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.