## Economath — a device designed to fool the feebleminded

from **Lars Syll**

Many American undergraduates in Economics interested in doing a Ph.D. are surprised to learn that the first year of an Econ Ph.D. feels much more like entering a Ph.D. in solving mathematical models by hand than it does with learning economics. Typically, there is very little reading or writing involved, but loads and loads of fast algebra is required. Why is it like this?

The first reason is that mathematical models are useful …

A second beneficial reason is signalling. This reason is not to be discounted given the paramount importance of signalling in all walks of life … Smart people do math. Even smarter people do even more complicated-looking math …

A third reason to use math is that it is easy to use math to trick people. Often, if you make your assumptions in plain English, they will sound ridiculous. But if you couch them in terms of equations, integrals, and matrices, they will appear more sophisticated, and the unrealism of the assumptions may not be obvious, even to people with Ph.D.’s from places like Harvard and Stanford, or to editors at top theory journals such as Econometrica. A particularly informative example is the Malthusian model proposed by Acemoglu, Johnson, and Robinson in the 2001 version of their “Reversal of Fortune” paper …

What’s interesting about the Acemoglu et al. Malthusian model is that they take the same basic assumptions, assign a particular functional form to how population growth is influenced by income, and arrive at the conclusion that population density (which is proportional to technology) will be proportional to income …

The crucial assumption, unstated in words but there in greek letters for anyone to see, was that income affects the level of population, but not the growth rate in population. Stated differently, this assumption means that a handful of individuals could and would out-reproduce the whole of China and India combined if they had the same level of income … Obviously, this is quite a ridiculous assumption when stated in plain language. A population can grow by, at most, a few percent per year. 100 people can’t have 3 million offspring. What this model does successfully is reveal how cloaking an unrealistic assumption in terms of mathematics can make said assumption very hard to detect, even by tenured economics professors at places like MIT. Math in this case is used as little more than a literary device designed to fool the feebleminded …

Given that this paper then formed part of the basis of Acemoglu’s Clark medal, I think we can safely conclude that people are very susceptible to bullshit when written in equations …

Given the importance of signaling in all walks of life, and given the power of math, not just to illuminate and to signal, but also to trick, confuse, and bewilder, it thus makes perfect sense that roughly 99% of the core training in an economics Ph.D. is in fact in math rather than economics.

Indeed.

No, there is nothing wrong with mathematics *per se*.

No, there is nothing wrong with applying mathematics to economics.

Mathematics is one valuable tool among other valuable tools for understanding and explaining things in economics.

What is, however, totally wrong, are the utterly simplistic beliefs that

• “math is the *only* valid tool”

• “math is *always and everywhere* self-evidently applicable”

• “math is all that really counts”

• “if it’s not in math, it’s not really economics”

*• *“almost *everything* can be adequately understood and analyzed with math”

One must, of course, beware of expecting from this method more than it can give. Out of the crucible of calculation comes not an atom more truth than was put in. The assumptions being hypothetical, the results obviously cannot claim more than a vey limited validity. The mathematical expression ought to facilitate the argument, clarify the results, and so guard against possible faults of reasoning — that is all.

It is, by the way, evident that the

economicaspects must be the determining ones everywhere: economic truth must never be sacrificed to the desire for mathematical elegance.

Neoclassical mainstream economists have wanted to use their hammer, and so have decided to pretend that the world looks like a nail. Pretending that uncertainty can be reduced to risk and that all activities, relations, processes and events can be adequately converted to pure numbers, have only contributed to making economics irrelevant and powerless when confronting real-world financial crises and economic havoc.

**How do we put an end to this intellectual cataclysm? How do we re-establish credence and trust in economics as a science? ****Five changes are absolutely decisive.**

(1) **Stop pretending that we have exact and rigorous answers on everything**. Because we don’t. We build models and theories and tell people that we can calculate and foresee the future. But we do this based on mathematical and statistical assumptions that often have little or nothing to do with reality. By pretending that there is no really important difference between model and reality we lull people into thinking that we have things under control. We haven’t! This false feeling of security was one of the factors that contributed to the financial crisis of 2008.

