Mathematics, psychology, decisions

I attended a conference on the mathematics of finance last week. It seems that things would have gone better in 2007/8 if only policy makers had employed some mathematicians to critique the then dominant dogmas. But I am not so sure. I think one would need to understand why people went along with the dogmas. Psychology, such as behavioural economics, doesn’t seem to help much, since although it challenges some aspects of the dogmas it fails to challenge (and perhaps even promotes) other aspects, so that it is not at all clear how it could have helped.

Here I speculate on an answer.

Finance and economics are either empirical subjects or they are quasi-religious, based on dogmas. The problems seem to arise when they are the latter but we mistake them for the former. If they are empirical then they have models whose justification is based on evidence.

Naïve inductivism boils down to the view that whatever has always (never) been the case will continue always (never) to be the case. Logically it is untenable, because one often gets clashes, where two different applications of naïve induction are incompatible. But pragmatically, it is attractive.

According to naïve inductivism we might suppose that if the evidence has always fitted the models, then actions based on the supposition that they will continue to do so will be justified. (Hence, ‘it is rational to act as if the model is true’). But for something as complex as an economy the models are necessarily incomplete, so that one can only say that the evidence fitted the models within the context as it was at the time. Thus all that naïve inductivism could tell you is that ‘it is rational’ to act as if the  model is true, unless and until the context should change. But many of the papers at the mathematics of finance conference were pointing out specific cases in which the actions ‘obviously’ changed the context, so that naïve inductivism should not have been applied.

It seems to me that one could take a number of attitudes:

  1. It is always rational to act on naïve inductivism.
  2. It is always rational to act on naïve inductivism, unless there is some clear reason why not.
  3. It is always rational to act on naïve inductivism, as long as one has made a reasonable effort to rule out any contra-indications (e.g., by considering ‘the whole’).
  4. It is only reasonable to act on naïve inductivism when one has ruled out any possible changes to the context, particularly reactions to our actions, by considering an adequate experience base.

In addition, one might regard the models as conditionally valid, and hedge accordingly. (‘Unless and until there is a reaction’.) Current psychology seems to suppose (1) and hence has little to help us understand why people tend to lean too strongly on naïve inductivism. It may be that a belief in (1) is not really psychological, but simply a consequence of education (i.e., cultural).

See Also

Russell’s Human Knowledge. My media for the conference.

Dave Marsay

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About Dave Marsay
Mathematician with an interest in 'good' reasoning.

7 Responses to Mathematics, psychology, decisions

  1. Blue Aurora says:

    Glad to see you posting again, Dr. David Marsay.

    Speaking of mathematicians and the global financial crisis of 2007/2008…what is your view on Steve Keen’s mathematical model for Hyman P. Minsky’s Financial Instability Hypothesis?

    The article was published in 1995 in the Journal of Post Keynesian Economics…here is the citation for it.

    Keen, Steve. “Finance and Economic Breakdown: Modeling Minsky’s “Financial Instability Hypothesis”.” Journal of Post Keynesian Economics 17.4 (1995): 607-635.

    And here is a link to the article.

    http://www.debtdeflation.com/blogs/wp-content/uploads/papers/Keen1995FinanceEconomicBreakdown_JPKE_OCRed.pdf

    More recently, Steve Keen received a grant from the INET for an economic simulation computer programme called “MINSKY”. And even more recently, Keen has achieved his minimum fundraising target on Kickstarter.

    Furthermore, there are mathematicians from the venerable Fields Institute in Canada that are working with Steve Keen. Professor Matheus R. Grasselli of McMaster University is one of these people. Grasselli and his graduate student, Bernardo Costa-Lima, have published in the journal Mathematics and Financial Economics an article analysing the contents of Keen’s 1995 model.

    http://link.springer.com/article/10.1007%2Fs11579-012-0071-8

    If you aren’t at a university right now, then see this link below. Grasselli provides a free copy from his website.

    http://www.math.mcmaster.ca/~grasselli/GrasselliCostaLima_MAFE_published.pdf

    Keen’s model of Minsky’s Financial Instability Hypothesis is based off the mathematical models of the late Richard M. Goodwin, a heterodox economist that was fond of mathematical techniques…especially when it came to the Lotka-Volterra equations.

