the parameters are not, then a constraint can be constructed using Zellners technique of Seemingly Unrelated Least Squares SULS to ensure that the estimated proportions sum to one.