Economics programs written in *Mathematica*

Thomas Cool, June 30 1996, Report no 96-07

Consultancy & Econometrics, email Cool@CAN.NL

Summary

The program *Mathematica* is being discovered by economists. This paper introduces a number of programs that help to provide a working and teaching environment. Keywords are: Chi2, CrossTable, Decision, Dbase, DifData, Finance, Graphics, Inference, Logic, Minimax, Modeling, Sampling, Statistics, Calculus, CES, Economic`Common, Economic`Optimise, IADS, Lagrange, LevelCES, Applied General Equilibrium Analysis, Neural Networks, Nonlinear Estimate, Leontief, List, Manager, Matrices, Tool, Chain Indices, Declare, Genetic Programming.

Introduction

It seems to me that *Mathematica* may be one of the revolutions of mankind. The invention of the wheel, the alphabet, hygiene, the steam engine, women's lib, ... What penicilline is to an infected person, what Adam Smith's *Wealth of Nations* means for civilisation, is what *Mathematica* will likely be to human inquiry.

Generations of mathematical geniusses have been designing an elegant and compact language to state their theorems and proofs: mathematics. This language is now being implemented on the computer, so that you can proceed along as you think.

The best way to see what this actually means, is to use *Mathematica*.

These present notebooks and packages have been developed for economics. I'm econometrician involved in decision support, and these tools have served and still serve their purpose. Also, I like to have my software neat and well documented, so that I can turn to it quickly when I need it again. My conjecture is that others could use it too.

These applications may help others:

- to get the job done
- to get a feel of
*Mathematica* - to get a feel of the discussed problems
- to have fun
- or, to create higher level complexity.

Keywords on ...

Applied General Equilibirum Analysis

Extend on Asahi Noguchi's packages, see Varian (1993). [Note 1]

Solve systems of production and utility functions and plot 2D diagrams for arbitrary sectors and factors. Plot their time trajectories.

Have easy access to the (Dynamic) Leontief Model.

Calculus

Substitute y = f[x] back into D[y, x] to get a simpler expression.

A general routine to use Lagrange multipliers.

Decision Making

Logic and inference.

Statistical decision theory including game theory (e.g. minimax).

Crosstables, and ChiSquare tests (in higher dimensions).

Data

Database, datafiles, using packages as datafiles, data contexts, data dictionary

Econometrics

Use NonlinearFit for estimation of equations and systems of equations, with an estimated variance for the estimated parameters.

Errors in variables for one equation.

Lags, Arima and some tests of the WRI Time Series Pack.

Economics

Some general efficiency, minimal cost, maximal profit, and factor demand routines. Applications on the CES, LevelCES and IADS functions, while providing the proper limits for Leontief, Cobb-Douglas and Line functions.

Standard representation of factors, price, coefficients and key parameters. Write your own function using the standard, and call the general routines.

Economics Papers

A solution approach to problems of unemployment and inflation, using *Mathematica* as a word processor, while including many graphs created with it.

Using Dutch data of 1950-1995 for a further explanation of the analysis on unemployment. Provide your own data and test the analysis for your own country.

See how you might apply Chi2 tests to Frauds in the European Community.

Let the gasoline price at the center of a metropolitan area be higher than in the surrounding rural area.

Finance

Flat rates & basics.

Try the WRI Finance Package and use some additional features

Genetic Programming

Define a population, a fitness criterion, and evolve. [Note 2]

Graphics

Plans, events, bond durations, calendar dates.

Use arrow diagrams to clarify relations between variables.

Linear Algebra

Create block diagonal matrices

Modeling

Make a model with various lags, and simulate it for a period. Store the various runs, and compare the outcomes.

Neural Networks

Use a "master" packages for Freeman's packages, see Freeman (1994).

Statistics

See Decision Making.

Chain indices. Using approximate US data as an example.

System Enhancement

Speed up the loading of common routines, and use separate contexts: Common, Declare, Graphics, List, Manager and Tool

Have various packages share common keywords with AddedUsage, store and reset definitions without saving, inspect and show levels and dimensions

Notebooks and Packages

The Cool Economics Pack consists of "notebooks" and "packages". Notebooks are the user-friendly interface of *Mathematica* with the user. The packages contain the routines.

The following lists the available packages (though with the "Cool`" prefix deleted):

{AGE`, Arima`, Arrowise`, Calculus`, CES`,

Chaindex`, Chi2`, Common`, Context`, CrossTable`,

Dbase`, Decision`, Declare`, Dictionary`,

DifData`, Economic`Common`, Economic`Optimise`,

Estimate`, Finance`, FlatRate`, GenePro`,

GP`Estimation`, Graphics`, IADS`, Inference`,

Lagrange`, Lags`, Leontief`, LevelCES`, List`,

Logic`, Lseqlist`, Manager`, Matrices`, Minimax`,

MissingData`, Model`, Neural`, PackLine`,

ReadData`, Sampling`, ShowPlan`,

Statistics`Common`, Time`, Tool`}

Technical Notes & Availability

The "Cool Eonomics Pack" contains about 200 files and takes 6.5 MB on hard disk. Binary files ("*.mb") that control the lay-out have been deleted.

Loading all packages - and the *Mathematica* packages that are relied on - takes about 2700 KB internal memory.

The *Mathematica* packages that are relied on and which are supplied by others, are: (1) the standard packages supplied from WRI, (2) for resetting: CleanSlate` (3) for Finance: the Finance Package of WRI, (4) for applied general equilibrium analysis: Asahi Noguchi & Silvio Levy's MyFindRoot` (Varian (1993)), (5) for math: Varian's SymbOpt` (see Varian), (6) for neural networks: Freeman (1994). For copyright considerations, only the CleanSlate` package is included here, and you are advised to buy the Varian book. (But you may also look into MathSource, see info@wri.com.)

Documentation is provided in & by the notebooks only.

The software has a semi-commercial status. I’ve decided to give it a licensed status, and to ask a small price for it. My hope is that there will be sufficient revenue to provide for the expense of a manual, and that sort of thing.

Thomas Cool

Scheveningen

The Netherlands

E-mail Cool@Can.nl

http://www.can.nl/~cool

References

J.A. Freeman, "Simulating neural networks with *Mathematica*", Addison Wesley, 1994

J. Kleid, "Genetic Programming with *Mathematica*", Son Of a Bit Software 1994, available from MathSource

H.R. Varian (ed), "Economic and financial modeling with *Mathematica*", Telos 1993

http://www.can.nl/~cool

http://www.wri.com

Note

This is an update of the report of 1995 with the same titel, Report-no: Thomas Cool 95-03. Programs have been added, others improved and integrated. This paper now is in Word for Windows, to allow for a wider distribution.

Footnotes