IDEAS home Printed from https://ideas.repec.org/a/bpj/jecome/v9y2020i1p29n2.html
   My bibliography  Save this article

Adjustments of Rao’s Score Test for Distributional and Local Parametric Misspecifications

Author

Listed:
  • Bera Anil K.
  • Doğan Osman

    (Department of Economics, University of Illinois at Urbana-Champaign (UIUC), Champaign, IL, USA)

  • Bilias Yannis

    (Department of International and European Economic Studies, Athens University of Economics and Business, Athens, Greece)

  • Yoon Mann J.

    (Department of Economics, California State University at Los Angeles, Los Angeles, CA, USA)

  • Taşpınar Süleyman

    (Economics Program, Queens College, The City University of New York, New York, NY, USA)

Abstract

Rao’s (1948) seminal paper introduced a fundamental principle of testing based on the score function and the score test has local optimal properties. When the assumed model is misspecified, it is well known that Rao’s score (RS) test loses its optimality. A model could be misspecified in a variety of ways. In this paper, we consider two kinds: distributional and parametric. In the former case, the assumed probability density function differs from the data generating process. Kent (1982) and White (1982) analyzed this case and suggested a modified version of the RS test that involves adjustment of the variance. In the latter case, the dimension of the parameter space of the assumed model does not match with that of the true one. Using the distribution of the RS test under this situation, Bera and Yoon (1993) developed a modified RS test that is valid under the local parametric misspecification. This involves adjusting both the mean and variance of the standard RS test. This paper considers the joint presence of the distributional and parametric misspecifications and develops a modified RS test that is valid under both types of misspecification. Earlier modified tests under either type of misspecification can be obtained as the special cases of the proposed test. We provide three examples to illustrate the usefulness of the suggested test procedure. In a Monte Carlo study, we demonstrate that the modified test statistics have good finite sample properties.

