Applied
General
Equilibrium (AGE) models were pioneered by
Herbert ScarfHerbert Eli "Herb" Scarf in Philadelphia, PA is an American mathematical economist and Sterling Professor of Economics at Yale University. He is a member of the American Academy of Arts and Sciences...
at
YaleRapidMiner is an environment for machine learning and data mining experiments. It allows experiments to be made up of a large number of arbitrarily nestable operators, described in XML files which are created with RapidMiner's graphical user interface...
University in 1967, in two papers, and a follow up book with Terje Hansen in 1973, with the aim of empirically estimating the Arrow-Debreu
General equilibriumGeneral equilibrium theory is a branch of theoretical neoclassical economics. It seeks to explain the behavior of supply, demand and prices in a whole economy with several or many markets, by seeking to prove that equilibrium prices for goods exist and that all prices are at equilibrium, hence...
model with empirical data, to provide "“a general method for the explicit numerical solution of the neoclassical model”
(Scarf with Hansen 1973: 1)
Scarfs method was an algorithm (based on simplical subdivisions) that would narrow a ‘net’ around the possible solution to the quantified general equilibrium problem.
Applied
General
Equilibrium (AGE) models were pioneered by
Herbert ScarfHerbert Eli "Herb" Scarf in Philadelphia, PA is an American mathematical economist and Sterling Professor of Economics at Yale University. He is a member of the American Academy of Arts and Sciences...
at
YaleRapidMiner is an environment for machine learning and data mining experiments. It allows experiments to be made up of a large number of arbitrarily nestable operators, described in XML files which are created with RapidMiner's graphical user interface...
University in 1967, in two papers, and a follow up book with Terje Hansen in 1973, with the aim of empirically estimating the Arrow-Debreu
General equilibriumGeneral equilibrium theory is a branch of theoretical neoclassical economics. It seeks to explain the behavior of supply, demand and prices in a whole economy with several or many markets, by seeking to prove that equilibrium prices for goods exist and that all prices are at equilibrium, hence...
model with empirical data, to provide "“a general method for the explicit numerical solution of the neoclassical model”
(Scarf with Hansen 1973: 1)
Scarfs method was an algorithm (based on simplical subdivisions) that would narrow a ‘net’ around the possible solution to the quantified general equilibrium problem. With enough iteration, the net was tightened sufficiently to choose a cut off point, giving a price vector that could clear the market.
Brouwer's Fixed Point theorem states that a continuous mapping of a simplex into itself has at least one fixed point. This paper describes a numerical algorithm for approximating in a
sense to be explained below, a fixed point of such a mapping (Scarf 1967a: 1326).
Scarf never built an AGE model, but hinted that “these novel numerical techniques might be useful in assessing consequences for the economy of a change in the economic environment”
(Kehoe et al. 2005, citing Scarf 1967b). His students elaborated the Scarf algorithm into a tool box, where the price vector could be solved for any changes in policies (or exogenous shocks), giving the equilibrium ‘adjustments’ needed for the prices. This method was first used by Shoven and Whalley (1972 and 1973), but was used up through the 1970s by Scarf’s students and students’ students.
Scarf’s simplex method was quite appealing to the economic theorists at the time, who wanted constructive proofs for the existence of equilibrium. Lance Taylor noted that as a solution algorithm, it ignored 2nd derivatives and curvature information, thus being much less effective than Newton methods for the highly convex model specifications which AGE modelers at the time were creating.
Furthermore, in a recent article, Velupillai (2006) proves how the AGE models, can not be precisely solved numerically and points out that "From a very elementary (classical) recursion theoretic standpoint it is easy to show the absence of a computable (and constructive) content" (Velupillai 2006: 366).
AGE and CGE models
AGE models developed separately and independently from
Computable general equilibriumComputable general equilibrium models are a class of economic models that use actual economic data to estimate how an economy might react to changes in policy, technology or other external factors...
(CGE) models, as illustrated in Mitra-Kahn (2008). However, today the two terms are used inter-changeably, and the Arrow-Debreu theoretical background of AGE models, is then attributed to CGE models, which are in widespread use across the world. This is a confusion as the AGE literature has no connections with the CGE models until the mid 1980's when AGE models are going out of fashion due to the high cost of implementing them, and the AGE modellers begin to adopt the CGE methods of using Social Accounting Matrices for their data set-ups, and macro balancing equations as opposed to Arrow-Debreu and General Equilibrium Theory.
AGE models, being based on Arrow-Debreu general equilibrium theory works in a different manner than CGE models. The model first establishes the existence of equilibrium through the standard Arrow-Debreu exposition, and then inputs data into all the various sectors, and then apply Scarf’s algorithm (Scarf 1967a, 1967b and Scarf with Hansen 1973) to solve for a price vector that would clear all markets instantly. This algorithm would narrow down the possible relative prices through a simplex method, which kept reducing the size of the ‘net’ within which possible solutions were found. AGE modelers then consciously choose a cutoff, and set an approximate solution as the net never closed on a unique point through the iteration process.
CGE models, are based on macro balancing equations, and use an equal number of equations (based on the standard macro balancing equations) and unknowns solvable as simultaneous equations, where exogenous variables are changed outside the model, to give the endogenous results. This process is uncontroversial, but also completely separate from AGE modelling and formal
general equilibriumGeneral equilibrium theory is a branch of theoretical neoclassical economics. It seeks to explain the behavior of supply, demand and prices in a whole economy with several or many markets, by seeking to prove that equilibrium prices for goods exist and that all prices are at equilibrium, hence...
theory.
See also
- Computable general equilibrium
Computable general equilibrium models are a class of economic models that use actual economic data to estimate how an economy might react to changes in policy, technology or other external factors...
models or CGE models
- General equilibrium
General equilibrium theory is a branch of theoretical neoclassical economics. It seeks to explain the behavior of supply, demand and prices in a whole economy with several or many markets, by seeking to prove that equilibrium prices for goods exist and that all prices are at equilibrium, hence...
theory
- Arrow-Debreu