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IDENTIFICATION IN TRIANGULAR SYSTEMS USING CONTROL FUNCTIONS

Published online by Cambridge University Press:  24 September 2010

Maximilian Kasy
Maximilian Kasy*
Affiliation:
University of California, Berkeley
*
*Address correspondence to Maximilian Kasy, Department of Economics, UC Berkeley, 508-1 Evans Hall 3880, Berkeley, CA 94720-3880; e-mail: maxkasy@econ.berkeley.edu.
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Abstract

This note discusses identification in nonparametric, continuous triangular systems. It provides conditions that are both necessary and sufficient for the existence of control functions satisfying conditional independence and support requirements. Confirming a commonly noticed pattern, these conditions restrict the admissible dimensionality of unobserved heterogeneity in the first-stage structural relation, or more generally the dimensionality of the family of conditional distributions of second-stage heterogeneity given explanatory variables and instruments. These conditions imply that no such control function exists without assumptions that seem hard to justify in most applications. In particular, none exists in the context of a generic random coefficient model.

Information

Type
NOTES AND PROBLEMS
Information
Econometric Theory , Volume 27 , Issue 3: SPECIAL ISSUE ON INVERSE PROBLEMS IN ECONOMETRICS , June 2011 , pp. 663 - 671
Copyright
Copyright © Cambridge University Press 2011

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References

REFERENCES

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