Generalization of a Result on "Regression, Short and Long"

This paper is concerned with the problem of combining a data set that identifies the conditional distribution P (y|x) with one that identifies the conditional distribution P (z|x), in order to identify the regressions E (y|x, middot) identical with [E (y|x, z = j), j element of Z] when the conditional distribution P (y|x, z) is unknown. Cross and Manski (2002) studied this problem and showed that the identification region of E (y|x, middot) can be precisely calculated, when y has finite support. Here we generalize Cross and Manski's result showing that the identification region can be precisely calculated also in the case in which y has infinite support.