Saturday, February 12, 2011

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.


  1. I like the comment section on Thoma's page, but I am reading the LeBaron paper, it is great and as I read it I convert to my channel model (in my head), but it is hard to comment on this simple window. So I move to Thoma's site.

  2. Yep. We're still here. We read as regularly as you post ;-). Keep on keeping us informed.

  3. Nick, thanks... that comment made me smile. I'd gladly trade quantity for quality as far as traffic is concerned. I have a couple of dozen half-written posts lying around, just need to find the time and motivation to wrap them up and publish. My goal is a steady state of about one a week.

  4. Any chance of a podcast of the discussion with Farmer et al.?

  5. excellent quickie

    the rationality of crowds ... mean

    is that about the assumption ????

    it really is a pure sim if you assume a mechanical reality to the economy
    ie a model-able system
    no matter how dynamical and fragile

    i know saying a system is historical lacks sharp contours as a notion
    but it seems harmless as an assumption

    if we can interact with a system in in performance improving ways
    we can build a clinical science no ???

    macro effective demand
    management :

    enhancing "remedies"
    like larger fiscal deficits
    for a high unemployment
    seemingly sluggish state
    of a market based
    for profit corporate dominated credit driven economy

    why require more till we reach some impasse
    where this remedy is no longer effective

    okay if we push to long and to hard
    with the deficit measures
    vide the notorious 70's
    we need to improve our handling of side effects like
    wage push inflation

    i stray

    but to this purpose
    maybe we don't need any more then a successful crtique of rat ex models
    perhaps we are not required to build a better mouse trap
    if we can use doc keynes patent elixir to "cure " the ill

  6. i guess i'm to in love with late godwin for my own goodwin

    complexity of causation as a claim doesn't have to mean
    hayekian quiessence macro policy wise
    we can see the record certain macro policy works about as expected lots of times least from a clearly defined class point of view
    what more do you need

    the plague of idle-ness is past
    the patients are back on their feet

  7. Tim, I don't think the conference was recorded but here's a quick overview of the panel discussion.

    Guesnerie and Farmer both argued that rational expectations need not be abandoned wholesale, that there are some applications for which it is a reasonable and useful modeling hypothesis. Farmer went further, arguing that the focus should be on instability rather than any particular methodology, and that one could build models of instability and crisis with or without RE. Frydman thought that all the models presented at the conference suffered from the same flaws at RE and referred to his own recent work in order to make this point - I have not read this work and will therefore withhold comment. Marcet's comments I have summarized above - he thinks that we have gone well beyond the early learning literature (which was largely about convergence to RE) and are now building models of expectation dynamics to address positive questions.

    Paine, complexity does not have to mean quiescence, quite right and well put.

    Matt, I looked at your comments on Mark's page but haven't yet been able to grasp your argument...

  8. If you post it, we will come. It is appreciated.

  9. Thanks for the post. For an engineer, this was informative. For example, I had not really seen a mathmatical definition of the rational expectations hypothesis anywhere, the reference to the Muth paper certainly helps.

    Do you know if there is any work on stability of the rational expectations equilibrium? I guess this is an econophysics-y question, but I guess I am interested in modeling assumptions where small deviations/shocks from the rational expectations distributions are corrected. Perhaps the question does not make sense. Also do people look at higher moments other than expectations?

    I see you address some of the convergence question above, but does skewness/kurtosis play a part?

  10. Archisman, I think that the stability of rational expectations equilibrium paths under the dynamics of disequilibrium adjustment is an enormously important and under-explored research area in economics. I've discussed this issue in previous posts, for instance here.

  11. Are there generic predictions that are associated with particularly classes of models? If so, how do the differ?

    For example, what are Mr. LeBaron's models revealing that behavioral models do not?

    I also wonder if behaviorial economics doesn't have a supply side impact, even if traders themselves are aware of exploitable cognitive failures to act rationally, since most trading takes place with other people's money. Continued survival in the financial markets has as much to do with an ability to convince wealthy individuals to use them in making investments as it does with actual return maximizing prowess. A trader with a better strategy for securing high returns might have a harder time raising capital than a trader with a strategy that makes sense to investors despite its limitations.

  12. Andrew, these are important and valid points. Regarding the latter, this is the basis of the "limits to arbitrage" literature: investors may withdraw from loss making funds just when the expected returns are highest. And yes, investor psychology can help us understand why.

    But what I resist is to reach for behavioral explanations reflexively for every empirical puzzle. For example, both Laibson and LeBaron presented models to explain the same set of facts: short run momentum, mean-reversion, and volatility clustering. Laibson's model had homogeneous investors who make forecasts based on much shorter lags than those generating the data. Le Baron had a population of forecasting rules in competition with each other.

    Did the models yield different predictions? No, because they were designed to account for the same set of facts. So how do we evaluate them? On the basis of two criteria: robustness and explanatory power.

    As Marcus Brunnermeier pointed out (politely) in his comments on the Laibson paper, the data generating process itself was assumed to create momentum and mean reversion, which was then amplified by investor behavior. This assumes (to a degree) what one is trying to explain. In contrast, LeBaron made no such assumption about the data generating process so his model had greater explanatory power.

    Furthermore, the behavioral model was not robust: small changes in assumptions would result in entirely different predictions. Allow investors using longer lag lengths to enter the market and they will take over, altering the model's predictions in the process. Again, Le Baron's model was more robust along this dimension: it was not obvious, at least to me, how a new forecasting rule omitted from his model would have done better than the incumbent rules.

  13. A very helpful explanation. Thank you.

  14. obviously agents operate with different "move - position"
    choice systems
    as well as data bases

    my intuition as one
    " adds in "
    varieties of systems
    the market behaviour
    approach each other
    and yet we have influenzas that shake the grip of these systems
    and generate rational ..if collectively self defeating ..

    i share joe stigs paradigm preference for rational agents
    but i don't think it "matters " in "simulating " collective behaviours of markets
    that are constantly generating internal contradiction
    ie endogenous shocks

    uncertainty in the end overwhelms rational
    "method " because inherent spontaneous chaotic variability triumphs ..until the market "blows up " or is harnessed

  15. andrew's
    using " other peoples money"
    ie introducing
    agent principal incentive contradictions
    brings on another set of dimensions entirely

    fraud swindle puffery you name
    the marketing of "ability "
    with its deceptions fads etc

    are markets self correcting along these dimensions
    only if crashing into a wall is
    labeled a braking system ??

  16. I enjoy your blog posts. You are a very careful thinker, and I appreciate your effort.

    In a conference such as the one you reference, do authors and commenters distinguish theoretical efforts at a priori analysis from quasi-empirical efforts to model the functioning of actual and specific institutions?

  17. Thanks Bruce, the effort is considerable but mostly worthwhile. To answer your question - not explicitly. But both types of analysis were on display at this particular conference.

  18. I'm extremely late to this party, but would you happen to have the program for the conference you linked in the beginning?

    The link redirects to the department home page.

  19. Yes, for some reason the link no longer leads to the conference page, and I can't find the program online anywhere. Sorry about that.