Friday, 14 October 2011

Robert Lucas attacked by chaos machine

Robert Lucas, a godfather of the rational expectations movement has come in for a lot of criticism recently.  Here's my own brief attempt.

Imagine an artificial economy with just two actors, who each have to guess game theory style at the likely behaviours, economically, of the other.  They both are fully cognisant of each other's economic models.  All they need to do is apply those rules to apply a decent best guess of model parameters - the legendary sloppy assumptions - and we'll sit back and watch well known macro-economic phenomena emerge from their identically specified micro-level models of themselves as economic actors.

Now lets imagine those models shared a similar property (as many many models do) with the logistic function, $X(n+1)=rX(n)(1-X(n))$, namely they are riddled with chaos.  Our two agents might agree perfectly on each other's model and what's more be correct but when it comes to apprximating the model parameters, needless to say, they cannot guess the other's starting value with infinite precision.  The result, over certain wide ranges of the parameter phase space - is utter chaos.  All it takes for rational expectations to be shown to be inadequate is some likelihood of such radical non-linearity in real (no pun intended) sets of micro-founded models of agent interactions within the wider rational expectations movement.

How would a rational exceptions robot respond to the possibility, or even more strongly, the knowledge that their models had 'dark areas'.  I guess the sensible thing to do is to apply probabilistic approximations around those regimes.  And those heuristics too would probably be amenable to the rational expectations approach.  I guess the rational expectations agent can operate under radical uncertainty.  But what if there were clear patterns of information which cry out for some kind of rational expectations model to develop, while an entirely different initial parameter set results in a different rational-seeming system to lure the unsuspecting rational economic agent.  And what's worse, where do you draw the line between uncontroversially certain parts of your model, and the stable-seeming boundaries at the edge of chaos?

1 comment:

  1. I had the above thought while reading one of the afore-mentioned kickings