Coupled Dynamics in the Phillips Machine Model of the Macroeconomy

In this paper it is claimed that the Phillips machine is a nonlinear mechanism. Phillips (1950) presented his machine as being described with a linear differential equation. In this paper it is claimed that the machine is better described with a system of nonlinear difference.-differential equations. This system itself is approximated by a set of nonlinear differential equations. This differential equations are of the Hicks-Goodwin flexible multiplier accelerator type. Consistently with this conjecture and following Phillips’ suggestion we have presented a ‘digital’ simulation of two coupled would-be Phillips machines.computable economics; flexible-accelerator, coupled dynamical systems, Goodwin, Phillips machine, MONIAC

Technological Progress in Italian Regions: Some Comparisons

In this paper we study technological progress in a set of representative Italian regions. The analysis is conducted using input-output data. We construct the technological frontiers and calculate new indices of technological progress (see Fredholm and Zambelli 2009 and Zambelli and Fredholm 2010). The empirical results are robust and seem to be interesting. We find, for the years 2001 and 2004 that Trentino and Sicily are the regions, among those examined, with the largest number of technologically advanced productive methods, while Veneto and Lombardy are characterized by poor relative technological performance. Given the micro data about observed productivity this result is, at first, surprising, but we provide an interpretation. In the case of the Trentino region the technological progress is actually exploited so that the region is near to full employment and the income generated is relatively high. In the case of Sicily our results show that there is a great potential for growth which is not exploited. Veneto and Lombardy seem to be cases in which the embodied technological progress is not high, this indicates, ceteris paribus, a low potential for future growth or, alternatively, that the development has occurred in the past. Good performance is also indicated by Emilia Romagna.Technological Progress, Technological Frontier, Productivity, Regional Economy

An Algorithmic Measurement of Technical Progress

In this paper we propose a measure of technological progress which is based on the information embedded in standard input-output tables. Well known duality properties enables one to establish a connection between the quantities necessary as inputs and the associated output and some auxiliary prices (like the wage-profit curves). We claim that properly tailored wage-profit frontiers may provide a basis for the measurement of technological progress. But the computation of these wage-profit frontiers is not trivial. A brute force algorithm for the computation of the wage-profit frontiers has high combinatorial complexity that would make its precise computation intractable. But thanks to an efficient algorithm that we have been able to devise we can now compute it. We consider this to be an important and original contribution. Here we present and apply this algorithm. Due to this improvement we can now use these wage-profit frontiers as benchmarks against which to measure technological progress: two new indices have been defined. These new tools have have been applied to the OECD input-output data 1970-2005 and the reslts are presented here.Technological Change, Convergence, Input-output analysis, Technological Frontier, Computational Techniques

Continuity, Discontinuity and Dynamics in Mathematics & Economics - Reconsidering Rosser's Visions

Barkley Rosser has been a pioneer in arguing the case for the mathematics of discontinuity, broadly conceived, to be placed at the foundations of modelling economic dynamics. In this paper we reconsider this vision from the broad perspective of a variety of different kinds of mathematics and suggest a broadening of Rosser’s methodology to the study of economic dynamicsContinuity, Discontinuity, Economic Dynamics, Relaxation Oscillations

The Epistemology of Simulation, Computation and Dynamics in Economics Ennobling Synergies, Enfeebling 'Perfection'

Lehtinen and Kuorikoski ([73]) question, provocatively, whether, in the context of Computing the Perfect Model, economists avoid - even positively abhor - reliance on simulation. We disagree with the mildly qualified affirmative answer given by them, whilst agreeing with some of the issues they raise. However there are many economic theoretic, mathematical (primarily recursion theoretic and constructive) - and even some philosophical and epistemological - infelicities in their descriptions, definitions and analysis. These are pointed out, and corrected; for, if not, the issues they raise may be submerged and subverted by emphasis just on the unfortunate, but essential, errors and misrepresentationsSimulation, Computation, Computable, Analysis, Dynamics, Proof, Algorithm

Computability and Algorithmic Complexity in Economics

This is an outline of the origins and development of the way computability theory and algorithmic complexity theory were incorporated into economic and finance theories. We try to place, in the context of the development of computable economics, some of the classics of the subject as well as those that have, from time to time, been credited with having contributed to the advancement of the field. Speculative thoughts on where the frontiers of computable economics are, and how to move towards them, conclude the paper. In a precise sense - both historically and analytically - it would not be an exaggeration to claim that both the origins of computable economics and its frontiers are defined by two classics, both by Banach and Mazur: that one page masterpiece by Banach and Mazur ([5]), built on the foundations of Turing’s own classic, and the unpublished Mazur conjecture of 1928, and its unpublished proof by Banach ([38], ch. 6 & [68], ch. 1, #6). For the undisputed original classic of computable economics is Rabinís effectivization of the Gale-Stewart game ([42];[16]); the frontiers, as I see them, are defined by recursive analysis and constructive mathematics, underpinning computability over the computable and constructive reals and providing computable foundations for the economist’s Marshallian penchant for curve-sketching ([9]; [19]; and, in general, the contents of Theoretical Computer Science, Vol. 219, Issue 1-2). The former work has its roots in the Banach-Mazur game (cf. [38], especially p.30), at least in one reading of it; the latter in ([5]), as well as other, earlier, contributions, not least by Brouwer.

Computation in Economics

This is an attempt at a succinct survey, from methodological and epistemological perspectives, of the burgeoning, apparently unstructured, field of what is often – misleadingly – referred to as computational economics. We identify and characterise four frontier research fields, encompassing both micro and macro aspects of economic theory, where machine computation play crucial roles in formal modelling exercises: algorithmic behavioural economics, computable general equilibrium theory, agent based computational economics and computable economics. In some senses these four research frontiers raise, without resolving, many interesting methodological and epistemological issues in economic theorising in (alternative) mathematical modesClassical Behavioural Economics, Computable General Equilibrium theory, Agent Based Economics, Computable Economics, Computability, Constructivity, Numerical Analysis