(2) **Stop the childish and exaggerated belief in mathematics giving answers to important economic questions**. Mathematics gives exact answers to exact questions. But the relevant and interesting questions we face in the economic realm are rarely of that kind. Questions like “Is 2 + 2 = 4?” are never posed in real economies. Instead of a fundamentally misplaced reliance on abstract mathematical-deductive-axiomatic models having anything of substance to contribute to our knowledge of real economies, it would be far better if we pursued “thicker” models and relevant empirical studies and observations.

(3) **Stop pretending that there are laws in economics**. There are no universal laws in economics. Economies are not like planetary systems or physics labs. The most we can aspire to in real economies is establishing possible tendencies with varying degrees of generalizability.

(4) **Stop treating other social sciences as poor relations.** Economics has long suffered from hubris. A more broad-minded and multifarious science would enrich today’s altogether too autistic economics.

(5) **Stop building models and making forecasts of the future based on totally unreal micro-founded macromodels with intertemporally optimizing robot-like representative actors equipped with rational expectations.** This is pure nonsense. We have to build our models on assumptions that are not so blatantly in contradiction to reality. Assuming that people are green and come from Mars is not a good – not even as a ‘successive approximation’ – modelling strategy.

Mathematics is a language with a characteristic of brevity. The symbols used in the language should be understood. People without this understanding can be misled. The very purpose of learning mathematics is to understand the language so that one is not misled. Once you learn mathematics you will know what is in store for economics. The irony is that we train students in problem solving rather than learning the language.

For example, x=2, when 2x=4. Mathematics allow us to solve problems. However, if ‘x’ is not defined properly the equation is meaningless. Economics assumes that humans are rational. However, if we try to quantify rationality we get into trouble. Everybody behaves according to their rationality. However, the decisions depend upon the inputs and the particular algorithm applied.

Mathematics is a language as P.A. Samuelson said. But it is not a simple language. It is a took to think logically. It is often extremely difficult to think logically and mathematics sometimes help us to think logically.

Of course, we must be aware of the limits of logical thinking. Economy is a complex system and it is more and more difficult when the complexity increases. In view of this, we should develop a new tool that are comparable to conceptual reasoning and mathematics which were in the case of economics mainly developed in the 19th and 20th century respectively. One possibility is agent-based simulation. For the moment, most of simulation results are rubbishes. Even though, without developing a suitable tool of investigation, we cannot advance. It is necessary to enhance this new method at the side of conceptual and mathematical reasoning. See my paper:

A Guided Tour of the Backside of Agent-Based Simulation, Chapter 1 (pp.3-50) in Kita et al. (2016) Realistic Simulation of Financial Markets, Tokyo: Springer Japan.

The present trouble with neoclassical economics is, as Lars point them, that (1) neoclassical economists are not aware of limits of mathematics, (2) that they are forgetting the importance of conceptual works.

Mathematics and Economics are two different subjects. Economists used math to explain simple concepts in their field. It works well in simple situations, where mathematics can be used. Mathematics does not consider human behavior. On the other hand, Economics has to consider human behavior. When Economics considers human behavior then probabilistic determinism could be the answer.

> Mathematics and Economics are two different subjects.

I do not confusing the two. Please see what I have written on Lars’s post:

On the irrelevance of game theory

https://rwer.wordpress.com/2018/01/12/on-the-real-world-irrelevance-of-game-theory/#comments

In my comment at January 13, 2018 at 1:24 am, I wrote

Game theory is a part of mathematics. It is analytical and contains no empirical contents. [But] Lars should not blame game theory because it contains no empirical contents. Does he blame mathematics because it contains no empirical contents? Lars should argue the way the game theory is applied in analyzing economic phenomena. (the first paragraph)

We are still evolving. The constraints we see outside are the constraints inside. However, we have to live within these constraints. We ought to find the best possible solution for a given problem within these constraints.

