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Tinbergen’s Macro-Dynamics: Instability and the Possibility of Collapse

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Modeling Economic Instability

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After his involvement in the early meetings of the Econometric Society, Tinbergen started to work on different macro-dynamic models able to account for economic instability. In 1934, he built a model generating new types of economic movements which eventually led him in 1936 to consider the possibility of having two equilibria, one stable, one unstable, with damped or self-sustained cycles around the high equilibrium and a collapse once the economy reaches the low equilibrium. Tinbergen saw these models, with reference to Fisher’s 1933 classic Econometrica paper on debt deflation, as a way to interpret the potential of a crisis to trigger the collapse of the economy.

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  1. 1.

    Paul Ehrenfest, a renowned physicist who had organized several important meetings in the Netherlands between Einstein, Bohr, and other physicists debating the emerging theories, killed himself shortly before the meeting of the Econometric Society, where he was scheduled to lecture (Dekker, 2020: 69).

  2. 2.

    Indeed it would seem both anachronistic and false to call them macroeconomists; although they anticipated and discussed much of what came later under the name of macroeconomics, their primary focus was set on the dynamic features of these macroeconomic processes, something that became a bit lost in the macroeconomic translation.

  3. 3.

    See Dimand (2019: 180 ff.) for a background on Fisher’s paper.

  4. 4.

    See Knoester and Wellink (1993: 19–20) on this address and the rest of the paper as well as their book on the wider context of the talk, one of five given by Tinbergen in front of the Association, that became the Netherlands Economic Association in 1950 and received the “Royal” epithet in 1987.

  5. 5.

    Not many years later, Tinbergen proposed a similar argument in the framework of utility theory: if marginal utility was taken to be diminishing, and if depressions lasted as long or even longer than booms, it was evident for him that social utility could be increased by damping out the fluctuations around their mean (Tinbergen, 1938a: 77).

  6. 6.

    Tinbergen uses here and later the term “labiele” which also exists in French, German and English but whose meaning seems best translated as “unstable”.

  7. 7.

    “Further investigation of the equilibrium equations (of, for example, Cassel or Walras) which determine the size of production, the level of prices, etc. in a stationary society, shows that there is not one equilibrium (in the sense of economic science), but that in general different equilibria are possible with the same technical and psychological data. It is quite possible, and even most likely, that with some form of utility functions and technical coefficients, two equilibria at least exist, both stable, one for instance with significant unemployment and the other without” (Tinbergen, 1932: 60). Rodenburg (2010: 10) mentioned Tinbergen’s argument in the context of his debate with the Dutch economist Goudriaan on dynamics and equilibrium.

  8. 8.

    “Presence of two stable equilibrium points means, as can be easily ascertained, that there are two points P1 and P2, in which the profit line of 1 has a horizontal tangent and that of 2 has a vertical tangent. This nevertheless means that any change in the number of workers in one’s own enterprise results in a reduction in profit: the condition for a stable equilibrium. In the figure, the action of separate companies always means a movement along vertical lines (for firm 2) or horizontal lines (firm 1)” (Tinbergen, 1932: 62).

  9. 9.

    “Only an organized action–changing the number of workers in both firms at the same time–creates a movement along other lines. Now, from the point P1, one can only reach the point P2 without going through ‘regions of lower gain’, if one stays within the hatched curvilinear quadrilateral. And again, this is only possible if one does not go along horizontal or vertical lines” (Tinbergen, 1932: 62).

  10. 10.

    “After all, one of the essential conditions for the existence of a state of equilibrium in the sense of these two authors [Walras and Cassel] is precisely that, at the prices applicable to that situation, the supply of all end products and production factors, including human labor, is fully absorbed by demand. The equations in which this condition is expressed are therefore an indispensable constituent of the whole system of ‘equilibrium equations’ through which, in the thinking of the aforementioned authors, the economic phenomena are examined” (Koopmans, 1932: 682).

  11. 11.

    Fisher mocked the plethora of cycle theories based on “over- or under-production, over- or under-consumption, over- or under-spending, over- or under-saving, over- or under-investment, and over or under everything else” (Fisher, 1933: 339), which did not go beyond the idea of an economy cycling around its equilibrium. Fisher also doubted that the pendulum metaphor may be of any help to account for the movement of the economy as we showed it in Chap. 3.

  12. 12.

    It has been argued elsewhere (Dimand, 2005), that Fisher’s analysis was close to the concept of a corridor of stability developed several decades later, in another context, by Leijonhufvud (1973) and  Harrod (1973).

  13. 13.

    This policy of stabilizing the business cycle is further clarified later on: “It is now determined that these economic schemes are influenced by such an economic policy, which leads to a stabilization of the purchasing power quantities that appear on the consumer goods market per unit of time. This stabilization will be largely equivalent to a neutral supply of money, since the most important fluctuations in the amount of purchasing power spent per unit of time on consumer goods are probably caused by the alternating creation and hoarding of purchasing power” (Tinbergen, 1934: 298).

  14. 14.

    “To solve this basic problem, you first have to be clear about how the economic movement is caused, that is, you have to have a business cycle theory” (Tinbergen, 1934: 289).

  15. 15.

    Tinbergen thought that a peaceful coexistence between theories was possible, and perhaps even necessary: “reality must be seen as a combination of these alternatives in an unknown proportion” (Tinbergen, 1934: 293).

  16. 16.

