Checking if the straitjacket fits

Pesaran and Smith (2011) concluded that DSGE models were sometimes a straitjacket
which hampered the ability to match certain features of the data. In this paper we look at
how one might assess the fit of these models using a variety of measures, rather than
what seems to be an increasingly common device - the Marginal Data Density. We apply
these in the context of models by Christiano et.al (2014) and Ireland (2004), finding they
fail to make a match by a large margin. Against this, there is a strong argument for
having a straitjacket as it enforces some desirable behaviour on models and makes
researchers think about how to account for any non-stationarity in the data. We illustrate
this with examples drawn from the SVAR literature and also more eclectic models such
as Holston et al (2017) for extracting an estimate of the real natural rate.