Ln-9 Ragnar Frisch and the history of econometrics
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- Utility Measurement (and related issues)
- The axiom system for quantifying utility. 1. Local axioms 1.1 Determination
- ( P , b ) 1.2 Transitivity
- ), then ( P , a )
- ), then ( P , α + γ )
- ( P , a ) or ( P , a )
- Frisch on business cycles
- The empirical determination of economic relations
- Three kinds of relations: (1) structural relations, (2) inflated confluent relations, and (3) deflated confluent relations
- Some other Frisch achievements The Frisch-Waugh-Lovell Theorem
- Capital Theory and Dynamic Economics
- Depression and Circulation Planning
- Production Theory Innovations in the formulation of theory: modelling, static/dynamic, conjectural and micro/macro concepts
- Static/dynamic analysis vs. stationary/chaging phenomena. Economic examples Static analysis Dynamic analysis
- Changing phenomena
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LN-9 Ragnar Frisch and the history of econometrics
Ragnar Frisch 1895-1973
Frisch, christened Ragnar Anton Kittil Frisch, was born in Oslo as the only child in a family with a jewellery business in the centre of Oslo. He was naturally expected to eventually take over the business after his father. (The firm had been established by Frisch’s grandfather in 1856; the Frisch name may have come to Norway with a mining engineer brought over from Saxony to work the silver mines at Kongsberg about 200 years earlier.) After school Frisch duly started as an apprentice in the well known Oslo firm David-Andersen. It is an often told story that Frisch’s mother, realizing how intellectually gifted Ragnar was, insisted that he along with the apprenticeship should take up a university study. Economics was because it was short and easy. Frisch graduated as cand.oecon. in 1919 and completed his probation work as a goldsmith in 1920. None of the two teachers of economics when Frisch studied (Oskar Jæger and Thorvald Aarum) were known outside Scandinavia. It was a study of limited depth but it may have served well as an introduction to the literature. Frisch did well in the exams. In one of exam papers - the question asked for a discussion of pro’s and con’s of progressive taxation – Frisch wrote something which may be read as his scientific credo: “We must not allow ourselves to be intimidated by the apparently impossible. History shows that man has a remarkable ability to make good on Aristotle’s maxim: Make the immeasurable measurable.” The unnamed “immeasurable” entity here was “utility”. Frisch was inspired as we shall see by Jevons, perhaps by others as well. We have studied earlier some persons who took up economics for serious study after they had become rich through luck or work. With Frisch it is the other way around. After his probation work his father made him equal partner in the business. That didn’t make him rich exactly but reasonably well off. Frisch chose to spend about 3 years with his wife abroad for further study. Most of the time he spent in Paris but he also visited UK and other countries. He followed some lecture series but mostly he read voraciously and studied on this own: mathematics, statistics and economics. After returning to Oslo Frisch became universitetsstipendiat, gave some lectures and prepared a doctoral dissertation in theoretical statistics (the first in Norway) and defended it in 1926. In that year he also published his first article in economics (in a Norwegian mathematical journal). This paper, titled Sur un problème d’économie pure, is often cited, mainly for the opening paragraphs: “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 possible, into a science in the strict sense of the word.” (Frisch 1926/1971: Sur un problème d’économie pure [On a problem in pure economics])
What Jevons actually said on the page Frisch referred to was that “the price of a commodity is the only test we have of the 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 of the final degree of utility - the all-important element in Economics.” Frisch’s idea or turning economics into a science was really a commitment and nothing else may have been so important to him at that time. He had surveyed economics at a time of great progress in science. Economics was lagging far
behind, there was no doubt about that, despite having had great pioneers. Frisch wanted both to promote the idea of an economic science and address some of the challenges in such a science, for which he had already fount the name
Immediately after the 1926 article Frisch started to elicit support from others for the idea of econometrics and work systematically towards establishing both an organization and a journal to promote econometrics in this broad sense. Frisch was in fact building a comprehensive network covering many countries. The effort was eventually brought to an important stage of fruition at the foundation of the Econometric Society in 1930 in USA in December 1930 and the journal Econometrica two years later. Frisch worked towards this goal with Irving Fisher, Joseph Schumpeter, François Divisia and Eugen Slutsky, among others, but there is no exaggeration to say that Frisch was the driving force in this venture, which became a rather important step in the internationalization and the scientization of economics. The Econometric Society adopted a constitution, drafted by Frisch, where the key sentences expressing the aim of the Society were as follows: “The Econometric Society is an international society for the advancement of economic theory in its relation to statistics and mathematics. … Its main object shall be to promote studies that aim at a unification between 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.” The term econometrics has later come to have a narrower meaning than Frisch originally intended, more like the study of statistical methods for the application of
We add into the story a few biographical details on Frisch. In 1926 got a Rockefeller Fellowship and visited USA in 1927. In 1928-29 he was teaching in Oslo. Frisch’s father died, the family firm was in dire straits and Frisch may have considered to give up economics as a professionnel career. It was at that time that Yale University (Irving Fisher) invited him for one year. Frisch restructured the company, left it it the hands of a manager before he left to spend a year and half in USA in 1930-31. Most of Frisch’s scientific ideas seems to have originated in during this visit. While he was away he was appointed Professor of economics and statistics in Oslo. After Frisch’s return to Oslo the University Institute of Economics was established with Rockefeller from 1932 as a research institute at the university but not part of it.
