Motivated by Manski and Tamer (2002) and especially their partial identification analysis
of the regression model where one covariate is only interval-measured, we offer several contributions.
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 estimates, and illustrate the superiority of MMD over MMM.
For MMD, we propose a simple shortcut for estimation.
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