Paper for the Summer Meeting of the Econometric Society, Duke University,
June 21-24, 2007.
Session: History of econometrics
Ragnar Frisch’s conception of econometrics
by
Olav Bjerkholt and Ariane Dupont
1. Introduction
Ragnar Frisch has arguably a stronger claim on the meaning of econometrics than anyone else.
He coined the term (in French) in his very first essay in economics, Sur un problème
d’économie pure (Frisch, 1926a).1 The term itself may naturally be read from its Greek
etymological origin as “measurement in economics.” The opening lines of his essay ran as
follows:
“Intermediate between mathematics, statistics, and economics, we find a new discipline which
for lack of a better name, may be called econometrics. Econometrics has as its aim to subject
abstract laws of theoretical political economy or “pure “economics to experimental and
numerical verification, and thus to turn pure economics, as far as is possible, into a science in
the strict sense of the word.” (Frisch, 1971a).
The definition was thus motivated by a desire to “turn economics … into a science.” Frisch’s
concept of a science was contemporary physics, not least the theory of relativity. Scattered
remarks he made various places indicated that for economics to become a science it should
adapt and adhere to the principles and procedures of modern physics, which in Frisch’s
formative years had made spectacular advances.2 Note also that Frisch does not really propose
a new discipline, econometrics exists and is to be found “intermediate between mathematics,
statistics and economics.” He mentioned the great interest in econometric research in recent
years. The proposed new term should rather serve to delineate what was scientific in
economics from what was not.
That econometrics aimed at “subject abstract laws … to experimental and numerical
verification” could reasonably be read as a plea for (better) econometric methods, in the
current usage of this term. But that was only part of Frisch’s purpose. He was as much
concerned with how theory should be formulated in economics to fulfil positivistic scientific
It was discovered in 1934 that the term had been coined in German – Oekonometrie – by Pavel Ciompa in 1910,
but in the sense of book-keeping, see Bjerkholt (1998:33), cf Econometrica 4, 95.
2
A source of inspiration for Frisch in this regard must have been the lecture series given by Albert Einstein at
the University of Oslo in 1920, shortly after observations of the solar eclipse in 1919 had confirmed in a
spectacular way the predictions of the general theory of relativity. It was Einstein’s first lecture series outside
Germany about the general theory of relativity (Johansen, 2005).
1
2
requirements. That meant concepts to be given empirical meaning through operational
definitions, and statements of economic relationships to be formulated such that they at least
under ideal conditions could be tested against observations. Frisch’s conception of
econometrics in the essay might, however, be said to reside not so much in his verbal
definition as in what he actually attempted to do in his 1926 essay.
The meaning of the term econometrics later shifted to a narrower meaning: the study of
statistical method for the application of economic models. The shift was not least due to the
wartime work of Frisch’s pupil and assistant Trygve Haavelmo, who carefully titled his
treatise The Probability Approach in Econometrics to indicate that it was an approach within
the Frischian conception of econometrics. At the Cowles Commission the probability
approach, as outlined by Haavelmo, became from 1944 the core and essence of econometrics,
from then on a sub-discipline of economics.3
After the publication of his 1926 essay Frisch introduced his new term and its proposed
connotation to fellow economists, mathematicians and statisticians, resulting eventually in the
foundation of the Econometric Society in 1930, see Bjerkholt (1998). Frisch drafted the key
formulations in the Econometric Society’s constitution stating its aim as “promote studies that
aim at a unification of the theoretical-quantitative and the empirical-quantitative approach to
economic problems and that are penetrated by constructive and rigorous thinking similar to
that which has come to dominate in the natural sciences.”4 Frisch had adopted from physics
‘quantification’ as a new keyword.5 The constitution paragraph also pointed to the natural
sciences as an ideal for economics to emulate with regard to “rigorous thinking.”
Ragnar Frisch’s role in the foundation of econometrics in the 1930s is well known and his
scholarly contributions in this period are dealt with at length in the history of econometrics.6
Among the early econometricians Frisch became known for his measurement of marginal
utility, the main topic of his 1926a essay and the monograph Frisch (1932). In the history of
econometrics he is above all recognized for his propagation and impulse explanation of
business cycles (Frisch, 1933b) and for his confluence analysis cum bunch map method for
analysing simultaneous economic relationships (Frisch, 1934).7
The authors have unearthed from Frisch’s archival remains various documents which shed
more light on Frisch’s ideas and overall conception of econometrics. Among these are a series
of eight lectures on the “theory and methods of econometrics” given by Frisch at the Poincaré
Institute at the University of Paris in 1933, as well as extensive lecture notes from Yale
The Haavelmo revolution in econometrics is rendered in the history of econometrics as Haavelmo’s profound
contribution after he was no longer under the sway of Frisch and converted to probability reasoning by Jerzy
Neyman. The story is not as simple as that, it may be closer to the truth to say that Haavelmo developed his
probability approach within the framework of the econometric ideas of Frisch, cf Bjerkholt (2005,2007).
Haavelmo’s concern with the estimation of simultaneous equations and the autonomy of relations was taken over
from Frisch. Although Frisch never sketched anything in the direction of Haavelmo’s probability approach, he
was deeply concerned with probability in economics, and has somewhat unfairly been depicted in the literature
as an “anti-probabilist”.
4
The constitution was stated on the inside back cover of Econometrica for several decades.
5
That term can also be traced back to 1926 and was first used in Norwegian (Frisch, 1926b).
6
See e.g. Morgan (1990), Hendry and Morgan (1995).
7
Despite his achievements and his active role in the early econometric community, it may be argued that
Frisch’s overall econometric conception is somewhat underrepresented in the history of economics literature.
Some of his key papers became less well known as they were published only in Norwegian (even only as
mimeographs), others in little accessible publications. Frisch is also to blame as on several occasions he
promised forthcoming publications which did not appear, perhaps because he hoped for more complete and
satisfactory results, but in the end not getting around to publish at all. Leading journals also refused to publish
papers heavily loaded with mathematical reasoning, this was indeed used as an argument for an econometric
journal.
3
3
University in 1930. The Paris lectures were meant to be published by the Poincaré Institute,
but Frisch never finalized the manuscript.
These and other documents elaborate on Frisch’s scientific views, how he aimed at modelling
economics on physics by transferring methodological principles, and on the methods he
proposed for economics, such as his axiomatization of individual behaviour, his refined
explication of concepts such as static/dynamic and equilibrium, his structural modelling
approach which soon became the basis for macroeconomics, his time series methods, and his
involvement with the probabilistic nature of the real world of economics, an involvement
which stretched from practical procedures for modelling and estimation to deep
epistemological concerns. The points mentioned have to do with the formulation of theory,
explanations in economics and numerical quantification, but one can discern in Frisch’s
conception a broader role for the econometrician, covering at one end economic data and the
relationship between theory and data and at the other end policy preparation for welfare and
improvement of human conditions.
The article is part of a project to trace the construction of Frisch’s econometric
project. We try to show how he was led to define econometrics, the loosely formulated idea of
a connection of economic theory, statistics and mathematics was not a completely new idea at
the time, but Frisch gave it a more specific definition. It is his originality in this endeavour
that we want to emphasize to shed light on the coherence of Frisch’s works and to grasp the
econometric vision driving his research program and underlying his efforts to found the
Econometric Society, cf Dupont-Kieffer (2003).
In order to grasp the essence of the Frischian definition of econometrics we follow
the steps which structured his research program. During his first years Frisch worked towards
showing how econometrics could be done and practiced. His aim was to integrate in
economics an empirical approach around the notions of measurement and structure. He
opened thus for modelization, requiring the construction of the bridge between economic
theories and observational data. The construction was based on the firm belief that “reality”,
e.g. as represented by statistics, could not be understood without a theoretical framework.
Frisch argued for axiomatics as a foundation for the measurement of marginal utility. The
model became the venue for the articulation of economics, mathematics and statistics. To
build up econometrics on a methodology of modelization resulted in Frisch’s attempts to draw
a borderline between econometrics and quantitative empirical economics (as developed by the
American institutionalists).
A part of the article is devoted to retracing the steps that led Frisch towards
proposing the propagation-impulse model. The latter is not only a response to the question
raised by the decomposition of time series about the nature of business cycles. It is also about
showing that the choice of the accelerator is not circumstantial but the outcome of a reflection
over the role of investment in the formation and development of fluctuations, and even more
the result of a research for an explanation of the deviation of the economic system from its
equilibrium position. To a considerable extent we let Frisch’s views be conveyed by his own
statements.
2. The making of an econometrician
Frisch was an only child and destined to take over the Frisch family’s jeweller shop in Oslo.
He excelled in school and while he was in training to become a silversmith he also followed,
at his mother’s suggestion, the two-year program in economics at the University of Oslo.
When he had completed his probation work as a silversmith his father made him partner in the
business, which made Frisch relatively well off and allowed him to be a silent partner while
4
he pursued his scientific interests. He was abroad for almost three years, mostly in Paris,
where he without being enrolled in any study delved deeply into mathematics and statistics
and mingled with French mathematicians, statisticians and economists.
At the end of his stay in Paris Frisch may have regarded himself more as a statistician than as
an economist. He published some papers in mathematical statistics in the early 1920s and took
part in an international mathematical congress in 1925. After his return to Oslo he submitted a
doctoral dissertation in mathematical statistics, and defended it at the end of 1926, the first
dissertation in statistics at the University of Oslo (Frisch, 1926c). Frisch had planned a final
chapter in the dissertation that he in the end left out, with only a trace in the conclusion of
what he had wanted to discuss in it:
The inverse problem: how to reconstruct from an empirical distribution the scheme, which has
given birth to the observed distribution, is a problem of a rather different kind. To deal with it
in depth one cannot avoid entering into philosophical issues and in particular into the theory of
knowledge. It seems to us that too often the scholars in statistics and mathematics have refused
to enter into these philosophical issues, instead confining themselves only to deal with
technical questions. That is the reason in our opinion why the critical interpretation of the
foundation and the methods of statistics has not kept in step with the development of
techniques and the increasing range of applications of our discipline in the social as well as in
the natural sciences. (Frisch, 1926c, transl. by the authors).
Exactly what Frisch had in mind when he wrote this, is not easy to say, but his observation
suggests a key role for statistics not only in the analysis of empirical data, but perhaps also in
the theoretical understanding of the real world. Was there an influence from the role of
uncertainty in quantum mechanics? Was there already a concern with the limitations of our
knowledge of the outer world when observations have been contaminated by stochastic
disturbances (cf. section 8)?8
Frisch was clearly concerned about profound methodological issues but dealt with them at
times by throwing around catchphrases like “… theoretical economics is about to enter the
phase of development at which natural sciences, particularly theoretical physics long have
been, the phase in which the theory gets its concepts from the observational technique”
(Frisch, 1926b; Frisch’s emphasis). He added that experiments or observations that served as
a foundation for the definition of concepts did not have to be workable at present, for the
logical definition it would suffice that they were workable in principle, existing as a logical
construction, similar to the light signal experiments in the theory of relativity. 9
Among scholars Frisch studied in Paris was Irving Fisher, whose 1891 dissertation he studied
in a French edition (Fisher, 1917). He shared with Fisher the idea that to achieve a more
scientific economics it was necessary to adapt the principles and methods of the natural
sciences. Frisch and Fisher were, however, one generation apart and their respective
references to physics may have had a similar gap, Fisher still in a Newtonian world, Frisch in
the age of relativity. They were, however, on similar tracks in trying to make the elusive
concept of utility subject to empirical estimation.
