Reflections on the Probability Space Induced by Moment Conditions with Implications for Bayesian Inference

A. Ronald Gallant

Journal of Financial Econometrics, 2016, vol. 14, issue 2, 229-247

Abstract: Often a structural model implies that certain moment functions expressed in terms of data and model parameters follow a distribution. An assertion that moment functions follow a distribution logically implies a distribution on the arguments of the moment functions. This fact would appear to permit Bayesian inference on model parameters. The classic example is an assertion that the sample mean centered at a parameter and scaled by its standard error has Student’s t-distribution followed by an assertion that the sample mean plus and minus a critical value times the standard error is a Bayesian credibility interval for the parameter. This article studies the logic of such assertions. The main finding is that if the moment functions have one of the properties of a pivotal, then the assertion of a distribution on moment functions coupled with a proper prior does permit Bayesian inference. Without the semi-pivotal condition, the assertion of a distribution for moment functions either partially or completely specifies the prior. In this case, Bayesian inference may or may not be practicable depending on how much of the distribution of the constituents remains indeterminate after imposition of a noncontradictory prior. An asset pricing example that uses data from the U.S. economy illustrates the ideas.

Date: 2016
References: View complete reference list from CitEc
Citations: View citations in EconPapers (8)

Downloads: (external link)
http://hdl.handle.net/10.1093/jjfinec/nbv008 (application/pdf)
Access to full text is restricted to subscribers.

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:oup:jfinec:v:14:y:2016:i:2:p:229-247.

Ordering information: This journal article can be ordered from
https://academic.oup.com/journals

Access Statistics for this article

Journal of Financial Econometrics is currently edited by Allan Timmermann and Fabio Trojani

More articles in Journal of Financial Econometrics from Oxford University Press Oxford University Press, Great Clarendon Street, Oxford OX2 6DP, UK. Contact information at EDIRC.
Bibliographic data for series maintained by Oxford University Press ().