Interval Regression Models with;Endogenous Explanatory Variables

We consider the estimation of linear models where the dependent variable is observed by intervals and some continuous regressors may be endogenous. Our approach is fully parametric and two estimators are proposed: a two-step estimator and a limited-information maximum-likelihood estimator. The results can be summarised as follows: the two-step estimator may offer some computational advantages over the LIML (Limited Information Maximum Likelihood) estimator, and a Monte Carlo experiment suggests that its relative efficiency is rather satisfactory. The LIML estimator, however, is probably simpler to implement and has the advantage of providing a framework in which several testing procedures are more straightforward to perform. The application of TSLS (Two-Stage Least Squares) to a proxy of the dependent variable built by taking midpoints, on the other hand, leads to inconsistent estimates. An example application is also included, which uses Australian data on migrants' remittances.