In the preface to the 1925 reprint of his dissertation Fisher wrote the following: “The
suggestion in this booklet that so-called “marginal utility” may be measurable statistically is
now being followed up. Within a few months, I expect to publish the first attempt of this sort
8
Frisch left notes about the omitted chapter with title suggested as Le problème inverse, Contingence et
causalité, Etude sur la conception statistique des connaissance humaine et sur les fondements de la statistique
mathematique. Frisch confronted an “inversion problem” in his business cycle project, see section 7.
9
After this references to physics Frisch hastened to add that there were differences in the research method. “The
methods of natural science cannot without reflection be copied for use in economics.” Frisch (1926b: 302-303).
5
and to discuss its possible practical use in deciding on the proper rate of progression for an
income tax.” Fisher published his attempted statistical of marginal utility in a festschrift for
John Bates Clark (Fisher, 1927). While Fisher was proofreading this paper in 1926 he
received a reprint of Frisch (1926a), sent to him by Frisch who until then had not been in
touch with Fisher. Fisher recognized immediately that Frisch had hit upon a more promising
method than his own and hastily wrote a note to be attached to his own paper when it was
distributed as a reprint, to notify American readers of the achievement of the unknown
Friosch from Norway.
In Frisch (1926a) the purpose of the essay was stated as “an attempt to realize the dream of
Jevons.”10 Frisch postulated additivity and separability properties of the utility function that
allowed him to estimate the demand function for sugar, as well as, and more important, the
marginal utility of income (as a function of income), using household data from a cooperative
association in Paris. Although Frisch had taken a cue from Jevons, a more direct impetus for
his study had come from Irving Fisher, who in his dissertation had outlined how the
measurement of utility could be solved, adding: “To do this statistically is of course a more
difficult, though by no means hopeless proceeding.”11 Thus the parallel efforts of Fisher and
Frisch both originated in Fisher’s 1892 dissertation.
Frisch’s estimation technique in 1926 was not impressive with regard to statistical techniques,
but the point he wanted to bring home was the measurability of marginal utility when guided
by theory.12 The primacy of theory was one of Frisch’s main tenets, analysis of economic data
was futile unless it was inspired and led by theory. Or as he stated it more spectacularly: “The
observation material is and remains a dead mass until it is animated by a constructive
theoretical speculation.”13
In February 1927 Frisch went to the U.S.A. with a Rockefeller fellowship. He met with Irving
Fisher for the first time. He asked him and Allyn Young for lists of people who shared his
interest in what he had defined as econometrics and tried to meet with them all. They were not
that many.14 Naturally, he took the opportunity to promote Divisia’s and his own idea of an
econometric association, it was a European idea but its realization would at the end take place
in the USA.
During the year he stayed in the USA he completed two treatises, during that year, both
reflected his emphasis on statistics as the key to a more scientific economics. One was The
In Jevons’ Theory of Political Economy from 1971 Jevons had stated:
… the price of a commodity is the only test we have of the [marginal] utility of the commodity to the
purchaser, and if we could tell exactly how much people reduce their consumption of each important
article when the price rises, we could determine, at least approximately, the variation in the final degree
of utility – the all-important element in Economics. (Quoted from Chipman (1998:59).
11
Fisher (1925: 20). In Frisch’s copy of the French edition he had underlined the corresponding sentence:
“Quant à l’établissement de cette courbe en conformité de données statistiques, c’est une autre affaire et bien
plus difficile, quoiqu’il n’y ait nullement lieu de désespérer de sa réussite.” Fisher (1917:24), cf. Bjerkholt (1995:
xxiv-xxv).
Frisch’s ambition to measure the marginal utility of income had been foreshadowed in his exam paper on
taxation issues in 1919, containing the following bold passage: “Man must not be afraid of what seems
impossible to do. History has shown that human beings possess a wonderful gift of being able to obey the saying
of Aristotle : ‘measure the nonmeasurable!’” (Andvig & Thonstad, 1998:6).
12
Frisch’s theoretical assumptions were more restrictive than he realized at first, as they implied homotheticity,
as shown by Burk (1936). The full story is told in Chipman (1998:59-67).The interest in “measurement of
marginal utility” which in Frisch’s version implied cardinality, waned after the rediscovery of Slutsky (1915)
and the demand revolution in the mid-1930s.
13
Frisch (1931a), translated by the author.
14
Allyn Young provided a list of “practically everyone in the field of mathematical economics”, the list
contained eight names, see Bjerkholt (1998:33).
10
6
Analysis of Statistical Time Series (Frisch, 1927) and the other the Correlation and Scatter
essay on the analysis of multidimensional economic data (Frisch, 1929a). Both treatises were
critical of current practices. Frisch may at the time have been one of very few aware of the
problems related to empirical analysis of economic time series data due to their nonexperimental character and simultaneity of economic relationships.
Frisch (1927) was a treatise on methods of time series analysis, critical of the current methods
in use for of determining trends and cycles in economic time series data. Frisch argued against
“total methods” for determining the components of a time series, such as Fourier analysis and
periodograms, in favour of “differential methods” to be applied in the environment of a single
point, see Morgan (1990: 83-90). Frisch’s point was that economic cycles were changing in
their characteristic properties and “total methods” were bound to fail. Frisch (1927) was never
properly published, but Frisch summarized the main ideas in Frisch (1928), introducing the
term changing harmonics to express the idea of changing cyclical properties, using an
analogy from mechanics to make his point:15
Suppose we have a chain of n pendula: To a long pendulum with a great mass is attached a
much shorter pendulum with a much smaller mass, and so on. Suppose the whole system is in
movement in a field of gravitation whose intensity is slowly changing. The length of the
individual pendula may also be slowly changing. The fluctuations of the lowest pendulum
measured from the vertical through the point of suspension of the system, is given. The
problem is to determine the individual components, i.e. determine the fluctuations of each
pendulum measured from the vertical through its own point of suspension. (Frisch, 1928: 231).
If the interval of observation was long enough to encompass a significant change in the
intensity of the gravitational field or in the length of the pendula, no kind of curve fitting with
constant period sine functions would be successful. In particular the harmonic components
determined by ordinary harmonic analysis would have no real significance. This use of a
physical model or analogy is yet another example of Frisch following in the footpath of Fisher
whose dissertation was amply illustrated by pictures of Fisher’s constructions of mechanic or
hydraulic models. They had similar inclinations to think in terms of physical analogies to
visualize an economic mechanism. When drawing on analogies with physics Frisch hastened
to add that “…the methods of natural science cannot unreflectedly be copied for use in
economics.” Frisch (1926b: 302-303).
The appearance of Slutsky (1927) during Frisch’s visit to the U.S.A. in 1927 came to have
crucial inspirational influence on his thinking about how cycles were created and maintained,
namely. Slutsky wrote in Russian but the five page English summary conveyed the main
point of the paper, namely “to show that cyclic processes may originate owing to a summation
of the mutually independent chance causes, and that these chance waves may show a certain
regularity being an imitation, in a lesser or greater degree, of the strictly periodical
fluctuations” (Slutsky, 1927: 156). Slutsky’s assertion that manipulation, such as smoothing
of statistical data by moving averages, could generate artificial waves, appealed immediately
to Frisch, thinking of an economy as represented by a (linear) dynamic structural model
exposed to stochastic shocks.
The Rockefeller fellowship was for three years, of which Frisch had planned to spend the last
two in Europe. But shortly after Frisch’s arrival in Europe Frisch’s father became seriously ill
and later died. This put Frisch’s entire career in jeopardy. He surrendered the fellowship to
take care of the family business which was in dire straits. He confided to Irving Fisher in the
spring of 1929 that he was considering giving up his scientific career to take care of the
family business and his economic responsibilities. Fisher responded by arranging for an
15
Thus the idea of ‘changing harmonics’ originated in Frisch (1927b), while he coined the term later.
7
invitation from Yale University as Visiting Professor.16 Frisch arrived at Yale University in
February 1930, a visit that would last until June 1931, with decisive importance for the
development of Frisch’s scientific ideas and for the emergence of econometrics, including the
foundation of the Econometric Society half way through Frisch’s stay in the USA.
In the spring of 1931 Frisch was by a special act of the Norwegian Storting (Parliament)
called to a new chair in economics and statistics at the University of Oslo to prevent him from
accepting an offer – generously equipped with research resources – from Yale University.
After his return to Oslo negotiations with Rockefeller Foundation about the establishment of a
research institute at the University of Oslo was initiated and brought to fruition. From 1932
Frisch was director of his own Institute of Economics at the University of Oslo with research
assistants and computing equipment as he could afford, an econometric laboratory it might
well be called.
3. Axiomatics
Frisch’s axiomatic approach related to the measurement and was first set out in Frisch (1926a).
It was introduced by yet another of his theory of science maxims: “The real advances in a
science of the outside world begin on the day that it is realized that vague common sense
notions must be replaced by notions capable of objective definition.” The vague notion Frisch
referred to here was that of cardinal utility, a central, but not well founded concept in
economics. Frisch’s conception of utility adhered to those of Fisher and Pareto, both of whom
he found had contributed substantially to quantify the concept of utility. But Frisch argued
that an objective definition of utility had not yet been achieved, as the axioms on which such a
definition must be based had not been displayed. That is what he set out to do in his essay.
The axioms were simple. A central feature of Frisch’s approach to axioms for homo
œconomicus was the distinction between the initial position given as vector of economic
goods x=(x1,x2,…,xn) and a displacement (finite or infinitesimal) of the initial situation given
by a vector p=(p1,p2,…,pn). x, y and z were used for denoting initial points, while p, q, r and s
denoted displacements.
The preference comparisons in Frisch’s axiom system are between combinations of a position
with a displacement. His axioms were as given in the table below. The symbol f is used for
preferred to.
Frisch’s axioms in On a Problem in Pure Economics, 1926
Axioms relating to a given position
Axioms relating to different positions
Axiom of choice
Axiom of choice
The choice of (x,p) vs. (x,q) is always
determined as preferred or indifferent.
Axiom of coordination
(x,p) f (x,q) & (x,q) f (x,r),
16
The choice of (x,p) vs. (y,q) is always
determined as preferred or indifferent.
Axiom of coordination
(x,p) f (y,q) & (y,q) f (z,r),
It is hard to believe that Frisch after his achievements up to 1929 would consider giving up his scientific career.
Fisher was quite wealthy; he gave Yale the money for inviting Frisch and then offered Frisch a similar amount to
be his personal advisor and assistant. Fisher gave his commitment before the stock market crash which
eventually wiped out Fisher’s entire wealth.
8
implies (x,p) f (x,r)
Axiom of addition
implies (x,p) f (z,r)
Axiom of addition
(x,p) f (x,q) & (x,r) f (x,s),
implies (x,p+r) f (x, q+s).
(x,p) f (y,q) & (x,r) f (y,s),
implies (x,p+r) f (y, q+s).
(p, q, r and s infinitesimal.)
(p, q, r and s infinitesimal.)
