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Been reading The Textbook of Computable General Equilibrium (CGE) by Hosoe et al as a bit of side interest later in life.

Much of the book (and the CGE set-up generally) obviously follows naturally from intermediate micro/macro classes I've taken previously.

However, one thing I'd never considered prior to the book was the estimation of utility coefficients required for CGE calibration (or at least CGE calibration where welfare change is concerned).

For example, in Hosoe et al's CGE mock example the share coefficients in the two-good (bread + milk) Cobb-Douglas utility function are given as: $\alpha_1 = 0.2; \alpha_2 = 0.8$.

But if we take for granted utility is latent, and therefore has to be estimated somehow econometrically (perhaps in Hicksian terms), then could anyone help with suitable estimation methods/R packages out there for estimating the share coefficients?

Or alternatively, given that many CGEs have the majority of their parameters calibrated from the social accounting matrix (SAM), then is it possible to arrive at the share coefficients using a SAM?

Lots of (naive) questions, sorry. All help would be appreciated.

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