The Methodology of a Computable Economist

Stephen KinsellaNew School for Social Research

stephen.kinsella@gmail.com

What is Computable Economics?

An algorithmic approach to economics

Can’t answer the questions economic life poses with the standard tools

Make new ones

Use Recursion theory

Supply & Demand

x = (!, x;A, t)

x

!

x

A

t

Prices of Goods for Sale

Price Vector

Transition Coefficient Matrix

Time

Change in Price Vector

1 Pick some functional form & discretise it

xt = xt!1 + !xt!1 + Axt!1 + C

2 Compute the Taylor Series

xT

n!(C+Axt!1+!xt!1)+!

Ax"

t!1 + !x"

t!1

"

t+

#

1

2Ax

""

t!1 +1

2!x

""

t!1

$

t2+

#

1

6Ax

"""

t!1 +1

6!x

"""

t!1

$

t3+O

4t

3 Find some parameters and solve

xT

n = 0

Errors

Data Measurement Model~Parameters Numerical methodsUse of a computerTruncation Errors

J. von Neumann and H.H. GoldstineNumerical Inverting of Matrices of High OrderProceedings of the American Mathematical Society,188-202,1947

Stability

The requirements of economic theory cannot be met by even the most precise

digital computer.

K.V. Velupillai, Computability, Complexity and Constructivity in Economic Analysis, Blackwells, 2005, pg. 160.

How to Solve the problem?

InductionProblem of Reductio solved if

1. the evidence for the inductive inference is characterised recursion-theoretically;

2. the mathematical rules confirming the evidence are also specified as algorithms.

Simulation