Why economic models constantly crash15 June, 2015 at 16:07 | Posted in Economics | 1 Comment
To understand real world decisions and unforeseeable changes in behaviour, stationary probability distributions are of no avail. In a world full of genuine uncertainty — where real historical time rules the roost — the probabilities that ruled the past are not necessarily those that will rule the future.
In most aspects of their lives humans must plan forwards. They take decisions today that affect their future in complex interactions with the decisions of others. When taking such decisions, the available information is only ever a subset of the universe of past and present information, as no individual or group of individuals can be aware of all the relevant information. Hence, views or expectations about the future, relevant for their decisions, use a partial information set, formally expressed as a conditional expectation given the available information. Moreover, all such views are predicated on there being no unanticipated future changes in the environment pertinent to the decision. This is formally captured in the concept of ‘stationarity’. Without stationarity, good outcomes based on conditional expectations could not be achieved consistently … Unfortunately, in most economies, the underlying distributions can shift unexpectedly. This vitiates any assumption of stationarity. The consequences for ‘dynamic stochastic general equilibrium models’ [DSGEs] are profound … The mathematical basis of a DSGE model fails when distributions shift. This would be like a fire station automatically burning down at every outbreak of a fire. Economic agents are affected by, and notice such shifts. They consequently change their plans, and perhaps the way they form their expectations. When they do so, they violate the key assumptions on which DSGEs are built … It seems unlikely that economic agents are any more successful than professional economists in foreseeing when breaks will occur, or divining their properties from one or two observations after they have happened. That link with forecast failure has important implications for economic theories about agents’ expectations formation in a world with extrinsic unpredictability. General equilibrium theories rely heavily on ceteris paribus assumptions – especially the assumption that equilibria do not shift unexpectedly. The standard response to this is called the law of iterated expectations. Unfortunately, as we now show, the law of iterated expectations does not apply inter-temporally when the distributions on which the expectations are based change over time. To explain the law of iterated expectations, consider a very simple example – flipping a coin. The conditional probability of getting a head tomorrow is 50%. The law of iterated expectations says that one’s current expectation of tomorrow’s probability is just tomorrow’s expectation, i.e. 50%. In short, nothing unusual happens when forming expectations of future expectations. The key step in proving the law is forming the joint distribution from the product of the conditional and marginal distributions, and then integrating to deliver the expectation … The law of iterated expectations need not hold when the distributions shift. To return to the simple example, the expectation today of tomorrow’s probability of a head will not be 50% if the coin is changed from a fair coin to a trick coin that has, say, a 60% probability of a head.
Time is what prevents everything from happening at once. To simply assume that economic processes are stationary — or even ergodic — is not a sensible way for dealing with the kind of genuine uncertainty that permeates open systems such as economies. It only leads to forecast failures and crashed models.
When we cannot accept that the observations, along the time-series available to us, are independent … we have, in strict logic, no more than one observation, all of the separate items having to be taken together. For the analysis of that the probability calculus is useless; it does not apply … I am bold enough to conclude, from these considerations that the usefulness of ‘statistical’ or ‘stochastic’ methods in economics is a good deal less than is now conventionally supposed … We should always ask ourselves, before we apply them, whether they are appropriate to the problem in hand. Very often they are not … The probability calculus is no excuse for forgetfulness.