Clarity and Obfuscation in the Use of Mathematics for Economic Reasoning

Goya Sleep of Reason

The Tony Lawson paper discussed on this blog the other day seems already to have begun to cause ripples in the heterodox community. The Real World Economics Review Blog has run a piece by Lars Syll on the paper and the responses have been rather varied.

One of the interesting claims that I noticed was that some people were saying that mathematics, due to its formal nature, provided economists with clarity. This was then typically followed up with appeals to how economics might become a science by increasingly mathematising. This argument seems entirely dubious to anyone who has ever investigated how science functions. But I do not here wish to either discuss whether economics is a science or if scientists working in other fields really do aspire to mathematical clarity rather than creative innovation.

Instead I would like to consider in what sense mathematics can provide economists with clarity in thinking through certain issues and in what sense it might do just the opposite. I think that a good example of mathematics providing clarity is the case of the Keynesian multiplier, which I have discussed on this blog before. The multiplier, when both imports and consumption are taken into account, generally looks something like this:

Multiplier Equation 1.3We can then manipulate this algebraically to get equilibrium income as such:

Muliplier EquilibriumHere is an example of a mathematical presentation providing clarity. Even without inputting any numbers into the equation we can immediately discern the factors that will generate equilibrium income, Yt*. It will be a component of autonomous consumption, C0, investment, I, government spending, G, and exports, X, minus autonomous imports, M0. It will also be positively multiplied by the consumption multiplier, c, and negatively multiplied by the import multiplier, m.

We know this because the components of income, as just laid out a moment ago, are in the numerator of the equation, while the multipliers are in the denominator. The multipliers are also being subtracted from/added to 1. The larger the denominator, the smaller the numerator and vice versa. So, anything that “subtracts” from the denominator — e.g. the consumption multiplier — will increase the numerator, while anything that “adds” to the denominator — e.g. the import multiplier — will decrease the numerator.

As we can see, even though this piece of algebra looks somewhat mysterious to someone not familiar with it, nevertheless to the trained eye it is actually possible to intuitively interpret it in a very tangible way. This, I think, is why it provides an example of a use of mathematics that at once provides clarity and insight into the underlying relationships.

Compare this presentation, however, with your typical econometric study. Such studies contain innumerable “black boxes” in that the reasoning behind the assumptions made is often entirely unclear. When it is not unclear and is made explicit (Wynne Godley’s forecasts at the Levy Institute are a model of econometric clarity, for example) one quickly sees that such assumptions are entirely arbitrary — often calling into question the entire endeavor.

One thus spends hours attempting to interpret and reconstruct such a study and, all too often, one comes away realising that the assumptions lead one inevitably to interpret the results as being almost entirely arbitrary. Keynes noted this well in his critique of Tinbergen when he wrote:

The labour it involved must have been enormous. The book is full of intelligence, ingenuity and candour; and I leave it with sentiments of respect for the author. But it has been a nightmare to live with, and I fancy that other readers will find the same. (Pp568)

Indeed, one recognises the labour that goes into such studies — especially if you have undertaken one yourself — but at the same time untangling it becomes “a nightmare to live with”. Why? Because such studies do not promote clarity at all. Instead they promote complete and total obscurantism. The mathematical symbols and manipulations become like a dense fog which the reader has to concentrate the depths of their attention and intelligence upon in order to dissipate, only to find that there is often nothing of substance there in any case.

This is not to say that econometrics is entirely useless. As Keynes says in the Tinbergen critique:

This does not mean that economic material may not supply more elementary cases where the method will be fruitful. Take, for instance, Prof. Tinbergen’s third example-namely, the influence on net investment in railway rolling-stock of the rate of increase in traffic, the rate of profit earned by the railways, the price of pig iron and the rate of interest. Here there seems a reasonable prima facie case for expecting that some of the necessary conditions are satisfied. (Pp567-568)

What Keynes is saying is that if we have a number of variables that we can assume to be very closely and immediately related then the econometric method may prove fruitful. I’ve always thought that a nice example of such a paper that did this entirely correctly was Basil Moore’s classic Unpacking the Post-Keynesian Black Box: Bank Lending and the Money Supply where Moore is extremely careful to lay out and justify the causal relationships before he engages in any econometric analysis.

Alas, however, the question as to what is the “correct” manner in which to undertake such a study remains impossibly hard to define. That gives users of the technique who have not bothered (or have not been able) to think through its methodological problems free reign to engage in nonsense. The reason for this is precisely because these mathematical techniques have a tendency, not to clarity at all, but to obscurantism and the moment one gives people a ticket allowing them to engage in obscurantist practices one runs the risk of spiking the proverbial punch.

The same points could be made in a slightly different manner about mathematical models. But the results are clear: while in certain instances mathematics can be used to increase clarity, in others it can be used to engage in obscurantism. The reason why I think that there should be only a limited place for mathematics in economics is because the risks in allowing it a prominent place are too great as it is the usefulness and relevance of economics as a discipline which is at stake.

