All entries for November 2009

Faith and falsification: the case of Competitive Equilibrium

From our religious correspondent

This is not a meeting of the Pope and the Archbishop to discuss matters ecumenical: but it may be the next best thing! For here in the top floor of the Maths department of a well-known British university, a leading economist and his colleague are explaining to their mathematical counterparts the mysteries of General Equilibrium Theory; and, what’s more, showing why the Competitive Equilibrium paradigm (CEp) has scientific validity. Some, they say, have argued that the idea that people maximise utility by using markets is so general as to be empty: but this charge is refuted on the grounds that the theory generates predictions that can be falsified. These predictions take the form of inequalities; and the mathematical issue up for discussion is how best to find these inequalities.

No specific evidence or concrete examples are offered: but a helpful characterisation is given in the context of a consumer buying two goods, x and y, with opportunity sets which depend on relative prices. A figure is drawn on the board, see below, and is used to argue that the kind of behaviour which, if widely observed, would refute the CEp is where a consumer wants to lots of good y when it is expensive relative to x, see point A, but wants to buy less of y when, on a separate occasion, it has become much cheaper , see point B.

Observations of points such as A and B would, apparently, count as falsifying CEp; and the crucial inequalities are those that rule out of such choices

Some technical discussion ensues as to whether the Tarski-Seidenberg theorem might be used in this context -- with no common ground among the mathematicians. But what of alternative theories, one mathematician asks: could ‘herd behaviour’ not generate observations like A and B? Is there not an alternative paradigm – of behavioural economics – that is consistent with such choices? From the CEp perspective, he is reminded, such choices constitute irrational behaviour; and the proposed alternative is not clearly formulated and lacks clear predictions (and so, by implication, lacks the scientific credibility claimed for CEp).

As this learned discussion proceeds, however, something peculiar is occurring: like the mountain beside the lake in Wordsworth’s Prelude - that seems to change shape and rear up on high as he rows towards it - the figure on the board seems to be changing and acquiring new significance. Instead of y and x, the words ‘Housing’ and ‘Liquid assets’ appear ; and the episodes now have labels attached to them, ‘House price Bubble’, and ‘Credit Crunch’. See Figure 2 for an artist’s impression.

Oblivious of this development, the speaker continues with eloquent exposition of the scientific credo being espoused. Behind him on the board, however, there is this example, familiar to all in the room, that seems to constitute a refutation of the theory that is being advanced! People wanted to buy houses when they were expensive and now - after the housing bubble has burst - they greatly prefer liquid assets (as long as they are government guaranteed)!

Should someone not draw the speaker’s attention to what is on the board behind him? Well, there are issues, like houses and liquid assets not being consumer products; so it’s more like portfolio allocation than consumer choice; and besides there are dynamic factors at work here,…

But, at this point, time runs out and the meeting ends promptly. All participants leave the room to another group, who - in preparation for their session - wipe the board quite clean.

So it is that the crucial issue - of whether the Tarski-Seidenberg theorem will open the way to a more general approach to the scientific testing of CEp – has been left unresolved, at least for now!

27 November 2009

Footnote

In early papers showing that asset prices varied a good deal more than the underlying fundamentals, the economist Robert Shiller cast doubt on the idea that asset prices are in fact forecasts of future fundamentals. Later, in his famous book entitled Irrational Exuberance, published before the US stock market collapse of 2001, he warned that US share prices were seriously overvalued. He followed this with a similar forewarning of the ending of the housing bubble, based largely on long run data he had collected on US house prices. In both cases he appeals to behavioural factors. (So too do he and Akerlof in their latest book.)

Shiller, R. J. (2000). Irrational Exuberance, Princeton NJ: Princeton University Press

                    (2008). The Subprime Solution, Princeton, NJ: Princeton University Press

Akerlof, George and Robert Shiller (2009). Animal Spirits, Princeton NJ: Princeton    

                                                                                                            University Press

Marcus Miller : 29 Nov 2009 23:43 |  Tags: Competitive Equilibrium Scientific Valididiation |  Comments (0) |  Close comments |  Report a problem