With suitable mathematical regularity conditions added the axioms relating to a given position
determine ordinal demand functions, while the axioms relating to different positions imply
cardinality. Frisch was aware that only ordinal utility could be derived from observable choice,
but empirical observations could be extended with interview data that would provide a
foundation for cardinal utility. Frisch declared himself as an adherent of cardinal assumptions,
often with an appeal to “everyday experience”.17
Frisch’s axiomatics was by and large bypassed in the discussion of his approach to utility
measurement before WWII. One reason may have been the limited distribution of (Frisch,
1926a) but perhaps also that the idea was a little ahead of its time. Frisch’s utility
measurement effort in Frisch (1926a) got considerable attention after his monograph,
completed at Yale, appeared (Frisch, 1932), but it did not include the axiom system.18
At the joint meetings of the American Economic Association and other association in
December 1927 Frisch took part in a discussion on the “present status and future prospects of
quantitative economics,” chaired by F.C. Mills who invited Frisch to submit his statement for
publication. Frisch submitted but in the end the editor decided to publish only the statements
of the invited panelists.19 Frisch’s prepared statement is nevertheless of interest as he took the
opportunity to argue in favour of an axiomatic approach:
We speak of one statistical procedure as giving a better result than another. The idea
underlying this distinction is evidently that a statistical procedure is considered as a sort of
approximation by which we try to determine the numerical magnitude or intensity of a certain
phenomenon or the character of a certain function. … we engage in this kind of approximation
work without knowing exactly what we are trying to approximate. We engage seriously in
target shooting without having any target to shoot at. The target has to be furnished by
axiomatic economics.
The axiomatic process of target making must necessarily be rather abstract, a fact which
accounts, perhaps, for its lack of popularity in these days when it is considered quite a virtue to
disregard abstract thinking in economics. It is abstract, but neither in the sense of a logic game
nor in the sense of metaphysical verbiage, of which we have had some in economics, at times.
Axiomatic economics will construct its quantitative notions in the same way as theoretical
physics has constructed its quantitative notions. ( Frisch/Mills, 21 February, 1928, National
Library of Norway).
Frisch’s statement conveyed his critical attitude towards empirical studies of theoretically not
very well defined relationships.
17
The axioms served to quantify static utility theory, Frisch made an attempt towards developing dynamic utility
theory in Frisch (1929b).
18
Of seminal contributions on the measurement of utility in the mid-1930s such as Lange (1934), Samuelson
(1937), and Alt (1936) only Lange (1934) referred to Frisch (1926a), but without mentioning the axioms.
19
The panelists included W.C. Mitchell, E.B. Wilson and others, see Mills et al. (1928).
9
In the Poincaré lectures in Paris in 1933 Frisch put strong emphasis on an axiomatic approach
towards establishing logical and quantitative definitions for the construction of a quantitative
theory of economic relations. In the first of eight lectures, The philosophical foundations of
econometrics, the axiomatic method, utility as quantity, he presented a set of axioms which
extended the 1926 axioms. He introduced a connectivity axiom which using the 1926 notation
can be written as
If (P,a) f (Q,b) & (P+a,α) f (Q+b, β), implies (P,a+α) f (Q,b+β)
(Here P and Q were positions, a and b finite displacements (which when added to a
position defined a new position), while α and β were infinitesimal displacements.)
Another axiom was the point determination (or position) axiom, which he wrote
If (P→R) f (P→S), then (Q→R) f (Q→S)
where the comparison is between moves from one position to another, and thus the
axiom expressed that the ranking of the terminal position was independent of the
starting point.
Among the other axioms, the affinity axiom, expressed the usual integrability condition for
utility ranking derived from the 1926 axioms (in 1933 renamed as local and interlocal axioms)
to be represented by a utility function. Frisch discussed the relative independence of the
axioms and among other results proved that:
If we have connectivity, then the point determination axiom and the integrability axiom are
equivalent. But if the connectivity axiom is not satisfied, the integrability axiom and the point
determination axiom express two different things. (…) We can thus have point determination
without having connectivity and integrability. We can also have point determination with
integrability, but without connectivity. This result is perhaps surprising, but has an entirely
natural explanation if we keep in mind the fundamental role played by the connectivity axiom.
That axiom suffices to show you the kind of analyses through which we can ensure the
compatibility and independence of the various axioms. (Frisch, 1933a).
Thus this axiomatic and more general approach was Frisch’s framework for settling the
integrability issue.20
After the Poincaré lectures (which never got published) Frisch did not pursue further or
publish his work on the axiomatization of demand behaviour. He attended the Cowles
Commission Research Conference in 1937, where he gave a series of three lectures on
General Choice-Field Theory, with a sketch of a further generalization of the system of
axioms of the Poincaré lecture. The choice-field theory was introduced as “applying for
instance to the behaviour of the entrepreneurs in a capitalistic society as well to the chief of
production in a planned economy and to the housewife who decides how much to use on food,
clothing, shelter, etc.” From the six page summary in the conference report it seemed to be
more like repackaging of earlier work than new ideas. Frisch worked again on the utility
axioms at the end of the war after been released from incarceration, but this time for the
purposes of preparing a comprehensive presentation (in Norwegian) for students. It was
20
Frisch also told his French audience that this was hot issue on the other side of the Atlantic:
At the current time great efforts have been exerted by Americans such as Professors Schultz, Hotelling
and Davis and by Dr Waugh, whom I have the pleasure of seeing in this auditorium, and who has been
studying theoretically and statistically the structure of choice fields, e.g. the integrability condition and
its role in the market mechanism. I believe that the axiomatic analysis of choice will give a solid base
for these kinds of studies. (Frisch, 1933a).
10
conceived (by students) as difficult stuff and dropped from the curriculum after some years.
Frisch rewrote the core part as a paper for Econometrica (Frisch, 1959).21
4. The responsibility of the econometrician
The responsibility of the econometrician was the title of Frisch’s article in Econometrica,
marking his return as editor after the war time isolation (Frisch, 1946). The article reflected
Frisch’s almost euphoric enthusiasm of being at the centre of events for the application of
econometrics after war time imprisonment and clandestine involvement with preparation of
post war reconstruction. It conveyed the impression that econometrics was indeed a tool for
solving social and economic problems.
The motivation behind Frisch’s view of the need for a more scientific economics had indeed
not been driven purely by an intellectual interest in science as a human activity. When he
lectured as visiting professor to students at Yale in the autumn term 1930 he impressed upon
his students that the need for econometrics was an issue of far-reaching consequences for
mankind’s future, in fact a matter of life and death:
“Man has proved sufficiently intelligent to create a huge economic machine capable of
producing a great variety of useful things. But he has not been sufficiently intelligent to
understand how to handle this big machine. He stands beside his big machine, not knowing
how to steer it, only hoping that the running of the machine will be not too disastrous to
him. … We may only think, for instance, of the situation, which occur again and again in the
production cycle; huge productive forces, machinery, and labor being idle at the same time as
there are millions of people who want very badly a great variety of things which could be
produced by the idle machinery and labor. Not only has man been able to create a big
economic machine which he cannot handle, but he is making it bigger and bigger and more
complicated all the time. He is constantly getting more handicapped in his attempt to steer
it. … It is a race of life and death, and man is certain to lose if he does not succeed in
developing economics into the state of a true science, that is, a study based not only on fact
collection, but also on constructive theoretical thinking.” (Frisch 1930: 3).
Frisch was not the only one with such concerns. The disastrous economic situation in 1930,
both in the U.S.A. and in Europe, gave a good opportunity for emphasizing to the students the
social importance of an econometric approach, for a better understanding of what was
happening in the economy and to do something about it. But Frisch was not opportunistic. His
conception of the econometric domain was a broad one. He presented it in his lecture in
simple language as “five types of mental activity”, see Box 1.
Box 1. Five types of mental activities in which the econometrician has to engage
1. The descriptive procedure.
One sort of question which the scientist has to answer is: What happened? What is the
situation? What course did the events follow? In order to answer these questions he has to
engage in descriptive, historical and experimental work. In some sciences, like economics,
direct experiment is more or less impossible and the scientist must rely largely on the
descriptive and historical answers to the questions here considered.
2. The understanding procedure.
Another sort of questions which the scientist has to answer is: Why did it happen? Why did
this situation exist? Why did the events follow the course they did? The answers to these
It became one of Frisch’s most cited articles. It included an appendix on integrability conditions, which was
also appended to the translation of Frisch (1926a) on Frisch (1971).
21
11
questions constitute the rational part of the investigation. By the power of his mind the
scientist tries to bring some reasonable order into the happening and the things he observed.
3. The prediction procedure.
The questions here are: What will happen? What will the course of events be in the future? In
order that this sort of questions shall have a meaning, the phenomenon must be such that it
cannot easily be controlled by man. If it can be fairly completely controlled, no forecasting
problem really exists.
4. The human purpose decision.
Here the questions are: What do we wish shall happen? What do we wish the situation to be?
The three first sorts of questions are exclusively of an intellectual character. On the contrary
the sort of questions here considered is of an ethical or moral sort. It cannot be answered
unless we adopt some sort of standard of social values. If the answer to such a question shall
be socially significant, it must, of course, in some way or another weigh the opinions of the
different individuals. It is not a question of what you or I personally think in this matter, but of
what is a socially fair position.
5. Social engineering.
The question here is: What can we do to produce such happenings or such situations? This last
sort of question is the most complicated we can ask. In order to give a significant answer to
this sort of question, we have to build on an analysis of all the first four sorts of questions.
(Frisch, 1930).
We may note in passing here that Frisch spread his life-time work as an econometrician over
all these five activities. Frisch was not a theory builder, he did not really have a theoretical
program, but he was highly concerned about the nature of theory. He was not a data collector,
but he designed national accounting systems, he was neither a forecaster nor a policy maker,
but he had strong views on how to conduct both kinds of activities, etc. Thus we find Frisch
covering all five activities, but primarily concerned with the methodology of the activity.
Although each of the five categories of activities had its theoretical components, economic
theory as such belonged under the “understanding procedure.” The whole point of theory was
to understand the real world by bringing, according to Frisch, “a rational order into things”,
by which he meant to modelization, to make a model of the phenomenon under consideration.
This may sound commonplace today, but it was not a common conception around 1930. It
was not a common procedure to model an economic (sub-)system and express is as a
determined sets of equations. Frisch introduced the idea to his student audience in the
following way:
“The observational world itself, taken as a whole in its infinite complexity and with its infinite
mass of detail, is impossible to grasp. Taken in its entirety, in its immediate for of sense
impressions, it resembles, so to speak, a jelly-like mass on which the mind cannot get a grip.
In order to create the points where the mind can get a grip, we make an intellectual trick: In
our mind we create a little model world of our own, a model world which is not too
complicated to be overlooked, and which is equipped with points where the mind can get a
grip, so that we can find our way through without getting confused. And then we analyse this
little model world instead of the real world.” (Frisch 1930: 5).
Frisch then tried to convey the essentials of the art of modelling. The model world builder is a
sovereign in the model world. He can decide which features and characteristics the model
world shall have and the relations between various phenomena in the model world, as long as
we do not break the rules of formal logic.” But are the decisions regarding the constitution of
the model world then “ruled completely by free fantasy or caprice?” No, because the model
world shall serve a purpose, it shall help to adopt a way of thinking that will “ultimately be
useful in our fight for control over nature and social institutions.” The model world shall
12
picture “those indefinable things in the real world which we might call ‘essentials’ … with
regard to our own ends.”
But are there criteria to judge if the model world conforms to this ideal. No, there are no
criteria that can be formulated as a definite logical rule:
“We have nothing except a mysterious, inborn ‘sense of smell’ which as a rule will guide us so
that we finally get on the right track. This is precisely the reason why the scientist is to be
considered as a logical sovereign in his model world. He is just like a wise, absolute monarch.
