## Econometrics — the danger of calling your pet cat a dog

from **Lars Syll**

Since econometrics doesn’t content itself with only making optimal predictions, but also aspires to explain things in terms of causes and effects, econometricians need loads of assumptions — most important of these are additivity and linearity. Important, simply because if they are not true, your model is invalid and descriptively incorrect. And when the model is wrong — well, then it’s wrong.

The assumption of additivity and linearity means that the outcome variable is, in reality, linearly related to any predictors … and that if you have several predictors then their combined effect is best described by adding their effects together …

This assumption is the most important because if it is not true then even if all other assumptions are met, your model is invalid because you have described it incorrectly. It’s a bit like calling your pet cat a dog: you can try to get it to go in a kennel, or to fetch sticks, or to sit when you tell it to, but don’t be surprised when its behaviour isn’t what you expect because even though you’ve called it a dog, it is in fact a cat. Similarly, if you have described your statistical model inaccurately it won’t behave itself and there’s no point in interpreting its parameter estimates or worrying about significance tests of confidence intervals: the model is wrong.

Our admiration for technical virtuosity should not blind us to the fact that we have to have a cautious attitude towards probabilistic inferences in economic contexts. Science should — as Keynes once put it — help us penetrate to “the true process of causation lying behind current events” and disclose “the causal forces behind the apparent facts.” We should look out for causal relations, but econometrics can never be more than a starting point in that endeavour since econometric (statistical) explanations are not explanations in terms of mechanisms, powers, capacities or causes. Firmly stuck in an empiricist tradition, econometrics is only concerned with the measurable aspects of reality. But there is always the possibility that there are other variables — of vital importance and perhaps unobservable and non-additive — that were not considered for the model. Those who were can hence never be guaranteed to be more than potential causes, and not real causes. A rigorous application of econometric methods in economics really presupposes that the phenomena of our real-world economies are ruled by stable causal relations between variables. To warrant that assumption one, however, has to convincingly establish that the targeted acting causes are stable and invariant so that they maintain their parametric status after the bridging. They seldom do.

To suppose that a complex system with feedbacks “linear:” is crazy. To do econometrics on a nonstationary, hence nonergodic and nonstochastic, system is illegal.

The only thing econometrics does is fit data to arbitrary equations to data sets. None of what is called a model can be anything other than this. If the appropriate theoretical equation was known then it would be self evident that it has been “convincingly establish[ed] that the targeted acting causes are stable and invariant”. All it needs is a first principles analysis and adherence too the quantity calculus. Unfortunately all the efforts to understand economic behaviour have lead to utter confusion because the scientific method has not been followed.

Hey, my pet cat IS a dog and I can prove it. All dogs are small-to-medium size furry creatures. All pet dogs eat out of dishes placed on the floor near the refrigerator. All dogs have various moods and attitudes, which they sometimes express with their teeth and claws. No dog can be fully understood by a human. Well, then: Moka (the pet cat in question) is a small-to-medium size furry creature with moods and attitudes, often resorts to teeth and claws to let us know what’s going on, and is fed in a dish on the floor. We definitely don’t understand her, so QED. Oh, I forgot to mention the most important premise, which I borrow from Milton Friedman (see his hilarious essay “Methodology in Positive Economics”). All syllogisms which appear to more-or-less hold water are valid, therefore the foregoing syllogism is valid, since treating something AS IF it’s true is pretty much the same as treating it as ACTUALLY true. Did I mention QED?

Lars repeats himself. But econometrics is not obliged to assume either linearity or additivity – however often he says it is. Given enough data we can estimate non-linear equations with interaction or multiplicative effects. The data is the usual limitation. I won’t repeat myself further but I’ll tell a little story. A few years back the financial markets were hung up on the monthly US trade deficit. The forecasts being made in the market were poor so I estimated an econometric equation – that one was linear actually. Over the next 15 months the equation was inside the market forecast 14 times. The firm employing me made millions. Not particularly socially useful and I didn’t see much of the money. But when people tell me econometrics is useless I think of that and a number of other experiences. And I know they don’t know what they are talking about.

Do you work for a hedge fund Gerald?

I was working for an investment bank at the time. I retired from the financial sector years ago.

Sorry to bore people by coming back but I would like to establish a consensus. I do not think people on this blog are as far apart as the rhetoric would imply. Let me try some propositions and see if Lars and others assent.

