GENERALIZATION OF A RESULT ON “REGRESSIONS, 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) to identify the regressions E(y|x,·) [identical with] [E(y|x,z = j),j [set membership] 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. a b
c1 Address correspondence to Francesca Molinari, 492 Uris Hall, Ithaca, NY 14853-7601, USA; e-mail: firstname.lastname@example.org
a We are grateful to the co-editor Paolo Paruolo, an anonymous referee, Maria Goltsman, Nick Kiefer, Tymon Tatur, and Tim Vogelsang for useful comments. Any remaining errors are our own responsibility.
b Financial support from Northwestern University's Dissertation Year Fellowship is gratefully acknowledged.