He knows that this is the only way of ultimately obtaining his ends. He listens to the
suggestions of facts but takes care to consider them as non-obligatory.” (Frisch 1930: 6).
The model world sovereign is guided, naturally, by observed empirical laws, which in
idealized form may be incorporated in the model world, like downward sloping demand
curves. But empirical generalizations might be enough:
“often the investigator will equip his model world with something more than this. By a heroic
guess, he will add something which is entirely outside the body of observation at his disposal.
It is exactly in this kind of heroic guesses, transgressing the observational facts, that the great
constructive minds distinguished themselves from the average scientific worker.” (Frisch 1930:
7).
What then was the nature of such “transobservational notions”? Frisch suggested two kinds of
such notions. One could be an object, not resembling anything from actual observation.
Another was a new relation between phenomena which by themselves were well known from
actual experience, but had never been observationally related because “the phenomena are of
such kind that they cannot be observed together directly with the given technique of
observation.” Frisch’s example of a transobservational object was drawn from physics, the
classic example of the atom. But as a transobservational relation he suggested the relation
“between the diminishing return of land and the fact that rent exists.” Both facts were known
long before Ricardo, but “the relation between them was not seen until revealed by the
abstract speculations of Ricardo,” contradicting the explanations given by the Physiocrats and
Adam Smith.
Frisch thus introduced his theory of scientific investigation, and the idea of economic
modelling, in an intuitive non-formalized way. He downplayed the distinction he had
introduced between “object” and “relation” as conventional, not one of principle. Something
which is a relation in a “microcosmic” model world might be a relation in a “macrocosmic”
model world. He then elaborated upon the need for exploring the model world. Despite the
fact that we have ourselves created it we cannot overlook all consequences, systematic
investigations of the model world are needed.
Within this framework Frisch defined empirical laws vs. rational laws, touched upon
induction and deduction, and elaborated further upon what was meant by “explanation” within
a model. He also discussed probability, sorting out various concepts of probability and hinted
at how the model itself could be formulated in a probabilistic way, leading to probabilistic
rather than necessary rational laws being derived from it. He finally discussed at some length
the concept of ‘cause’, although it was “perfectly possible to do without altogether:”
“If we strip the word ‘cause’ of its animistic mystery, and leave only that part which science
can accept, nothing is left except a certain way of thinking, an intellectual trick, a shorthand
symbol, which has proved itself to be a useful weapon, legitimate or illegitimate, in our fight
with nature and social institutions. As I see it the scientific (as distinguished from the
scholastic), problem of causality is essentially a problem regarding our way of thinking, not a
problem regarding the nature of the exterior world.” (Frisch 1930: 13).
13
At the end of his introduction he returned again to the indispensability of theory for a real
understanding of the phenomena under consideration. The phenomena often make much noise
and attract attention to things that are inessential for a real understanding, things which
“…are only apt to capture the pure empiricist and keep him at some laborious and sterile tasks
of fact getting. The key to the phenomena is very often furnished by some feature which seems
utterly unimportant from the empirical point of view. This is why the purely empirical and socalled institutional approach to economics is so dangerous. If we go to our economic or social
investigations under the motto that we shall “let the facts speak for themselves,” what we will
hear will very often be childish talk. When it comes to really understanding a phenomenon, to
gain an insight into its nature, not only to be familiar with its appearances, then the
discrimination, this mysterious sense of smell which the real theorist uses in the construction
of his model world, becomes basic. The only road to wisdom has been and will ever be to hear
all things and believe little. That is why in the deeper problems of science the crucial
contribution towards a real understanding of the phenomenon is always furnished by one of
these heroic guesses transgressing observational facts.” (Frisch 1930: 20-21).
Frisch mentioned Albert Einstein’s theory of relativity as a “grandiose example” of a heroic
guess and also Isaac Newton’s explanation of the orbit of the moon:
“In his imaginative mind he constructed a model world where bodies attracted each other with
a force proportional to the masses of the bodies and inversely proportional to the square of
their distances. He started exploring this model world and found that certain bodies would
move in certain orbits, and one of these orbits that could be computed from the law of his
model world, was the orbit of the moon. The real discovery was brought about by a brain, not
by a staff of patient observers. All the observational material would have been a dead mass if
not animated by a theorist of genius. (Frisch 1930: 22).
Business cycles had been the topic of the day for all the years Frisch had taken an interest in
economics. Large amounts been collected and analyses in business cycle institutes. In Frisch's
view a few of these laborious investigations had been “wasted because the investigations have
not been animated and directed by constructive theoretical thinking.” And even when it was
not directly wasted it did not have the assumed relevance for understanding economic
fluctuations, because the data collection for economic analysis needed to be guided by
theoretical insights.
Reading Frisch's lecture notes for the Yale lectures 1960 the thought is close at hand that
when he spoke about “heroic guesses” and “transgressing the observational facts” he had in
mind his own forthcoming contribution to the explanation of business cycles. Most likely he
had already solved in his own mind the problem of how approximately regular, maintained
cycles could be explained, but not yet written out the model that would illuminate his theory.
Frisch ended his introductory lecture with drawing a line between his own econometric
approach and economists adhering to “historical, institutional, ands similar schools in
economics”:
The idea that it should be possible to “explain” the things of this world by any other mental
process than the one built on rationality, that is, on “theory”, seem to me a fundamental naivity
of the extremists of the historical and institutional schools in economics.” (Frisch 1930: 25).
5. Innovations in the formulation of theory: modeling,
static/dynamic, conjectural and micro/macro concepts
Frisch’s general idea of modelling as sketched in the previous section was underlying his
structural modelling approach, as used in his business cycle modelling and also in the
confluence analysis, but the methodology of structural modelling was never properly
presented and published in English. Frisch’s further effort at “quantifying theory” comprised
14
various suggestions of innovations in the formulation of theoretical statements. We shall here
deal with his fairly well known attempt to give a more precise meaning and usage to the
concepts of ‘static’ and ‘dynamic’. Then we consider Frisch’s attempt to formalize market
structures and introduce conjectural actions as market behaviour, which may be regarded as
an early game-theoretic approach. For both of these we draw on Frisch’s discussion in the
Poincaré lectures. Finally, we make some remarks on the term and concept of
‘macroeconomic’ which may reasonably be regarded as having its origin in Frisch.
Frisch’s definition of statics/dynamics was motivated by the imprecise usage of these terms
and the lack of precise definition of concepts. The confused use of statics and dynamics often
reflected unclear notions about equilibrium, say that a situation was dynamic if it was out of
equilibrium. The Frischian distinction between dynamics and statics may likely have been the
outcome of the opposition between Frisch and Wesley C. Mitchell on that issue. Mitchell was
a pioneer in business cycle analysis and argued for the necessity of developing a dynamic
perspective. But in Mitchell’s historical framework for the dynamic perspective, he explained
each phase of the cycle as developing into another one, each phase characterized by
historically specific features. But to Frisch the necessity of how and why one phase turned
into another one could only be provided by an analytical perspective, not by a historical one.
The issue gave Frisch an opportunity to draw a borderline between his own econometrics and
Mitchell’s empirical quantitative economics. Attracted as he was to the subject matter of
Mitchell’s field of research, it lead Frisch to specify more clearly his own methodology,
namely structural modelling, cf Dupont-Kieffer (2001,2003).
Contrary to the institutionalist approach the new disciplinary field had, according to Frisch no
historical dimension and cannot be defined without reference to equilibrium concept.22 Indeed,
one cannot define the business cycles by reading only statistical monographs and sketching
out causal relations that might connect the objects of investigation (production, investment,
consumption, money) by the only decomposition and analysis of the statistical time series as
Mitchell and the American Institutionalists seem to do. Frisch advocated the need to interpret
statistical data within frameworks of precise theoretical hypotheses. These hypotheses
respresented by simultaneous economic relations must be statistically evaluated and
empirically tested.
Frisch’s first formulated his notion that these concepts should be used to characterize the
methods of analysis and not the phenomena themselves, in a lecture in Copenhagen in 1928.
published in Norwegian (Frisch 1929b). Perhaps recognizing that his innovation had not been
well distributed he chose it as one of the topics for the Poincaré lectures. In Frisch’s
terminology a phenomenon, e.g. an economic system could be stationary or changing, while
the model for analysing such a system could be either static or dynamic:
What will then be the difference between a static theory and a dynamic theory? I propose the
following distinction: a relation, with all variables entering into it referring to the same point
in time is a static relation, while a relation comprising variables referring to different points in
22
Dupont-Kieffer (2003, Ch.2) shows that the work of Frisch on business cycles in the late 1920s was not in
outspoken opposition to Mitchell’s work but rather muted. Frisch came out with more markedly against the
institutionalist methodology in his controversy with John Maurice Clark in 1931 (Frisch, 1931c). One should
focus especially on Frisch’s review of Ǻkerman thesis where he first distinguishes forced and free oscillations of
a system whose natural position is an equilibrium (Frisch, 1931a). This analysis is at the opposite of Mitchell’s
who was considering successive up and down waves, leads and lags without referring to the equilibrium concept
as an analytical key. The second point on which Frisch grounds his analytical point of view on BC is the
definition of dynamics (Frisch, 1929a): he defines the study of dynamics as the way by which the system moves
from one equilibrium position to another), whereas Mitchell and Burns (1946) define it as the study of the
irreversible transformations in a monetary society occurring through depressions and growths. We can speak of
an analytical dynamics in the case of Frisch and, in the case of Mitchell, we think of a historical dynamics.
15
time is a dynamic relation. A static theory will be an analysis with only static relations,
according to this definition. Likewise, a dynamic theory will be an analysis comprising at least
one relation which is dynamic in the sense I have indicated. (Frisch, 1933a, Lecture 3)
Was static analysis then to be used for stationary phenomena and dynamic analysis for
changing phenomena? No, not at all. Frisch counterpoised these two dichotomies by
attempting to show that all four combinations of them might be perfectly meaningful, i.e. (1)
static analysis of stationary phenomena, (2) static analysis of changing phenomena, (3)
dynamic analysis of changing phenomena, and (4) dynamic analysis of stationary phenomena.
In the Poincaré lecture he illuminated the issue by using both a mechanical example and an
economic example for all four combinations to drive his point home. We bypass the
mechanical example here, it was very mechanical with a rod of iron fixed at one end to a pivot
and at the other end to an iron ring, inside which there is a small ball, which can slide inside
the ring.The economic example may seem slightly contrived for a modern reader, it went as
follows.
Economic
examples
Static analysis
Dynamic analysis
Stationary
phenomena
1. Consider the demand for a given
good, assuming that the price
immediately finds its new level after a
change in the quantity. If we have found
by observation that the price rests
stationary during a certain time, then it
will be natural to introduce the idea of a
static demand curve. In other words we
can try to explain the constancy of the
price by the constancy of the quantity in
the market. We will then have explained
a stationary phenomenon by a static
theory.
4. Finally, if we want to explain the
final level of the price and its constancy
in a more profound way, e.g. why
economic forces tend towards a stable
equilibrium represented by the
asymptotic level of the price, then it
will be necessary to enter into the
picture a dynamic theory to show the
interplay between forces, namely how
the dynamic elements of the situation
tend to generate a stable level. We
would thus have to analyse a stationary
phenomenon by means of a dynamic
theory.
Changing
phenomena
2. On the other hand, if we have
observed during some time a systematic
development in the price and at the
same time a systematic development in
the quantity, it may seem plausible to
try to express this by means of a static
demand curve. Then, we will have
analysed a changing phenomenon by
static theory.