Frisch’s role in the foundation of the Econometric Society and his research at that time made him quite well known internationally, especially among younger talented economists who joined the Society. Frisch was a very active participant at the European meetings of the Econometric Society and also editor of Econometrica for many years. More on Ragnar Frisch can be found on a special web page: http://www.sv.uio.no/econ/om/tall-og-fakta/nobelprisvinnere/ragnar-frisch/ What were Frisch’s scientific concerns in the 1930s? This is more or less the same as asking what his conception of econometrics was. Econometrics was about quantification – theoretical quantification and empirical quantification. Theoretical quantification meant to make theoretical concepts measurable. A most important theoretical concept was – utility, used by many but often in imprecise and vague ways. Perhaps one could say that Frisch was more oriented towards methodological challenges than theoretical developments.
1926 Sur un problème d’économie pure [On a problem in pure economics] 1932 New Methods of Measuring Marginal Utility, Tübingen 1936
Annual survey of general economic theory: The problem of index numbers, Econometrica 1959
A complete scheme for computing all direct and cross demand elasticities in a model with many sectors, Econometrica Utility was a prime object for theoretical quantification. To measure (marginal) utility was the challenge Jevons had formulated and what Frisch had stated in his exam paper. Frisch was naturally influenced by his close reading of Jevons, Pareto, Edgeworth, Irving Fisher and Slutsky. Frisch proposed an axiomatic approach as the foundation for the existence of utility functions in individuals, implying that the individual indifference curves/utility function could be regarded as the outcome of answers to choice questions suggested by the axioms. Frisch would have seen this as very close to the thinking of Pareto and Fisher and without the psychological overtones of Edgeworth. We can only give a very brief indication of Frisch’s axiomatic approach here. Frisch formulated such choice axioms in the 1926 paper, as the following:
1. Local axioms 1.1 Determination
(P,a)
1.2 Transitivity
If (P,a)
1.3 Additivity
If (P,α)
2. Interlocal axioms 2.1 Determination (P,a)
2.2 Transitivity If (P,a)
2.3 Additivity If (P,α)
There were further axioms and mathematical requirements we leave aside here. Frisch sketched a proof of how a utility function could be determined from the axioms (the integrability problem). An important point is that the local axioms would suffice to give ordinal utility, that is a preference ordering as indifference curves, while fulfilment of the interlocal axioms would result in cardinal utility. Frisch tended to be cardinalist, he found that people were willing to make the kind of comparisons expressed by the interlocal axioms. The 1926 article also comprised empirical estimation of the marginal utility of income as a function of income and a price index, from household data Frisch had got hold during his study years in Paris. The results, or rather the assumptions Frisch had made to achieve the results, were contested in some of the reviews of the paper and inspired related work. The empirical analysis demonstrated a very important tenet the Frisch held, namely that empirical work should be based or led by theory. Frisch undertook a more extensive investigation in the 1932 book with a wider range of methods and several applications. A further application of utility theory was in price index theory, and the questions of true cost-of-living indexes. This was interest Frisch shared with Fisher who was great authority of indexes, but also a very technical topic.
