[Gretl-users] Re: BACE Estimation difficulties
On 27.08.2022 23:22, Brian Revell wrote:
Hi Sven
the dependent variable and independent variables are different and X
only contained a single indep. variable and y a single dep. variable.
So as far as I can see the error message is nonsense. It should be
possible to estimate a Bayesian regression with a single indep
variable eg a Bayesian trend function.
Well,
just for clarification: BACE approach is not purely Bayesian, since it
relays on OLS estimates. This is because in BACE we assume extremely
diffuse prior on regression parameters and we use BIC as an
approximation of marginal data density. Although Raftery over 25 years
ago named this approximation "crude" he showed that it works fine. Of
course such setup impose strict prior assumptions, which in fact tends
to RIC (Risk Inflation Criterion). You can find more in: Eduardo Ley
and Mark F.J. Steel (2009), "On the effect of prior assumptions in
Bayesian model averaging with applications to growth regression",
Journal o Applied Econometrics 4(24).
So, the whole BACE method is approximation, but again: it works quite
well. For example, to replicate classical BMA analysis by Carmen
Fernández, Eduardo Ley, Mark J.F. Steel (2001), "Model Uncertainty in
Cross-Country Growth Regressions", Journal of Applied Econometrics, Vol.
16, No. 5, pp. 563-576 you should just set 'avg_model_size=k/4' (where k
is a number of variables).
Marcin
--
Marcin Błażejowski