{"id":1918,"date":"2010-07-01T11:10:09","date_gmt":"2010-07-01T11:10:09","guid":{"rendered":"http:\/\/meeseeks:5080\/blog\/?p=1918"},"modified":"2010-07-01T11:10:09","modified_gmt":"2010-07-01T11:10:09","slug":"the-glass-bead-game-of-mathematical-economics","status":"publish","type":"post","link":"https:\/\/vukutu.com\/blog\/2010\/07\/the-glass-bead-game-of-mathematical-economics\/","title":{"rendered":"The glass bead game of mathematical economics"},"content":{"rendered":"

Over at the economics blog, A Fine Theorem<\/a>, there is a post about economic modelling.
\nMy first comment is that the poster misunderstands the axiomatic method in pure mathematics.\u00a0 It is not the case that “axioms are by assumption true”<\/em>.\u00a0 Truth is a bivariant relationship between some language or symbolic expression and the world.\u00a0 Pure mathematicians using axiomatic methods make no assumptions about the relationship between their symbolic expressions of interest and the world.\u00a0\u00a0 Rather they deduce consequences from the axioms, as if<\/em> those axioms were true, but without assuming that they are.\u00a0\u00a0\u00a0 How do I know they do not assume their axioms to be true?\u00a0 Because mathematicians often work with competing, mutually-inconsistent, sets of axioms, for example when they consider both Euclidean and non-Euclidean geometries, or when looking at systems which assume the Axiom of Choice and systems which do not.\u00a0\u00a0 Indeed, one could view parts of the meta-mathematical theory called Model Theory<\/em> as being the formal and deductive exploration of multiple, competing sets of axioms.
\nOn the question of economic modeling, the blogger presents the views of Gerard Debreu<\/a> on why the abstract mathematicization of economics is something to be desired.\u00a0\u00a0 One should also point out the very great dangers of this research program, some of which we are suffering now.\u00a0 The first is that people \u2014 both academic researchers and others \u2014 can become so intoxicated with the pleasures of mathematical modeling that they mistake the axioms and the models for reality itself.\u00a0 Arguably the widespread adoption of financial models assuming independent and normally-distributed errors was the main cause of the Global Financial Crisis of 2008, where the errors of complex derivative trades (such as credit default swaps) were neither independent nor as thin-tailed as Normal distributions are.\u00a0 The GFC led, inexorably, to the Great Recession we are all in now.
\nSecondly, considered only as a research program, this approach has serious flaws.\u00a0 If you were planning to construct a realistic model of human economic behaviour in all its diversity and splendour, it would be very odd to start by modeling only that one very particular, and indeed pathological, type of behaviour examplified by homo economicus<\/em>, so-called rational economic man<\/em>.\u00a0\u00a0 Acting with with infinite mental processing resources and time, with perfect knowledge of the external world, with perfect knowledge of his own capabilities, his own goals, own preferences, and indeed own internal knowledge, with perfect foresight or, if not, then with perfect knowledge of a measure of uncertainty overlaid on a pre-specified sigma-algebra of events, and completely unencumbered with any concern for others, with any knowledge of history, or with any emotions, homo economicus <\/em>is nowhere to be found on any omnibus to Clapham.\u00a0 Starting economic theory with such a creature of fiction would be like building a general theory of human personality from a study only of convicted serial killers awaiting execution, or like articulating a general theory of evolution using only a hand-book of British birds.\u00a0\u00a0 Homo economicus <\/em>is not where any reasonable researcher interested in modeling the real world would start from in creating a theory of economic man.
\nAnd, even if this starting point were not on its very face ridiculous, the fact that economic systems are complex adaptive systems should give economists great pause. \u00a0 Such systems are, typically, not continuously dependent on their initial conditions, meaning that a small change in input parameters can result in a large change in output values. \u00a0 In other words, you could have a model of economic man which was arbitrarily close to, but not identical with, homo economicus<\/em>, and yet see wildly different behaviours between the two.\u00a0 Simply removing the assumption of infinite mental processing resources creates a very different economic actor from the assumed one, and consequently very different properties at the level of economic systems.\u00a0 Faced with such overwhelming non-continuity (and non-linearity), a naive person might expect economists to be humble about making predictions or giving advice to anyone living outside their models.\u00a0\u00a0 Instead, we get an entire profession labeling those human behaviours which their models cannot explain as “irrational”.
\nMy anger at The Great Wen of mathematical economics arises because of the immorality this discipline evinces: \u00a0 such significant and rare mathematical skills deployed, not to help alleviate suffering or to make the world a better place (as those outside Economics might expect the discipline to aspire to), but to explore the deductive consequences of abstract formal systems, systems neither descriptive of any reality, nor even always implementable in a virtual world.<\/p>\n","protected":false},"excerpt":{"rendered":"

Over at the economics blog, A Fine Theorem, there is a post about economic modelling. My first comment is that the poster misunderstands the axiomatic method in pure mathematics.\u00a0 It is not the case that “axioms are by assumption true”.\u00a0 Truth is a bivariant relationship between some language or symbolic expression and the world.\u00a0 Pure […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[23,25,50],"tags":[],"class_list":["post-1918","post","type-post","status-publish","format-standard","hentry","category-decision-theory","category-economics","category-mathematics","p1","y2010","m07","d01","h11"],"_links":{"self":[{"href":"https:\/\/vukutu.com\/blog\/wp-json\/wp\/v2\/posts\/1918","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vukutu.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/vukutu.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/vukutu.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/vukutu.com\/blog\/wp-json\/wp\/v2\/comments?post=1918"}],"version-history":[{"count":0,"href":"https:\/\/vukutu.com\/blog\/wp-json\/wp\/v2\/posts\/1918\/revisions"}],"wp:attachment":[{"href":"https:\/\/vukutu.com\/blog\/wp-json\/wp\/v2\/media?parent=1918"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vukutu.com\/blog\/wp-json\/wp\/v2\/categories?post=1918"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vukutu.com\/blog\/wp-json\/wp\/v2\/tags?post=1918"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}