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Some Recent Developments in Econometric Inference

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  • Arnold Zellner

Abstract

Recent results in information theory, see Soofi (1996; 2001) for a review, include derivations of optimal information processing rules, including Bayes' theorem, for learning from data based on minimizing a criterion functional, namely output information minus input information as shown in Zellner (1988; 1991; 1997; 2002). Herein, solution post data densities for parameters are obtained and studied for cases in which the input information is that in (1) a likelihood function and a prior density; (2) only a likelihood function; and (3) neither a prior nor a likelihood function but only input information in the form of post data moments of parameters, as in the Bayesian method of moments approach. Then it is shown how optimal output densities can be employed to obtain predictive densities and optimal, finite sample structural coefficient estimates using three alternative loss functions. Such optimal estimates are compared with usual estimates, e.g., maximum likelihood, two-stage least squares, ordinary least squares, etc. Some Monte Carlo experimental results in the literature are discussed and implications for the future are provided.

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Bibliographic Info

Article provided by Taylor & Francis Journals in its journal Econometric Reviews.

Volume (Year): 22 (2003)
Issue (Month): 2 ()
Pages: 203-215

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Handle: RePEc:taf:emetrv:v:22:y:2003:i:2:p:203-215

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Related research

Keywords: Econometric inference; Bayes' theorem; Information theory; Learning; Optimal estimation;

References

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  1. Sawa, Takamitsu, 1972. "Finite-Sample Properties of the k-Class Estimators," Econometrica, Econometric Society, vol. 40(4), pages 653-80, July.
  2. Zellner, Arnold, 1996. "Models, prior information, and Bayesian analysis," Journal of Econometrics, Elsevier, vol. 75(1), pages 51-68, November.
  3. Zellner, Arnold, 1980. "A Note on the Relationship of Minimum Expected Loss (MELO) and Other Structural Coefficient Estimates," The Review of Economics and Statistics, MIT Press, vol. 62(3), pages 482-84, August.
  4. Zellner, A., 1988. "Optimal Information-Processing And Bayes' Theorem," Papers m8803, Southern California - Department of Economics.
  5. Min, Chung-ki & Zellner, Arnold, 1993. "Bayesian and non-Bayesian methods for combining models and forecasts with applications to forecasting international growth rates," Journal of Econometrics, Elsevier, vol. 56(1-2), pages 89-118, March.
  6. Russell L. Lamb & Francis X. Diebold, 1996. "Why are estimates of agricultural supply response so variable?," Finance and Economics Discussion Series 96-8, Board of Governors of the Federal Reserve System (U.S.).
  7. Golan, Amos & Judge, George G. & Miller, Douglas, 1996. "Maximum Entropy Econometrics," Staff General Research Papers 1488, Iowa State University, Department of Economics.
  8. Zellner, Arnold & Chen, Bin, 2001. "Bayesian Modeling Of Economies And Data Requirements," Macroeconomic Dynamics, Cambridge University Press, vol. 5(05), pages 673-700, November.
  9. 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.
  10. Jeffrey T. LaFrance, 1999. "Inferring the Nutrient Content of Food With Prior Information," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 81(3), pages 728-734.
  11. Zellner, Arnold, 1978. "Estimation of functions of population means and regression coefficients including structural coefficients : A minimum expected loss (MELO) approach," Journal of Econometrics, Elsevier, vol. 8(2), pages 127-158, October.
  12. Park, Soo-Bin, 1982. "Some sampling properties of minimum expected loss (MELO) estimators of structural coefficients," Journal of Econometrics, Elsevier, vol. 18(3), pages 295-311, April.
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