    What are your thoughts on these papers? What are your thoughts that there are people at the Fields Institute working with heterodox economists?

    Finally Dr. Marsay, do you have any comment on the use of the term “ergodicity” and “non-ergodicity” in economics? I know that ergodicity is defined pretty specifically and rather technically by mathematicians and other specialists on this matter. Paul Davidson, the founding editor of the Journal of Post Keynesian Economics, accuses the “mainstream” of having an “Ergodic Axiom” which states that financial markets are “ergodic”. Davidson argues that the financal markets are in fact, “non-ergodic”. What are your thoughts?

    Here are some links to articles where Davidson uses the terms “ergodic” and “non-ergodic”.

    http://www.jstor.org/stable/4537730 (1982)

    http://www.jstor.org/stable/4538058 (1987)

    http://www.jstor.org/stable/1942706 (1991)

    http://www.jstor.org/stable/4538504 (1996)

    http://www.jstor.org/stable/4538847 (2003)

    http://econ.bus.utk.edu/publications/davidsonpapers/realworld%20econrview(2).pdf (2012)

    • Dave Marsay says:

      Thanks. I have a considerable backlog, which I hope to clear this week. Meanwhile, there was a talk noting that economies are not ergodic, and noting that many economists seem to suppose that it is. Yawn. I am not aware of any sense in which it is sensible for policy-makers to assume ergodicity. But I am not clear that talking about ergodicity is a good way to engage with policy wonks, or that assumptions of ergodicity are a ‘root cause’. Watch this space for more.

  2. Reblogged this on Get "fit for randomness" [with Ontonix UK] and commented:
    According to naïve inductivism we might suppose that if the evidence has always fitted the models, then actions based on the supposition that they will continue to do so will be justified. (Hence, ‘it is rational to act as if the model is true’). But for something as complex as an economy the models are necessarily incomplete, so that one can only say that the evidence fitted the models within the context as it was at the time…

  3. Or it may be that people try to coordinate because them holding the same asset class keeps the price high. At least for some time. http://www.financialconventions.com/herding-or-conventions/ 😉

    • Dave Marsay says:

      I was thinking about general dogmas, such as ‘the end of boom and bust’ rather than specific beliefs such as ‘this is a good stock’. Many people get up early to buy stocks that have been recommended, wait for the many to buy them, and then dump to take a quick profit. Occasionally they may get caught out, such as when there is some bad news that morning. It seems to me that this is all part of regular trading, and that traders can adapt to make a reasonable profit. My concern is more about the global co-ordination of thinking stocks (and borrow-to-let housing) virtually risk-free propositions. (But good blog.)

      • I’m also refering somehow more to a “timing” task than to a stock picking task. There are so many stocks that it is not easy to coordinate to choose some of them (although if you have a bloomberg terminal and make some classic stock screening you may end up with the same list as many of your pears). But it is much more natural to emagine how investors coordinate between entire asset classes, because there aren’t as many of them, like when switching from one type of risky assets (stocks), to another (high yield bonds) or to a less risky class (investment grade or cash) etc.

        In respect to the adoption of a flawed model to value securities, this may be the result of the coordination purpose it plays. The fact that some were able to sell the securities at approximately the same price they payed for it (because others used the same bell curve distribution as they did) enforced the legitimacy of the model. The more it was used the more it appeared correct because it had an influence on asset prices by coordinating market valuations to what the model suggested.

  4. Dave Marsay says:

    Vladimir, I agree with you (and Keynes and Soros) that the less tangible assets are, the more they are subject to reflexivity: they can tend – for a while – to behave as they are expected to behave. But there are other factors. The financial industry routinely process in ‘risk’, by which it means volatility, which it judges historically. In the short-run (if Keynes et al are correct) this ‘neutral attitude to risk’ is ‘correct’ and those who adopt it will do better than those who are more far-sighted – in the short run. The long-run impact depends on who you are. For example if you are young-ish and saving for retirement then to maximize your expected pension pot you ‘should’ be more risk averse than a fund manager would typically be, even though in the short-run others will do better than you. So the problem is not just co-ordination, although that does make things worse.

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