This lecture introduces supply side of GTAP model.
Production system
We start with introducing the production tree and producers' behavior
Model factors with by mobility:
- Perfectly mobile factors (move freely across sectors)
- Imperfectly mobile factors, or Sluggish factors
APE
In this lecture, we introduce a new concept: Allen partial elasticities of substitution (APEs), which is necessary to apply restrictions below and reduce the number of parameters we need to estimate.
The key to understand the producers' system in GTAP is to distinguish three elasticities of substitution:
- full elasticity of substitution: the elasticity of the ratio of two inputs / goods to a production / utility function with respect to the ratio of their marginal products / utilities (at competitive market, the ratio of marginal product equals the ratio of price)
- Unweighted output-constant cross-price elasticity of demand: the elasticity of input i with respect to the price of input j, holding output constant
- cost-share weighted constant-output cross-price elasticity of demand, or Allen partial elasticity of substitution
Relationship between three elasticities is given in the note of Allen partial elasticity of substitution, And APEs can be calculated from the full elasticity of substitution with Keller's formula.
Restrictions
In modeling research, one major challenge is to obtain estimates of a large number of parameters. To overcome the challenge, we use restrictions, a series of assumptions to reduce the number of parameters needed to solve the model.
The note of restrictions on the production function explains the theoretical foundation of restrictions. You may recall in the note of production system above, we use the CES as the functional form for producers. The section of CES function is one of the particular restrictions discussed here.
And the note of restrictions on a specific production function gives a simple and more clear example.