Definition
Weak separability
The MRS between two variables in the same group is unaffected by the level of the third variable in other groups
Strong separability
The MRS between two variables (can be not from the same group) is unaffected by the level of the third variable in other groups
In GTAP, we use weak separability to restrict the number of parameters
For example, in the nested production function Y = G(VA(K,L),F,M,S),
where:
- F: food
- M: manufacture
- S: services
- L: land
- K: capital
The VA factor (K, L) are separated from intermediate inputs (F, M, S) means:
- the optimal mix of primary factor (K, L) is invariant to the price of intermediate inputs (F, M, S)
- the APE (Allen's partial elasticity of substitution) between any primary factor and intermediates is the same:
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, for all j in {F, M, S}
So by assuming separability, we further reduce the number of APEs to be estimated (see restrictions).