Click on “Douglas L. Campbell”, above and discover an interesting young American economist whose first post-PhD professorial position appears to be teaching in Moscow! Fascinating, in this day and age of neo-McCarthyism. Plus, he’s got lots to say. Thanks, Lars.

I noticed that too :-)

Economies are graphs, as in networks with nodes and edges. What’s interesting about economies is not aggregates but connections: Are value flows centralized (big capitalism) or distributed (small firms)? Are money flows roughly symmetric to value (fairness) or very different (exploitation). What do families look like in the graph? Firms? Cities? Are people well connected in stable networks or are they precarious or unemployed (cut connections)? Is money flowing in cycles or does it just accumulate in a few nodes? What do markets do? (they facilitate the making of connections). What is money? (it’s a distributed algorithm for finding closed paths in the value graph).

The fault of economics is not using too much calculus per se, it’s dealing with scalars n the first place. Estimating aggregate quantities is not interesting. Almost anything interesting you can say or question about an economy is a statement about graphs. Economies are graphs, study them with graph theory.

Is someone going to start a course teaching economics founded on graph theory, and can I work for you?

Good post, a system-orientation of examining not the parts but the nodes, flows and relationships. If you haven’t already seen it and can find a copy, check Kenneth Boulding’s A Reconstruction of Economics (196?), which has some wonderful graphs. You can see some of it here: http://babel.hathitrust.org/cgi/pt?id=uc1.b4149471;view=1up;seq=22

I have been considering using graph theory to disarticulate hidden supply chains in the software industry. These supply chains use numerous technologies to hide their presence in an attempt to deceive job seekers on different levels. The ultimate goal of these hidden supply chains are to capture and dominate the market for “contingent” workers. Thanks for reminding me of an unfinished project :-)

Quote from above: (3) Stop pretending that there are laws in economics…

Rather than assert that there are no laws, it might be better to say that so far conventional analysis has not yet demonstrated a single law. So far the attempts have been woefully inept. The requirements for theoretical validity are almost universally ignored. Known laws of physics are frequently violated in the models imagined. Dimensional analysis which would prove the erroneous nature of the models is hardly ever considered.

Frank, please cite the “known laws” you are referring too, as that would be helpful.

Neoclassical growth theory violates the second law of thermodynamics.

Each and every analysis based on production functions violate dimensional analysis. Dimensions must be small negative or positive integers — e.g. metres per second the dimension of the metre is 1, the dimension of the second is -1.

Accelerations has units of metres per second per second (or per second squared) — m dimension is 1, s dimension is -2. There is no production function which has small + or – integer values. They all contain indices which have real values — all such analysis violates dimensional analysis.

Also mathematical errors:

Logarithms are frequently used in conventional production theory.

Equations are Y = f(K,L) and y = f(k,l) where the lower case letters are the logarithms of the upper case letters.

Logarithms can not be taken of dimensional quantities only of scalar values. The mathematics used is plainly wrong.

Thanks, I appreciate that.

Frank Salter > Neoclassical growth theory violates the second law of thermodynamics.

This comment requires a more detailed explanation. Any economic growth, if it is considered as closed system, violates the second law of thermodynamics. Moreover, it violates more classical law of conservation of mass and energy. This means that any economic system is an open system when it is seen as a physical system.

Human economy can grow because it is a dissipative structure (Ilya Prigogine’s naming), which is a subsystem of a larger system and has a flow of energy (or mass) between the subsystem and the outside of the subsystem. Any living thing is a dissipative structure. It can conserve its macroscopic forms and activity only when it takes foods in and discharge excreta out. Aspiration is a similar mechanism.

Human economy is a dissipative structure, but often we forget that it is a dissipative structure. This is a crucially important point when we consider environmental problems. No economy can be an equilibrium system.

