Belief Heterogeneity

There was an interesting conference at Columbia yesterday (though not nearly as interesting as the momentous events unfolding elsewhere at the time). The theme was "Heterogeneous Expectations and Economic Stability" and this is how the organizers (Ricardo Reis and Mike Woodford) described the goal of the meeting:

Conventional models in both macroeconomics and finance are based on the hypothesis of rational expectations, under which all agents are assumed to have common expectations, corresponding to the probabilities implied by the economist’s model. The adequacy of this familiar hypothesis has been called into question by recent events, however, notably the instability resulting from the boom and bust in real estate prices. The purpose of this conference is to bring together researchers exploring alternative approaches to modeling the dynamics of expectations, with particular attention to applications in macroeconomics and finance. We have sought to bring together proponents of a variety of approaches, who may not frequently engage one another, in the hope of reaching conclusions about which directions are most promising at this time.

And, indeed, the collection of papers presented were methodologically diverse. Although any such classification is bound to be coarse and imperfect, there seem to be four different directions in which research on expectations is proceeding. First, there is the approach of near-rational expectations, in which intertemporal optimization and Bayesian rationality are maintained but allowance is made for heterogeneous prior beliefs. Then there is the behavioral approach, which endows agents with heuristics based on regularities identified in laboratory experiments. Third, there is the evolutionary approach, which allows for a broad range of competing forecasting rules with the population composition shifting over time under pressure of performance differentials. And finally, the empirical approach, which treats expectations as a state variable to be measured using survey or market data and explained just as one would explain output or inflation. Each of these perspectives was on prominent display at the conference.

Regular readers of this blog (if there are any left, given the recent decline in my rate of posting) will know that I am deeply skeptical of the behavioral approach to trading strategies, for the simple reason that behavior in high stakes environments with strong selection pressures driving entry and exit is unlikely to be psychologically typical in the sense of reflecting outcomes of lab experiments with standard subject pools. What might be a common behavioral trait in the population at large could be extremely rare among traders, especially if such traits can be exploited with ease by other market participants. By the same token, behavior that is pathological in the lab could well become widespread in financial markets from time to time. As a result my favored approach to trading strategies in general and forecasting rules in particular is ecological.

Not surprisingly, then, the presentation I found most appealing was that of Blake LeBaron. Blake is a pioneer in the development of agent-based computational models of financial markets, and the paper he presented belonged to this class. A large number of different forecasting strategies, some based on fundamental information and others on technical data analysis, compete with each other and with a traditional buy-and-hold strategy in his model. The resulting trading dynamics give rise to asset price returns that exhibit both moderate levels of short-run momentum as well as mean reversion over longer horizons. Moreover, the long run population of forecasting rules is ecologically diverse, with both passive and active strategies well represented.

During the panel discussion at the end of the conference, Albert Marcet observed that the conference itself was symptomatic of a revolution in economic thought that is currently underway, prompted in large measure by the global financial crisis. If methodologies such as agent-based computational economics start to be published in major journals and attract attention from the most promising graduate students, then there really will be a revolution underway. But I'm not convinced that we're there yet.

One final thought. The conference organizers described the rational expectations hypothesis as one "under which all agents are assumed to have common expectations, corresponding to the probabilities implied by the economist’s model." This is an accurate characterization as far as the contemporary implementation of the hypothesis is concerned, but it is important to note that this is not the hypothesis originally advanced by John Muth in his classic paper. In fact, Muth cited survey data exhibiting "considerable cross-sectional differences of opinion" and was quite explicit in stating that his hypothesis "does not assert... that predictions of entrepreneurs are perfect or that their expectations are all the same.'' In Muth's version of rational expectations, each individual holds beliefs that are model inconsistent, although the distribution of these diverse beliefs is unbiased relative to the data generated by the actions resulting from these expectations. It is a wisdom of crowds argument, rather than one based on individual rationality.

Viewed in this manner, there a sense in which the heterogeneous prior models (with diverse beliefs centered on a model consistent mean) represent both a departure from the rational expectations hypothesis as currently understood, as well as a return to the original rational expectations hypothesis as formulated by Muth. The history of economic thought is full of such rather strange twists and turns.