Physicists on this blog have complained that economists seem concerned to work out the logical implications of model worlds without being concerned, or concerned enough, about whether they can explain reality. I agree with that. They have also acknowledged that economic phenomena are the result of a complex, evolving system which is partly self referential and adapts in response to what is discovered about it. It exceeds our powers to develop fully general models of such a system, certainly ones with unique solutions. I agree with that.

The response has to be a certain eclecticism whereby we develop different partial and incomplete models in an attempt to understand particular situations. Understand here means get some intuitive understanding of some of the principal forces at work. It is seldom if ever appropriate to apply such a partial model without adaptation in a given situation and you have to allow for plenty of fudge factors – as any engineer would do when using abstract physical theories in practice. One must not expect too much, certainly not a general truth. Yet a familiarity with the suite of models available and past failures and successes is useful when forecasting or developing polic advice. What to use is a matter of judgement and it will at best produce conclusions specific to a place and time. The limits of extrapolation are learned from experience.

I do not wish to defend all the contents of most economics text books, nor do I have the least sympathy for DSGE, rational expectations assumptions or real business cycle models, which are exercises in misplaced ingenuity. Most economists know this but a certain methodological conformity results from the sociology of the academic economics trade. Such models generally and unsurprisingly fail empirical tests. They would not have achieved popularity if economists were more concerned with empirical corroboration and less with producing deductive theorems from attractive but unverified axioms. We agree on that.

Surely, then, we should give some respect to efforts at empirical testing, be they statistical or experimental. It is somewhat perverse, having damned economists for anti-empirical scholasticism, to then damn root and branch all efforts to bring evidence to bear systematically. Of course any method can be misused, data can be mined, failures can be hidden, samples used selectively. All of these crimes have been committed. The fact that police corruption exists, that suspects have been fitted up with false evidence for conviction is also true. It invites an appropriate scepticism but it is not an argument that we can dispense with forensic science, the police force or the criminal justice system. We deplore the failures and corruption, not the ideal.

If economics is to make any progress, sensible use of econometrics is one of the ways it will happen. Indeed if econometricians had higher status relative to economic theorists a lot of errors might have been avoided. Bad practice is rife and should be criticized when it occurs; to claim that good practice is impossible, however, is to say we can never test propositions against data by statistical methods. It is to encourage economics to remain in the dark ages.

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I am sorry, Gerald, not only for pressing the wrong button but for not agreeing with a lot of your propositions. You may see why if you study what I wrote in response to Geoff Davies on “Radical Misleading Calculations” (Oct 23 at 2.58 pm), where what you call statistical testing is what I have called Reduction, and what you call experimental testing I call Induction.

You say, “Understand here means get some intuitive understanding of some of the principal forces at work”. Physicists think of fields or forces acting at a distance, but a communications engineer has to think of how languages (encoded signals) work and how brains receive, interpret and act up on them, which is not down to forces in the signal but to our ability to detect them, interpret their variations and know how to respond.

You say, “It exceeds our powers to develop fully general models of such a system, certainly ones with unique solutions”. For those not familiar with a paradigmatic example of what a fully general model is, that is true, but consider an analog clock with four quarters, where one can say the hands tend to be somewhere between any two to the exclusion of the others, though cumulatively they will pass through 0-3 quarters. This following from the definitions of whole numbers and the independence of directions at right angles. Those familiar only with slave control by force cannot be expected to understand controlling by mathematically independent PID signals, as in guided missiles; nor the proposition that Keynes moved on in his theory from continuous price control in the second (P) quadrant to control of cumulative unemployment in the third (I) quadrant. Entrepreneurs eventually create that in the fourth (D) quadrant by reinvesting to control profits, unless this “going off course” is corrected.

Is our danger that of calling or pet “economics” instead of “an outdated control system”?

Gerald Holtham: I am in total agreement with your last paragraph however what you envisage appears to be impossible. I continue to point out that what can constitute possible ‘valid’ theory is very well understood. Any valid theory must conform to the quantity calculus. Curve fitting does NOT provide any information by which theory developed. ANY arbitrary equation can be fitted to the data. If one inspects ALL conventional quantitative economic theory, both orthodox and heterodox, NOT ONE cab be valid theory. That the equations fit the data is not a logical argument to justify that the fitted equations are theoretically valid. Correlation does NOT imply causation. That there is NO valid theory may seem an extreme statement. It is not. It is the absolute truth. What is necessary is to develop theory from first principles. This is why the physical sciences are so successful and economics is a failure. My paper, Transient Development RWER-81, develops abstract production theory. Even when presented with the truth, economists appear incapable of recognising it.

