A blog on financial markets and their regulation
Bayesians in Finance
November 17, 2009Posted by on
At the EconLog blog, Bryan Caplan asks
why academic economists are not Bayesians. Caplan was talking about a
Bayesian approach to the validity of economic theories. Stephen Gordon
responded with a post
about why economists do not use enough of Bayesian econometrics. Both
questions are valid and should cause some introspection.
The issue is probably even more important in finance where key
parameters are estimated with such large confidence intervals that the
prior does not get washed out by the sample. In fact, I think that one
of the defining characteristics of finance as a discipline is that
first moments (for example, mean returns) are estimated very poorly
even with extremely large samples while second moments (variances) are
somewhat better estimated.
For example, Aswath Damodaran has an interesting paper last month
discussing the difficulties of estimating the Equity Risk Premium
reliably. Damodaran states bluntly that:
At the risk of sounding harsh, the risk premiums in academic
surveys indicate how far removed most academics are from the real
world of valuation and corporate finance and how much of their own
thinking is framed by the historical risk premiums they were exposed
to back when they were graduate students.
What Damodaran is really saying is that despite being exposed to
recent academic research using centuries of global stock market data,
the posterior distributions of most academics are still strongly
influenced by the prior distributions formed during their student
days. In such a situation, there is merit in making the prior
distribution quite explicit rather than leaving it implicit.
Classical statistics also involves priors; the tragedy is that in
that framework, there are only two kinds of priors:
- Dogmatic priors which totally ignore what the data says, and arbitrarily
set some parameters to zero or some other special value.
- Diffuse (or improper) priors which impose no priors beliefs at all
and leave everything to the data.
Bayesians can however use the more interesting priors which reflect
non trivial prior beliefs that can be overruled by the data.
At a different level, I think it is also essential to incorporate
Bayesian learning into theoretical models. Rational expectations
models are richer when they recognize that even with large samples,
posterior distributions could have large error variances.