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Specification tests based on MCMC output

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  • Li, Yong
  • Yu, Jun
  • Zeng, Tao

Abstract

Two test statistics are proposed to determine model specification after a model is estimated by an MCMC method. The first test is the MCMC version of IOSA test and its asymptotic null distribution is normal. The second test is motivated from the power enhancement technique of Fan et al. (2015). It combines a component (J1) that tests a null point hypothesis in an expanded model and a power enhancement component (J0) obtained from the first test. It is shown that J0 converges to zero when the null model is correctly specified and diverges when the null model is misspecified. Also shown is that J1 is asymptotically χ2-distributed, suggesting that the second test is asymptotically pivotal, when the null model is correctly specified. The main feature of the first test is that no alternative model is needed. The second test has several properties. First, its size distortion is small and hence bootstrap methods can be avoided. Second, it is easy to compute from MCMC output and hence is applicable to a wide range of models, including latent variable models for which frequentist methods are difficult to use. Third, when the test statistic rejects the null model and J1 takes a large value, the test suggests the source of misspecification. The finite sample performance is investigated using simulated data. The method is illustrated in a linear regression model, a linear state-space model, and a stochastic volatility model using real data.

Suggested Citation

  • Li, Yong & Yu, Jun & Zeng, Tao, 2018. "Specification tests based on MCMC output," Journal of Econometrics, Elsevier, vol. 207(1), pages 237-260.
    • Handle: RePEc:eee:econom:v:207:y:2018:i:1:p:237-260
    DOI: 10.1016/j.jeconom.2018.08.001
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    1. Zheng, John Xu, 2000. "A Consistent Test Of Conditional Parametric Distributions," Econometric Theory, Cambridge University Press, vol. 16(5), pages 667-691, October.
    2. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    3. Arnaud Doucet & Neil Shephard, 2012. "Robust inference on parameters via particle filters and sandwich covariance matrices," Economics Papers 2012-W05, Economics Group, Nuffield College, University of Oxford.
    4. Whitney K. Newey & Richard J. Smith, 2004. "Higher Order Properties of Gmm and Generalized Empirical Likelihood Estimators," Econometrica, Econometric Society, vol. 72(1), pages 219-255, January.
    5. Wooldridge, Jeffrey M., 1992. "A Test for Functional Form Against Nonparametric Alternatives," Econometric Theory, Cambridge University Press, vol. 8(4), pages 452-475, December.
    6. George Poyiadjis & Arnaud Doucet & Sumeetpal S. Singh, 2011. "Particle approximations of the score and observed information matrix in state space models with application to parameter estimation," Biometrika, Biometrika Trust, vol. 98(1), pages 65-80.
    7. Jones, Galin L. & Haran, Murali & Caffo, Brian S. & Neath, Ronald, 2006. "Fixed-Width Output Analysis for Markov Chain Monte Carlo," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1537-1547, December.
    8. Horowitz, Joel L., 1994. "Bootstrap-based critical values for the information matrix test," Journal of Econometrics, Elsevier, vol. 61(2), pages 395-411, April.
    9. Yongmiao Hong, 2005. "Nonparametric Specification Testing for Continuous-Time Models with Applications to Term Structure of Interest Rates," The Review of Financial Studies, Society for Financial Studies, vol. 18(1), pages 37-84.
    10. Li, Yong & Liu, Xiao-Bin & Yu, Jun, 2015. "A Bayesian chi-squared test for hypothesis testing," Journal of Econometrics, Elsevier, vol. 189(1), pages 54-69.
    11. Chernozhukov, Victor & Hong, Han, 2003. "An MCMC approach to classical estimation," Journal of Econometrics, Elsevier, vol. 115(2), pages 293-346, August.
    12. T. S. Breusch & A. R. Pagan, 1980. "The Lagrange Multiplier Test and its Applications to Model Specification in Econometrics," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(1), pages 239-253.
    13. Presnell, Brett & Boos, Dennis D., 2004. "The IOS Test for Model Misspecification," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 216-227, January.
