There is a tradition of trying to have models replicating statistical features of the business cycle, this is what the real business cycle theory is about: find a model that seems to mimic the data reasonably well, so that one can then use the model to study the impact of some policies. These models have had mixed results, in particular regarding the labor market, but this is somewhat understandable, as these models are obviously abstractions and they are not fitted to the data. But the point is that one has a structural model that can be applied for something useful.
So when I stumbled upon a recent paper by James Morely, Jeremy Piger and Pao-Lin Tien on reproducing business cycle facts, I was expecting something along the lines described above. Not so. This paper is about fitting VAR models and the like with non-linear effects to business cycle features. What would this be good for? These statistical model are good for short-term forecasting, and then you try to minimize some criterion like out-of-sample forecasting errors. Why would you try to have these models try to mimic business cycle features? They are not even good for any policy use, as they are reduced form models. Beats me.