According to Spanos 2014 Revisiting Haavelmo's Structural econometrics: Bridging the gap between theory and data Dynamic Stochastic General Equilibrium models are statistically inadequate, in such an order of magnitude as to render them useless.
The most serious problem with DSGE models is that they are often statistically inadequate. Advocates of DSGE modeling, however, have put forward a number of arguments to explain away the unreliability of their evidence, such as ‘the price one has to pay for rigorous and policy-relevant theoretical models’ (Lucas, 1980, p. 696), or simply inevitable: “The models constructed within this theoretical framework are necessarily highly abstract. Consequently, they are necessarily false, and statistical hypothesis testing will reject them. This does not imply, however, that nothing can be learned from such quantitative theoretical exercises.” (Prescott, 1986, p. 10)
Part of my research involves using a partial equilibrium models to simulate a particular segment of an economy.
Considering the above, what methods would you start with to show that a given equilibrium model is statistically unreliable?