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Characterizations of identified sets delivered by structural econometric models

Author

Listed:
  • Andrew Chesher

    (Institute for Fiscal Studies and University College London)

  • Adam Rosen

    (Institute for Fiscal Studies and Duke University)

Abstract
This paper develops characterizations of identifi?ed 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 signifi?cant role. Building on a de?finition of observational equivalence for incomplete models the development uses results from random set theory which guarantee that the characterizations deliver sharp bounds, thereby dispensing with the need for case-by-case proofs of sharpness. The use of random sets de?ned on the space of unobserved variables allows identi?cation 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 till now. Application of many of the results of the paper requires no familiarity with random set theory.

Suggested Citation

  • Andrew Chesher & Adam Rosen, 2016. "Characterizations of identified sets delivered by structural econometric models," CeMMAP working papers CWP44/16, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:cemmap:44/16
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    File URL: https://www.ifs.org.uk/uploads/cemmap/wps/cwp441616.pdf
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    References listed on IDEAS

    as
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    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Andrew Chesher & Adam Rosen, 2015. "Characterizations of identified sets delivered by structural econometric models," CeMMAP working papers CWP63/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Arie Beresteanu, 2016. "Quantile Regression with Interval Data," Working Paper 5991, Department of Economics, University of Pittsburgh.
    3. Steven T. Berry & Philip A. Haile, 2018. "Identification of Nonparametric Simultaneous Equations Models With a Residual Index Structure," Econometrica, Econometric Society, vol. 86(1), pages 289-315, January.
    4. Thomas M. Russell, 2020. "Policy Transforms and Learning Optimal Policies," Papers 2012.11046, arXiv.org.

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    More about this item

    Keywords

    instrumental variables; endogeneity; excess heterogeneity; limited information; par- tial identfii?cation; random sets; incomplete models; English auctions.;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation

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