Modeling Household Behavior

Leontief

Easy to parameterize but the implicit zero elasticity of substitution is unrealistically low in most situations.

Cobb-Douglas

Also easy to parameterize. Imposes unitary substitution and income elasticities. The unitary substitution elasticity may or may not be reasonable, but it is well known from the literature on demand models that few goods have a unitary income elasticity.

Constant Elasticity of Substitution (CES)

Relaxes the imposed substitution elasticities in the Leontief and Cobb-Douglas models. Does not address the income elasticity problem: income elasticities are still constrained by the functional form to equal one.

Linear Expenditure System

Relaxes the unitary income elasticity assumption. Straightforward to estimate.

Translog

Flexible but more difficult to parameterize. Large number of parameters makes it difficult to estimate on short datasets. Also requires that the curvature restrictions in the integrability conditions be checked by hand after estimation.