## Econometrics — a con art with no relevance whatsoever to real world economics

from **Lars Syll**

Econometrics looks “sciency”. Once in a seminar presentation I displayed two equations, one taken from

Econometricaand the other from theJournal of Theoretical and Experimental Physicsand challenged the audience to tell me which is which. No one volunteered to tell me which is which, including at least one hard-core econometrician. Economics is a social science where the behaviour of decision makers is not governed purely by economic considerations but also by social and psychological factors, which are not amenable to econometric testing. This is why no economic theory holds everywhere all the time. And this is why the results of empirical testing of economic theories are typically a mixed bag. And this is why econometricians use time-varying parametric estimation to account for changes in the values of estimated parameters over time (which means that the underlying relationship does not have the universality of a law). And this is why there are so many estimation methods that can be used to produce the desired results. In physics, on the other hand, a body falling under the force of gravity travels with an acceleration of 32 feet per second per second – this is true anywhere any time. In physics also, the boiling point of water under any level of atmospheric pressure can be predicted with accuracy.Unlike physicists, econometricians are in a position to obtain the desired results, armed with the arsenal of tools produced by econometric theory. When an econometrician fails to obtain the desired results, he or she may try different functional forms, lag structures and estimation methods, and indulge in data mining until the desired results are obtained (torture produces a confession even when applied to data). If the empirical work is conducted for the purpose of writing an academic paper, the researcher seeks results that are “interesting” enough to warrant publication or results that confirm the view of the orthodoxy. And it is typically the case that the results cannot be replicated. Physicists do not have this luxury – it is unthinkable and easily verifiable that a physicist manipulates data (by using principal components or various econometric transformations) to obtain readings that refute Boyle’s law. Economists study the behaviour of consumers, firms and governments where expectations and uncertainties play key roles in the translation of economic theory into real world economics. These uncertainties mean that econometric modelling cannot produce accurate representation of the working of the economy.

Mainstream economists often hold the view that if you are critical of econometrics it can only be because you are a sadly misinformed and misguided person who dislike and do not understand much of it.

As Moosa’s eminent article shows, this is, however, nothing but a gross misapprehension.

And just as Moosa, Keynes certainly did not misunderstand the crucial issues at stake in his critique of econometrics. Quite the contrary. He knew them all too well — and was not satisfied with the validity and philosophical underpinnings of the assumptions made for applying its methods.

Keynes’ critique is still valid and unanswered in the sense that the problems he pointed at are still with us today and ‘unsolved.’ Ignoring them — the most common practice among applied econometricians — is not to solve them.

To apply statistical and mathematical methods to the real-world economy, the econometrician has to make some quite strong assumptions. In a review of Tinbergen’s econometric work — published in *The Economic Journal* in 1939 — Keynes gave a comprehensive critique of Tinbergen’s work, focusing on the limiting and unreal character of the assumptions that econometric analyses build on:

**Completeness**: Where Tinbergen attempts to specify and quantify which different factors influence the business cycle, Keynes maintains there has to be a complete list of *all* the relevant factors to avoid misspecification and spurious causal claims. Usually, this problem is ‘solved’ by econometricians assuming that they somehow have a ‘correct’ model specification. Keynes is, to put it mildly, unconvinced:

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 being able to apply econometrics — the system we try to analyse has to have a large degree of ‘homogeneity.’ According to Keynes most social and economic systems — especially from the perspective of real historical time — lack that ‘homogeneity.’ As he had argued already in *Treatise on Probability* (ch. 22), it wasn’t always possible to take repeated samples from a fixed population when we were analysing real-world economies. In many cases, there simply are no reasons at all to assume the samples to be homogenous. Lack of ‘homogeneity’ makes the principle of ‘limited independent variety’ non-applicable, and hence makes inductive inferences, strictly seen, impossible since one of its fundamental logical premises are not satisfied. Without “much repetition and uniformity in our experience” there is no justification for placing “great confidence” in our inductions (TP ch. 8).

And then, of course, 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 there is a stable spatio-temporal relationship between the variables his econometric models analyze. But as Keynes had argued already in his *Treatise on Probability* it was not really possible to make inductive generalisations based on correlations in one sample. As later studies of ‘regime shifts’ and ‘structural breaks’ have shown us, it is exceedingly difficult to find and establish the existence of stable econometric parameters for anything but rather short time series.

**Measurability:** Tinbergen’s model assumes that all relevant factors are measurable. Keynes questions if it is possible to adequately quantify and measure things like expectations and political and psychological factors. And more than anything, he questioned — both on 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 (still a standard assumption in econometrics). Keynes argues that in such a complex, organic and evolutionary system as an economy, independence is a deeply unrealistic assumption to make. Building econometric models from that kind of simplistic and unrealistic assumptions risk 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 seen, inapplicable. Mechanical probabilistic models have little leverage 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 can’t be a goal in itself. Good econometric models are means that make it possible for us to infer things about the real-world systems they ‘represent.’ If we can’t show that the mechanisms or causes that we isolate and handle in our econometric models are ‘exportable’ to the real world, they are of limited value to our understanding, explanations or predictions of 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

atomiccharacter 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

quawholes 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 study 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 laws and relations about entities in models that presuppose causal mechanisms and variables — and the relationship between them — being linear, additive, homogenous, stable, invariant and atomistic. But — when causal mechanisms operate in the real world they only do it in ever-changing and unstable combinations where the whole is more than a mechanical sum of parts. Since statisticians and econometricians — as far as I can see — haven’t been able to convincingly warrant their assumptions of homogeneity, stability, invariance, independence, additivity as being ontologically isomorphic to real-world economic systems, Keynes’ critique is still valid. As long as — as Keynes writes in a letter to Frisch in 1935 — “nothing emerges at the end which has not been introduced expressively or tacitly at the beginning,” I remain doubtful of the scientific aspirations of econometrics.

In his critique of Tinbergen, Keynes points us to the fundamental logical, epistemological and ontological problems of applying statistical methods to a basically unpredictable, uncertain, complex, unstable, interdependent, and ever-changing social reality. Methods designed to analyse repeated sampling in controlled experiments under fixed conditions are not easily extended to an organic and non-atomistic world where time and history play decisive roles.

Econometric modelling should never be a substitute for thinking. From that perspective, it is really depressing to see how much of Keynes’ critique of the pioneering econometrics in the 1930s-1940s is still relevant today. And that is also a reason why we — as does Moosa — have to keep on criticizing it.

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.

Keynes, letter to E.J. Broster, December 19, 1939

A very good post Thank you Prof.Syll. I would simply say that econometrics cannot be a valid method in a non ergodic process because a necessaty condition to do econometrics is stationarity

Yet people observe phenomena, think they detect patterns and suppose they will be stable enough for predictions. How could decisions be made otherwise in the everyday business of life? Moosa and Syll’s arguments do not apply just to econometrics. Taken to their ultimate conclusion they are epistemological and assert that nothing can be said about evolving systems. Well, perhaps that is true in some transcendental sense but meanwhile we have to do the best we can. All conclusions in life and in science are provisional and conjectural.

Econometrics like more casual empiricism can be done well or badly, intelligently or stupidly, dogmatically or with an open mind. But are these gentlemen saying that statistical analysis can never reveal anything in economics that is not obvious to simple observation? Evidently that is untrue. What is revealed is never a “law” and will obviously be contingent in space and time. That follows from the nature of society and economic data. Statistical analysis nevertheless has an indispensable place in social studies whether economics, psychology, medicine or sociology.

Econometrica may be boring and contain articles of no evident application but there is a sound reason for the growth of statistical theory. Physicists do not have to contend with lousy data. They can set up a controlled experiment and repeat it to generate as much data as they need. If the data are well conditioned simple statistics is good enough. Economists do not have that luxury. Economic data contains measurement errors, multicollinearity, erratic distributions and a host of other issues. Econometric theory is concerned with how to extract information as efficiently as possible from a sparse and noisy data set. Economists use more fancy statistical methods than physicists not out of perversity but because their data is lousier. Statistical sophistication cannot make up for lousy data and you cannot extract information that isn’t there but that is no reason for using simple statistics that you know are inappropriate, ignoring problem of which you are aware.

Finally I want to rebut Moosa’s suggestion that econometrics and mathematical expressions of particular economic theories are the same thing. Not at all. Econometrics is the application of statistics to economic phenomena in order to test hypotheses, or the calibration of empirical regularities in order to make forecasts. If econometricians ruled the world the theory of “rational expectations”, so popular for so long among theorists, would never have enjoyed much currency. It ruined the limited predictive power of every macroeconometric model into which it was introduced. It was the failure to believe the data that allowed a misleading theory to persist so long.

As long as the models used are mere curve fitting, econometric models can only represent the data set to which they were fitted. To expect more demonstrates a lack of understanding of science. If groups of dimension-one had been fitted then meaningful theoretical results would have been achieved. Until this is done no progress will made.

Curve fitting for the business of prediction without explanation is a perfectly reasonable pragmatic approach to the practical problem of forecasting. In an evolving system any prediction beyond the data sample is hazardous but what is the alternative: never attempt prediction or just guess? .If a testable theory is produced it will make conditional predictions subject to domain specifications. \If historical data meet the domain restrictions the theory can be tested. Given the noisy nature of economic data, the test will generally be statistical. Econometrics is useful for both these functions. One should not, of course, confuse the two.

Sapiens are unique among the genus Homo in that it does create culture. Most anthropologists attribute that to changes in the human brain and nervous system that occurred about 30,000 years ago. These changes give Sapiens something no other species on earth has – imagination. This gave the species an evolutionary advantage over both other Homo species and over other animals on earth. Sapiens could plan hunts and food gathering without having to experience beforehand the routes, times, and land for these actions. Sapiens could imagine these from similar experiences in the past. Sapiens’ evolutionary and cultural history shows it well equipped to find patterns in experiences.

The socio-cultural systems created by Sapiens take many forms. Some are stable but not chaotic. After perturbations (data changes, structural changes, etc.), these will return to that non-chaotic pattern. Some are nonlinear. There are many forms of nonlinearity. A nonlinear system may be stable in chaotic ways. So, patterns exist in the system, but they are chaotic patterns. Other nonlinear systems are strange. Meaning they are unstable and chaotic. There is no visible pattern. If perturbed, the pattern afterwards cannot be predicted. And of course, some systems change from one pattern to another over time. Sometimes more than once. Geometry is a friend here, as it allows us to identify the different patterns quickly by their geometric shapes.

Considering some examples. Within limits of given time, structure, and elements, some systems are predictable. For example, a city council that always rubber stamps the mayor’s decisions. Or, the church that never questions the decisions of its minister. Either or both patterns may change, even quickly, if, for example the mayor’s decisions bankrupt the city or the minister’s decisions create large public protests and disruptions. With such problems the local people may insist that each city council decision be reviewed, and if necessary reversed by a “peoples’ board.” This creates a stable chaotic system. Or, going on the people may demand a new public election for each necessary or believed necessary decision. This is an unstable chaotic system. All this limited, of course by time, actants involved, and the place of the confrontations.

In the social sciences, including economics chaos theory is the study of complex non-linear systems of social complexity. It is not about disorder but rather about complex systems of order. Chaos theory aims to find the general order of these social systems, and particularly social systems that are like each other. The assumption here is that the unpredictability in a system can be represented as overall actions, which gives some amount of predictability, even when the system is unstable and chaotic. Even chaotic systems are not random systems. Chaotic systems have order, with some determinants of overall actions. Econometrics, and other forms of statistical methods can be useful in the examination of stable-nonchaotic systems. It’s of little use for the examination of stable-chaotic systems and is out of its depth entirely with unstable-chaotic systems. Differential equations is useful for considering parts of these two kinds of systems, but cannot reveal the systems in total or over long time spans. Work on developing chaotic mathematics continues. Though study of chaotic social systems often requires little or no mathematics to be beneficial and revealing.

One final comment. “In physics, on the other hand, a body falling under the force of gravity travels with an acceleration of 32 feet per second per second – this is true anywhere any time. In physics also, the boiling point of water under any level of atmospheric pressure can be predicted with accuracy.” This statement applies to earth. Physicists assume it applies 2, 20, 5000 light years from earth. Maybe it does. But that’s a physics problem, not an econometric one.