We may never know the answer. But it’s pretty obvious the posterior is multimodal. For example, Chib/Ramamurthy (2010): “Tailored randomized block MCMC methods with application to DSGE models”, Journal of Econometrics, 155, pp. 19-38 have pointed out that the mode reported in the original Smets/Wouters (2007) paper is not actually the mode. \bar \pi (constepinf) is estimated lower while \bar \l (constelab) is higher.