Published online by Cambridge University Press: 12 December 2005
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) to
identify the regressions E(y|x,·)
≡ [E(y|x,z =
j),j ∈ Z] when the conditional
distribution P(y|x,z) is
unknown. Cross and Manski (2002,
Econometrica 70, 357–368) studied this problem and showed
that the identification region of
E(y|x,·) can be precisely
calculated when y has finite support. Here we generalize the
result of Cross and Manski, showing that the identification region can be
precisely calculated also in the case in which y has infinite
support.