Econometrics lost its way by using data derived from one

another (in a hurry to deliver a report) and not from original sources.

Frank Salter, Your point, if I have understood it, is that if aggregate data are derived by adding up individual instances (eg aggregate consumption is the sum of individual acts of consumption in a given period) then any function that applies to the aggregate must be linear, otherwise it cannot be the sum across individual functions. It is true that functions that are not additively separable cannot be derived from individuals’ behavioural functions. Hence your objection to aggregate Cobb Douglas production functions. Some macroeconomic models deal with monetary aggregates and use linear functions so it is not obvious what you have against them. A more general point is that your view is inherently reductionist in that it excludes the possibility of emergent properties of an aggregate that cannot be derived from the characteristics of the individual. The individual molecules of a gas follow Brownian motion; it is meaningless to talk of changes in their volume or pressure. Yet a body of gas made up of such molecules has volume, temperature and pressure and obeys Boyles law – which describes a non-linear relation between those characteristics. When Boyle told you that – before anyone knew about the behaviour of molecules and statistical mechanics – would you have accused him of “curve fitting”?

It is quite possible that there are no stable emergent properties in macoeconomies, in which case the “quantity calculus” won’t help us because there is no reason at all to suppose that individual behaviours are linear. Most studies of individual industrial processes for example show them to obey the law of variable proportions and not to be linear. Your model aggregates only because it is too simple in the first place.

The desire to derive all macroeconomic equations from the maximising behaviour of individuals led to the idiocies of so-called New Classical economics. The derivation was impossible so they invented fictions like the “representative consumer” or representative firm” but these are not real “micro-foundations”. Currently we can only link the individual with the aggregate by simulation of so-called agent based models. It’s that or curve-fitting.

I never expect the relationships to be linear ever. If they were they would have been determined already. If they were, econometricians would have discovered this immediately.

I have no problems with the Cobb-Douglas relationship when it seen effectively as an arbitrary equation. It has no greater resonance than that. The moment anyone seeks to promote it to ‘theory’, they are totally wrong. They are making a category error.

I am unable to say that monetary aggregates are not useful, but there is no reason at all for them to be useful. I believe that they often align with a different parameter. I can prove that the natural unit of output quantity is labour-time. This would allow Marx the claim the labour theory of value. But is only so if the monetary values are an affine transformation of the output quantity. This may be seen in my paper. Solow’s data does just that. (Transient Developmpent, RWER-81, section 4.5) Of course, Solow’s aggregate production function, based on abstract production theory, is only a concrete representation of the data even though my equation (31) p, 159 is derived from the abstract theory. Please note the dot which should be above the q is missing.

Emergent properties arise naturally from the solution to the equations particularly when integration is carried out to form aggregates. In my paper you can see that the algebraic solution describes individual manufacturing projects whereas the the integration describes industries. I was quite surprised to find chow significant the maintenance term was when I derived the solutions.

I see no difficulty in curve fitting in any way. It is a powerful technique. Boyle fitted an equation which conforms to the quantity calculus. My criticism is not one of curve fitting as such. It is the claim to theoretical validity for equations which do NOT conform to the quantity calculus which I criticise. Another significant technique used in the physical sciences is understanding the significance of groups of dimension one, These are essential to understanding the effects of scaling. Economists claim incorrectly that some effects are greater or less than scale.

If you read my paper, you will see that the abstract production theory it describes demonstrates extremely stable emergent properties. Using the Solow data from 1909 to 1949, a period encompassing normality, the great depression and two world wars, demonstrates stable emergent properties.

You talk of the law of variable proportions. I talk of scaling laws describable by groups of dimension one.

I have NO model. The the aggregation is valid is demonstrated by the fact that my relationships explain why every relationship described by economists, Kaldor’s stylised facts, Verdoorn’s law, Okun’s Lawe etc., are what they are. My relationships only describe abstract production theory. They do NOT describe growth.

I agree with your final paragraph.

However, I wish to emphasise that it is the failure to work correctly with quantities that explains the failure of orthodox and heterodox economic theories.

DaveTaylor. to the extent that experimentalists want to apply their results outside the framework of their experiment, they are indeed relying on induction. That is always risky because one can never be sure that all possible influences have been controlled in the experiment. Nevertheless in some circumstances it is reasonable to hope it will work. Statistical testing is no different. You are seeing if a stochastic model is consistent with past data, as a necessary condition for having confidence in it. If you use it for forecasting or policy you run the same risk as the experimentalist because it is impossible to put in a model every factor that could conceivably influence the outcome; there are bound to be omitted variables. So it is induction again and equally risky; I am not sure why you call it reduction. But what is the alternative – to not experiment or not test models on past data?

There seems to be a view that unless propositions can be deduced from a general theory of human behaviour they are valueless. If you believe that you are entitled to despair. Fortunately human behaviour is characterised by quite a lot of inertia. In situations that are not too novel that enables us to understand and even predict what is going on. But we don’t have full understanding of the system and can always be surprised. I’m afraid I don’t understand your clock analogy but controlling an economy is far more complicated than controlling a guided missile. Very little read-across there.

Reduction because (qua Popper) one is falsifying, not proving (i.e. eliminating non-problems). Experiments test a particular application of theory; testing models against empirical data doesn’t test the underlying logic of the model. That happens in the ‘revolutionary’ phase of science, when the underlying logic is recognised at a more primitive (earlier) level and deductively retested for consistency before being tried out on applications. The clock analogy is about the circular form of complex number providing a language to make distinctions before any have had time to evolve. On the issue of “controlling an economy” (an economy being defined by the range of its token money) has anyone really any right to do more than advise unless real harm is being done?

Gerald, try reading the section on Chomsky’s “Deep Structure and Surface Structure ” in https://en.wikipedia.org/wiki/Transformational_grammar, which is very much where I am coming from. Our Algol68 added “deep structure” [modes of interpretation” to Algol60.

So how did ] (on the right of the QUERTY keyboard) end up as ” (uppercase 2 on the left of my keyboard)? More and more I think there must be an error in my Word program which reads a ‘top-down’ stack as a ‘first-in, first out’ one. Deep structure!

Frank, I take the point that formulations like aggregate production functions may or may not be useful but they are not a theory. Mind you, I’m not sure if anyone claimed they were. They have been used as a component of a “theory” of growth and income distribution but if it is a theory at all it is not coherent. Perhaps we agree on that.

I read your paper, albeit quickly. Some points of your reply still puzzle me. Are you saying that increasing or decreasing returns to scale are impossible because inconsistent with the quantity calculus or have I misunderstood you? In practice scale effects can appear through improvements in technique and therefore productive efficiency. Is your point that a theory would have to specify efficiency units and incorporate them explicitly in order to generate a theory?

The natural unit of output quantity is labour time, you say. There are several difficulties. One is that labour is not homogenous. Without buying the whole neo-classical story, there is a reason why brain surgeons are paid differently from porters. One can integrate the labour time taken in training the brain surgeon in principle, though not in practice, but it is doubtful f that would resolve the problem. Secondly practical macroeconomics deals with aggregates of very different commodities that are compiled into single quantities using prices and monetary values. A persistent, some would say fatal, objection to the labour theory of value is that it correlates very poorly with actual prices. If you find a diamond by luck on a river bed you can sell it for the same price as if you had spent a week digging it out of a deposit. Labour time will be a poor explanation for any aggregation of production, because the aggregation is done using market prices.

I am therefore not sure whether you are saying that economists are missing a trick when they attempt to theorise at the level of the macroeconomy or whether you are saying that such theorising is a priori illegitimate given the way macroeconomic aggregates are constructed.

I am not sure that you are correct in saying that production functions are not seen as theory. After all the Cobb-Douglas paper title is “A theory of production”. My memory of most of the papers is that the authors seem to believe that what they they have described IS theory.

By the way the papers on growth are mainly based on a paper containing elementary mathematical errors. Many of these authors claim the original describes reality. I have no explanation for this.

My analysis is based on constant returns to scale. It is consistent with the Solow data which Solow describes as diminishing returns to scale. Engineers are very familiar with scaling laws. Similarity is determined by the application of groups of dimension one, such as the Reynolds and Mach numbers. Clearly economists do not use groups of dimension one and have a misunderstanding of scaling. I have a developed an abstract growth theory. It is consistent with constant returns scale. I am saying that if anyone claims increasing or decreasing returns to scale, they have not understood the nature of scaling.

