Wednesday 3 June 2015

Mathiness: not just a problem of macro-economics

I was aware of the "mathiness" discussion initiated by the macro-economist Paul Romer, but have only recently read the articles because while the discussion was taking place I was finishing of an article for The Mathematical Intelligencer that presents a remarkably similar argument (noting that mathematicians consider a coffee cup and doughnut to be the same).

Romer's concern is in the field of economic growth - an area I am unfamiliar with -  but two related statements caught my attention
For the last two decades, growth theory has made no scientific progress  toward a consensus. ... The question posed here is why the methods of science have failed to resolve the disagreement between these two groups.
and, postulating on why science has failed to come to a consensus, Romer offers an explanation as "mathiness"
Like mathematical theory, mathiness uses a mixture of words and symbols, but instead of making tight links, it leaves ample room for slippage between statements in natural versus formal language and between statements with theoretical as opposed to empirical content.
My article for the Intelligencer is titled "Finance and Mathematics: where is the ethical malaise" and was written in response to a series of articles  about the role of mathematics in financial crises.  I begin my piece
Discussions of the role of mathematics in finance appearing in The Mathematical Intelligencer can be split into two classes. Marc Rogalski and Jonathan Korman capture a widespread fury at a collapse in commercial ethics while Ivar Ekeland  and Peter Haggstrom off er economic facts. The conclusions of Rogalski and Korman can be summarised as that mathematicians should spurn the financial world; Haggstrom and Ekeland point to technocratic solutions, characterised by better regulation. I do not buy into the argument that the problems of finance can be solved by regulations, it is, as both the U.K. and U.S. governments have identified, an ethical problem.
I go onto to explain that mathematics has not been neutral in recent financial crises
In their submission to the Parliamentary Commission on Banking Standards in 2013 the Bank of England was highly critical of how some fi rms have used advanced mathematical techniques to 'pull the wool' over the eyes of the regulator [para. 89] while U.S. authorities identified that this type of mathematical sleight of hand played a part in the 'London whale' episode [p 14]. The existence of the Gaussian copula as a 'truth-teller' of the value of complex debt portfolios played a central role in the Crisis of 2007-2009, justifying the actions of banks, despite its short-comings being known to mathematicians. In the early 1970s, the Black-Scholes-Merton framework played an important part in legitimising the re-emergence of financial derivatives markets. As long ago as 1877 a large, corporate, insurer defended their actions in undermining fraternal/mutual insurers to legislators with the argument that
 "There are certain fundamental rules . . . which can only be understood by actuaries, and it is impossible for me to go into here [p 198]"
 In my piece, for the mathematics community, I note that while mathematicians might see these abuses, which I am fairly certain could be ascribed to 'mathiness' as coined by Romer, as being abuses of mathematics, we do bear some responsibility.

Many mathematicians, but probably only a minority, argue that there is an issue with mathematics in that it is often used to obscure rather than enlighten.  Part of this trope is the presentation of mathematics as a mystical key that can unlock hidden truths:

In economics, my favourite example is Samuelson's account of how he 'discovered' Bachelier's thesis, much as Indiana Jones might uncover a magical artefact

(From the BBC programme "The Midas Formula/The Trillion dollar Bet")

This all might seem benign in to context of encouraging people to engage with mathematics, but when combined with he dominant philosophical paradigm of Foundationalism and finance, problems emerge.

Foundationalism sees language as being made up of statements that are either true or false and complex statements are valid if they can be deduced from true primitive statements. This approach is exemplified in the standard mathematical technique of axiom-theorem-proof and so arguments presented mathematically are automatically imbued with the quality of 'truth' and so hold authority.

I then give a Habermasian explanation of what happens when mathematics and finance come together.
the Enlightenment led to the objectification of nature and its mathematisation, which in turn leads to 'instrumental mindsets' that look to optimally achieve predetermined ends in the context of an underlying need to control external events. Where as during the seventeenth and eighteenth centuries public spaces emerged, the public sphere, which facilitated rational discussion that sought the truth in support of the public good, through the nineteenth century, mass circulation mechanisms came to dominate the public sphere and these were controlled by private interests. As a consequence, the public became consumers of information rather than creators of a consensus through engagement with information.
Habermas, and Pragmatic philosophy more generally, offer an antidote by switching the emphasis of what language says (whether it is true or false) to what it does
Specifically, the function of language is to enable different people to come to a shared understanding and achieve a consensus, this is de fined as discourse. Because discourse is based on making a claim, the claim being challenged and then justified, to be successful discourse needs to be governed by rules, or norms. The most basic rules are logical and semantic, on top of these are norms governing procedure, such as sincerity, and finally there are norms to ensure that discourse is not subject to coercion or skewed by inequality.
This is the basis of my claim that Reciprocity is a Foundation of Financial Economics.

With regard to the 'mathiness' discussion it is interesting to see that Romer argues the issues are in the collapse of 'economic norms', so are diagnosis and treatment appear aligned.  My criticism of Romer is mild, and it is that he has not presented his case in the context of Pragmatism, which would provide him with a firmer foundation for his case (I recommend Haack and Misak  as bedrocks).

However, I do not see my contribution as calming the criticism there has been for Romer, because my suggestion is the issue is not with one, or another, local mis-understanding but a fundamental issue with the dominant pardigm supporting science.  Economists might disagree on their growth models but they are likely to agree that science is based on Foundationalism.  This said, the problems Romer, and I, identify are pervasive, with science being unable to resolve many problems ranging from finance to climate change.

1 comment:

  1. I am not sure this really would resolve this problem, which is more of an issue with goals and intent than language. But, in the sense that expressive power does help to communicate intent more clearly, I can see one possible approach. The expressive power of mathematics is very flexible, but very low level. Thus, complex ideas require very long and abstruse mathematics, obscuring their meaning and making errors easy to hide.

    This has a analogy in programming languages: assembly language vs. high-level languages. Code written in assembly language is difficult to understand and debug compared to the equivalent in a high-level language. It has the superior flexibility, but it is also far less productive to use. I would suggest one approach might be to use a more expressive and compact language than mathematics that still retains the rigor. High-level programming language constructs are fairly universal and widely understood, so they might be used as an approach. Classes and control structures should be valuable to economics.

    I do think we are on the cusp of a new scientific paradigm and that economics will be one of the pioneer disciplines.


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