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Pitfalls of Estimating the Marginal Likelihood Using the Modified Harmonic Mean

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  • Joshua C.C. Chan
  • Angelia L. Grant

Abstract

The modified harmonic mean is widely used for estimating the marginal likelihood. We investigate the empirical performance of two versions of this estimator: one based on the observed-data likelihood and the other on the complete-data likelihood. Through an empirical example using US and UK inflation, we show that the version based on the complete-data likelihood has a substantial finite sample bias and tends to select the wrong model, whereas the version based on the observed-data likelihood works well.

Suggested Citation

  • Joshua C.C. Chan & Angelia L. Grant, 2015. "Pitfalls of Estimating the Marginal Likelihood Using the Modified Harmonic Mean," CAMA Working Papers 2015-08, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    • Handle: RePEc:een:camaaa:2015-08
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    Cited by:

    1. Cross, Jamie & Nguyen, Bao H., 2017. "The relationship between global oil price shocks and China's output: A time-varying analysis," Energy Economics, Elsevier, vol. 62(C), pages 79-91.
    2. Jamie L. Cross & Chenghan Hou & Bao H. Nguyen, 2018. "On the China factor in international oil markets: A regime switching approach," Working Papers No 11/2018, Centre for Applied Macro- and Petroleum economics (CAMP), BI Norwegian Business School.
    3. repec:wrk:wrkemf:20 is not listed on IDEAS
    4. Chan, Joshua C.C. & Eisenstat, Eric & Koop, Gary, 2016. "Large Bayesian VARMAs," Journal of Econometrics, Elsevier, vol. 192(2), pages 374-390.
    5. Hajargasht, Gholamreza & Rao, D.S. Prasada, 2019. "Multilateral index number systems for international price comparisons: Properties, existence and uniqueness," Journal of Mathematical Economics, Elsevier, vol. 83(C), pages 36-47.
    6. Antonio Pacifico, 2021. "Structural Panel Bayesian VAR with Multivariate Time-Varying Volatility to Jointly Deal with Structural Changes, Policy Regime Shifts, and Endogeneity Issues," Econometrics, MDPI, vol. 9(2), pages 1-35, May.
    7. Chan, Joshua C.C. & Grant, Angelia L., 2016. "Modeling energy price dynamics: GARCH versus stochastic volatility," Energy Economics, Elsevier, vol. 54(C), pages 182-189.
    8. Jamie L. Cross & Aubrey Poon, 2020. "On the contribution of international shocks in Australian business cycle fluctuations," Empirical Economics, Springer, vol. 59(6), pages 2613-2637, December.
    9. Joshua C. C. Chan, 2020. "Large Bayesian VARs: A Flexible Kronecker Error Covariance Structure," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(1), pages 68-79, January.
    10. Diegel, Max, 2022. "Time-varying credibility, anchoring and the Fed's inflation target," Discussion Papers 2022/9, Free University Berlin, School of Business & Economics.
    11. Siddhartha Chib & Minchul Shin & Fei Tan, 2023. "DSGE-SVt: An Econometric Toolkit for High-Dimensional DSGE Models with SV and t Errors," Computational Economics, Springer;Society for Computational Economics, vol. 61(1), pages 69-111, January.
    12. Benjamin K. Johannsen & Elmar Mertens, 2021. "A Time‐Series Model of Interest Rates with the Effective Lower Bound," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 53(5), pages 1005-1046, August.
    13. Doğan, Osman, 2023. "Modified harmonic mean method for spatial autoregressive models," Economics Letters, Elsevier, vol. 223(C).
    14. Siddhartha Chib & Minchul Shin & Fei Tan, 2020. "High-Dimensional DSGE Models: Pointers on Prior, Estimation, Comparison, and Prediction∗," Working Papers 20-35, Federal Reserve Bank of Philadelphia.
    15. Pacifico, Antonio, 2020. "Structural Panel Bayesian VAR with Multivariate Time-varying Volatility to jointly deal with Structural Changes, Policy Regime Shifts, and Endogeneity Issues," MPRA Paper 104292, University Library of Munich, Germany.
    16. Gary Koop & Stuart McIntyre & James Mitchell & Aubrey Poon, 2018. "Regional Output Growth in the United Kingdom: More Timely and Higher Frequency Estimates, 1970-2017," Economic Statistics Centre of Excellence (ESCoE) Discussion Papers ESCoE DP-2018-14, Economic Statistics Centre of Excellence (ESCoE).
    17. Stylianos Asimakopoulos & Marco Lorusso & Francesco Ravazzolo, 2023. "A Bayesian DSGE Approach to Modelling Cryptocurrency," Working Papers No 09/2023, Centre for Applied Macro- and Petroleum economics (CAMP), BI Norwegian Business School.
    18. Joshua C. C. Chan, 2018. "Specification tests for time-varying parameter models with stochastic volatility," Econometric Reviews, Taylor & Francis Journals, vol. 37(8), pages 807-823, September.
    19. Joshua C. C. Chan & Eric Eisenstat, 2018. "Bayesian model comparison for time‐varying parameter VARs with stochastic volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(4), pages 509-532, June.
    20. Aubrey Poon, 2018. "Assessing the Synchronicity and Nature of Australian State Business Cycles," The Economic Record, The Economic Society of Australia, vol. 94(307), pages 372-390, December.

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    More about this item

    Keywords

    Bayesian model comparison; state space; unobserved components; inflation;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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