Really, the most natural thing to do with the consumption-based model is to estimate it and test it, as one would do for any economic model. Logically, this investigation comes before "puzzles" which throw away information (correlation, multiple assets, time-variation of moments). The puzzles are not tests, they are useful diagnostics for why tests fail.
4.1 Hansen and Singleton
The classic consumption-based model test is due to Hansen and Singleton [87, 89]. The influence ...