We investigate identification in semi-parametric binary regression models, y = 1(xβ+υ+ε > 0) when υ is either discrete or measured within intervals. The error term ε is assumed to be uncorrelated with a set of instruments z, ε is independent of υ conditionally on x and z, and the support of −(xβ + ε) is finite. We provide a sharp characterization of the set of observationally equivalent parameters β. When there are as many instruments z as variables x, the bounds of the identified intervals of the different scalar components βk of parameter β can be expressed as simple moments of the data. Also, in the case of interval data, we show that additional information on the distribution of υ within intervals shrinks the identified set. Specifically, the closer the conditional distribution of υ given z is to uniformity, the smaller is the identified set. Point identified is achieved if and only if υ is uniform within intervals.

The famous events of May 1968, starting with student riots, threw France into a state of turmoil. As a result, normal examination procedures were abandoned, and the pass rate for various qualifications increased enormously. The lowering of thresholds at critical stages of the education system enabled a proportion of students to pursue more years of higher education than would otherwise have been possible. For those on the margin of passing their examinations, additional years of higher education increased future wages and occupational levels. Interestingly, the effect is also transmitted across generations and is reflected in the educational performance of children.