Two things though have always bothered me in the actual practice of DSGE modelling.
The first is the use of the "Calvo rule" for modelling how firms change their prices. This method assumes that firms have a constant probability of changing their price and that said probability does not vary with how long it has been since they last changed their price (i.e. it has a constant hazard).
The second is the increasing number of ad-hoc "real rigidities" that are routinely added to the models to help them fit the data. Things like adjustment costs for capital, labor, and leisure, among others. They are not derived from theory, their correct functional forms are far from obvious, and in my view, they make the claim that we can do real counterfactual policy analysis with the models fairly suspect.
I have been told by practitioners that the Calvo rule is innocuous. They say that is a literally false assumption that is convenient, yet does not play a major role in the models' dynamics.
Two new papers show that, at least in some cases, this is not correct. In "The cost of tractability and the Calvo pricing assumption" (available here), Fang Yao shows that, in the model he studies, replacing the Calvo rule with a price adjustment rule where the hazard function is increasing, makes the inflation dynamics of the model fit the data better without incorporating real rigidities! He also shows that money shocks have a bigger impact with the increasing hazard price adjustment rule.
In other words, in his model, the Calvo rule is not innocuous and replacing it with a more realistic rule lessens the need for incorporating real rigidities into the model and changes conclusion about the importance of nominal shocks for explaining model dynamics. Two birds with one stone!
Another recent paper, "Heterogeneous price setting behavior and aggregate dynamics" (available here) by Carvalho and Schwartzman not only allows for non-constant hazards but allows more than one type of price adjustment rule to be followed in the economy. They find that allowing such heterogeneity in price adjustments has large effects on model dynamics, specifically that it creates larger amounts of monetary non-neutrality.
Shout it from the rooftops!
Hat tip to Gabriel M