Gempack
Encyclopedia
GEMPACK is a modeling system for CGE
economic models, produced
and used at the Centre of Policy Studies (CoPS), Monash University
, Australia
, and sold by CoPS to other CGE modellers.
Some of the more well-known CGE models solved using GEMPACK
are the GTAP
model of world trade, and the MONASH, MMRF, ORANI-G and TERM models used at CoPS.
All these models share a distinctive feature: they are formulated as a system of differential equations in percentage change form;
however, this is not required by GEMPACK.
for the model can be readily constructed from a
table of transaction values (such as an input-output table or a social accounting matrix
) that satisfies certain basic
accounting restrictions. GEMPACK builds on this feature by formulating
the CGE model as an initial value problem
which is solved
using standard techniques.
The GEMPACK user specifies her model by constructing a text file listing model equations and variables, and showing how variables relate to value flows stored on an initial data file.
GEMPACK translates this file into a computer program which solves the model, ie., computes how model variables might change in response to an external shock. The original equation system is linearized (reformulated as a system of first-order partial differential equations).
If most variables are expressed in terms of percentage changes (akin to
log changes
) the coefficients of the linearized system are usually very simple functions of database value flows.
Computer algebra is used at this point to greatly
reduce (by substitution) the size of the system.
Then it is solved by multistep methods such as the Euler method,
midpoint method
or Gragg's modified Midpoint method.
These all require solution of a large system of linear equations;
accomplished by sparse matrix
techniques.
Richardson extrapolation
is used to improve accuracy.
The final result is an accurate solution of the original non-linear equations.
This linearized approach, originally devised to solve medium-sized CGE models on early computers, has since proved capable (on modern computers) of solving very large models. Additionally it has lent itself to some interesting extensions, such as: a Gaussian quadrature
method of estimating confidence intervals for model results from known distributions of shock or parameter values; a way to formulate inequality constraints or non-differentiable equations
as complementarities
; and a technique to decompose changes in model variables due to several shocks into components due to each individual shock.
The underlying numerical approach is complemented by several
GUI
programs that:
ease viewing of large multidimensional arrays often found in CGE databases;
manage complex (e.g., multi-period) simulations; and
allow interactive exploration and explanation of simulation results.
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...
economic models, produced
and used at the Centre of Policy Studies (CoPS), Monash University
Monash University
Monash University is a public university based in Melbourne, Victoria. It was founded in 1958 and is the second oldest university in the state. Monash is a member of Australia's Group of Eight and the ASAIHL....
, Australia
Australia
Australia , officially the Commonwealth of Australia, is a country in the Southern Hemisphere comprising the mainland of the Australian continent, the island of Tasmania, and numerous smaller islands in the Indian and Pacific Oceans. It is the world's sixth-largest country by total area...
, and sold by CoPS to other CGE modellers.
Some of the more well-known CGE models solved using GEMPACK
are the GTAP
GTAP
GTAP is a global network of researchers who conduct quantitative analysis of international economic policy issues, especially trade policy. They cooperate to produce a consistent global economic database, covering many sectors and all parts of the world...
model of world trade, and the MONASH, MMRF, ORANI-G and TERM models used at CoPS.
All these models share a distinctive feature: they are formulated as a system of differential equations in percentage change form;
however, this is not required by GEMPACK.
Main features
A characteristic feature of CGE models is that an initial solutionfor the model can be readily constructed from a
table of transaction values (such as an input-output table or a social accounting matrix
Social accounting matrix
A Social Accounting Matrix represents flows of all economic transactions that take place within an economy . It is at the core, a matrix representation of the National Accounts for a given country, but can be extended to include non-national accounting flows, and created for whole regions or area...
) that satisfies certain basic
accounting restrictions. GEMPACK builds on this feature by formulating
the CGE model as an initial value problem
Initial value problem
In mathematics, in the field of differential equations, an initial value problem is an ordinary differential equation together with a specified value, called the initial condition, of the unknown function at a given point in the domain of the solution...
which is solved
using standard techniques.
The GEMPACK user specifies her model by constructing a text file listing model equations and variables, and showing how variables relate to value flows stored on an initial data file.
GEMPACK translates this file into a computer program which solves the model, ie., computes how model variables might change in response to an external shock. The original equation system is linearized (reformulated as a system of first-order partial differential equations).
If most variables are expressed in terms of percentage changes (akin to
log changes
Logarithmic derivative
In mathematics, specifically in calculus and complex analysis, the logarithmic derivative of a function f is defined by the formulawhere f ′ is the derivative of f....
) the coefficients of the linearized system are usually very simple functions of database value flows.
Computer algebra is used at this point to greatly
reduce (by substitution) the size of the system.
Then it is solved by multistep methods such as the Euler method,
midpoint method
Midpoint method
In numerical analysis, a branch of applied mathematics, the midpoint method is a one-step method for solving the differential equation y' = f, \quad y = y_0...
or Gragg's modified Midpoint method.
These all require solution of a large system of linear equations;
accomplished by sparse matrix
Sparse matrix
In the subfield of numerical analysis, a sparse matrix is a matrix populated primarily with zeros . The term itself was coined by Harry M. Markowitz....
techniques.
Richardson extrapolation
Richardson extrapolation
In numerical analysis, Richardson extrapolation is a sequence acceleration method, used to improve the rate of convergence of a sequence. It is named after Lewis Fry Richardson, who introduced the technique in the early 20th century. In the words of Birkhoff and Rota, ".....
is used to improve accuracy.
The final result is an accurate solution of the original non-linear equations.
This linearized approach, originally devised to solve medium-sized CGE models on early computers, has since proved capable (on modern computers) of solving very large models. Additionally it has lent itself to some interesting extensions, such as: a Gaussian quadrature
Gaussian quadrature
In numerical analysis, a quadrature rule is an approximation of the definite integral of a function, usually stated as a weighted sum of function values at specified points within the domain of integration....
method of estimating confidence intervals for model results from known distributions of shock or parameter values; a way to formulate inequality constraints or non-differentiable equations
as complementarities
Linear complementarity problem
In mathematical optimization theory, the linear complementarity problem arises frequently in computational mechanics and encompasses the well-known quadratic programming as a special case...
; and a technique to decompose changes in model variables due to several shocks into components due to each individual shock.
The underlying numerical approach is complemented by several
GUI
Graphical user interface
In computing, a graphical user interface is a type of user interface that allows users to interact with electronic devices with images rather than text commands. GUIs can be used in computers, hand-held devices such as MP3 players, portable media players or gaming devices, household appliances and...
programs that:
ease viewing of large multidimensional arrays often found in CGE databases;
manage complex (e.g., multi-period) simulations; and
allow interactive exploration and explanation of simulation results.
See also
- RunGEMRunGEMRunGEM is a freeware component of the commercial modelling package, Gempack, written at Monash University.It is mainly used for solving computable general equilibrium models. It does not allow a user to change a model's specification or to create a new model.-External links:*...
: a freeware solving component for Gempack - GAMSGeneral Algebraic Modeling SystemThe General Algebraic Modeling System is a high-level modeling system for mathematical optimization. GAMS is designed for modeling and solving linear, nonlinear, and mixed-integer optimization problems. The system is tailored for complex, large-scale modeling applications and allows the user to...
: another modeling system often used to solve CGE models.