Oodwin Model

‘The appearance,’ writes [Thalberg], ‘of yet another study dealing with Keynes’ General Theory does not, of course,

make the air electric with expectancy.’ This, I fear is true, but in this slender volume Mr Thalberg has given us a

very neat and interesting account of an aspect of the Keynesian system.’ Amartya Sen, Review of A Keynesian Model Extended by Explicit Demand and Supply Functions for Investment Goods by B.Thalberg, EJ, Vol. 73, Mar., 1963.

ASSRU Newsletter Date September 15, 2012 Vol. 2, # 1

ASSRU Newsletter July 15, 2013 Vol. 3, # 1

Algorithmic Social Sciences Research Unit (ASSRU)

In Memoriam Björn Thalberg (1924-2013)

Björn Thalberg belonged to the interregnum –

the enlightened generation of economists of the

Golden Quarter Century of Keynesian

Economics and its policy successes: 1947 –

1972. The generation that had a complete

mastery of the ‘four’ (actually six) defining

classics of the age of the neoclassical synthesis:

Value and Capital by John Hicks, the

Foundations of Economic Analysis by Paul

Samuelson, Money, Interest and Prices by

Don Patinkin and Roy Allen’s ‘trilogy’ on

Mathematical Analysis for Economists,

Macro-Economic Theory and Mathematical

Economics.

This mastery was built on the foundations of

what I have come to call the ‘Oslo Tradition’* –

that which was built on the outstanding

pioneering works by Ragnar Frisch, Trygve

Haavelmo and, later, Leif Johansen, to which

adding the name of Jan Tinbergen, Bent Hansen

and Herman Wold was only natural, at least as

far as Thalberg’s own intellectual building

blocks were concerned.

These were unusually solid foundations and

students of my generation, who did not foresee

the demise of the neoclassical synthesis, were

privileged to be taught – particularly in

macroeconomics – the concepts and tools that

were not only considered necessary for

disciplined thinking , but also absolutely

essential for an enlightened approach to active

economic policy.

Thalberg’s own interests in, and fundamental

contributions to, Macrodynamics, Methods of

mathematics in macroeconomics, Econometrics,

Computationally underpinned simulations and

Nonlinear endogenous business cycle theory

were the result of his intellectual – direct and

indirect - inspirations from the teachings and

writings of Ragnar Frisch, Trygve Haavelmo,

Richard Goodwin, Roy Allen and A.W.Phillips

(in his stabilization policy incarnation) most

directly, and indirectly from his mastery of the

classics by Wicksell and Keynes.

Because he was such a humble, old fashioned

(in all its good and decent senses), scholar-

gentleman, because he – like Schumpeter –

never referred to his own work during the

lectures I had the pleasure and privilege of

attending, it was only with some effort that I

came to realize how masterly his knowledge of

the General Theory was (as amply testified by

Sen’s above sensitive and characteristically

scholarly review of Thalberg’s elegant yet,

sadly neglected, Keynes Booklet).

I trace a development of his macrodynamics, from

the Haavelmo-inspired ‘Mod K’ of the early

1960s, to the Extensions of the Goodwin Model, of

the mid-1960s, to, finally, the ‘stabilization’ phase

determined by forging the above two rich

formalizations to a framework which generalized

Phillips’ EJ contributions of 1954 & 1957.

On the way, explicit considerations of delivery

lags and order-book timings (from the Corfu

Conference to ‘Mod K’), ‘time-to-build’ and the

important supply considerations in both

consumption and investment goods productions,

intractable nonlinearites tamed by simulations, at

least pro tempore, and finally, those transparent

policy themes that Phillips embodied in the

MONIAC, were all part of the classy lectures on

advanced macroeconomics we were privileged to

follow, in our graduate studies in the department

of economics at the University of Lund.

*Thalberg is reluctant to call this ‘tradition’ a ‘school’ in

the sense in which one refers to the ‘Stockholm School’,

is unfortunately in terms of a reference to a specious

characterization attempted by Björn Hansson in his

seriously deficient study, based on his deeply flawed

Cambridge doctoral dissertation. He, and others, who

indulge in referring to a ‘Stockholm School’ forget that

the two important contributions to the monetary theory,

being forged by Wicksell’s younger followers, led by

Lindahl and Myrdal of a senior generation and

continued by Hammarskjöld, Lundberg, Alf Johansson,

Ingvar Svennilsson and Bent Hansen of a younger

generation, were NOT part of this group: Ohlin &

Palander, who added the appellation ‘Stockholm’

(against the explicit protests of the above younger

generation). I develop these themes in my forthcoming

essay, Hammarskjöld, Wigforss & Ohlin.

