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Generalized Instrumental Variable Models

Chesher, AD; Rosen, AM; (2017) Generalized Instrumental Variable Models. Econometrica , 85 (3) pp. 959-989. 10.3982/ECTA12223. Green open access

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Abstract

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 singlevalued 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.

Type: Article
Title: Generalized Instrumental Variable Models
Open access status: An open access version is available from UCL Discovery
DOI: 10.3982/ECTA12223
Publisher version: https://doi.org/10.3982/ECTA12223
Language: English
Additional information: © 2017 The Econometric Society. This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Instrumental variables, endogeneity, excess heterogeneity, limited information, partial identification, random sets, incomplete models, English auctions.
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL SLASH
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of S&HS
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of S&HS > Dept of Economics
URI: https://discovery.ucl.ac.uk/id/eprint/1539920
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