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Bayesian Trace Statistics for the Reduced Rank Regression Model


  • Strachan, R.W.
  • Inder, B.


Estimation of the reduced rank regression model requires restrictions be imposed upon the model. Two forms of restrictions are commonly used. Earlier Bayesian work relied on the triangular method of identification which imposes an a priori ordering on the variables in the system, however, incorrect ordering of the variables can result in model misspecification. Bayesian estimation of the reduced rank regression model without ordering restrictions was presented in Strachan (1998) and follows the classical approach of Anderson (1951) and Johansen (1998). This method of estimation avoids placing restrictions on the space spanned by the reduced rank relations and simplifies testing of restrictions on that space. In this paper, a method for estimating approximate marginal likelihoods and Bayes factors is presented for this model, using Laplace approximations for integrals. These Bayes factors algebraically resemble the Johansen trace statistic (1995), hence the title. We consider the model with rank r and no restrictions on the reduced rank relations.

Suggested Citation

  • Strachan, R.W. & Inder, B., 1999. "Bayesian Trace Statistics for the Reduced Rank Regression Model," Monash Econometrics and Business Statistics Working Papers 13/99, Monash University, Department of Econometrics and Business Statistics.
  • Handle: RePEc:msh:ebswps:1999-13

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    References listed on IDEAS

    1. Erev, Ido & Roth, Alvin E, 1998. "Predicting How People Play Games: Reinforcement Learning in Experimental Games with Unique, Mixed Strategy Equilibria," American Economic Review, American Economic Association, vol. 88(4), pages 848-881, September.
    2. Itzhak Gilboa & David Schmeidler, 1995. "Case-Based Decision Theory," The Quarterly Journal of Economics, Oxford University Press, vol. 110(3), pages 605-639.
    3. Borgers, Tilman & Sarin, Rajiv, 2000. "Naive Reinforcement Learning with Endogenous Aspirations," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(4), pages 921-950, November.
    4. Borgers, Tilman & Sarin, Rajiv, 1997. "Learning Through Reinforcement and Replicator Dynamics," Journal of Economic Theory, Elsevier, vol. 77(1), pages 1-14, November.
    5. Colin Camerer & Teck-Hua Ho, 1999. "Experience-weighted Attraction Learning in Normal Form Games," Econometrica, Econometric Society, vol. 67(4), pages 827-874, July.
    6. Sarin, Rajiv & Vahid, Farshid, 1999. "Payoff Assessments without Probabilities: A Simple Dynamic Model of Choice," Games and Economic Behavior, Elsevier, vol. 28(2), pages 294-309, August.
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    More about this item


    Reduced rank regression; marginal likelihoods; Bayes factors; Bayesian analysis;

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General

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