Partial Identification in Monotone Binary Models: Discrete Regressors and Interval Data

We investigate identification in semi-parametric binary regression models, "y"= 1("x""β"+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 - ("x""β"+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 "β"_"k" 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. Copyright © 2008 The Review of Economic Studies Limited.