A note on partial identification of regression parameters in regression with interval-valued dependent variable

Abstract

We consider linear regression where the dependent variable is unobservable. Instead we can observe only an upper and lower bound. In this setup, the regression parameters need not be consistently estimable. We make certain stochastic assumptions, as weak as possible, on the random process generating the observable intervals and derive tight bounds for the regression parameters. The bounds are consistently estimable and the estimators are functions of the observable quantities only. We also restate the result in terms of set-estimators for regression models with interval-valued data.