The four Professors during Velupillai’s years, in the

late 1970s, in Lund:

Ingemar Ståhl, Bo Södersten, Björn Thalberg & Bengt Höglund

Velupillai & Thalberg at the latter’s home, in Lund, Christmas 1979

The ASSRU Logo From L to R (Clockwise):

Turing, Simon, Brouwer, Goodwin, Sraffa & Keynes

Page 2 ASSRU NL v.3 #1

Thalberg’s fundamental work in macrodynamics was inspired and influenced by the pioneering contributions of his teachers, Frisch & Haavelmo, and his distinguished contemporaries, Goodwin and Phillips – the latter two on nonlinear cycle theory and macroeconomic stabilization policy. Leif Johansen’s influence was of an entirely different ‘dimension’.

Thalberg’s last letter to me, in response to my request for a brief note on remembrances of

his years at Cambridge, with Goodwin and the Phillips Machine.

Festschrift in honour of Thalberg

Thalberg’s ‘Extension of the Goodwin Model’ Phillips Stabilization in a Keynes-Goodwin Model

Björn Thalberg’s wonderful lectures on macroeconomics which I

had the pleasure and privilege to attend as a graduate student at

Lund, in Spring 1972, were seriously underpinned by an appeal

to the ‘correspondence principle’. Coming from an applied

mathematics background, with emphasis on the mathematical

methods of physics – in the Hilbert-Courant tradition – I was

astonished to discover that there was such a thing also in

economics – knowing, till then, only the famous Niels Bohr

version which was formulated to reconcile classical and quantum

physics. It was, therefore, quite natural for me to mention the

‘correspondence’ between the two versions, the Bohr and the

Hicks-Samuelson formulations, in an appendix to my ‘essay’ for

Thalberg’s course. Imagine my surprise, when I received a

meticulously annotated ‘essay’ back, with a suggestion that I

write up the appendix so that Thalberg could get it published in

the Swedish Journal of Economics – which he did, in 1973!

Of all my own work, the ones that Thalberg found most

satisfying were those that built on the Frischian tradition of

decision models, framed so as to facilitate interactions between

an economic theoretical modeller and an actual politician, like a

Finance Minister*.

Thalberg’s almost passionate allegiance to Leif Johansen, as a

scholar of impeccable integrity – matching his own – was most

elegantly and persuasively evident in his long and thorough

survey of his great Norwegian contemporary’s contributions to

economics, published in 2000 in the Norsk Økonomisk Tidsskrift.

The 157 page document – and this brings the story only till

December, 1961 - is meticulously detailed and is also a reflection

on the Oslo Tradition in which he and Leif Johansen were

schooled. The most impressive feature of this study is the

sympathetic, yet wholly objectively argued, endorsement of Leif

Johansen’s vast and varied visions of economics, economic

theory and applied economics. This is particularly so for Leif

Johansen’s two enduring contributions to macroeconomics – his

‘Putty-Clay’ model and the path-breaking monograph on A Mutli-

Sectoral Study of Economic Growth**

.

The thoroughness is strengthened by detailed quotations even

from Leif Johansen’s Cambridge diaries***

.

Page 3 ASSRU NL v.3 # 1

. *Hicks, in a letter to me of 23 December, 1983, wrote,

regarding what he called my ‘Frischian paper’: ‘The paper you

sent me made me think of Dobb Lindahl and Wigforss (I once

had lunch with them together). No doubt Frisch had someone

in Norway with whom he could have similar relations.’ A

reading of this letter gave Thalberg immense pleasure. **

Thalberg was careful to attribute the false claim that this

classic study was the pioneering contribution to what came to

be called CGE modelling, to Lars Begman. I have discussed

this, and related false claims, in my detailed simulation paper

dedicated to Thalberg (OUP, 2013). CGE modelling, linking

the Brouwer fix point theorem to a (Walras)-Arrow-Debreu

equilibrium, was the creation of Uzawa and Scarf (see my

forthcoming EPW paper, too). ***The entry for 6/11/1958 gave me particular pleasure: ‘The

Department had a visit by A.W. Phillips from London who

gave a talk on ‘Buffer stocks and price stabilization. …

Kaldor, Joan Robinson, Goodwin and Meade, among others,

were present. Kaldor tried to steal the show, J.R was not easy

to follow. Goodwin was the one who understands all and was

always ready to intervene in a supportive way.’ (My

translation from the original Norwegian; italics added). It gave

me enormous satisfaction to write my JEBO paper of 1993,

linking Goodwin’s classic Growth Cycle with Leif Johansen’s

Classical Model of Growth, both published in the Dobb

Festschrift.

