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Generalized Instrumental Variable Models

Publication ,  Journal Article
Chesher, A; Rosen, AM
Published in: Econometrica
May 1, 2017

This paper develops characterizations of identified sets of structures and structural features for complete and incomplete models involving continuous or discrete variables. Multiple values of unobserved variables can be associated with particular combinations of observed variables. This can arise when there are multiple sources of heterogeneity, censored or discrete endogenous variables, or inequality restrictions on functions of observed and unobserved variables. The models generalize the class of incomplete instrumental variable (IV) models in which unobserved variables are single-valued functions of observed variables. Thus the models are referred to as generalized IV (GIV) models, but there are important cases in which instrumental variable restrictions play no significant role. Building on a definition of observational equivalence for incomplete models the development uses results from random set theory that guarantee that the characterizations deliver sharp bounds, thereby dispensing with the need for case-by-case proofs of sharpness. The use of random sets defined on the space of unobserved variables allows identification analysis under mean and quantile independence restrictions on the distributions of unobserved variables conditional on exogenous variables as well as under a full independence restriction. The results are used to develop sharp bounds on the distribution of valuations in an incomplete model of English auctions, improving on the pointwise bounds available until now. Application of many of the results of the paper requires no familiarity with random set theory.

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Published In

Econometrica

DOI

EISSN

1468-0262

ISSN

0012-9682

Publication Date

May 1, 2017

Volume

85

Issue

3

Start / End Page

959 / 989

Related Subject Headings

  • Econometrics
  • 3803 Economic theory
  • 3802 Econometrics
  • 3801 Applied economics
  • 1403 Econometrics
  • 1402 Applied Economics
  • 1401 Economic Theory
 

Citation

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MLA
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Chesher, A., & Rosen, A. M. (2017). Generalized Instrumental Variable Models. Econometrica, 85(3), 959–989. https://doi.org/10.3982/ECTA12223
Chesher, A., and A. M. Rosen. “Generalized Instrumental Variable Models.” Econometrica 85, no. 3 (May 1, 2017): 959–89. https://doi.org/10.3982/ECTA12223.
Chesher A, Rosen AM. Generalized Instrumental Variable Models. Econometrica. 2017 May 1;85(3):959–89.
Chesher, A., and A. M. Rosen. “Generalized Instrumental Variable Models.” Econometrica, vol. 85, no. 3, May 2017, pp. 959–89. Scopus, doi:10.3982/ECTA12223.
Chesher A, Rosen AM. Generalized Instrumental Variable Models. Econometrica. 2017 May 1;85(3):959–989.
Journal cover image

Published In

Econometrica

DOI

EISSN

1468-0262

ISSN

0012-9682

Publication Date

May 1, 2017

Volume

85

Issue

3

Start / End Page

959 / 989

Related Subject Headings

  • Econometrics
  • 3803 Economic theory
  • 3802 Econometrics
  • 3801 Applied economics
  • 1403 Econometrics
  • 1402 Applied Economics
  • 1401 Economic Theory