3. If the market does not adjust rapidly,
the quantity may depend not solely
upon the price, but also on the rate of
change of the price (and other dynamic
elements). Such a theory would explain
the movement of the price, the rapidity
of its fall before it starts to increase
again, etc. This will be an example of a
dynamic theory of a changing
phenomenon.
Frisch (1933a, L3)
Summing up in a pragmatic way these simple cases, he also gave the reason forhios insistence
on a dynamic model for his business cycle approach:
These examples show you how it can be justified from the specific concrete conditions and
also according to the underlying object of investigation sometimes to apply a static theory and
sometimes a dynamic theory. The justification of a simple analysis by a static theory is often
the fact that the phenomenon under investigation adjusts very rapidly to the changing factors it
depend upon. And likewise if the adjustment speed is not very great the static analysis can still
by justified if the changes in the factors do not happen very frequently and if we only are
16
interested in long run effects. But if the adjustment of the phenomenon under various
conditions is not rapid, because there are frictions or inertia and if, even more, the conditions
the phenomenon depend upon, change frequently, then a static analysis will not have a raison
d’être. That is precisely the situation where it is absolutely necessary to develop a dynamic
theory if we want a true analysis of the phenomena under consideration. (Frisch, 1933a, L3).
Frisch did not publish much on his conception of equilibrium, but dealt with it at some length
e.g. in the Yale lectures, distinguishing between assumption-equilibrium and situationequilibrium. The “assumption-equilibrium” referred to the model world, it was a definition of
the characteristics of the model world. Hence, it had no meaning to ask whether it was
fulfilled or not. The “situation-equilibrium” on the other hand referred to the real world, as a
characterization of a situation.
A stationary equilibrium is not the same as a static equilibrium, not any more than a rainstorm
is the same as that part of meteorology which is concerned with rainfall. The stationary
equilibrium is something characterized by a particular kind of situation that might arise under
certain circumstances, the emergence of which it is the object of theory to explain, and this
explanation may be attempted either by a static theory (involving the idea of static assumption
equilibria) or by a dynamic theory (involving the idea of dynamic assumption equilibria).
(Frisch 1930:72).
The Yale lectures also elaborated upon the concept of moving equilibrium which was implicit
in Frisch’s business cycle model.
A completely different idea for quantifying theory that also had to do with equilibrium
concepts was Frisch’s attempt to formalizing market structures. As part of that he introduced
conjectural action which in a sense anticipated a game-theoretic approach. As Frisch did not
follow up this line of thought further, except in unpublished lecture notes, it cannot be called
more than an attempt. He presented these ideas in the Poincaré lectures.23
Frisch had been inspired in this work an article by Bowley some years earlier on strategic
types and also by the Danish economist Frederik Zeuthen. Frisch introduced and discussed the
following list of strategic types in the market:
Strategic types
I. Elementary adjustment
A. Quantity adjuster
B. Stochastic price adjuster
C. Option receiver
D. Option issuer
II. Parametric action
A. Autonomous action
B. Conjectural action
C. Superior action
III. General negotiation
Under the elementary adjustment the quantity adjuster needs no comment. Now if quantity is
given instead of the price, say if the buyer asks the producer at which price he can deliver a
certain quantity of goods at a specified quality, it is tender situation. The individual has one
23
Frisch (1933a, L2). Frisch offered a paper (in French) based on this lecture when asked for a contribution to a
festschrift for Westergaard, published 1933, it was republished in English in the 1950s.
17
parameter, i.e. the price, at his disposal, but he cannot be sure that he can finalize the
transaction. He is a stochastic price adjuster. Frisch offered some clues on the shape and
position of the “stochastic supply curve” implied by this strategic type. The option receiver is
in a take-it-or-leave-it situation, he is offered both price and quantity. While the option issuer
is someone who is in a position to force other agents to act as option receivers
The stochastic supply curve and the forced supply curve
For the less elementary case of parametric action each agent, Frisch calls them polists,
controls a number of parameters. The total number of parameters may be large. Each polist’s
benefit depends upon the parameters set by himself and by the others. The distinction between
the three kinds of parametric action is the attitude of the polists in this generalized competitive
or game-theoretic situation. The autonomous action is the case where each polist acts as if a
small change in his own parameters will not induce any change in the parameters of the others.
Hence, it is generalization of a Cournot market.
Then the conjectural action case is when each polist takes into account the possibility that a
change in their own parameters will induce a change in the parameters of the others,
namely that each polist acts as if the possible changes in the parameters of others will be
(differentiable) functions of the changes in his own parameters. We introduce the elasticities:
(1)
k
zih z j
z  k h
z j zi
hk
ij
expressing the change in the parameter i of polist no. h which polist no. k believes will be
induced when he changes his own parameter j. These coefficients do not necessarily express
what will actually happen, when polist no. k change a little his parameter j, but rather what
polist no. k believes will happen. For this reason I call these coefficients conjectural
coefficients or conjectural elasticities, as different from elasticities expressing what will
actually happen.
18
Finally, in the case of superior adjustment we assume that one group of polists act
autonomously, while another group of polists can play, so to say, upon the mechanism defined
by the polists of the first group. The conjectural element entering into the considerations of the
polists of the second group is constituted only by conjectural coefficients among the
individuals of that group themselves. In this case we say that the second group act under a
regime of superior adjustment. (Frisch, 1933a, L2).
On the basis of the defined kinds of parametric action Frisch defined various derived concepts,
particularly what he called the attraction force of the various parameters, to analyze equilibria,
friction and cyclical oscillations in autonomous and conjectural regimes. One of the
applications Frisch had particularly in mind and which he developed further in Norwegian
lectures was the labour market with the interaction of trade unions and employers.
From time to time textbooks and articles that macroeconomics emerged before the term
‘macroeconomic’ was much used. The first use of the term ‘macroeconomic’ in a properly
published publication is most likely in Tinbergen’s League of Nations volume for the 1938
conference in Cambridge. As indicated there the term was in oral use. Frisch introduced the
pair of terms ‘microeconomic/macroeconomic’ in his Norwegian lectures in 1933, but his
preferred terms were ‘microdynamic/macrodynamic’, as used in Frisch (1933b). The
‘micro/macro’ pair of terms was used in other sciences.
More important than the term itself is the more direct indication of macroeconomic as a level
of modelling, which originated in Frisch (1933b). It is interesting here to note that it was
introduced together with the idea of national accounts to proved the data needed for
macroeconomics. This was in line with Frisch’s view of the need for close coordination
between theoretical concepts and empirical observation, cf. his 1926 assertion that “the theory
gets its concepts from the observational technique” as quoted in section 2 and the quotes at
the beginning of the next section. It is worthwhile here to quote the passage from Frisch
(1933b), that may reasonable be taken as the first proposal of a macroeconomic sub-discipline
of macroeconomic theory and modeling:
When we approach the study of business cycles with the intention of carrying through an
analysis that is really dynamic and determinate in the above sense, we are naturally led to
distinguish between two types of analysis: the micro-dynamic and the macro-dynamic types.
The micro-dynamic analysis is an analysis by which we try to explain in some detail the
behaviour of a certain section of the huge economic mechanism, taking for granted that certain
general parameters are given. (…)
The macro-dynamic, on the other hand, tries to give an account of the fluctuations of the
whole economic system taken in its entirety. Obviously in this case it is impossible to carry
through the analysis in great detail. … we must deliberately disregard a considerable amount
of the details of the picture. We may perhaps start by throwing all kinds of production into one
variable, all consumption into another, and so on, imagining that the notions “production”,
“consumption”, and so on, can be measured by some sort of total indices. (Frisch, 1933b: 172173).
6. The empirical determination of economic relations
One of Frisch’s assertions was that astronomy as a field of study was more “scientific” than
any other field of study. This was so because
“… in astronomy the fusion between theory and observation has been realised more perfectly
than in the other fields of study. … the astronomical observations are filled into the theoretical
structure. It is this unification that raises astronomy to the dignity and significance of a true
science. Also in economics we have had theoretical speculations, but most of the time it has
not been that kind of theory which is built with a view to being verified by observations.
19
Economic theory has not as yet reached the stage where its fundamental notions are derived
from the technique of observations.” (Frisch 1930: 1).
Perhaps this could be misinterpreted, as another attempted revival of Newtonian science as an
ideal for economics, but that is not at all what Frisch is after. He contrasts the “unification” he
praised in astronomy with the situation in economics. Not that there was a lack of
observational data in economics, on the contrary since the 19th century an overwhelming
statistical and historical material of economic facts had been compiled, but economics would
not really take off as a science.
“But these observations have not been guided and animated by constructive theoretical
thinking in the same way as the astronomical observations. Theory and observations in
economics have gone along in a more or less disconnected way. There have been cycles of
empiricism and rationalism. At times when it became too obvious that economics did not
progress so rapidly as, for instance, astronomy, physics and biology, even though theoretical
thinking had been applied to it some economists would lose confidence altogether in
theoretical thinking in this field and plunge themselves into a pure empirical fact collection in
the hope that such a blind grappling with facts should reveal something of the nature of the
complicated phenomena with which the economist is faced. Then again it became obvious that
such a pure empiricism did not lead anywhere, theoretical speculations in economics had a
revival and the abstract-minded type of people ruled the ground for a while. (Frisch 1930: 1-2).
Rather than such cycles what was needed economics was a “new fusion between theory and
observation” in economics. To achieve that it was required with a “theoretical structure which
is such that it is capable of being connected directly or indirectly with actual numerical
observations.” What was needed? Frisch had answers:
“The true theorist in economics has to become at the same time a statistician. He has to
formulate his notions in such a way that he gets a possibility of ultimately connecting his
theory with actual observations. I know of no better check on foggish thought in economic
theory than to have the theorist specify his notions in such a way as if he were to apply the
notions immediately to some actual or hypothetical statistical material.” (Frisch 1930: 2).
Frischian econometrics can be viewed as a new methodology built around structural
modelling24. Structural modelling should then be understood as a new methodology for
connecting theoretical quantification and empirical quantification. The model appears in
Frisch’s works as the core of the scientific investigation on the one hand, and as the tool for
connecting theoretical and empirical quantitative economics on the other. Frisch’s modelling
concept is close to that articulated by Morgan and Morrison (1999):
Models are one of the critical instruments of modern science. (…) they function as
instruments of investigation (…). It is because they are neither one thing nor the
other, neither just theory nor data, but typically involve some of both (and often
additional ‘outside’ elements), that they can mediate between theory and the world.
(Morgan and Morrison, 1999, 10-11).
Frisch (1929a) was a profound and inventive introduction to data analysis, that provided the
basis for Frisch’s later work on simultaneity and confluent relations. It remained almost
neglected in the literature, notwithstanding the fact that it foreshadowed both principal
component analysis, credited to Harold Hotelling 1933, and Generalized Least Squares,
credited to Alexander C. Aitken 1935. Frisch’s treatise also scores high on new concepts and
methods of presentation, including the first use of linear algebra for econometric analysis, the
latter often credited to Aitken.
24
Frisch was not talking stricto sensu about structural modelling. But, since 1928, he has been thinking out the
idea that an econometric model has to be built up from autonomous and confluent equations.
