A Note on Regressions with Interval Data on a Regressor

We reconsider the partial identification analysis of the regression model in Manski and Tamer (2002) where one covariate is only interval-measured and present two additional sets of results. Manski and Tamer (2002) propose two estimation approaches in this context, focussing on general results. The modified minimum distance (MMD) estimates the true identified set and the modified method of moments (MMM) a superset. Our first contribution is to characterize the true identified set and the superset. Second, we complete and extend the Monte Carlo study of Manski and Tamer (2002). We present benchmark results using the exact functional form for the expectation of the dependent variable conditional on observables to compare with results using its nonparametric estimate. We illustrate the superiority of MMD over MMM, as well as the advantage of adopting a geometric estimation approach in both cases