The natural unit of output is labour-time. This is provable using the quantity calculus. I show in appendix A of “Transient Development” that mathematically the orthodox general statement of production functions means that capital must also be labour-time. Labour does not have to be homogeneous for this be true. The significant point it that it is the natural unit. This does not imply that labour-time represents value. So all your examples are true but do not just represent labour-time but also widgets as well. Apply widget to be anything you wish. Labour-time is the abstract unit not a concrete one of productivity.

Money is a useful numeraire if and only if it is an affine transformation of labour-time. I agree with you that the labour theory of value is unsupportable as I point out above. Your diamond example introduces productivity. It is concrete example not a abstract one.

I think if you read the papers which use labour-time rather that money, they seem to give understandable results, which implies affine transformations.

I don’t think your final paragraph is a true representation of macroeconomics. If you consider my paper then you can see that the mathematics is consistent with every empirical relationship recognised by macroeconomics, Kaldor’s stylised facts, Okun’s and Verdoorn’s laws. It also predicts that the Verdoorn coefficient and the intercept of the aggregate production function have the same value. They are. So the relationships I found is the complete production theory but it is not growth theory. That is different.

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If one peels back the history of the so-called

intrinsic valueof diamonds one finds that the value—market price of diamonds—is a manufactured manipulation by a monopolist and slick marketing; little more than pure fiction and capitalism’s propaganda. In other words, both thescarcityandintrinsic valueof diamonds purportedly reflected in the market price are fiction, ergo diamonds are bullshit..

Wages are like diamonds; subject to manipulation by the asymmetric power of capitalists and corporatism who can easily undermine unions by “shedding” employees and turning a wage rate negation into a market manipulation price competition (to wit, here, here, and here).

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Perhaps the difficulty is that you are looking for underlying physical quantities in economic equations. But in economics, equations nearly always just equate monetary values. The production function other than for a single process cannot be understood as the production of widgets; it is the production of monetary value – a collection of diverse items only made commensurable by their price. The explanatory variables can also be measured as values: the value of labour input and the rental value of the capital used in the production process. The equation thus displays dimensional homogeneity. The dimension is monetary value, whether expressed in pounds, dollars or euros (conversion factors are available). The equations may be nonsense but they are consistent with the quantity calculus. Labour, not being homogenous, has to be aggregated using wages. If you use man hours in the production function you need a multiplicative efficiency constant measuring the average value produced per man hour to preserve dimensional homogeneity.

Such a relation does not constitute a fundamental theory but not because it fails to obey a quantity calculus. Recall too that certain conservation laws that apply in physics and chemistry may not have clear equivalents in economics. Therefore I am not clear that your strictures are correct.

” in economics, equations nearly always just equate monetary values”.

Given how perverse and misleading economist’s equations are, the question is, should they? Economics needs to be about sustaining the biosphere, not balancing bankers’ books.

I refer you to my comments Oct 29 09.23. You are repeating your previous comments which I have shown to be not quite correct.

The equations you claim as consistent with the quantity calculus are NOT. If you believe that I am wrong, please give an example of ones that are consistent.

Whatever happens in physical reality MUST obey the laws of physics.

Frank, I fear we are both repeating ourselves without getting through to the other party. Labour time cannot explain prices therefore it cannot explain aggregates that are arrived at by summing values not physical quantities. Equations that relate one set of monetary values to another set are dimensionally homogenous and therefore consistent with the quantity calculus. Your point seems to be that economics cannot be reduced to a branch of physics and is therefore illegitimate. Well, it can’t be reduced to physics. If you can show any economic proposition is actually inconsistent with a physical law you are entitled to reject it. You are not entitled to reject it because it cannot be derived from a physical law. It has to be judged on its own terms, like propositions in biology or psychology.

An equation relating an indivdual’s consumption measured in currency units to her income measured in currency units is not inconsistent with the quantity calculus. There are issues when relating aggregate consumption to aggregate income because the parameters depend not only on the psychology of individuals but on their weights in the aggregation. As these change so will the parameters. This is a general problem for macroeconomics.

Yes, Gerald. Even in the case of an individual one cannot resolve variations in taste by taking an average of them. One may be able to make valid correlations of behaviour with average positions in a complex number plane, but being in the “North East” sector is different from being in any of the NW, SE and SW sectors and variation can only be accommodated in a model by accepting that as fact. For a behavioural model of this see Myers-Briggs personality analysis. The physical reasons for the personality differences are to be found in our split brains controlling both feelings and action, which themselves may be inwards or outwards directed..