20
It is really in this paper we have the origin of the ideas that led to the focus on simultaneity
and autonomy in Haavelmo’s probability approach. Frisch studied in a completely nonprobabilistic setting how observations scattered and clustered in observation space when
relations were represented by geometric planes of different order, noting the mathematically
trivial fact that when two relations were assumed to be fulfilled at the same time the
observations would be scatter on or close around the interface of the two planes representing
the relations.
This led him to the reflection that when we analyse a part of the real world, which he then
would think of as represented by a structural equation system, we would not in general be able
to determine from data the individual relationships, as the observations all would be found
along the interfaces of the jointly fulfilled relations. He has the idea then in the late 1920s,
without fully working it through in all consequences, but clearly he was thinking at that time
in terms of autonomous and confluent relationships as concepts for describing this situation.
We know he had coined these terms in 1931, but surely had the connotation defined before
that.25 His main project was the explanation of business cycles. What bothered him was then
the limits set by simultaneity for to what extent we could identify (without using this term) the
model from data. Hence, the problem of simultaneity was closely connected to his business
cycle approach, although in the history of econometrics, e.g. Morgan (1990), Frisch business
cycles and his confluence analysis are dealt with as two very separate issues, but to Frisch
they were closely connected..
The terms autonomous/autonomy were in fact not used in print before Haavelmo’s Probability Approach in
1944. Haavelmo referred to an unpublished mimeograph by Frisch in 1938, while Frisch had coined the terms in
1931.
25
21
Frisch’s confluence analysis book was not published until 1934, it was actually an artyicle
that grew out of hand, not planned and designed as a textbook. In Poincaré lecture no. 6, The
statistical construction of econometric functions, autonomous and confluent equations, the
danger of analysis of many variables, he introduced the key issues, briefer but also in a more
attractive way than in the 1934 book. The difference between structural (autonomous) and
confluent relations he introduced by an example.26 We should note that Frisch was very
inventive in coining new terms as he needed them, this is helpful but this can also be
confusing as he sometimes used different terms at different times.
Three kinds of relations: (1) structural relations, (2) inflated confluent relations, and (3)
deflated confluent relations
y is the log of the area of a rectangle, x1 log of the base and x2 log of the height.
(1)
y  x1  x2 .
Consider rectangles with base equal to height, i.e.
(2)
x1  x2
For this class of rectangles we shall have
(3)
y  2x1 .
another formula for the same case, not very much used but nevertheless absolutely correct, is
3
11
y  x1  x2 .
(4)
7
7
When x1 = x2, then (4) expresses correctly the area of the square, more generally
(5)
(with b1  b2  2 )
y  b1x1  b2 x2
The structural relation (1) can be verified with no regard for whether other relations are
satisfied; it is an autonomous relation, holding identically in the right-hand side variables.
The deflated confluent relation (3) distinguished from the structural relation by being satisfied
only when relation (2) is true. Also (3) is true identically in the right-hand variables.
The inflated confluent relation (4), contrariwise, is satisfied only if (2) is true, and it is not
identically true in the variables.
Thus for the structural relation and also for deflated confluent relation, the coefficients have a
well defined meaning, while in the case of the inflated confluent relation this not the case,
only the sum of the two constants which have any significance. Frisch commented:
Suppose that we have by a priori considerations reached the conclusion that the area of
a rectangle must be of the form (4) where b1 and b2 are certain constants, and assume
that we have at our disposal a certain number of rectangles, given as pieces of
homogenous cardboard, and that we weigh each piece. If there is an assortment of
rectangles of different length and height, we shall find that we can determine b1 and b2
as equal to unity, with a small error of no importance. But, on the other hand, let us
suppose that the empirical material at our disposal only comprises squares. If we then
try to determine b1 and b2 by calculating the regression of y with regard to x1 and x2 by
the least squares method, one will find that b1 is of the form error/error and the same
for b2.
26
The example was used also at a conference in Stockholm in 1931, with proceedings in Norwegian.
22
Suppose someone attacks the problem by means of theoretical scheme which implies
at the same time the hypothesis that the area can be written as in (4), and the
hypothesis that x1 is equal to x2, then the matter becomes serious. The theoretical
position of the problem itself is then such that if the statistical data really fulfilled the
theoretical conditions which have been assumed, then this will prevent that the
available data material can give any information about the parameters of the theory
adopted. (Frisch (1933a:L6).
Recognizing the problem of simultaneity for the identification of economic relationship,
Frisch tried to establish a battery of methods to mitigate the problem, not least investigate
how closely the unidentifiable coefficients could be approximated by making suitable
assumptions. One line of reasoning as set out in the Poincaré lectures went as follows:
Let the relationship under consideration be
(1) y  b0  b1 x1  .....  bn xn  ibi xi
but with the rank of the swarm of observations equal to ρ less than n. Then there exists a set of
ρ variables, e.g. x1 ,..., x , such that all variables can be expressed as linear functions of those
ρ variables.

(2) xi   aij x j
j 0
0 i  j
(i  0,1,..., n) for i ≤ ρ we have aij  eij  
1 i  j
Since the variables x1 ,..., x are linearly independent the coefficients aij for i>ρ may be
determined by the statistical material. Thus all the aij coefficients may be considered as
known. Inserting (2) in the structural condition (1) we see that the variable y also must be
expressed as a linear form in the basic set, i.e. that we have a relation of the form:

y   Bj x j
(3)
j 0
Since the ρ variables of the basis constitute a linearly independent set, the coefficients B in (3)
may be determined by the statistical material, provided that the swarm of observations
( y, x1 ,..., x ) is not degenerate. We are going to utilize the a and B coefficients to be able to
express the nature of the information which the data furnish on the structural coefficients b
entering relation (1).
From the construction of (3) we have that
n
B j   bi aij
i 0
In other words
(4) B j  b j  R j
( j  0,1,...,  ) where
Rj 
n
b a
i   1
i ij
We shall call the B j ’s the confluence coefficients and the bi ’s the structural coefficients.
Equation (4) states that the confluence coefficients which we can determine from the
statistical data under consideration are equal to the corresponding structural coefficients apart
from a residual R which is a linear form in the structural coefficients of (1). The aij
coefficients, are known while the coefficients bρ+1,…,bn are not known. These coefficients are
just arbitrary parameters indicating how the indetermination enters into the problem. It seems
23
to me that this is a quite natural way of formulating this indetermination, particularly since we
may have supplementary information bearing upon just the structural coefficients bρ+1,…,bn.
We may for example know certain upper limits on their absolute values and in that case we
see that it will be easy to indicate an upper limit to the error committed by setting the
confluent coefficients equal to the structural coefficients. In other cases it might be possible to
evaluate the limit of the domain of variation of the parameters bρ+1,…,bn, and in that case the
information one might derive on the structural coefficients b1,…,bρ will be even more precise.
In the case of n-ρ=1 the nature of this limitation can be expressed graphically in a very
simple way:
Domain of variation of structural coefficients in the case of only one arbitrary
parameter ( n    1 )
A final point with Frisch’s empirical methodology is his frequently repeated appeal for
interview data as a direct source of information which not easily can be acquired in any other
way. It can be found from the mid-1920s until the end of his life, in somewhat different
contexts. He argued in the 1920 for interviews as a source for direct information about how
the marginal utility varied with income.27 In the 1930s he was concerned with the limits
simultaneity set to our knowledge about autonomous relations and he argued for interview
information as a way of overcoming that, see Frisch (1938), and he also did in the Poincaré
lecture discussed above. He came back to this point in the post war context of applying
27
See Frisch (1926b:330), as quoted in Bjerkholt (1995, footnote 35).
24
econometrics for urgent practical purposes, cf Frisch, 1948. It appeared as a forerunner of the
method of stated preferences:
We must look for some other means of getting information about the numerical character of
our structural equations, The only possible way seems to be to utilize to a much larger extent
than we have done so far the interview method, i.e. we must ask persons or groups what they
would do under such and such circumstances. In doing so we must, of course, watch our step
very carefully to avoid bias in the answers. … There are two things we may do in order to
assure the answers to be as reliable as possible. In the first place we may use questions which
are worked out in such a way that the information we seek does not come directly from the
answers themselves but rather from the solution of a system of equations connecting the
answers, i.e. we try to conceal as much as possible from the interview persons the true object
of the interviewing. In the second place, we will have a check on the answers by noticing
whether or not the relations we derive from them, check with the covariational equations
which we derive form the usual kind of statistics. (Frisch, 1948:6).
In the 1950s and 1960s he developed a sophisticated technique along these lines to determine
the preferences of politicians and policy-makers, see Bjerkholt and Strøm (2001). His last
research project dealt with this, Frisch (1970a).28
7. Probabilistic shocks and deterministic laws: the explanation of
business cycles
Frisch’s achievement in business cycle analysis is best known for the model he presented in
his Propagation and Impulse essay in the festschrift for Gustav Cassel (Frisch, 1933b). The
model, also known as the rocking horse model, is based on an idea developed by Knut
Wicksell in 1907, making the distinction between the impulse effects, when the rocking horse
is hit by a wooden stick, and the propagation effects, the movement of the rocking horse.29
28
29
He also dealt with it in a somewhat joking way in last speech to students of his department:
Assume that my wife and I have had dinner alone as we usually do. For dessert two cakes have
been purchased. They are very different, but both are very fine cakes and expensive according to our standard. My wife hands me the tray and suggests that I help myself. What
shall I do? By looking up my own total utility function I find that I have a strong preference for
one of the two cakes. I will assert that this introspective observation is completely irrelevant
for the choice problem I face. The really relevant problem is: which one of the two cakes does
my wife prefer? If I knew that the case would be easy. I would say “yes please” and take the
other cake, the one that is her second priority. But here a problem of reliable data emerges. If I
know exactly what she prefers, the case is resolved, but what if I am in doubt about that? The
problem cannot be solved by asking her: “Which one do you prefer?” She would then say: “I
am completely indifferent, take which one you prefer.” Neither is the case resolved by saying:
“You help yourself first,” because then the same problem will arise for her. Hence, the
simplest thing I can do is to utilize earlier experience and make the decision on that basis. In
some cases my assessment of her preferences may be so vague and indeterminate that I to
some degree must rely on my own total utility, i.e. make some compromise between the two
preference scales. (Frisch, 1971b:6, transl. from Norwegian).
Frisch credits Wicksell for the idea of erratic shocks hitting a system, accounting with the explicit theory that
the source of energy which maintains the economic cycles is erratic shocks. Wicksell should have conceived,
according to Frisch, more or less definitely of the economic system as being pushed along irregularly. These
irregular jerks may cause more or less regular cyclical movements. Frisch illustrates it by this illustration:" If you
hit a wooden rocking-horse with a club, the movement of the horse will be different from that of the club "
(Frisch, 1933a, 79). Frisch derived this illustration from Wicksell’s article of 1907 referenced by Frisch as
Wicksell, " Krisernas Gåta ", Statsøkonomisk Tidsskrift, 255-286. In fact, it seems that the first reference of
Wicksell to this idea has to be sought in Wicksell, " Karl Petander : Goda och dårlige tider ", Ekonomisk Tidssrift,
1918,71.
25
Frisch (1933b) stands out as Frisch’s only contribution to business cycle analysis. It was
preceded in time by the Poincaré lectures, which discussed the explanation of cycles
particularly in lecture 5, The creation of cycles by random shocks, synthesis between a
probabilistic point of view and the point of view of deterministic dynamic laws. The
explanation of business cycles was part of Frisch’s most ambitious research project before
World War II, but the intended main publications from the project never appeared. For this
reason the project must be deemed an unsuccessful one.
