Bayesian Specification Analysis in Econometrics

authors: John Geweke, William McCausland year: 2001 See in Zotero

Literature Notes

Overview

In order to decide between different models, you can use specification analysis to see how close certain parts of a model are to aspects of reality (the statistician must do decide what parts of reality to approximate - what is important). First choose a ‘vector of interest’ ($\omega$) which is just some statistics/ function to be computed from the date (usually associated with some meaning or theory). Then use predictive specification or postpredictive specification.

Predictive Specification

General question: Does the predictive distribution (and $\omega$ given the predictive distribution) fit what you think it should given the model?

Postpredictive Specification

General question: Does the posterior predictive density (and $\omega$) fit the expectation given the model?

Notes

• Complete model - Must be equiped with prior distribuiton for unobservables and likelihood function for observables. To use specification analysis you need to have a complete model.
• Specification analysis (especially checking with the predictive speficiation) is a good way to decide on which prior to use. Its especially interesting since it has an element of explicit subjectivity as different people would use different $\omega$ vectors.