Leif Johansen, the Correspondence Principle and Frisch’s Decision Models

Almost exactly forty one years ago, on

1st July, 1972, I was appointed a ‘3:e

Amanuens’ – the lowliest level of the

academic rung - in the department of

economics, at the University of Lund. I

never had the slightest doubt that it was

entirely due to the fact that Björn

Thalberg, as head of the department of

economics, opted for me. It was my first

ever academic appointment and finally

gave me the chance to devote all of my

time to economic studies. Till then, I had

worked as a cement factory labourer, in

the far south of Sweden – in Limhamn –

often 16 hours on every formal holiday,

living in the factory barracks.

He even ‘engineered’ a temporary

appointment for me, as an ‘Acting

Professor’ for the princely period of 8

weeks! No doubt this left lingering

bitterness in the tongues of many of my

more senior colleagues in Lund, which

was not slow in manifesting itself very

shortly and led to my eventual peripatetic

life.

The initial lowly appointment was the

beginning of my lifelong indebtedness to

Thalberg, as I look back now, at the

academic and intellectual trajectory my

wandering life has taken.

The topics on which I gradually began to

work on were all based on the seeds that

were planted in those early years under

Thalberg’s enlightened guidance.:

Macrodynamics, capital theory, growth

theory, the theory of economic policy,

history of economic thought,

mathematical methodology in economics,

computationally underpinned simulation,

Brief Personal Reminiscences

Page 4 ASSRU NL v.3 # 1

optimal control & dynamic programming

and, above all, nonlinear endogenous

business cycle theory. The worlds of

Frisch, Haavelmo, Keynes, Goodwin,

Samuelson, Leif Johansen and Phillips

loomed large in the visions I was carving

for myself, sitting and learning at his noble

feet.

Alas, his enthusiasm for Econometrics, in

the Haavelmo tradition, never left any

trace on my intellectual development.

From 1980 for the next 33 years, till

almost the eve of his death, I kept in touch

with him, via old-fashioned penned letters

on paper and card, telephone and, as times

changed, by means of e-mails. He visited

me in London, Florence and Galway.

One day, just before his official

retirement, he came home to me,

unannounced, in the Skalderviken, bearing

a ‘kranskaka’. He wanted to persuade me

to apply for his Chair. I was reluctant, but

agreed, just to please him. Of course, I did

not succeed, nor did I expect to do so. In

the path to that failure – one of many in

Lund - I also learned, through him, how

dormant viciousness had reared its

Caliban head, in the form of rumours,

spread by two of my former colleagues:

Göte Hansson and Björn Hansson. It

pained him, later, to ring and inform me of

their Iago-like deed – and to ‘name’ them.

It was one of three occasions when he

expressed his sadness, in his reserved way,

at not being able to ‘protect’ me, in Lund.

I considered my friendship with Thalberg

one of the jewels that crowned my life –

both personal and intellectual.

‘One day in [Autumn]

1971 Vela appeared at

my lectures in Lund. A

few days later we met in

the street and talked

together a long time. ..

He had arrived in

Sweden .. in 1970,

where he … worked as a

labourer at a cement

factory, and did at the

same time attend classes

in Swedish. .. One day in

Kyoto he came across

Gunnar Myrdal’s Asian

Drama and became so

fascinated that he

decided to go to Sweden.

Many years later Myrdal

got wind of the story

and they had several

long conversations in

Stockholm.’ Thalberg (in the Festschrift ed., by

Zambelli, Routledge, 2010, p.287)

A card from BT to KV, from the Norwegian fjords & a letter from Lund to Florence, BT

to KV

Three books on themes central to the research

program and methodology of ASSRU, were

edited by affiliated members of ASSRU

including chapters by Velupillai and Velupillai &

Zambelli, during the academic year 2012/13:

I. Velupillai’s comprehensive chapter on

Postkeynesian Precepts for Nonlinear,

Endogenou, Nonstochastic, Business

Cycle Theories is included in Vol. 1 of

The Oxford Handbook of Post-

Keynesian Economics, Edited by G.C.

Harcourt & Peter Kriesler, Oxford

University Press, 2013.

II. A Computable Universe:

Understanding Computation &

Exploring Nature as Computation,

edited by Hector Zenil, with a Foreward

by Sir Roger Penrose, World

Scientific/Imperial College Press,

December/January, 2012/13.

III. Irreducibility and Computational

Equivalence: 10 Years After

Wolfram’s A New Kind of Science,

edited by Hector Zenil, Springer, 2013.

‘Now we are Four’

The four ‘surviving’ ASSRU members, at Velupillai’s home, on

the occasion of his 65th birthday.

The following articles have been published in

2012/13 by the resident members of ASSRU:

1. A Nonlinear Model of the Trade Cycle:

Mathematical Reflections on Hugh

Hudson’s Classic, K. Vela Velupillai, V.