It is far, far more difficult to engage in obfuscation and magical nonsense when using plain English than it is when using mathematics; not to mention the fact that it is far easier to catch people out. And as a general rule-of-thumb it is probably not unfair to say that as the number of equations grows, the lack of clarity tends to increase and so too do the difficulties in sorting the wheat from the chaff. It is thus the multiplication and proliferation of equations that tends to give rise to nightmares. I think that is what Lawson, Syll and others are getting at when they express skepticism over too heavy a use of mathematics in economics.


About pilkingtonphil

Philip Pilkington is a London-based economist and member of the Political Economy Research Group (PERG) at Kingston University. You can follow him on Twitter at @pilkingtonphil.
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8 Responses to Clarity and Obfuscation in the Use of Mathematics for Economic Reasoning

  1. B says:

    So the main problem is the tendency of some mathematical techniques to obscurantism or the inappropriate use of them by some economists?

    Honesty and clarity about the assumptions depend on the author. By stating them clearly, the reader would not have to “spend hours attempting to interpret and reconstruct the study”. Probably one of the reason why econometricians don’t provide such explanations at the beginning of their papers is that they “presuppose a certain amount of prior education.” in econometrics, which is consistent with an axiomatic-deductivist approach where one has to build on previous “advancements” by its community. The problem today is that even the first axioms were arbitrary and inaccurate, threatening the entire framework based on it. And for other less-evident assumptions, the lack of explanations is just fraudulent.

    But I would not be so categorical about mathematics, because the major problem seems to be the economists, not mathematics. It is the economist who has to recognize the inadequacy of linear and simple mathematics when he tries to describe our world. Or it is him who has to figure out that mathematics is not a neutral tool when he tries to modify reality to build a tractable model. As Paul Davidson said, blame the axioms and the economists who claim these axioms are universal truths.

    This debate reminds me the one about guns in the US. Who are responsible, weapons or the guys using it? Same thing for alcohol and in fact a lot of things.

    I’m not ready to discard complicated mathematical models because I see no reason to believe that such models cannot be based on sound foundations and manipulated very carefully by honest and pragmatic economists. I may be overoptimistic.

    • I am not just referring to papers that don’t lay out their economic assumptions. I am referring to papers that have not properly tarried with the methodological implications. For example, Tinbergen’s original paper is quite clear when judged against many contemporary econometric papers and yet the argument Keynes has to make against it is so dense that it is almost difficult to read. If you read an econometric paper properly you have to do most of the mental somersaults that Keynes did in his critique. It’s exhausting.

      Again, to be clear: I am not just referring to papers that don’t lay out their economic assumptions, I am talking about papers that have not understood the implicit assumptions which econometric techniques themselves make. This makes up the vast majority of the literature which is, we might say, unreflective in this sense. Indeed, much of this literature, if it were refelctive would simply not exist.

  2. Thomas Bergbusch says:

    Great post.

  3. Ramanan says:

    “It will also be positively multiplied by the consumption multiplier, c, and negatively multiplied by the import multiplier, m.”

    Yikes – have you ever really studied basic Keynesian Macro?

    c and m are not multipliers

    The multiplier is the whole thing multiplying the flow variables and here it is


    Fun you are out to criticize me and struggle in such basic things.

    Your next para is even more mega confused and struggling.

    • Don’t be silly…

      In economics, a multiplier is a factor of proportionality that measures how much an endogenous variable changes in response to a change in some exogenous variable.

      For example, suppose variable x changes by 1 unit, which causes another variable y to change by M units. Then the multiplier is M.

      Ramanan, I think you’re a good economist but stop this. It’s desperately silly.

      • Ramanan says:

        Again you quote something to make it look like it supports you but it doesn’t. It is again the opposite here.

        You can see in those Wikipedia articles regarding how multipliers are different from propensities.

        You confuse propensities to the multiplier. As simple as that.

        propensity to … ≠ multiplier

        For example m is the propensity to import.

        Usually multipliers are greater than 1 (and hence the name multiplier) and propensities less than 1.

        But the bigger issue which I intentionally withheld in my previous comment was the next para where you say something changes the denominator and it changing the numerator. It is not like that – it changes left hand side instead of the numerator.

        For example if the propensity to import increases, there is no reason to think that (what are assumed to be) exogenous variables automatically change. Because that is what exogenous variable is – a type of input. So for example there is no reason to think that government expenditure automatically changes. That is a decision of the government. It can be changed today or the next year.

        Anyway – careful about these things!

      • pilkingtonphil says:

        Perhaps. But I think that you’re just being picky here. The mistakes you and others are making regarding the BoP crisis are far more fundamental as they make up the substance of your argument.

  4. Jan says:

    Great read Philip.Interesting take on the whole math in econ thing and i haven´t read much by Tony Lawson as i should, but it seems he deserve to spend much more time on!Keep the good work up Philip!

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