    This approach to fluctuations and stability was later labeled by Samuelson “stability in the second kind” (Samuelson, 1941: 101), who considered it in the context of a stock model in 1941 without reference to nonlinearities (see Chap. 8).

  17. 17.

    Tinbergen referred to Kalecki’s own approach at the Leiden meeting which was similar; his paper had not yet been published but this simplification of the integral is apparent, for instance in Kalecki (1935: 287). The lag duration and other parameters were not the result of a statistical analysis but were chosen to give economically meaningful fluctuations or movements.

  18. 18.

    Justifying this in his 1936 paper, he wrote that abandoning the linearity assumption led to the absence of a systematic solution, but “since the results, it seems to me, are extraordinarily remarkable, something should be said about them” (Tinbergen, 1936: 212).

  19. 19.

    It was also already referenced in his 1935 survey as the “Wagemann Festschrift” paper (Tinbergen, 1935a: 295).

  20. 20.

    An application reproducing this model is available at

  21. 21.

    The term model had not yet appeared; the first time it was used was in a paper presented by Tinbergen at the Namur meeting of the Econometric Society and published in 1935 (Tinbergen, 1935d). The term was slow to catch on as many econometricians still referred often to “schemes” rather than models.

  22. 22.

    An increase will have the best effect during the ascendant phase of the cycle, while the inverse is true for a decrease, somewhat counterintuitively.

  23. 23.

    An application reproducing those trajectories for Tinbergen’s two cases can be found here:

  24. 24.

    The change in equilibrium is not visible in the figures above, the same as in Tinbergen’s article, because he limited himself to simple cases where \( A=K=P=a=1 \), that entailed the peculiar fact that production remained at the same level after a change in wages / prices, while prices and purchasing power adapted to the new level. Other values of parameters and constants can very well give rise to a change in equilibrium for all three variables (prices, production and demand) after a change in wages.

  25. 25.

    Tinbergen underlined that for a smaller increase in wages, the movement of production was at first upward rather than downward. This led him to hypothesize that there existed a finite value in wage increase, somewhere between 5 and 10%, that would perfectly stabilize the economy and eliminate the cycle.

  26. 26.

    “Of course this implies the conclusion that the cause of great depressions, such as the one we are actually in, is in some way or another connected with the present form of organization of industry and trade” (Frisch, 1934: 259, original emphasis).

  27. 27.

    “They will reach a point where they simply cannot restrict purchases any more, no matter what the further consequences may be” (Frisch, 1934: 264).

  28. 28.

    “In order to make the scheme more realistic, we ought to allow the magnitude of the existing debt to exert an influence on the buying policy of the parties at a given instant. Professor Irving Fisher has recently drawn attention to the rôle played by debts in the dynamics of the business cycle” (Frisch, 1934: 265).

  29. 29.

    As we have seen, the expansion of credit acted negatively on the rate of change of consumption. In both cases, the effect is to stabilize the system (see Chap. 4).

  30. 30.

    Dupont-Kieffer  (2012) argued that Frisch tried to “reconcile planning, individual freedom and market economy” (2012: 288) in several radio talks made at the same time, but in the end the allocation plan advocated by Frisch in the monograph gave little place to personal freedoms and initiative. At this particular moment in time, he seems to have taken a more radical step toward the planification of production, than in other works where he may have argued in favor of a more indirect type of intervention.

  31. 31.

    The document was entitled “The Non-Curative Power of the Capitalistic Economy—A Non-Linear Equation System Describing how Buying Activity Depends on Previous Deliveries”.

  32. 32.

    This summary is drawn from the discussion quoted in Louçã (2007: 267–268), which was based on an unpublished manuscript from the Ragnar Frisch Archive. Louçã links this discussion with another between Frisch and Tjalling Koopmans which took place at the Vatican in 1963. But it seems to have been a homonymous Koopmans that was present at Namur (see the attendance list in Anon. [1936: 284]), the same J.G. that debated the possibility of unemployment in a walrasian system with Tinbergen around 1932. This does not change anything to our story as we are only interested in the 1935 discussion.

  33. 33.

    Louçã (2007: 276 ff.) recounts the episode.

  34. 34.

    “Examples of this type of equations can easily be found. Tinbergen will be able to tell you about some of his problems leading to equations of the type considered” (Frisch to de Wolff, October 15th, 1935, RFA).

  35. 35.

    The lectures, given in French, have been translated and published in Frisch (2009).

  36. 36.

    “I thought that when the Institut Poincaré invites a foreign scientist, the purpose would probably be to get acquainted with whatever valuable ideas he may have and that the object, only to a lesser degree, is to attract a large and popular audience. On the other hand, since the lectures are to be published in the Annales, I would rather like to work them out on a scientific rather than a popular basis” (Frisch to Fréchet, March 13, 1933, RFA).

  37. 37.

    See his comments on this problem in the 1936 Wagemann Festschrift paper (Tinbergen, 1936: 212), and in another paper published in Econometrica in 1938 (Tinbergen, 1938b: 31).

  38. 38.

    This was the position argued in 1938 for instance, in an offshoot of the LoN studies published in French: “The object of this [economic] policy being to obtain a more or less stabilized system, where there are only small deviations from the equilibrium movement, we have only to deal with cases where linear equations are valid” (Tinbergen, 1938b: 33–34).


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Assous, M., Carret, V. (2022). Tinbergen’s Macro-Dynamics: Instability and the Possibility of Collapse. In: Modeling Economic Instability. Springer Studies in the History of Economic Thought. Springer, Cham.

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