The idea of dissipative structure is important to change our image how economy works. Not only neoclassical economists but many heterodox economists consider that they can describe economy as an equilibrium theory. If economy is an an equilibrium system, its internal state is determined by boundary conditions. This is the true reason that neoclassical economists assumes full employment. If work forces is a kind of resources, it must be fully used. This is a natural boundary condition for neoclassical economists. There are some other important aspects that the idea of economy as dissipative structure hints us how the economic system works.

See my old paper (a talk at a conference):

Economy as a Dissipative Structure

https://www.researchgate.net/publication/236149834_Economy_as_a_Dissipative_Structure

I would like to expand the comment on the calculus of several variables. There is no existential problem in setting up differential equations in a number of variables.

The real problem arises when such a system is to be solved. It will, generally, have been expressed as one or more partial differential equations. Only the very simplest system will have an analytical solution. There are only a few text books dealing with analytical solutions to those partial differential equations capable of solution.

In general, this means that the only solutions available are numerical. For engineers, this is the usual manner of solving the problems arising in their various fields — fluid flow, transient heating, structural design etc.

The more dimensions being considered, the greater the difficulty of visualising the results — graphical output is an enormous help in their interpretation.

Having seen the many variables used by some economists in their hypotheses, it is almost beyond belief that any understanding would be achieved by this method — hence the inappropriate use of curve-fitting — at least there are computer programs to do this and their papers are published — unfortunately.

Yes, Frank – both to this and your second comment here yesterday: the logarithms applying only to scalars rather than dimensional quantities is nicely put.

have a look at what I’ve been saying on the role of logic in model building (here your equations) as against testing the models after they have been built:

https://rwer.wordpress.com/2018/02/10/the-flawed-premises-of-mainstream%E2%80%8B-economic-theory/#comment-131754

Paclos above: Great idea, but I would add Multifractals and power distributions.

Pavlos and C-R D

To learn and use different mathematics is a necessary idea. We may say that economists knows no mathematics other than calculus.The reason is simple. They (macro economists in particular) uses only scalars (As Pavlos put it.). In the old days in 1950’s, even neoclassical economists talked much about activity analysis and non-negative matrices.

From 1970’s to 1980’s, many economists talked about catastrophe, chaos, and multifractals. The Lèvy distribution (stable distribution other than normal distribution) that I mentioned in my comment to

More thoughts on the stock crash

https://rwer.wordpress.com/2018/02/06/more-thoughts-on-the-stock-crash/#comments

is a power law. Econophysicists are finding many cases of poweler laws in economy (not economics).

Perhaps Pavlos is thinking of random graph. Classical graph theory can be useful. I have successfully used bipartite graph to characterize sets of production techniques that has a unique stable value (a vector of wage rates and prices) for an international trade theory. [This result is not yet published but I will in the near future.]

To be a good creative economist, it is necessary to know many kind of mathematics, because different phenomena require different mathematics. In some cases, proper mathematics may not have been discovered. In that case, it is necessary to create a suitable mathematics. If one misunderstands that mathematics is calculus, one can only treat economics with one variable (or at maximum several variables).

It is not good to mathematics to scare and fool feeble-minded people, but economists should be a good mathematician. If not, they are slaves of mathematics. It is mathematics that use them.

> Econophysicists are finding many cases of poweler laws in economy (not economics).

Please read “many cases of power laws”.

> It is not good to mathematics to scare

I missed a word. Please read “It is not good to use mathematics to scare” ,,,

Yoshinori, if you’d read the paper I shared with you, you would have seen what Pavlos was talking about. (That’s the macro or conceptual level; the same structure applies at micro level in the same way as the methods of navigation apply to part as well as the whole of a journey.

If you had read my Collins “Dictionary of Mathematics” you would have realised that ‘Graph’ has different meanings: here

“4. (Graph Theory) A set of points (VERTICES) and line segments (EDGES) that connect some of these vertices, used bth in the study of TOPOLOGY and in COMBINATORICS and the construction of COMBINATORIAL ALGORITHMS. See also TREE”.