The underlying problem is the following: let e(u, p) express the minimum income to achieve utility level u under the price vector p. We can then define the true cost-of-living index as
Frisch discussed index issues in the 1936 Econometrica article, relating this index to other index formulae such as Laspeyres and Paasche indexes. Frisch’s approach to utility theory with cardinalist leanings lost momentum by the rediscovery of Slutsky’s paper in the mid-1930s as the focus shifted from utility to demand with no use for cardinal assumptions. Cardinal assumptions were sidelined but have however remerged in several contexts later. A late outgrowth of Frisch’s utility theory studies in the 1930s is the 1959 Econometrica paper, allowing easy determination of all demand price elasticities on the Frisch assumption of “want independence”. It is one of Frisch’s most cited papers. Also the origin for the concept of Frisch elasticity. There is a lot more that could be said about Frisch on preferences and utility but we round this off with a Frisch statement from his last speech to Norwegian students in 1971. The topic was something else but in the speech Frisch revisited his early interest in utility analysis and offered the following elaborate example of his way of reasoning: “In a realistic, theoretical foundation of social policy we must for each individual consider two entities: the own-utility and the conjectured utility of other persons. An example will make this clear. 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 utilise 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 1971, my translation)
It was stated jokingly but some important points were made here. Frisch was always interested in the art of eliciting information via structured interviews and argued for its importance in economics.
I have extracted a passage from a lecture entitled What is Economic Theory given by Frisch in a course at Yale 1930, where Frisch gives a beautiful explanation of what a model is. This is familiar to us but this level of abstraction in economic theory was not common at that time. “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 form of sense impressions, it resembles, so to speak, a jelly-like mass ... In order to create 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, ... And then we analyze this little model world instead of the real world. This mental trick ... constitutes the rational method, that is, theory. (...) When we create the model world it is up to ourselves to decide which features and characteristics the model world shall have and what kind of relations shall exist between the various phenomena and groups of phenomena in the model world. This we can do because we are sovereigns in the model world, so long as we do not break the rules of formal logic. This does not mean, of course, that our decisions regarding the constitution of the model world are ruled completely by free fantasy or caprice. 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. It shall picture those indefinable things in the real world which we might call ‘essentials’, meaning by that, of course, essentials with regard to our own ends. What kind of criterion have we then, by which to judge if our model world conforms to this ideal? We have no such criterion, – none 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 as so that we finally get on the right track. This is precisely the reason why the scientist is to be considered a logical sovereign in his model world. He is just like a wise, absolute monarch. He uses his prerogatives with tact and care. 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 non-obligatory. The laws of the model world will often consist only in...idealization of some observed empirical law. We observe ... that a given market... will be able to absorb a greater quantity of an article, the lower the price ... and ... we create a model world with a demand curve, sloping downward. But 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. A classic example ... of transobservational invention is the creation of a model world equipped with atoms. The atoms were at the time of their introduction into science, something far beyond the range of direct actual observations. (...). As an example of the second kind of invention, one could take the discovery of the relation between the diminishing return of land and the fact that rent exists. Both facts were well known long before Ricardo, but the relation between them was not seen until revealed by the abstract speculations of Ricardo. (...) Having created our little model world, we start out to explore it. This seems paradoxical. Should it be necessary to explore something which we have ourselves created? It certainly is in many cases. When we create a model world, i.e. define a scheme of thought, it is generally impossible at once to overlook all the consequences involved in the definition laid down. Most frequently this can only be done by systematic investigations. We only have to think of what is meant by a mathematical discovery. This kind of investigation constitutes an essential part of the rational process, namely the rational deduction. The creation of the model world itself constitutes the rational induction. (...) (Frisch, 1930) Frisch on business cycles 1933 Propagation Problems and Impulse Problems in Economic Dynamics Business cycle research, i.e. investigations into the more or less regular fluctuations in economic activity, emerged around the mid-19C, particularly through the work of Juglar 1862 but became much more comprehensive after post-WWI shocks reverberated. Kondratiev (ca 50 years), Juglar (ca 9 years) and Kitchin (3-4 years) were the most common cycles studied. Harvard launched the A- B-C method, business cycle research institutes mushroomed in Europe, (Morgan (1990: 41-68). Frisch is known in business cycle analysis mainly for the model and analysis he presented in the 1933 article, which also addressed important methodological. The specific model is of lesser importance than the methodological points Frisch tried to drive home. “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 1933).
