On Least Squares Estimation When the Dependent Variable is Grouped

Abstract

This paper examines the problem of estimating the parameters of an underlying linear model using data in which the dependent variable is only observed to fall in a certain interval on a continuous scale, its actual value remaining unobserved. A Least Squares algorithm for attaining the Maximum Likelihood estimator is described, the asymptotic bias of the OLS estimator derived for the normal regressors case and a "moment" estimator presented. A "two-step estimator" based on combining the two approaches is proposed and found to perform well in both an economic illustration and simulation experiments.