A few years ago - twelve, to be specific - an interesting paper appeared in the Journal of the Royal Statistical Society. That paper, "Bayesian measures of model complexity and fit", by Spiegelhalter et al., stirred up a good deal of controversy within the statistical community. That much is apparent even from the "discussion" that accompanied its publication. More than 4,600 Google Scholar citations later, it continues to attract widespread attention - though not that much among econometricians, as far as I can tell. An exception is the paper by Berg et al. (2004).
In their 2002 paper, Spiegelhalter et al. introduced a new measure of model fit. They termed it the "Deviance Information Criterion" (DIC). Briefly, here's how it's defined: