Keynes and Tinbergen on econometric modelling
24 Nov, 2025 at 00:16 | Posted in Statistics & Econometrics | Leave a comment
Mainstream economists often hold the view that Keynes’s criticism of econometrics was the result of a profoundly mistaken thinker who disliked and largely failed to understand it.
This, however, is nothing but a gross misapprehension.
To be careful and cautious is not the same as to dislike. Keynes did not misunderstand the crucial issues at stake in the development of econometrics. Quite the contrary—he knew them all too well, and was deeply unsatisfied with the validity and philosophical underpinning of the assumptions required to apply its methods.
Methodology must be suited to the nature of the object of study—that is, the ontology of the social world. Keynes’s critique of econometrics is fundamentally ontological: one cannot apply statistical tools designed for stable, repetitive systems (such as games of chance or classical physics) to a social reality that is inherently unstable, non-atomic, and permeated by human agency and genuine uncertainty (in the Knightian/Keynesian sense).
Keynes’s critique of the ‘logical issues’—the conditions that must be satisfied to validly apply econometric methods—remains valid and unanswered. The problems he identified are still with us today and are largely unsolved. To ignore them—the most common practice amongst applied econometricians—is not to solve them.
To apply statistical and mathematical methods to the real-world economy, the econometrician must make some rather strong assumptions. In a review of Tinbergen’s early econometric work, published in The Economic Journal in 1939, Keynes delivered a comprehensive critique, focusing on the limiting and unrealistic character of the assumptions upon which econometric analyses are built:
Completeness: Where Tinbergen attempts to specify and quantify the factors influencing the business cycle, Keynes maintains that one must have a complete list of all relevant factors to avoid misspecification and spurious causal claims. Typically, this problem is ‘solved’ by econometricians assuming they have somehow arrived at a ‘correct’ model specification. Keynes was, to put it mildly, profoundly sceptical:
It will be remembered that the seventy translators of the Septuagint were shut up in seventy separate rooms with the Hebrew text and brought out with them, when they emerged, seventy identical translations. Would the same miracle be vouchsafed if seventy multiple correlators were shut up with the same statistical material? And anyhow, I suppose, if each had a different economist perched on his a priori, that would make a difference to the outcome.
Homogeneity: To make inductive inferences possible—and to be able to apply econometrics—the system we try to analyse must have a large degree of ‘homogeneity’. According to Keynes, most social and economic systems—particularly from the perspective of real historical time—lack this ‘homogeneity’. As he had argued as early as his Treatise on Probability (Ch. 22), it was not always possible to take repeated samples from a fixed population when analysing real-world economies. In many cases, there is simply no reason at all to assume the samples are homogeneous. A lack of ‘homogeneity’ renders the principle of ‘limited independent variety’ inapplicable, and hence makes inductive inferences, strictly speaking, impossible, since one of their fundamental logical premises remains unsatisfied. Without “much repetition and uniformity in our experience,” there is no justification for placing “great confidence” in our inductions (TP Ch. 8).
Furthermore, there is also the ‘reverse’ variability problem of non-excitation: factors that do not change significantly during the period analysed can still very well be extremely important causal factors.
Stability: Tinbergen assumes a stable spatio-temporal relationship exists between the variables his econometric models analyse. But as Keynes had argued in his Treatise on Probability, it was not truly possible to make inductive generalisations based on correlations in a single sample. As later studies of ‘regime shifts’ and ‘structural breaks’ have demonstrated, it is exceedingly difficult to find and establish stable econometric parameters for anything other than rather short time series.
Measurability: Tinbergen’s model assumes that all relevant factors are measurable. Keynes questions whether it is possible to adequately quantify and measure elements such as expectations, and political and psychological factors. More than anything, he questioned—on both epistemological and ontological grounds—that it was always and everywhere possible to measure real-world uncertainty with the help of probabilistic risk measures. Thinking otherwise can, as Keynes wrote, “only lead to error and delusion.”
Independence: Tinbergen assumes that the variables he treats are independent (an assumption that remains standard in econometrics). Keynes argues that in a complex, organic, and evolutionary system such as an economy, independence is a profoundly unrealistic assumption. Building econometric models upon such simplistic and unrealistic assumptions risks producing nothing but spurious correlations and causalities. Real-world economies are organic systems for which the statistical methods used in econometrics are ill-suited, or even, strictly speaking, inapplicable. Mechanical probabilistic models have little purchase when applied to non-atomic, evolving, organic systems—such as economies.
It is a great fault of symbolic pseudo-mathematical methods of formalising a system of economic analysis … that they expressly assume strict independence between the factors involved and lose all their cogency and authority if this hypothesis is disallowed; whereas, in ordinary discourse, where we are not blindly manipulating but know all the time what we are doing and what the words mean, we can keep “at the back of our heads” the necessary reserves and qualifications and the adjustments which we shall have to make later on, in a way in which we cannot keep complicated partial differentials “at the back” of several pages of algebra which assume that they all vanish.
Building econometric models cannot be an end in itself. Good econometric models are a means to enable us to make inferences about the real-world systems they purport to represent. If we cannot demonstrate that the mechanisms or causes we isolate and manipulate in our models are applicable to the real world, then they are of little value to our understanding of, explanations for, or predictions about real-world economic systems.
The kind of fundamental assumption about the character of material laws, on which scientists appear commonly to act, seems to me to be much less simple than the bare principle of uniformity. They appear to assume something much more like what mathematicians call the principle of the superposition of small effects, or, as I prefer to call it, in this connection, the atomic character of natural law.
The system of the material universe must consist, if this kind of assumption is warranted, of bodies which we may term (without any implication as to their size being conveyed thereby) legal atoms, such that each of them exercises its own separate, independent, and invariable effect, a change of the total state being compounded of a number of separate changes each of which is solely due to a separate portion of the preceding state …
The scientist wishes, in fact, to assume that the occurrence of a phenomenon which has appeared as part of a more complex phenomenon, may be some reason for expecting it to be associated on another occasion with part of the same complex. Yet if different wholes were subject to laws qua wholes and not simply on account of and in proportion to the differences of their parts, knowledge of a part could not lead, it would seem, even to presumptive or probable knowledge as to its association with other parts.
Linearity: To make his models tractable, Tinbergen assumes the relationships between the variables he studies to be linear. This is still standard procedure today, but as Keynes writes:
It is a very drastic and usually improbable postulate to suppose that all economic forces are of this character, producing independent changes in the phenomenon under investigation which are directly proportional to the changes in themselves; indeed, it is ridiculous.
To Keynes, it was a ‘fallacy of reification’ to assume that all quantities are additive (an assumption closely linked to independence and linearity).
The unpopularity of the principle of organic unities shows very clearly how great is the danger of the assumption of unproved additive formulas. The fallacy, of which ignorance of organic unity is a particular instance, may perhaps be mathematically represented thus: suppose f(x) is the goodness of x and f(y) is the goodness of y. It is then assumed that the goodness of x and y together is f(x) + f(y) when it is clearly f(x + y) and only in special cases will it be true that f(x + y) = f(x) + f(y). It is plain that it is never legitimate to assume this property in the case of any given function without proof.
J. M. Keynes “Ethics in Relation to Conduct” (1903)
And as even one of the founding fathers of modern econometrics — Trygve Haavelmo — wrote:
What is the use of testing, say, the significance of regression coefficients, when maybe, the whole assumption of the linear regression equation is wrong?
Real-world social systems are usually not governed by stable causal mechanisms or capacities. The kinds of ‘laws’ and relations that econometrics has established are, in fact, laws and relations about entities within models. These models presuppose that causal mechanisms and variables—and the relationships between them—are linear, additive, homogeneous, stable, invariant, and atomistic. However, when causal mechanisms operate in the real world, they do so only within ever-changing and unstable combinations, where the whole is more than a mechanical sum of its parts.
Given that statisticians and econometricians—as far as I can see—have been unable to convincingly warrant their assumptions of homogeneity, stability, invariance, independence, and additivity as being ontologically isomorphic with real-world economic systems, Keynes’s critique remains valid. As long as—to quote Keynes in a 1935 letter to Frisch—”nothing emerges at the end which has not been introduced expressly or tacitly at the beginning,” I remain deeply sceptical of the scientific aspirations of econometrics. This is especially true when it comes to its use for making causal inferences, which often still rely upon counterfactual assumptions of exceptionally weak foundation.
In his critique of Tinbergen, Keynes highlights the fundamental logical, epistemological, and ontological problems inherent in applying statistical methods to a social reality that is fundamentally unpredictable, uncertain, complex, unstable, interdependent, and ever-changing. Methods designed for analysing repeated sampling in controlled experiments under fixed conditions are not easily extended to an organic, non-atomistic world where time and history play decisive roles.
Econometric modelling should never be a substitute for critical thought. From this perspective, it is profoundly depressing to observe how much of Keynes’s critique of the pioneering econometrics of the 1930s and 1940s remains relevant today.
The general line you take is interesting and useful. It is, of course, not exactly comparable with mine. I was raising the logical difficulties. You say in effect that, if one was to take these seriously, one would give up the ghost in the first lap, but that the method, used judiciously as an aid to more theoretical enquiries and as a means of suggesting possibilities and probabilities rather than anything else, taken with enough grains of salt and applied with superlative common sense, won’t do much harm. I should quite agree with that. That is how the method ought to be used.
J. M. Keynes, letter to E.J. Broster, December 19, 1939