Frisch (1933b) introduced the “propagation problem” as that of working out the cyclical
properties of a given “swinging system” when it is started in some initial situation. The
“impulse problem” was to explain how the damped cycles found as the solution of the
propagation problem, could give rise to maintained swings as observed for economic systems.
The Wicksell-Slutsky-Frisch paradigm was that a stream of “erratic shocks” energized the
damped swings of the economic system, the famous “rocking horse” model.30
The propagation mechanism of Frisch (1933b) was based on accelerator and replacement
mechanism, formulated as combined differential-difference equations. Frisch had undertaken
an investigation of reinvestment cycles in 1927, inspired by the work of Norwegian
economists Einarsen and Schønheider, but also Aftalion.
Due to Frisch’s incomplete publication of his work the Propagation and Impulse essay may
have been interpreted with too much emphasis on the content and properties of the specific
macroeconomic model as Frisch’s business cycle model per se.31 Frisch was showing off in
the festschrift article by his “discovery” that his model generated the two most common cycle
lengths in the conception of business cycle analysts at the time, and in addition predicted a
third shorter cycle. His real message was to demonstrate his overall paradigm for macro
analysis in economics (applicable in micro settings as well) and to corroborate that his quite
sophisticated paradigm offered the adequate structure for a scientifically appropriate
explanation of more or less regular fluctuations, see Morgan (1990: 99).32
The propagation-impulse mechanism was a qualitative result with a strong intuitive appeal,
the shocks energized the damped cycles of the “structural-economic theory” and prevented
them from dying out. But Frisch wanted more than that. Also the effect of the shocks could be
quantified, in its effect upon the cycles generated by the model. This was the changing
harmonics, which together with the structural-economic theory constituted the two key
elements in Frisch’s approach.
In Frisch (1933b) he defined a changing harmonic as: “…a curve that is moving more or less
regularly in cycles, the length of the period and also the amplitude being to some extent
variable, these variations taking place, however, within such limits that it is reasonable to
speak of an average period and an average amplitude.”
Slutsky’s work had showed that if one applied a moving average to erratic data, there would
emerge cycles with lengths related to that of the period of moving average. The existence of
these cycles could be proved both theoretically and experimentally. This was a phenomenon
of the same nature as the explanation of the maintenance of economic cycles and the creation
of new cycles.
See e.g. Morgan (1990), Ch.3.2 ”Frisch’s rocking-horse model of the business cycle”.
Also Boumans (1999) highly interesting discussion of Frisch approach his contribution from this angle.
32
Ironically, Frisch erred in his presentation. The model, which had been studied more than any other model of
business cycles, did not generate cycles, cf. Zambelli (2007).
30
31
26
The characteristics of the maintained cycles could be explained partly by the weight system
and partly by the distribution characteristics of the shocks. Already by 1934 Frisch had
arrived at the following general conclusions:
The fundamental characteristics regarding the time shape, as (1) the average length of the
cycles, (2) their relative average intensity, i.e. average amplitudes, and (3) the beating effect,
could all be explained only knowing the structural-economic solution, i.e. the weight
function.33 The absolute intensity of the cycles required knowledge of the average standard
deviation of the shocks, but not the actual distribution. Finally, the exact timing, the phase of a
given cycle, i.e. whether at a given moment it shall be in maximum or minimum, depended
upon the actual distribution of shocks. (Frisch 1934b).
Thus the dynamic structural-economic theory only furnished one part of the explanation – the
other and equally important part was the superstructure of the general theory of changing
harmonics.
What Frisch had showed in the Cassel festschrift contribution was that
if a set of variables are defined by a linear system (i.e. one whose structural dynamic equations
are linear in the unknown time functions), the time shape of one of the variables, when hit by
shocks, is obtained by extending to the shock series a moving summation whose weight
system, is exactly the same sort of curve as that which would have given the time evolution of
this variable, if no shocks had occurred. (Frisch, 1939: 640).
Or shorter and more succinctly: Economic theory furnishes the weight system, statistical
theory does the rest!
But Frisch’s full presentation of his model with all ramifications never materialized. A
manuscript for a major publication seems to have been ready for publication in 1933-34, but
never appeared.
One reason for this outcome was that Frisch had raised the ambition in his project to
encompass two kinds of shocks. The regular random Wicksellian rocking horse shocks
caused no changes to the model. Schumpeterian shocks on the other hand would
change the model. Frisch introduced different terms for these two kinds of shocks,
calling them aberrations and stimuli, respectively. Thus a new problem would be to
account for the effect of stimuli.34 The innovations were not randomly distributed, but
might still energize the swings of an economic system or even cause a “secular or
supersecular movement” by changing the economic mechanism (Frisch, 1933b, p.205).
But there was also another hard-to-reach ambition, namely “the inversion problem,” as stated
by Frisch in 1936. Suppose a statistical time series was given, produced by the propagationimpulse effect of energizing a theoretically explained cycle.
Is it possible to determine the weight curves by which the random disturbances have been
accumulated? And, second, is it possible to measure the random disturbances themselves. This
was the structural decomposition problem. (Frisch 1936b:16).
Considerable efforts were exerted at Frisch’s Institute pursuing these targets. The method of
attack was a combination of theoretical analysis and the construction of numerical models, but
apparently this never led to very definite and comprehensive results. The motivation for the
The “beating effect” was the variation in amplitudes and frequency that would occur in the fluctuations of a
time series which comprised more than one sinus component.
34
“The existence of stimuli entails much more far-reaching consequences. The total time shape will now be
more or less transformed, for instance damped cycles will become undamped in the long run, but will have a
disturbing effect over shorter intervals. The timing between the cycles may be changed from what it is in the
stimulus-free system, and entirely new, pure cumulation cycles will emerge.” (Frisch, 1938).
33
27
search for the solution to the inversion problem was that the ultimate purpose was to provide a
much better basis for forecasting. Instead of attempting more or less mechanical extrapolation
of statistical curves “one is led to consider forecasting as an extremely complex problem the
solution of which depends on a previous successful solution of the structural decomposition
problems.” The general idea of the forecasting problem, as rephrased from the Rockefeller
report, ran as follows:
The history of Ragnar Frisch’s approach to business cycle analysis leaves several puzzles.
Why did the success of the propagation-impulse model not lead Frisch towards the path that
Tinbergen chose of constructing real models of the macroeconomy and finding ways of
testing the model, perhaps better than Tinbergen’s, against statistical data? Did his way of
testing a model against data focus too much on the properties of observed vs. modeled cycles,
or was he just fascinated by the challenge of cracking “the inversion problem”, without
realizing that except for very simple models it would be too much for the equipment he had
available? His involvement with random shocks was profound, but his ambition of
determining them turned out to be futile. Perhaps the most positive outcome of Frisch’s effort
was that he may have inspired his chief assistent and student, Trygve Haavelmo, to turn the
problem around some years a later in his Probability Approach (Haavelmo, 1944).
8. The limits of knowledge: Frisch’s philosophy of chaos
In the last of the eight Poincaré lectures titled The meaning of social and mechanical laws,
invariance and rigidity, remarks on a philosophy of chaos, Frisch touched upon fundamental
cognitive issues related to the probabilistic nature of the outer world. He started out by the
notion of a scientific law as a mathematical relationship in a coordinate system, say ξ-space,
which by a non-singular transformation can be transformed with all its complexity preserved
into x-space.
If there are small irregularities in the observations the situation with regard to transformations
has fundamentally changed. In that case the nature of the transformation itself begins to exert
an independent influence upon the complexity of the outcome of observations. … In fact, if
the systematic law that we try to identify among irregular fluctuations, depends upon the
system within which it is observed, what is then left of the concept of a law itself?
I will speak about three aspects of this question. First, I shall make a somewhat technical
remark on the invariance of statistical laws, then say something on the reversibility of the
phenomena of the external world, and, finally, speak on the most important aspect, namely, the
rigidity of observable laws and the question is then to know to what extent we have
constructed the observed laws ourselves. These three aspects of the question will lead us
towards the same general conclusion, namely the absolute relativity of all our observations and
all our conclusions concerning the external world. We conclude with the conception of an
external world as being ultimately essentially chaotic. (Frisch, 1933a, L8).
His technical remark about the invariance of statistical laws was the following. Let a scatter of
observations be given in (x,y). A non-singular linear transformation will transform the scatter
from the two-dimensional space (x,y) to the two-dimensional space (u,v). If the scatter is not
completely disorganized we may choose a regression method and determine a regression line
through the scatter. Then Frisch poses the question of the relation between the regression line
in (x,y) transformed to (u,v) and the regression line determined by the same method in (u,v). It
is mathematically trivial that there is no invariance of most regression methods under a simple
linear transformation.
The scatter and regression line in (x,y)
28
The scatter transformed to (u,v) and the new regression line, the stippled line is the
transform of the original regression line.
29
Thus Frisch shed doubt on the invariance of economic laws, or perhaps the invariance of
regression methods. This was in fact a old topic for him as Frisch (1929a) had explored
invariant regressions.
On the reversibility of the phenomena of the external world Frisch made a visit to
thermodynamics and may have been on loose ground when he asserted:
Instead of saying that there exists a universal law of increasing entropy one may arrive
one day at proving a principle of conservation of entropy in the same way as one has a
principle of conservation of energy.
On the third issue about the rigidity of laws, however, Frisch formulated his assertion as the
following mathematical theorem:
For any given scatter of points in (x, y) which is not perfectly correlated, there exists a
non-singular transformation into (u,v), such that the correlation can be chosen
arbitrarily close to 1 and furthermore the regression coefficient of the transformed
mass of points can also be chosen freely.
The proof was mathematically trivial then as now, but Frisch elaborated persuasively upon its
implications:
In a large number, if not the majority, of the problems we meet with in social, in
biological and above all in physical series, it is nothing which imposes the choice of
one coordinate system rather than another. But where are we then? By a change of
variables we can make the appearance of a law disappear, or we can create a law and
give it the appearance we like.
But what is then the object of science? The incessant preoccupation of science is to
find theoretical schemas, new coordinate systems that fit better and better to the socalled facts. If science finds a discrepancy, it modifies its theoretical scheme, it
introduces other variables, and in short it makes a transformation. Having done that, it
declares triumphantly that now it has succeeded in finding a scheme fitting even better
with experience. What does that mean? It means that science has made transformations
closer to singular transformations than before. You probably find such a view of
science disgusting, you will like better to regard scientific activity as disinterested
research for objective truths which are perpetually outside us.
We have here arrived at the point where it is necessary to draw the final consequences
of the perspective I have presented for you here. It is necessary to translate this
perspective to the biological plane. Let us suppose that we have a biological being of
some sort which was first equipped with sense organs which could register the
influences (x,y). It lives in a chaotic world and it will have neither the means of
looking ahead nor the means of serving itself from the forces of nature. Thus it will
most likely be eliminated. But other biological beings will develop, perhaps some
supplied with sense organs influenced by (u,v). These beings live in a very beautiful
world; they will develop natural sciences for discovering the laws of the world. Their
science will research the same genre of singular transformations according to which
the biological transformation has taken place. But there is more. Science, encouraged
by its success, will probably engage in speculations and in research of new singular
transformations which go beyond by far the biological transformations, which have
defined the sense organs, and in that new domain, at the same time both abstract and
empirical, there are infinite possibilities of discovering new so-called laws of nature.
