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General Specification Testing With Locally Misspecified Models

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  • Bera, Anil K.
  • Montes-Rojas, Gabriel
  • Sosa-Escudero, Walter

Abstract

A well known result is that many of the tests used in econometrics, such as the Rao score (RS) test, may not be robust to misspecified alternatives, that is, when the alternative model does not correspond to the underlying data generating process. Under this scenario, these tests spuriously reject the null hypothesis too often. We generalize this result to generalized method of moments–based (GMM-based) tests. We also extend the method proposed in Bera and Yoon (1993, Econometric Theory 9, 649–658) for constructing RS tests that are robust to local misspecification to GMM-based tests. Finally, a further generalization for general estimating and testing functions is developed. This framework encompasses both likelihood and GMM-based results.

Suggested Citation

  • Bera, Anil K. & Montes-Rojas, Gabriel & Sosa-Escudero, Walter, 2010. "General Specification Testing With Locally Misspecified Models," Econometric Theory, Cambridge University Press, vol. 26(6), pages 1838-1845, December.
    • Handle: RePEc:cup:etheor:v:26:y:2010:i:06:p:1838-1845_99
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    Cited by:

    1. Montes-Rojas Gabriel, 2022. "Subgraph Network Random Effects Error Components Models: Specification and Testing," Journal of Econometric Methods, De Gruyter, vol. 11(1), pages 17-34, January.
    2. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2018. "Double/debiased machine learning for treatment and structural parameters," Econometrics Journal, Royal Economic Society, vol. 21(1), pages 1-68, February.
    3. Ming He & Kuan-Pin Lin, 2015. "Testing in a Random Effects Panel Data Model with Spatially Correlated Error Components and Spatially Lagged Dependent Variables," Econometrics, MDPI, vol. 3(4), pages 1-36, November.
    4. Federico Zincenko & Walter Sosa-Escudero & Gabriel Montes-Rojas, 2014. "Robust tests for time-invariant individual heterogeneity versus dynamic state dependence," Empirical Economics, Springer, vol. 47(4), pages 1365-1387, December.
    5. Anil K. Bera & Yannis Bilias, 2024. "Three Scores and 15 Years (1948-2023) of Rao's Score Test: A Brief History," Papers 2406.19956, arXiv.org, revised Oct 2024.
    6. Victor Chernozhukov & Juan Carlos Escanciano & Hidehiko Ichimura & Whitney K. Newey & James M. Robins, 2022. "Locally Robust Semiparametric Estimation," Econometrica, Econometric Society, vol. 90(4), pages 1501-1535, July.
    7. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2016. "Double/Debiased Machine Learning for Treatment and Causal Parameters," Papers 1608.00060, arXiv.org, revised Nov 2024.
    8. Doğan, Osman & Taşpınar, Süleyman & Bera, Anil K., 2021. "A Bayesian robust chi-squared test for testing simple hypotheses," Journal of Econometrics, Elsevier, vol. 222(2), pages 933-958.
    9. Taşpınar, Süleyman & Doğan, Osman & Bera, Anil K., 2017. "GMM gradient tests for spatial dynamic panel data models," Regional Science and Urban Economics, Elsevier, vol. 65(C), pages 65-88.
    10. Bera, Anil K. & Doğan, Osman & Taşpınar, Süleyman, 2018. "Simple tests for endogeneity of spatial weights matrices," Regional Science and Urban Economics, Elsevier, vol. 69(C), pages 130-142.
    11. Dogan, Osman & Taspinar, Suleyman & Bera, Anil K., 2017. "Simple Tests for Social Interaction Models with Network Structures," MPRA Paper 82828, University Library of Munich, Germany.
    12. Chaudhuri, Saraswata & Renault, Eric, 2020. "Score tests in GMM: Why use implied probabilities?," Journal of Econometrics, Elsevier, vol. 219(2), pages 260-280.
    13. Taspinar, Suleyman & Dogan, Osman & Bera, Anil K., 2017. "GMM Gradient Tests for Spatial Dynamic Panel Data Models," MPRA Paper 82830, University Library of Munich, Germany.
    14. Li, Haiqi & Fan, Rui & Park, Sung Y., 2018. "Generalized empirical likelihood specification test robust to local misspecification," Economics Letters, Elsevier, vol. 171(C), pages 149-153.

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