After having analysed business cycles with methods for time series analysis in, estimating cycle lengths, amplitudes etc. Frisch noted that none of those who launched theories tried to explain the cycles by means of a set of equations. NBER’s data intensive business cycle studies provided explanations in the form of narratives stating what causes made the economic activity go up what causes made it go down but not with explanations that could be summarized as a model. Some followed Jevons in finding the explanations for cycles outside the economy. Frisch shifted his attention to the question of the nature of a proper theoretical explanation of economic fluctuations. His theory of science led him to regard “cause”, so frequent in business cycle discussions, largely as a metaphysical term of little use in a more simultaneous theoretical framework. Frisch’s orientation
was towards finding the appropriate methods for analysing and explaining cycles, a prime example of an econometric problem. Frisch started out with the idea that a proper explanation ought to be found in terms of a simultaneous system of structural relations and the number of endogenous variables equal to the number of equations. These are simple ideas to us but were not so at that time. A model of the economy able to generate cyclical movements would have to be a dynamic model, a topic Frisch had studied very thoroughly. Of course, system of dynamic relations could be constructed to give cycles of any specific length. But to Frisch that seemed an unsatisfactory explanation because then the cyclical structure would depend on the exact values of parameters in these equations. With a little different values of parameters the system would either converge to stationary solution or diverge, both were unsatisfactory. Frisch’s approach was then to explain the roughly stable values of cycles over time as the interaction of a macroeconomic mechanism with an inherently dampened dynamic nature with random shocks from outside. Frisch thus introduced “propagation problem” as that of working out the cyclical properties of a given “swinging system” when it is started in some initial situation. And then 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. Frisch credited his great hero Wicksell as having been the first “who has been definitely aware of the two types of problems in economic cycle analysis – the propagation problem and the impulse problem – and also the first who has formulated explicitly the theory that the source of energy which maintains the economic cycles are erratic shocks.” Wicksell had introduced an imaginative analogy, that of a rocking horse being hit repeatedly by a club. The movements of the rocking horse is highly affected by the hits of the club, as Wicksell argued, the rhytm of movement of the rocking horse would be quite largely independent of hits by the club. Frisch also credited Slutsky for shown in his 1927/37 paper the effects of a series of random shocks. Frisch showed in the 1933 article that a small three-equation model generated the two most common cycle lengths in the conception of business cycle analysts at the time. But his real message was to demonstrate an overall paradigm for macro analysis in economics.
1929 Correlation and scatter in statistical variables, Nordisk Statistisk Tidskrift 1933 Pitfalls in the statistical construction of demand and supply curves, Leipzig 1934
Statistical confluence analysis by means of complete regression systems
After the term econometrics had been introduced it was used retrospectively, as by Morgan 1990, and also Schumpeter who used “the econometricians” to mean the Political Arithmetick practitioners, Cantillon and Quesnay. Frisch certainly shared the view that important early efforts in economcetrics had been done but he was also very critical of contemporary empirical work for determining, say demand and supply curves. He was also very sharp in his criticism. So what were his critical views? Let us look at something he said in 1930, namely that astronomy as a field of study more “scientific” than any other field 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. ... Economic theory has not as yet reached the stage where its fundamental notions are derived from the technique of observations.” (Frisch 1930). Frisch contrasted the “unification” he praised in astronomy with the situation in economics. Since 19C an overwhelming statistical and historical material of economic facts had been compiled, but economics would not really take off as a science. “...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. ...when it became too obvious that economics did not progress so rapidly as, for instance, astronomy, physics and biology, ... some economists would lose confidence altogether in theoretical thinking in this field and plunge themselves into a pure empirical fact collection ... 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). What was needed? Frisch had an answer: “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). These quotes convey the flavour of Frisch’s criticisms but then there are two more specific methodological points. There was a wave of empirical studies in American research in the 1920s. Frisch was not enthusiastic and made the following comment: “Den geschäftige statistiske materialinnsamler og korrelasjonsberegner vil kun gi et magert bidrag til analysen av de økonomiske fenomener så lenge han arbeider uten den plan og forståelse som et teoretisk-økonomisk tankeskjema gir. Den økonomiske statistikk sier oss ingenting hvis den ikke sees på bakgrunn av en bred teoretisk-økonomisk analyse. Denne bakgrunnen savner man imidlertid ikke sjelden ved de arbeider som leveres av den amerikanske kvantitative skole. … Observasjonsmaterialet er og blir en død masse inntil det animeres av en konstruktiv teoretisk spekulasjon.” (Frisch 1931, probably written 1928). Here is expounded the primacy of theory which Frisch held high as a principle. The other point is of deeper nature. Frisch viewed, as we have argued, the macroeconomic situation of an economy as something that could be understood as the joint result of the interaction of structural equations. Suppose we want to estimate one of these equations. Frisch then makes the point that the observations will be scattered and clustered in observation space according to the entire equations system. Let us say the system has two realtions, each in the same three variables, a sin the figure below.
