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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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    1. Jochmann, Markus & Koop, Gary & Potter, Simon M., 2010. "Modeling the dynamics of inflation compensation," Journal of Empirical Finance, Elsevier, vol. 17(1), pages 157-167, January.
    2. Alejandro Justiniano & Giorgio E. Primiceri, 2008. "The Time-Varying Volatility of Macroeconomic Fluctuations," American Economic Review, American Economic Association, vol. 98(3), pages 604-641, June.
    3. Chan, Joshua C.C. & Grant, Angelia L., 2016. "Fast computation of the deviance information criterion for latent variable models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 847-859.
    4. John Geweke, 1999. "Using simulation methods for bayesian econometric models: inference, development,and communication," Econometric Reviews, Taylor & Francis Journals, vol. 18(1), pages 1-73.
    5. Joshua C C Chan & Cody Y L Hsiao, 2013. "Estimation of Stochastic Volatility Models with Heavy Tails and Serial Dependence," CAMA Working Papers 2013-74, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    6. Francesco Bianchi, 2013. "Regime Switches, Agents' Beliefs, and Post-World War II U.S. Macroeconomic Dynamics," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 80(2), pages 463-490.
    7. repec:hal:journl:peer-00732535 is not listed on IDEAS
    8. Zheng Liu & Daniel F. Waggoner & Tao Zha, 2011. "Sources of macroeconomic fluctuations: A regime‐switching DSGE approach," Quantitative Economics, Econometric Society, vol. 2(2), pages 251-301, July.
    9. Markku Lanne & Arto Luoma & Jani Luoto, 2012. "Bayesian Model Selection And Forecasting In Noncausal Autoregressive Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(5), pages 812-830, August.
    10. Yong Li & Zeng Tao & Jun Yu, "undated". "Robust Deviance Information Criterion for Latent Variable Models," Working Papers CoFie-04-2012, Singapore Management University, Sim Kee Boon Institute for Financial Economics.
    11. McCausland, William J., 2012. "The HESSIAN method: Highly efficient simulation smoothing, in a nutshell," Journal of Econometrics, Elsevier, vol. 168(2), pages 189-206.
    12. James H. Stock & Mark W. Watson, 2007. "Why Has U.S. Inflation Become Harder to Forecast?," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(s1), pages 3-33, February.
    13. Koop, Gary & Potter, Simon, 2010. "A flexible approach to parametric inference in nonlinear and time varying time series models," Journal of Econometrics, Elsevier, vol. 159(1), pages 134-150, November.
    14. John Geweke, 1999. "Using Simulation Methods for Bayesian Econometric Models," Computing in Economics and Finance 1999 832, Society for Computational Economics.
    15. Joshua C.C. Chan & Angelia L. Grant, 2014. "Issues in Comparing Stochastic Volatility Models Using the Deviance Information Criterion," CAMA Working Papers 2014-51, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    16. Frühwirth-Schnatter, Sylvia & Wagner, Helga, 2008. "Marginal likelihoods for non-Gaussian models using auxiliary mixture sampling," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4608-4624, June.
    17. Chan, Joshua C.C., 2013. "Moving average stochastic volatility models with application to inflation forecast," Journal of Econometrics, Elsevier, vol. 176(2), pages 162-172.
    18. James H. Stock & Mark W. Watson, 2007. "Erratum to "Why Has U.S. Inflation Become Harder to Forecast?"," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(7), pages 1849-1849, October.
    19. Berg, Andreas & Meyer, Renate & Yu, Jun, 2004. "Deviance Information Criterion for Comparing Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 22(1), pages 107-120, January.
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    Cited by:

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    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. 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).
    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. Firmin Doko Tchatoka & Qazi Haque & Madison Terrell, 2022. "Monetary policy shocks and exchange rate dynamics in small open economies," CAMA Working Papers 2022-15, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    12. 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.
    13. 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.
    14. Doğan, Osman, 2023. "Modified harmonic mean method for spatial autoregressive models," Economics Letters, Elsevier, vol. 223(C).
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. 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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