Bayesian Method of Moments (BMOM) Analysis of Mean and Regression Models

Arnold Zellner

A chapter in Modelling and Prediction Honoring Seymour Geisser, 1996, pp 61-72 from Springer

Abstract: Abstract A Bayesian method of moments/instrumental variable (BMOM/IV) approach is developed and applied in the analysis of the important mean and multiple regression models. Given a single set of data, it is shown how to obtain posterior and predictive moments without the use of likelihood functions, prior densities and Bayes’ Theorem. The posterior and predictive moments, based on a few relatively weak assumptions, are then used to obtain maximum entropy densities for parameters, realized error terms and future values of variables. Posterior means for parameters and realized error terms are shown to be equal to certain well known estimates and rationalized in terms of quadratic loss functions. Conditional maxent posterior densities for means and regression coefficients given scale parameters are in the normal form while scale parameters’ maxent densities are in the exponential form. Marginal densities for individual regression coefficients, realized error terms and future values are in the Laplace or double-exponential form with heavier tails than normal densities with the same means and variances. It is concluded that these results will be very useful, particularly when there is difficulty in formulating appropriate likelihood functions and prior densities needed in traditional maximum likelihood and Bayesian approaches.

Keywords: Likelihood Function; Posterior Density; Prior Density; Predictive Density; Posterior Odds (search for similar items in EconPapers)
Date: 1996
References: Add references at CitEc
Citations: View citations in EconPapers (1)

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-2414-3_4

Ordering information: This item can be ordered from
http://www.springer.com/9781461224143

DOI: 10.1007/978-1-4612-2414-3_4

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().