Ragupathy & Stefano Zambelli,

Australian Economic Papers, Vol. 52 ,

2013.

2. Turing’s Economics: A Birth Centennial

Homage, Economia Politica, Vol. XXX,

#1.

3. A Journey Through the Corridors of a

Labyrinth, Interdisciplinary Journal of

Economics and Business Law, Vol. 2,

Issue 2, 2013.

4. Foley’s Thesis, Negishi’s Method,

Existence Proofs and Computations, in:

The Festschrift in Honour of Professor

Duncan Foley, edited by Lance Taylor,

Armon Rezai and Thomas Michl,

Routledge, London, 2013.

ASSRU Publications and Editorial Activities 2012/13

Page 5 ASSRU NL v.3 # 1

5. Three Notes on Alan Turing’s

Contribution to Emergence,

Problem Solving and

Constructive Mathematics: a. Reflections on Wittgenstein’s

Debates with Turing during his

Lectures on the Foundations of

Mathematics (pp. 77-79);

b. Turing on Solvable and

Unsolvable Problems & Simon

on Human Problem Solving (pp.

339-342);

c. Four Traditions of Emergence:

Morphogenesis, Ulam-von

Neumann Cellular Automatas,

the Fermi-Pasta-Ulam Problem

and British Emergentism (pp.

759-762);

By K. Vela Velupilllai in: Alan

Turing – His Work and Impact,

edited by S. Barry Cooper & J.

van Leeuwen, Elsevier Science,

2013.

6. The Relevance of Computation

Irreducibility as Computation

Universality in Economics by K.

Vela Velupillai, in: Irreducibility

and Computational

Equivalence: Wolfram Science

10 Years After the Publication

of A New Kind of Science,

edited by Hector Zenil, Springer,

2013.

7. Computability and Algorithmic

Complexity in Economics by K.

Vela Velupillai & Stefano

Zambelli, in: A Computable

Universe: Understanding and

Exploring Nature as

Computation, edited by Hector

Zenil, World Scientific/Imperial

College Press, 2012/13.

Visions

“If a complex structure is completely unredundant …. then it is its own simplest

description. We can exhibit it, but we cannot describe it by a simpler structure.”

Simon, 1962, p. 478; italics added.

Thus, Herbert Simon signalled one aspect of the basis of his approach to

complexity theory, in terms of what later came to be called Kolmogorov

Complexity. It is not surprising, after all Ray Solomonoff who, together with

Kolmogorov and Chaitin is considered one of the founding fathers of this approach

to complexity, presented his original paper on the subject at the famous Dartmouth

Conference.

Moreover, the setting of an evolving hierarchical system, in which Simon placed

this concept of complexity to fruitful use, was also underpinned by the notion of

near decomposability – culled, in the early 1950s, by Simon, from Goodwin’s

notion of unilaterally coupled, vertical and horizontal markets.

In addition, Simon was never an adherent of either untrammelled reductionism or

of fashionably emergent holism (cf, Simon, op.cit., p. 468).

Finally, the evolution of complexity, whether in hierarchic or other systems, in

space and time, was – for Simon – a special case of Human Problem Solving,

which was also the basis for his fundamental contributions to a theory of design

and discovery (where his original inspiration for the role of heuristics came from

Polya’s work in the domain of mathematics).

Christopher Alexander, who was intimately acquainted with Simon’s work on

human problem solving, even at the time of his own 1964 classic, was a

reductionist, who turned into its opposite, and an advocate of a version holism in

the sense of the British Emergentists by the time he came to write his outstanding

tetralogy on The Nature of Order.

The superficial similarities between Simon’s computability theoretic approach to

human problem solving, in general, and Alexander’s entirely different problem

solving visions for design, underpinned by ‘Cartesian Rationalism’ – all of which

he explicitly disowned (see quote below) – has led unserious and unscholarly

claims on the feasibilities of a so-called modular approach to economic modelling.

Simon extolled the virtues of method; Alexander disowned method.

Christopher Alexander & Herbert Simon

Design, Discovery, Complexity & Indecomposability

Page 6 ASSRU NL v.3 # 1

http://www.assru.economia.unitn.it/

Indeed, since [Notes on the Synthesis of Form] was published, a whole academic field has grown up around the idea of “design

methods” – and I have been hailed as one of the leading exponents of these so-called design methods. I am very sorry that this has

happened, and want to state, publicly, that I reject the whole idea of design methods as a subject of study… . In fact people who study

design methods without also practicing design are almost always frustrated designers who have no sap in them, who have lost, or

never had, the urge to shape things. Such a person will never be able to say anything sensible about “how” to shape things either. Christopher Alexander: Preface to the Paperback edition (1971) of Notes on the Synthesis of Form; italics added.