627

**Priors for Unit Root Models**

**Joseph B. Kadane, Ngai Hang Chan and Lara J. Wolfson**

### Abstract:

*In the recent debate about unit roots, part of the discussion now
centers on what prior is correct to use. From the perspective of
subjective Bayesians, this question seems ill posed. To the extent
that the likelihood is sharply peaked, the prior will not matter much.
To the extent that the likelihood is flat, the posterior depends
principally on the prior. A special consideration in unit roots models
is that the spaces , and have very
different economic implications. A better way to asses the role of the
prior is to study its connections with these implications through
prior elicitations.
*
In each of the intervals, a conjugate prior
(i.e. normal-inverse gamma) is fit to the elicited opinion of an
expert. Since the likelihood in each interval is normal, the
posterior is of the same form as the prior (i.e. piece-wise
normal-inverse gamma), so this family of priors is closed under
sampling.

A modification of existing methods for the normal linear model permits
elicitation of this expanded family of prior distributions. An
example elicitation of a macro-economist is discussed.

*
*

Here is the full postscript text for this
technical report. It is 238468 bytes long.