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GENERALIZATION OF A RESULT ON “REGRESSIONS, SHORT AND LONG”

Published online by Cambridge University Press:  12 December 2005

Francesca Molinari
Affiliation:
Cornell University
Marcin Peski
Affiliation:
Northwestern University

Abstract

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),jZ] 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.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.Financial support from Northwestern University's Dissertation Year Fellowship is gratefully acknowledged.

Type
Notes and Problems
Copyright
© 2006 Cambridge University Press

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References

Cross, P.J. (2000) Three essays in nonparametric identification. Ph.D. dissertation, University of Wisconsin–Madison.
Cross, P.J. & C.F. Manski (2002) Regressions, short and long. Econometrica 70, 357368.CrossRefGoogle Scholar
Okner, B.A. (1972) Constructing a new microdata base from existing microdata sets: The 1966 merge file. Annals of Economic and Social Measurement 1, 325362.Google Scholar
Ridder, G. & R. Moffitt (in press) The econometrics of data combination. In J.J. Heckman & E.E. Leamer (eds.), Handbook of Econometrics, vol. 6, forthcoming in 2006.
Rockafellar, R.T. (1970) Convex Analysis. Princeton University Press.
Sims, C.A. (1972) Comments and rejoinder (On Okner (1972)). Annals of Economic and Social Measurement 1, 343–345, 355–357.Google Scholar
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