    14. Hausman, Jerry, 2015. "Specification tests in econometrics," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 38(2), pages 112-134.
    15. Fan, Yanqin & Li, Qi, 1996. "Consistent Model Specification Tests: Omitted Variables and Semiparametric Functional Forms," Econometrica, Econometric Society, vol. 64(4), pages 865-890, July.
    16. Tauchen, George, 1985. "Diagnostic testing and evaluation of maximum likelihood models," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 415-443.
    17. Yoichi Miyata, 2004. "Fully Exponential Laplace Approximations Using Asymptotic Modes," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 1037-1049, December.
    18. Davidson, Russell & MacKinnon, James G, 1992. "A New Form of the Information Matrix Test," Econometrica, Econometric Society, vol. 60(1), pages 145-157, January.
    19. Nicolas Chopin, 2002. "A sequential particle filter method for static models," Biometrika, Biometrika Trust, vol. 89(3), pages 539-552, August.
    20. Drew Creal, 2012. "A Survey of Sequential Monte Carlo Methods for Economics and Finance," Econometric Reviews, Taylor & Francis Journals, vol. 31(3), pages 245-296.
    21. Qian M. Zhou & Peter X.-K. Song & Mary E. Thompson, 2012. "Information Ratio Test for Model Misspecification in Quasi-Likelihood Inference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 205-213, March.
    22. Kim, Jae-Young, 1994. "Bayesian Asymptotic Theory in a Time Series Model with a Possible Nonstationary Process," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 764-773, August.
    23. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    24. Chesher, Andrew & Spady, Richard, 1991. "Asymptotic Expansions of the Information Matrix Test Statistic," Econometrica, Econometric Society, vol. 59(3), pages 787-815, May.
    25. Susumu Imai & Neelam Jain & Andrew Ching, 2009. "Bayesian Estimation of Dynamic Discrete Choice Models," Econometrica, Econometric Society, vol. 77(6), pages 1865-1899, November.
    26. Orme, Chris, 1990. "The small-sample performance of the information-matrix test," Journal of Econometrics, Elsevier, vol. 46(3), pages 309-331, December.
    27. Lancaster, Tony, 1984. "The Covariance Matrix of the Information Matrix Test," Econometrica, Econometric Society, vol. 52(4), pages 1051-1053, July.
    28. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    29. Sascha Mergner & Jan Bulla, 2008. "Time-varying beta risk of Pan-European industry portfolios: A comparison of alternative modeling techniques," The European Journal of Finance, Taylor & Francis Journals, vol. 14(8), pages 771-802.
    30. Newey, Whitney K, 1985. "Maximum Likelihood Specification Testing and Conditional Moment Tests," Econometrica, Econometric Society, vol. 53(5), pages 1047-1070, September.
    31. Tingting Cheng & Jiti Gao & Peter CB Phillips, 2017. "Bayesian estimation based on summary statistics: Double asymptotics and practice," Monash Econometrics and Business Statistics Working Papers 4/17, Monash University, Department of Econometrics and Business Statistics.
    32. Gozalo, Pedro L., 1993. "A Consistent Model Specification Test for Nonparametric Estimation of Regression Function Models," Econometric Theory, Cambridge University Press, vol. 9(3), pages 451-477, June.
    33. Jae-Young Kim, 1998. "Large Sample Properties of Posterior Densities, Bayesian Information Criterion and the Likelihood Principle in Nonstationary Time Series Models," Econometrica, Econometric Society, vol. 66(2), pages 359-380, March.
    34. Andriy Norets, 2009. "Inference in Dynamic Discrete Choice Models With Serially orrelated Unobserved State Variables," Econometrica, Econometric Society, vol. 77(5), pages 1665-1682, September.
    35. Jianqing Fan & Yuan Liao & Jiawei Yao, 2015. "Power Enhancement in High‐Dimensional Cross‐Sectional Tests," Econometrica, Econometric Society, vol. 83(4), pages 1497-1541, July.
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    More about this item

    Keywords

    Specification test; Point hypothesis test; Latent variable models; Markov chain Monte Carlo; Power enhancement technique; Information matrix;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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