How can we determine plane I or plane II when the data are concentrated on the common line of these two planes. Frisch was struggling with what would later be know as the identification problem. In a simultaneous problem how can we identify the structural (or autonomous) relations.
In the 1929 book Frisch studied in a completely non-probabilistic 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 scattered on or close around the interface of the two planes representing the relations, as in the figure above. When we tried to estimate the equation of say plane I, not only was the data not distributed to allow precise estimates, what we would get was a confluent relations, i.e. some kind of mix of two structural relations. The 1934 book was written to develop methods to get around this problem. The Introduction states (p. 9): "The present study has been undertaken as an indispensable preliminary step for certain projects, namely statistical productivity studies and statistical construction of econometric functions (demand and supply curve and the like)...." The problems were not properly resolved until much later and on the basis of Trygve Haavelmo’s work.
At a lecture in Paris in 1933 Frisch gave an elementary and amusing presentation of the core of the problem:
Three kinds of relations: (1) structural relations, (2) inflated confluent relations, and (3) deflated confluent relations Let y be the log of the area of a rectangle, x 1 log of the base and x 2 log of the height. (1) 1
y x x = +
. Consider rectangles with base equal to height, i.e. (2) 1
x x =
For this class of rectangles we shall have (3)
1 2
x = . another formula for the same case, not very much used but nevertheless absolutely correct, is (4) 1
3 11 7 7 y x x = + . When x 1 = x 2 , then (4) expresses the area of the square, more generally (5) 1 1
2 2 y b x b x = + (with 1 2 2 b b + =
) 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, but is not identically true in the variables.
Some other Frisch achievements The Frisch-Waugh-Lovell Theorem In the course of his investigations of the relationship between sugar consumption and sugar prices, Frisch had to face up to the problem that, as was contended by a number of authors at that time, if there were a strong upward trend in consumption accompanied by a strong downward trend in price, it would be a mistake to de-trend the data series and then perform a regression on the de-trended series, called the "individual trend method" by Frisch and Waugh (1933), as opposed to including time explicitly as one of the explanatory variables (called the "partial time regression method"). It was the accomplishment of the paper by Frisch and Waugh (1933) to show that so long as the relations are assumed to be linear, both methods give exactly the same result. The Frisch- Waugh theorem was generalized by Reiersøl to any instrumental set of variables and was applied by Lowell (1963) to seasonal adjustment.
Frisch's earliest work on capital theory was his 1927 article on primary investment and reinvestment. The problem he considered was this: Suppose that at an initial time an investment is made in a number of different goods with different durabilities, and assume that each of these goods has a definite durability and is replaced as soon as it wears out. What will be the subsequent pattern of total reinvestment over time? He gave examples (such as the production of a wooden hammer, iron hammer, and steel hammer with respective durabilities of one, two, and three years) that would give rise to a very marked subsequent limit cycle, but showed that this was atypical (resulting from the distribution of prime numbers from 1 to 6); with finer class intervals, he showed that fluctuations in reinvestment will be damped, so that a smooth flow of reinvestment will be approached asymptotically. A few years later, Frisch presented his methodological approach to static and dynamic economics in a penetrating Norwegian paper (1929b),of which unfortunately only the introductory sections are available in English. Shortly thereafter, during a visit to the University of Minnesota, a lively discussion in the Campus Club with Alvin Hansen prompted Frisch to make his first well-known contribution to business-cycle theory (1931e). Not surprisingly, in view of his previous investigation, he again turned his attention to the cyclical nature of replacement investment. The occasion for the discussion was Hansen's treatment (1927, p. 113) building upon the "acceleration principle" introduced by Clark (1917, 1923), among others Clark had stated (1917, p. 220) that "the demand for maintenance and replacement of existing capital varies with the amount of the demand for finished products, while the demand for new construction or enlargement of stocks depends upon whether or not the Depression and Circulation Planning One of Frisch's most striking contributions (1934b) was born out of the experience of the Great Depression; it might have had greater impact if it had not been overshadowed by Keynes's General Theory, which appeared two years later.25 Frisch opened his book-length article with the following passage: “The most striking paradox of great depressions, and particularly of the present one, is the fact that poverty is imposed on us in the midst of a world of plenty. Many kinds of goods are actually present in large quantities, and other kinds could without any difficulty be brought forth in abundance, if only the available enormous productive power was let loose. Yet, in spite of this technical and physical abundance, most of us are forced to cut down consumption. We are compelled to make real sacrifices in order to economize in the use of these very goods and services that could easily be produced in abundance if we would only use our resources.” (Frisch 1934)
Frisch attributed the problem to a defect in the form of organization and to a situation in which groups "are forced mutually to undermine each other's position. ... This meaningless vicious circle is what I understand by the incapsulating phenomenon." The picture he painted was of a game that ended up in a sub-Pareto-optimal situation and even a prisoner's dilemma. But in some respects it also is a picture of unstable equilibrium.
