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Further Results on Bayesian Method of Moments Analysis of the Multiple Regression Model

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  • Zellner, Arnold
  • Tobias, Justin

Abstract

In this article we extend previous BMOM results by showing how information about a variance parameter and its relation to regression coefficients produces a rich class of postdata densities for regression parameters. Prediction and model selection techniques are also described. We also discuss the well-documented link between cross-entropy and the average log odds and then use this criterion in an experiment to compare results obtained from BMOM and Bayes approaches using data generated from known models. Copyright 2001 by American Economic Association.

Suggested Citation

  • Zellner, Arnold & Tobias, Justin, 2001. "Further Results on Bayesian Method of Moments Analysis of the Multiple Regression Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 42(1), pages 121-140, February.
  • Handle: RePEc:ier:iecrev:v:42:y:2001:i:1:p:121-40
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    1. Tack, Jesse, 2013. "A Nested Test for Common Yield Distributions with Applications to U.S. Corn," Journal of Agricultural and Resource Economics, Western Agricultural Economics Association, vol. 38(1), April.
    2. Kleibergen, Frank & Zivot, Eric, 2003. "Bayesian and classical approaches to instrumental variable regression," Journal of Econometrics, Elsevier, vol. 114(1), pages 29-72, May.
    3. Atkinson, Scott E. & Dorfman, Jeffrey H., 2005. "Bayesian measurement of productivity and efficiency in the presence of undesirable outputs: crediting electric utilities for reducing air pollution," Journal of Econometrics, Elsevier, vol. 126(2), pages 445-468, June.
    4. Scott Atkinson & Jeffrey Dorfman, 2005. "Multiple Comparisons with the Best: Bayesian Precision Measures of Efficiency Rankings," Journal of Productivity Analysis, Springer, vol. 23(3), pages 359-382, July.
    5. Shen, Edward Z. & Perloff, Jeffrey M., 2001. "Maximum entropy and Bayesian approaches to the ratio problem," Journal of Econometrics, Elsevier, vol. 104(2), pages 289-313, September.
    6. LaFrance, Jeffrey T., 1999. "An Econometric Model of the Demand for Food and Nutrition," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt2z5516c2, Department of Agricultural & Resource Economics, UC Berkeley.
    7. Komunjer, Ivana & Ragusa, Giuseppe, 2016. "Existence And Characterization Of Conditional Density Projections," Econometric Theory, Cambridge University Press, vol. 32(04), pages 947-987, August.
    8. Gao, Chuanming & Lahiri, Kajal, 2002. "A note on the double k-class estimator in simultaneous equations," Journal of Econometrics, Elsevier, vol. 108(1), pages 101-111, May.
    9. Rodney W. Strachan & Herman K. van Dijk, 2014. "Divergent Priors and Well Behaved Bayes Factors," Central European Journal of Economic Modelling and Econometrics, CEJEME, vol. 6(1), pages 1-31, March.
    10. Komunjer, Ivana & Ragusa, Giuseppe, 2009. "Existence and Uniqueness of Semiparametric Projections," University of California at San Diego, Economics Working Paper Series qt0wg3j51c, Department of Economics, UC San Diego.
    11. Agee, Mark D. & Atkinson, Scott E. & Crocker, Thomas D. & Williams, Jonathan W., 2014. "Non-separable pollution control: Implications for a CO2 emissions cap and trade system," Resource and Energy Economics, Elsevier, vol. 36(1), pages 64-82.
    12. R. A. L. Carter & A. Zellner, 2002. "The ARAR Error Model for Univariate Time Series and Distributed Lag Models," UWO Department of Economics Working Papers 20025, University of Western Ontario, Department of Economics.
    13. Antoine, Bertille & Bonnal, Helene & Renault, Eric, 2007. "On the efficient use of the informational content of estimating equations: Implied probabilities and Euclidean empirical likelihood," Journal of Econometrics, Elsevier, vol. 138(2), pages 461-487, June.
    14. Scott E. Atkinson & Jeffrey H. Dorfman, 2009. "Feasible estimation of firm-specific allocative inefficiency through Bayesian numerical methods," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(4), pages 675-697.
    15. LaFrance, J. T. & Beatty, T. K. M. & Pope, R. D. & Agnew, G. K., 2002. "Information theoretic measures of the income distribution in food demand," Journal of Econometrics, Elsevier, vol. 107(1-2), pages 235-257, March.
    16. Wu, Ximing, 2003. "Calculation of maximum entropy densities with application to income distribution," Journal of Econometrics, Elsevier, vol. 115(2), pages 347-354, August.
    17. Carter Richard A. L. & Zellner Arnold, 2004. "The ARAR Error Model for Univariate Time Series and Distributed Lag," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(1), pages 1-44, March.
    18. Zellner, Arnold, 2006. "S. James Press And Bayesian Analysis," Macroeconomic Dynamics, Cambridge University Press, vol. 10(05), pages 667-684, November.
    19. Zellner, Arnold & Ando, Tomohiro, 2010. "Bayesian and non-Bayesian analysis of the seemingly unrelated regression model with Student-t errors, and its application for forecasting," International Journal of Forecasting, Elsevier, vol. 26(2), pages 413-434, April.
    20. Zellner, Arnold, 2007. "Some aspects of the history of Bayesian information processing," Journal of Econometrics, Elsevier, vol. 138(2), pages 388-404, June.
    21. Zellner, Arnold, 2010. "Bayesian shrinkage estimates and forecasts of individual and total or aggregate outcomes," Economic Modelling, Elsevier, vol. 27(6), pages 1392-1397, November.

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