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A small sigma approach to certain problems in errors-in-variables models

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  • Hahn, Jinyong
  • Hausman, Jerry
  • Kim, Jeonghwan

Abstract

We propose a pragmatic approach to the errors-in-variables and nonlinear panel models. These models are often deemed impossible to estimate in their most general forms. For example, the higher order moments approach to errors-in-variables model fails when there is conditional heteroscedasticity. We propose estimating these models using approximate moments, using a Taylor series approximation applied to Kadane’s (1971) small sigma approach.

Suggested Citation

  • Hahn, Jinyong & Hausman, Jerry & Kim, Jeonghwan, 2021. "A small sigma approach to certain problems in errors-in-variables models," Economics Letters, Elsevier, vol. 208(C).
    • Handle: RePEc:eee:ecolet:v:208:y:2021:i:c:s0165176521003712
    DOI: 10.1016/j.econlet.2021.110094
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    References listed on IDEAS

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    1. Amemiya, Yasuo, 1985. "Instrumental variable estimator for the nonlinear errors-in-variables model," Journal of Econometrics, Elsevier, vol. 28(3), pages 273-289, June.
    2. Susanne M. Schennach, 2004. "Estimation of Nonlinear Models with Measurement Error," Econometrica, Econometric Society, vol. 72(1), pages 33-75, January.
    3. S. M. Schennach & Yingyao Hu, 2013. "Nonparametric Identification and Semiparametric Estimation of Classical Measurement Error Models Without Side Information," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(501), pages 177-186, March.
    4. Susanne M. Schennach, 2016. "Recent Advances in the Measurement Error Literature," Annual Review of Economics, Annual Reviews, vol. 8(1), pages 341-377, October.
    5. Jinyong Hahn & Jerry Hausman, 2010. "Estimation with Valid and Invalid Instruments," NBER Chapters, in: Contributions in Memory of Zvi Griliches, pages 25-57, National Bureau of Economic Research, Inc.
    6. Arthur Lewbel, 1997. "Constructing Instruments for Regressions with Measurement Error when no Additional Data are Available, with an Application to Patents and R&D," Econometrica, Econometric Society, vol. 65(5), pages 1201-1214, September.
    7. Timothy B. Armstrong & Michal Kolesár, 2021. "Sensitivity analysis using approximate moment condition models," Quantitative Economics, Econometric Society, vol. 12(1), pages 77-108, January.
    8. Isaiah Andrews & Matthew Gentzkow & Jesse M. Shapiro, 2017. "Measuring the Sensitivity of Parameter Estimates to Estimation Moments," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 132(4), pages 1553-1592.
    9. repec:adr:anecst:y:2005:i:79-80:p:02 is not listed on IDEAS
    10. Amemiya, Yasuo, 1990. "Two-stage instrumental variables estimators for the nonlinear errors-in-variables model," Journal of Econometrics, Elsevier, vol. 44(3), pages 311-332, June.
    11. Aigner, Dennis J. & Hsiao, Cheng & Kapteyn, Arie & Wansbeek, Tom, 1984. "Latent variable models in econometrics," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 23, pages 1321-1393, Elsevier.
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    Cited by:

    1. Andrei Zeleneev & Kirill Evdokimov, 2023. "Simple estimation of semiparametric models with measurement errors," CeMMAP working papers 10/23, Institute for Fiscal Studies.
    2. Kirill S. Evdokimov & Andrei Zeleneev, 2023. "Simple Estimation of Semiparametric Models with Measurement Errors," Papers 2306.14311, arXiv.org, revised Mar 2024.

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    More about this item

    Keywords

    Errors-in-variables; Small sigma;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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