30
Most likely these new adventures of science will have a repercussion on life and
perhaps even on the biological development of the species. There will be
interdependence between the biological evolution and the scientific development, very
similar to the relation between a demagogue and the people. Under the influence of
this mutual interdependence the biological and the scientific life will continue their
evolution. During this evolution science will certainly from time to time register new
fundamental discoveries. But the world which science in that way will discover, will
be very, very distant from being an objective world.
Why then do science? Because we can perhaps by that hope to soften at least a little
the pain of the species which develops, for evolution will always be accompanied by
pain, that is only universal and eternal principle which we never will have to question
the existence of.
Frisch chose to recapitulate this concluding part of the unpublished Poincaré lectures in his
Nobel address in 1970, suggesting it was topic close to his heart also 36 years later:
It is quite clear that the chances of survival of man will be all the greater the more man
finds regularities in what seems to him to be the “outer world”. The survival of the
fittest will simply eliminate that kind of man that does not live in a world of
regularities. … Science considers it a triumph whenever it has been able by some
partial transformation here or there, to discover new and stronger regularities. …If
“the ultimate reality” is chaotic, the sum total of the evolution over time – biological
and scientific – would tend in the direction of producing a mammoth singular
transformation which would in the end place man in a world of regularities. How can
we possibly on a scientific basis exclude the possibility that this is really what has
happened? This is a crucial question that confronts us when we speak about an
“ultimate reality”. Have we created the laws of nature, instead of discovering them?
(Frisch, 1970b:218-219)
9. Conclusion
By focusing on the technical and innovative aspects of the various works of Frisch, one may
miss the coherence of his research program. Indeed, what is at stake is the building up of a
new disciplinary field that is to say econometrics. One must cross different analysis from the
history of analysis to the history of statistics, through the history of Norway and the western
economies in the mid-wars. In addition, one has to put in a temporal perspective the various
propositions of Frisch relating to business cycles, price index, or economic policies, etc.
Econometrics is nowadays seen as a technique or at least as a set of various knowledge and
practices all coined by their high level of technical nature, this set of tools being useful for
both testing theoretical assumptions and designing policies. To write down the history of this
technique is necessary in order to reconstruct its whole complexity and to show that
econometrics cannot be reduced to its technical nature.
By reading Frisch and especially the Poincaré’s lectures in their entire coherence,
econometrics cannot be anymore as a set of different tools for analysis and forecasting. These
tools are only the vectors of a new way of defining the nature and the subject of the scientific
research in economics. The complexity of the work of Frisch is reflected indeed in the
specificity and the diversity of his research topics as it can be seen in the Poincaré’s lectures.
The complexity of his work is the only consequence of the difficulty to articulate a field of
research (at the cross-section of empirical quantitative economics and of theoretical
economics), various tools of analysis and measurement, and at last the development of a
methodology able to treat the different types of linking ‘theory’ and ‘facts’.
31
What cannot be seen in the Poincaré’s lectures is that not only Frisch is defining a new
research field based on the intertwining of empirical and theoretical quantification of
economic phenomena, but also he is attempting to articulate economic rationality and political
rationality. Indeed, Frischian econometrics has to be read in a broader perspective. Because
according to Frisch (lecture 8, but also Frisch (1926a) and the Nobel price lecture (1970),
science aims the discovery or at least the formulation of laws in order to avoid chaos. Laws
and heuristic aims are subordinated to philosophical and political ones: avoiding chaos
implies to rely on the scientific discoveries in order to bend facts and guarantee social order
and economic growth.
Frisch is the herald of the new way of dealing with economic facts but also of a new burden of
the economist. The complexity of Frisch work is mirrored as the two specificities that
characterised the work of economists just after the Second World War. The first specificity is
the way to articulate mathematical economics, statistical economics and statistical data
(collection and use). This new way relies on a particular philosophy of science/knowledge
that attempts to combine deductive reasoning and inductive understanding of the phenomena
ruling the economic and social world. These attempts lead Frisch to develop and design new
tools and the structural modelling methodology.
The second specificity regards to his particular way of defining econometrics jointly as a
heuristic tool and a political tool. At the very core of his definition and practice of
econometrics, an appeal to the social responsibility of the econometrician has to be founded.
The work of Frisch is clearly two-folded: on one hand structural modelling and on the other
economic policies. But to what extent these two aspects are separated? Are they
interdependent? Does the definition by Frisch of econometrics as a new research field in “a
more scientific perspective” as to say in “a more quantitative perspective” contain the seeds of
the political side of the econometrician task?
This interrelation of heuristic aims and political ones of Frisch work is underlined by Andvig
(1985). But Andvig does not see here the definition of a new discipline but just an answer
form Frisch to the historical context of the Great Depression. Andvig assumption is to relate
the social consequences of the Great Depression, the commitment of Frisch with the Labour
Party, the paramount outlay of rebuilding economies after WWII to the development of set of
planning tools and models by Frisch (“utopian project” Andvig, 1985, chap. 12). But we
assume that the beginning of a theory of political action can be sought in the definition of
econometrics as the unification of empirical quantitative economics and theoretical
quantitative economics. In a sense, lecture 8 is very helpful to answer this question.
This interdependence, either explained by the historical context or by the epistemology of
Frisch, has some consequences on the nature of the tools for analysis and forecasting but also
for planning. By investigating the way to set up these tools and how he combines them, the
ambivalence of Frischian econometrics can be enlightened and econometrics seen at the
crossing of normative and positive ambitions.
The economic crisis in the 1930s and the economic recovery of the early post-war years were
linked to an intense involvement of the successive Norwegian Government and trade unions
in economic affairs. From the mid-30s, the Norwegian economic policies were embedded in
the interaction between political decision makers and academic scholars, which was widely
institutionalised and flourished after 1945 with the founding of the Research Department of
Statistics Norway in 1950, which was in charge of the design of models of the growth path.
This interaction led Frisch and his pupils ruling the Ministry of Finance to produce new
statements and new heuristic tools (Lie, 1995; Lie and Roll-Hansen, 2001).
32
Frisch mobilises his econometrics defined as a set of tools and methodologies for economic
policy aims as he explains to his fellows researchers in academic issues and conferences and
to his fellow citizens in a plenty of newspapers articles (see Frisch, 1931d) and radio speeches
in the 1930s. Our aim is to relate this intertwining of knowledge and action to a specific
epistemology based on a mechanistic and deterministic physicalism35, which must allow
econometricians not to be trapped in the contradictions of the difficult articulation between
economic rationality and political substantive rationality36. Frisch is willing to avoid chaos
and seems confident on the ability of scientific economics- as to say econometrics- to be
produce laws that economists can rely on in order to build up countercyclical measures.
Indeed, Frisch’s work on business cycles leads him to accept the persistence of disequilibria.
This recognition along with the socio-economic consequences of the 1929 crisis explains his
need to turn econometric analysis into an instrument of implementing economic policies. His
first outlines of solutions, and in particular those proposed in the very long 1934 article
“Circulation Planning” (Frisch, 1934a), underline two significant elements of this theory: 1) if
the crisis is a breakdown of the whole economic machine, then economic policies must aim to
restart the machine and 2) economic policy should be restated as an optimisation problem
which can be solved through econometric calculation and modelling. It is not surprising that
the only solution he recommends in 1934 is similar to a process of “walrasian trial and
error”— that leads to the General Equilibrium—which a national clearing agency will be in
charge of. This solution leads Frisch to face the existence of a tension between an economic
analysis founded on the concept of equilibrium and the economic policies that aim to face
economic imbalances and to cope with the social and economic consequences of disequilibria.
It is the reason why, according to Frisch, econometricians have to mitigate analytical tools
and political tools. Economic policy then requires specific tools: at the first step, some shall
picture the economic mechanisms that actually run the Nation, and some shall present paths to
reach the wished economic state. Policy tools have to be distinct from those proposed by the
macrodynamic models but at the same time to complete them. Macrodynamic models present
the theoretical understanding of the fulfilment of the General Equilibrium as multi-sector
models and national accounting are their empirical counterpart, picturing the actual national
economy. At the second step, national budgets have to be set up showing the way to reach a
equilibrium (local or of second best), as we will show below.
After the Second World War, Frisch clearly equates economic policy to building up models of
economic planning37, and this in the name of protecting and guaranteeing political and
economic individual freedoms38, Frisch defines a more pragmatic and flexible methodology to
35
We refer here to the assumed identity between the physical world and the social one. See more in the next
section.
36
We borrow this distinction from Christian de Boissieu (1980) who refers to the “economic rationality” as the
core of the General equilibrium economics, and to the “political substantive rationality” as the core of the
theories of political action. The distinction is an attempt to distinguish the logic of analysis and the logic of
action in economics. The first is focusing on the understanding of the General equilibrium ideal concept. The
second is dealing with the instability of the economic systems and the difficulty for policies to reach the desired
General Equilibrium.
37
Frisch was very much involved in Norwegian politics and in the public debate by radio speeches and in
newspapers, and as an expert to the Government and the Labour Party. We focus here on the analytical and
epistemological side and grounds of his way of intertwining heuristic aims and politics. For more details about
his political commitment, see Andvig (1985), Bjerkholt (1995, 1998), Bjerve (1998) and Dupont-Kieffer (2003).
38
Frisch’s attachment to the market system is fundamental to understanding his step which tends to use
econometric tools to set up guidelines to planning production and exchanges activities: "the matter of wise
planning is to carry out several specific objectives, while preserving as much as possible the advantages of the
system of competition" (Frisch, 1965, 1198). As Louça (1999, 9) underlines, Frisch explains the advantages of
direct planning by comparing three other types of economic policy. Firstly, he notices the policies based on the
33
connect econometric modelling and national accounting. After the 1934 article on
“Circulation planning”, Frisch turns to a more pragmatic approach and defines a methodology
of the economic policy in two stages? that of selection and that of implementation? The first
is based on the definition of a preference function of the political agents and the second
depends on the construction of decision models. The latter are sectoral and multisector
structural econometric models
Consequently, this is the time, according to Frisch, for the political leaders to formulate their
objectives of social justice and economic development. His solution is to make economic
modelling a crucial element of economic policy, making it possible at the same time to
understand, forecast and act. Hence, Frisch makes a sharp distinction between the moment of
the selection and the moment of the implementation. Selection consists in laying down
specific economic objectives, and implementation consists in creating the organisations
charged with achieving these objectives. The phase of selection, i.e. of clarifying the
normative aims is more clearly specified by Frisch. He assumes that it is necessary to
distinguish between what concerns the structure of the economy (which the structure of the
model must account for) and what concerns national political aims. The moment of the
selection must clarify the preference function. That way of doing implies that the political
leaders start to formulate at this stage, through interviews by economists, their objectives of
social justice and economic development (GDP growth rate, environment goals, standards of
education, and of geographical balances). The task of the econometrician is then to lay down
these various even sometimes incompatible objectives. Selection consists in determining and
ordering the preferences of the political leaders for the future of the Nation/country. The
econometricians help them to formulate their preferences in a economic way, to indicate
whether and to what extent their wishes are compatible, and up to what degree these aims can
be accomplished, given the current state of the economy. And then, the econometricians
calculate the optimal solution to reach their goals.
Frisch’s ambition is to show that it is possible that one has to be satisfied one state which,
though less optimal from the point of view of the economic ‘rational choice’, has the
advantage of being manageable and socially satisfactory. Politicians and economists must
then accept that a ‘second best solution’ in an economic perspective is better desirable and
more from a social and political point of view.
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34
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