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A Framework for Eliciting, Incorporating, and Disciplining Identification Beliefs in Linear Models

Author

Listed:
  • Francis DiTraglia
  • Camilo García-Jimeno

Abstract

To estimate causal effects from observational data, an applied researcher must impose beliefs. The instrumental variables exclusion restriction, for example, represents the belief that the instrument has no direct effect on the outcome of interest. Yet beliefs about instrument validity do not exist in isolation. Applied researchers often discuss the likely direction of selection and the potential for measurement error in their papers but at present lack formal tools for incorporating this information into their analyses. As such they not only leave money on the table, by failing to use all relevant information, but more importantly run the risk of reasoning to a contradiction by expressing mutually incompatible beliefs. In this paper we characterize the sharp identified set relating instrument invalidity, treatment endogeneity, and measurement error in a workhorse linear model, showing how beliefs over these three dimensions are mutually constrained. We consider two cases: in the first the treatment is continuous and subject to classical measurement error; in the second it is binary and subject to non-differential measurement error. In each, we propose a formal Bayesian framework to help researchers elicit their beliefs, incorporate them into estimation, and ensure their mutual coherence. We conclude by illustrating the usefulness of our proposed methods on a variety of examples from the empirical microeconomics literature.

Suggested Citation

  • Francis DiTraglia & Camilo García-Jimeno, 2016. "A Framework for Eliciting, Incorporating, and Disciplining Identification Beliefs in Linear Models," NBER Working Papers 22621, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:22621
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Amir-Ahmadi, Pooyan & Drautzburg, Thorsten, 2017. "Identification Through Heterogeneity," Working Papers 17-11, Federal Reserve Bank of Philadelphia.
    2. Matthew A. Masten & Alexandre Poirier, 2017. "Inference on Breakdown Frontiers," Papers 1705.04765, arXiv.org, revised Oct 2017.
    3. Daron Acemoglu & Giuseppe De Feo & Giacomo De Luca, 2017. "Weak States: Causes and Consequences of the Sicilian Mafia," NBER Working Papers 24115, National Bureau of Economic Research, Inc.

    More about this item

    JEL classification:

    • B23 - Schools of Economic Thought and Methodology - - History of Economic Thought since 1925 - - - Econometrics; Quantitative and Mathematical Studies
    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation
    • C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs

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