In trying to work out some kind of solution to this difficult problem Frisch made the following remark: “We have here one of those cases – so frequent in economic practice – where it can be proved by abstract reasoning that a solution is not possible, but where life itself compels us nevertheless to find a way out.”
The problem was well expressed in a subsequent publication (1963, p. 2) as follows: “To illustrate ... we may think of the tailor and the shoemaker who were standing looking at each other with sorrowful faces. The sorrow stemmed from the fact that the tailor did not dare to order the shoes he needed because he was not sure that he would be able to sell any suit to the shoemaker, while the shoemaker did not dare to order the suit he needed because he was not sure that he would be able to sell any shoes to the tailor.
If we include also the baker, the fisherman and a few others in the picture we have a good illustration of what is meant by the multilateral balancing problem, and in particular we get an illustration of the need for a system which can assure everybody that he is taking part in a game where a multilateral balancing is automatically provided for.” One way to interpret these passages is that Frisch is showing the failure of Walras's law to hold in a dynamic economy. The worker, according to this law, will effectively demand the goods which he would purchase if he were to get the job he is looking for. The essential asymmetry between the buying and selling sides of the transaction is what leads to the breakdown; the selling must take place first. And all proofs of stability of competitive equilibrium assume Walras's law.26 25 It was preceded by an equally striking little book, Saving and Circulation
We first consider Frisch’s attempt to formalize market structures and introduce conjectural actions in markets, which may be regarded as an early game-theoretic approach. Frisch introduced and discussed the following list of strategic types in the market:
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 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. 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.
For 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. Autonomous action rules when each polist acts as if a small change in his own parameters will not induce any change among the others, hence it is generalization of a Cournot market.
Then conjectural action occurs when each polist takes into account the possibility that a change in 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)
∂ = ⋅ ∂
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 express what will actually happen, but rather what the agents (polists) believe will happen. Frisch calls these coefficients conjectural elasticities. (Frisch 1933).
The case of superior action means that one group of polists act autonomously, while another group exert conjectural action, playing, so to say, upon the behaviour of the first group. The conjectural element entering into the considerations of the second group is only among the this group.
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. Frisch’s first formulated his notion that the concepts of statics and dynamics 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).
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 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
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. 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.
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 (1933). Frisch did not publish much on his conception of equilibrium, but he dealt with it at some length e.g. in the Yale lectures, distinguishing between assumption- equilibrium and situation-equilibrium. 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).
The second major improvement in the analysis of business cycles brought about in the 1933 paper was the distinction between micro and macro analysis.
22 juni 1934. Lov om økonomisk embedseksamen ved Universitetet. 1
§ 1. Der skal av Det juridiske fakultet ved Universitetet holdes en økonomisk embedseksamen. § 2. Til denne eksamen skal kandidatene gjøre rede for sine kunnskaper i følgende fag og disipliner: . Socialøkonomikk og statistikk: Socialøkonomikkens teori, social- økonomikkens historie, næringspolitikk, socialpolitikk, sociologi, arbeidet som økonomisk og sociologisk faktor, økonomisk historie, bedriftsøkonomi (herunder landbruksøkonomi), finanslære» statistikkens teori og teknikk, sammenlignende økonomisk og sooial statistikk (herunder Norges næringsliv, landets økonomiske og sociale tilstand), forretningsstatistikk, sammenlignende befolkningsstatistikk og befolkningslære. Rettsvidenskap: Kort kursus i privatrett og forfatningsrett. Visse avsnitt av forvaltningsretten, herunder næringsrett, socialrett og finansrett. Der holdes både skriftlig og muntlig prøve.
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