Suggested Citation

  • Bera Anil K. & Doğan Osman & Bilias Yannis & Yoon Mann J. & Taşpınar Süleyman, 2020. "Adjustments of Rao’s Score Test for Distributional and Local Parametric Misspecifications," Journal of Econometric Methods, De Gruyter, vol. 9(1), pages 1-29, January.
    • Handle: RePEc:bpj:jecome:v:9:y:2020:i:1:p:29:n:2
    DOI: 10.1515/jem-2017-0022
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/jem-2017-0022
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.1515/jem-2017-0022?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Bera, Anil K. & Sosa-Escudero, Walter & Yoon, Mann, 2001. "Tests for the error component model in the presence of local misspecification," Journal of Econometrics, Elsevier, vol. 101(1), pages 1-23, March.
    2. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037.
    3. White,Halbert, 1996. "Estimation, Inference and Specification Analysis," Cambridge Books, Cambridge University Press, number 9780521574464.
    4. Jaggia, Sanjiv & Trivedi, Pravin K., 1994. "Joint and separate score tests for state dependence and unobserved heterogeneity," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 273-291.
    5. Andrews, Donald W.K. & Cheng, Xu, 2013. "Maximum likelihood estimation and uniform inference with sporadic identification failure," Journal of Econometrics, Elsevier, vol. 173(1), pages 36-56.
    6. Davidson, Russell & MacKinnon, James G, 1987. "Implicit Alternatives and the Local Power of Test Statistics," Econometrica, Econometric Society, vol. 55(6), pages 1305-1329, November.
    7. Pollard, David, 1985. "New Ways to Prove Central Limit Theorems," Econometric Theory, Cambridge University Press, vol. 1(3), pages 295-313, December.
    8. Kiefer, Nicholas M., 1985. "Specification diagnostics based on Laguerre alternatives for econometric models of duration," Journal of Econometrics, Elsevier, vol. 28(1), pages 135-154, April.
    9. Kiefer, Nicholas M, 1984. "A Simple Test for Heterogeneity in Exponential Models of Duration," Journal of Labor Economics, University of Chicago Press, vol. 2(4), pages 539-549, October.
    10. Osman Doğan & Süleyman Taṣpınar & Anil K. Bera, 2018. "Simple tests for social interaction models with network structures," Spatial Economic Analysis, Taylor & Francis Journals, vol. 13(2), pages 212-246, April.
    11. L. G. Godfrey & M. R. Veal, 2000. "Alternative approaches to testing by variable addition," Econometric Reviews, Taylor & Francis Journals, vol. 19(2), pages 241-261.
    12. Andrews, Donald W K, 2001. "Testing When a Parameter Is on the Boundary of the Maintained Hypothesis," Econometrica, Econometric Society, vol. 69(3), pages 683-734, May.
    13. Badi Baltagi & Seuck Heun Song & Byoung Cheol Jung, 2002. "Simple Lm Tests For The Unbalanced Nested Error Component Regression Model," Econometric Reviews, Taylor & Francis Journals, vol. 21(2), pages 167-187.
    14. Andre Lucas, 1998. "Inference on cointegrating ranks using lr and lm tests based on pseudo-likelihoods," Econometric Reviews, Taylor & Francis Journals, vol. 17(2), pages 185-214.
    15. Yuzo Honda, 1985. "Testing the Error Components Model with Non-Normal Disturbances," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 52(4), pages 681-690.
    16. Badi H. Baltagi & Dong Li, 2001. "LM Tests for Functional Form and Spatial Error Correlation," International Regional Science Review, , vol. 24(2), pages 194-225, April.
    17. Donald W. K. Andrews, 1999. "Estimation When a Parameter Is on a Boundary," Econometrica, Econometric Society, vol. 67(6), pages 1341-1384, November.
    18. Saikkonen, Pentti, 1989. "Asymptotic relative efficiency of the classical test statistics under misspecification," Journal of Econometrics, Elsevier, vol. 42(3), pages 351-369, November.
    19. Koenker, Roger, 1981. "A note on studentizing a test for heteroscedasticity," Journal of Econometrics, Elsevier, vol. 17(1), pages 107-112, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Jieun Lee, 2022. "Testing Endogeneity of Spatial Weights Matrices in Spatial Dynamic Panel Data Models," Papers 2209.05563, arXiv.org.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Jieun Lee, 2022. "Testing Endogeneity of Spatial Weights Matrices in Spatial Dynamic Panel Data Models," Papers 2209.05563, arXiv.org.
    3. Cho, Jin Seo & White, Halbert, 2010. "Testing for unobserved heterogeneity in exponential and Weibull duration models," Journal of Econometrics, Elsevier, vol. 157(2), pages 458-480, August.
    4. Godfrey, Leslie G & Orme, Chris D, 1996. "On the Behavior of Conditional Moment Tests in the Presence of Unconsidered Local Alternatives," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 37(2), pages 263-281, May.
    5. Fang, Ying & Park, Sung Y. & Zhang, Jinfeng, 2014. "A simple spatial dependence test robust to local and distributional misspecifications," Economics Letters, Elsevier, vol. 124(2), pages 203-206.
    6. Donald W. K. Andrews & Xu Cheng, 2012. "Estimation and Inference With Weak, Semi‐Strong, and Strong Identification," Econometrica, Econometric Society, vol. 80(5), pages 2153-2211, September.
    7. Timo Dimitriadis & Xiaochun Liu & Julie Schnaitmann, 2020. "Encompassing Tests for Value at Risk and Expected Shortfall Multi-Step Forecasts based on Inference on the Boundary," Papers 2009.07341, arXiv.org.
    8. 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.
    9. 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.
    10. Gregory Cox, 2022. "A Generalized Argmax Theorem with Applications," Papers 2209.08793, arXiv.org.
    11. Pedersen, Rasmus Søndergaard, 2017. "Inference and testing on the boundary in extended constant conditional correlation GARCH models," Journal of Econometrics, Elsevier, vol. 196(1), pages 23-36.
    12. Montes-Rojas, Gabriel & Sosa-Escudero, Walter, 2011. "Robust tests for heteroskedasticity in the one-way error components model," Journal of Econometrics, Elsevier, vol. 160(2), pages 300-310, February.
    13. Ketz, Philipp, 2018. "Subvector inference when the true parameter vector may be near or at the boundary," Journal of Econometrics, Elsevier, vol. 207(2), pages 285-306.
    14. Andrews, Donald W.K. & Cheng, Xu & Guggenberger, Patrik, 2020. "Generic results for establishing the asymptotic size of confidence sets and tests," Journal of Econometrics, Elsevier, vol. 218(2), pages 496-531.
    15. 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.
    16. 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.
    17. Bera, Anil K. & Sosa-Escudero, Walter & Yoon, Mann, 2001. "Tests for the error component model in the presence of local misspecification," Journal of Econometrics, Elsevier, vol. 101(1), pages 1-23, March.
    18. Dastoor, Naorayex K., 1997. "Testing for conditional heteroskedasticity with misspecified alternative hypotheses," Journal of Econometrics, Elsevier, vol. 82(1), pages 63-80.
    19. Bera Anil K. & Doğan Osman & Taşpınar Süleyman, 2019. "Testing Spatial Dependence in Spatial Models with Endogenous Weights Matrices," Journal of Econometric Methods, De Gruyter, vol. 8(1), pages 1-33, January.
    20. Jin Seo Cho & Peter C. B. Phillips & Juwon Seo, 2019. "Parametric Inference on the Mean of Functional Data Applied to Lifetime Income Curves," Working papers 2019rwp-153, Yonsei University, Yonsei Economics Research Institute.

    More about this item

    Keywords

    inference; Lagrange multiplier tests; locally misspecified models; QMLE; Rao’s score tests; robust LM tests; specification testing;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bpj:jecome:v:9:y:2020:i:1:p:29:n:2. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Peter Golla (email available below). General contact details of provider: https://www.degruyter.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.