I am curious to know why the Hicksian form of the CES is used in CGE models rather than the Marshallian form. I have a few hypotheses, but I am not sure which one is correct. If any?
Hypothesis 1: In a general equilibrium setting, the Hicksian and Marshallian forms of the CES should yield the same results. This is because Shepard's lemma guarantees that the functions are strictly convex and concave for supply and demand, meaning there is only one solution. Therefore, the utility would be the same in both scenarios, yielding equal demands for the goods. The solutions to the Lagrangian are only used to tie demand for each input to the utility or production curve.
Hypothesis 2: The Hicksian form may be easier to calibrate than the Marshallian form.
Hypothesis 3: The choice of the Hicksian form may be due to the mathematical formulation of the optimization problem in CGE models. In many CGE models, household consumption is maximized as the global objective of the optimization problem. This means that the Hicksian demand function is the appropriate choice, as it represents the demand for goods that maximizes household utility.
I would be grateful if someone could shed some light on this issue. I am particularly interested in knowing if I'm in the ballpark of a right answer above, or if there is another reason why the Hicksian form is used in CGE models.