Here are three posts by Delong who likes the model:
Here are three by Cowen, who dislikes the model:
I will leave aside the macroeconomics (no expertise). What I care about is how one should, and should not, critique "models".
Since a model is an abstraction, a simplification of reality, no model is above critique.
I consider the following types of critique not deserving:
1) The critique that the modeler makes an assumption,
e.g. "it fudges the distinction between real and nominal interest rates". Making assumptions is not inherently bad, making bad assumptions is a problem but not all assumptions are bad.
2) The critique that the modeler makes an assumption for mathematical convenience,
e.g. "Don't assume they are the same, just to squash the two curves onto the same graph." Almost all assumptions are made for mathematical convenience. The inappropriate use of the Gaussian assumption, that most unpardonable of sins according to Taleb, is almost always invented to render the math tractable. But not all assumptions that simplify the math are bad assumptions.
3) The critique that the model omits some feature,
e.g. "those aggregate curves are not invariant to expectations", because this critique is no different from saying the modeler makes an assumption (see #1) More, what is a "bad" assumption? How does one determine which assumptions are bad among the set of all possible assumptions?
4) The critique that the model doesn't fit one's intuition,
e.g. "the model leads you to believe that interest rates are more important than they probably are". The model should fit reality (the data); it doesn't need to fit anyone's intuition.
5) The critique that the model fails to make a specific prediction,
e.g. "this distinction really matters when you're trying to predict the macro effects of 'window breaking'". No model, especially a macroeconomic model that can issue a large number of predictions, will ever predict everything. Not all predictions are equally important. One must agree on which predictions are the most important to get right, and make judgment based on the entire list of predictions.
Above all, a serious critique must include an alternative model that is provably better than the one it criticises. It is not enough to show that the alternative solves the problems being pointed out; the alternative must do so while preserving the useful aspects of the model being criticized.
This whole debate reminds me of the climate change model controversies. I am not aware of an alternative model from those who dislike the consensus model. Until they offer such an alternative, their critique cannot be taken seriously, I'm afraid.
The underlying belief -- on both sides of the macroeconomic divide, it appears -- that someone's model can be proved "wrong" and thus discarded for all eternity is as dubious as the belief that a model can be proved "right".