I’ve previously mentioned W W Sawyer’s “Prelude to Mathematics” on Topology. Looking through my books, what we are talking about here turns up elsewhere in Sawyer under ‘maps and mappings’, illustrated with eleectric circuits. Chiang’s “Fundamental Methods of Mathematical Economics, 2nd Ed” contains not a suggestion of it, but “Mathematic of Organisation”, by Malita and Zidaroiu, has a chapter on it. Its significance for mapping the ordering of events time becomes obvious when one considers its use in Critical Path Analysis, in which the metrics are added back as annotations to the “edges”.

I might add I don’t remember Lars Syll’s critiques ever even mentioning this. With a background in electrics I’ve taken it for granted. Good for Pavlos for bringing it up here.

Sorry, davetaylor1. I have not read your paper yet. The graph I refer to by “classical graph” is exactly what you have defined (4 Graph Theory). In my case, the vertices are countries and commodities. Edges are production technique. They connect a country to a commodity. (This means in reality, there exists a firm in country A that posses the production technique that produce the commodity.) All edges connects a country in one part to a commodity in another part. Hence, a bipartite graph. In this setting, spanning trees ply a special role in determining the international value v = (w, p).

Good, Yoshinori. Still, if you had even skimmed my paper you would have seen the graph[4] diagrams. Mine are macro, i.e. global, contextually polarised and evolving, so your graph reduces to one edge in mine; but yours looks a good way of spatially mapping the micro world of “the state of the art” in places, production techniques and commodities. I’m aiming for an overview simple and obvious enough to be taught in schools, so that university students and future teachers could take it for granted as now they take the paradigm of buying something.

Having acquired Kenneth Boulding’s “Economics as Science” I was fascinated to find that too was aimed at school teachers, though with the science and relative economic sanity of 1968. It is sad to see how his concept of economics as a sub-system of other sciences – social, ecological, behavioural, political, mathematical, moral and future planning – has given way to economists “colonising” everything else. Sad too that he doesn’t mention graph [4]. What he does say is this (gently challenging economists):

“The amount of mathematics which is actually used in economics represents a relatively small proportion of the total corpus of modern mathematical knowledge. As time goes on, however, and as economists become more educated in the use of mathematics, we may well find that the more erudite branches of mathematics, such as group theory, the theory of numbers, and topology,which might almost be described as the theory of possible shapes, will be brought into use. Their present neglect may be more a matter of the relative unsophistication of economists, even mathematical economists, than of any fundamental inapplicability”.

Reverting to the topic of this thread, Lars’ defence of mathematics, economists ought to stop pretending mathematics is a hammer, try believing those who tell them it is a tool-box, and when trying to crack a nut – little hammers having proved ineffective – to look to see if there is a nut-cracker before (following the example of their professors) “taking a sledge hammer to crack a nut”.

It is true that when a man (even a woman too?) has a hammer, he want to crack something. That is often happening in economics. Other than some seminal papers, most of them are extensions or generalizations using the same technique. We can also say that they are slaves of mathematics. To be a master of mathematics, it needs really a high skill of mathematics.

I’m not sure I agree with your last sentence, Yoshinori. To be master rather than the slave of mathematics one surely needs to understand its scope, how it works and what makes particular bits of it applicable. One doesn’t have to be that skilled at doing it, especially if you “know a man who is”.

Here are two conceptual mathematical formulas based upon the Fibonacci sequence:

[ (monetary economy + private monopoly on credit creation) = enforced systemic monetary austerity, necessity to continually borrow and ever increasing power of the business model of Finance ]

[ (integration of policies of monetary gifting into digital money system + aligned regulations) = prosperous free flowingness of the new paradigm ]

Paradigms are single transformative concepts that fit seamlessly within a current framework and resolve the current paradigms most “intractable” problems. You can figure-figure-figure on data and theory and never perceive it, and, like now, all cutting edge reformers can suggest piecemeal but philosophically aligned policies to it and still not accomplish the holistic conceptual leap that consciously identifies it.