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Testing for the presence of measurement error

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  • Daniel Wilhelm

    (Institute for Fiscal Studies and University College London)

Abstract

This paper proposes a simple nonparametric test of the hypothesis of no measurement error in explanatory variables and of the hypothesis that measurement error, if there is any, does not distort a given object of interest. We show that, under weak assumptions, both of these hypotheses are equivalent to certain restrictions on the joint distribution of an observable outcome and two observable variables that are related to the latent explanatory variable. Existing nonparametric tests for conditional independence can be used to directly test these restrictions without having to solve for the distribution of unobservables. In consequence, the test controls size under weak conditions and possesses power against a large class of nonclassical measurement error models, including many that are not identifi ed. If the test detects measurement error, a multiple hypothesis testing procedure allows the researcher to recover subpopulations that are free from measurement error. Finally, we use the proposed methodology to study the reliability of administrative earnings records in the U.S., fi nding evidence for the presence of measurement error.

Suggested Citation

  • Daniel Wilhelm, 2018. "Testing for the presence of measurement error," CeMMAP working papers CWP45/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:cemmap:45/18
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    3. Michele Lalla & Maddalena Cavicchioli, 2020. "Nonresponse and measurement errors in income: matching individual survey data with administrative tax data," Department of Economics 0170, University of Modena and Reggio E., Faculty of Economics "Marco Biagi".
    4. Chetverikov, Denis & Wilhelm, Daniel & Kim, Dongwoo, 2021. "An Adaptive Test Of Stochastic Monotonicity," Econometric Theory, Cambridge University Press, vol. 37(3), pages 495-536, June.
    5. Crossley, Thomas F. & Fisher, Paul & Hussein, Omar, 2023. "Assessing data from summary questions about earnings and income," Labour Economics, Elsevier, vol. 81(C).
    6. Andrei Zeleneev & Kirill Evdokimov, 2023. "Simple estimation of semiparametric models with measurement errors," CeMMAP working papers 10/23, Institute for Fiscal Studies.
    7. Kirill S. Evdokimov & Andrei Zeleneev, 2023. "Simple Estimation of Semiparametric Models with Measurement Errors," Papers 2306.14311, arXiv.org, revised Mar 2024.
    8. Maddalena Cavicchioli & Michele Lalla, 2022. "Evidences from survey data and fiscal data: nonresponse and measurement errors in annual incomes," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(3), pages 587-615, September.
    9. Wossen, Tesfamicheal & Abay, Kibrom A. & Abdoulaye, Tahirou, 2022. "Misperceiving and misreporting input quality: Implications for input use and productivity," Journal of Development Economics, Elsevier, vol. 157(C).

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    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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