Monday, February 3, 2014

Rational Expectations and Animal Spirits

Along with the rest of modern macroeconomics, the rational expectations (RE) assumption has gotten quite a bit of flack lately. I don’t think all of it is deserved.  It is not the rational expectations (RE) assumption that is at fault: It is the rational expectations assumption in conjunction with the assumption of a unique equilibrium. 

In standard dynamic stochastic general equilibrium (DSGE) models there is a single rational expectations equilibrium. In the models I work with there are many rational expectations equilibria. Not just one, or two or three: but an infinite dimensional continuum of them. That is not a problem. It is an opportunity that I exploit to model the idea that beliefs matter. In my work, I close my models by adding an equation that I call a 'belief function'. The belief function is an effective way of operationalizing the Old Keynesian assumption of ‘animal spirits’. It is a forecasting rule that explains how people use current information to predict the future. That rule replaces the classical  assumption that the quantity of labor demanded is always equal to the quantity of labor supplied.

You might think that adding a belief function to operationalize animal spirits allows me to dispense with the rational expectations assumption since the belief function could be arbitrary. Not so. Even though we do not live in a stationary environment, our beliefs should be consistent with the outcomes that we would observe in a stationary world.  In such a world, beliefs should obey Abraham Lincoln’s dictum that “you can fool all of the people some of the time or some of the people all of the time but you can’t fool all of the people all of the time.”  In my view, that is the rational expectations assumption.

Suppose you are building a rational expectations model with a unique equilibrium. In that model, you would  not need to independently model a ‘belief function’.  The people in your model would need to forecast the future somehow, and presumably they would use some kind of forecasting rule.  But you would not need to know the parameters of that rule.  Whatever rule they use; it would have to be correct ‘on average’.

Stick with the unique RE assumption and suppose that the fundamentals change.  Perhaps there is a new Fed Chairperson, or perhaps someone invents a new technology. In a standard DSGE model, the rule that people use to forecast the future would need to change. The belief function in this world is endogenous.

Now move to my parallel universe where there is a continuum of RE equilibria.  In my universe the rule that people use to forecast the future is critical.  It is the belief function that selects the equilibrium. If people believe that there will be high unemployment; that belief will be self-fulfilling.

In my world, ask what happens if the fundamentals change.  Perhaps there is a new Fed Chairperson or perhaps there is a new technology.  In this world, the belief function selects a new equilibrium. Beliefs are fundamental!

Are beliefs really fundamental?  I think so. This is a not a radical idea; it is a new way of understanding an old one. Central bankers have known for a long time that expectations of future inflation are highly persistent. That persistence is often cited as one of the strikes against either the rational expectations assumption or the equilibrium assumption. I believe that both of those accusations are misplaced. Persistent expectations is a strike against rational expectations PLUS the uniqueness assumption. It is the uniqueness assumption that needs to go; not the rational expectations assumption which simply reflects a fact that we have known for a long time: Expectations are incredibly persistent. Welcome to my alternate reality!


  1. Hi Roger,

    “Welcome to my alternate reality!” And what a fascinating reality it promises to be, though some of us will need a more detailed map.

    You describe the rational expectations assumption in terms of Lincoln’s famous line, “You can fool all of the people some of the time or some of the people all of the time but you can’t fool all of the people all of the time.” I think Lincoln was actually saying that no person (political opportunist) can fool all of the people all of the time, whereas I think you’re claiming that all of the people (market participants) won’t make errant forecasts all of the time (in other words, there’s no “fooling” involved, or at least not much of it).

    If I’ve interpreted your view correctly – i.e., that everyone can’t make errant forecasts all of the time – then this would seem to a proposition no sane modeler of expectations could reject. Allowing a few market participants to forecast correctly from time to time isn’t a very demanding requirement.

    “Beliefs are fundamental!” It may be worth distinguishing between two kinds of beliefs: 1) beliefs about future states of nature, e.g., winter temperatures in New England next year; and 2) beliefs about future states of the economy that depend on conjectures about the future beliefs of others [Keynes’ “beauty contest”]. The first kind of beliefs can’t be self-fulfilling, but the second kind can be. By the same token, and more importantly, self-fulfilling beliefs need not be held by everyone. If a preponderance of firms believes employment will be high, then it will be high. But everyone’s expectations won’t be fulfilled. So, to conclude with a question, does your conception of a “belief function,” that is, your operationalization of “animal spirits,” assume that all agents experience the same degree of optimism or pessimism (or whatever measure of “animal spirits” you use in your model)?

    P.S. This is one of the most intriguing posts I’ve ever read!

  2. Thanks for your comment Greg.

    I'm a little more demanding than "allowing in a few market participants to forecast correctly from time to time". I want the belief function to have the property that it coincides with RE in stationary environments.

    Yes: it's worth separating beliefs about the state of nature from beliefs about others' beliefs.

    All of my existing work assumes homogenous beliefs. Agents are willing to trade because they have different preferences over outcomes. The issue of heterogeneity of beliefs is, for me, an important open question.

  3. Roger Farmer
    " Agents are willing to trade because they have different preferences over outcomes"

    Yes, but can there be *speculative* trade (in financial mkts) with multiple RE equilibria? The problem arises from Aumann's famous Agreeing to Disagree theorem.:
    " If two people have the same priors, and their posteriors for an event E are common knowledge, then these posteriors are equal."

    Also Milgram and Stokey (1982), Information, trade and common knowledge :
    "... when risk-averse traders begin at a Pareto optimal allocation (relative to their prior beliefs) and then receive private information (which disturbs the marginal conditions), they can still never agree to any non-null trade"

    The evidence for speculative trades in financial markets is, I think, pretty strong.

    Also, in the broader macroeconomy, a fair case can be made that the severity and persistence of the current recession has something to do with agents' pre-crisis plans not being realized.

    "The issue of heterogeneity of beliefs is, for me, an important open question."

    Good to read this. If only more equilibrium theorists were as open-minded, the criticism of RE would have been much more muted. After all, even most critics would concede that the idea of RE is certainly important in many contexts, and multiple equilibria perhaps even more so.

    1. Stokey and Milgrom no trade result assumes pareto optimality. Speculative trade can occur under RE if the world is pareto inefficient.

    2. hermanq and daniels
      Thanks for your comments.

      daniels is right about the no trade theorem. In my work, the set of participants is changing over time and that leads to trade in asset markets. I'm not sure how to identify a 'speculative trade'. In my work, everyone agrees about ex ante probabilities and that, I think, is what hermanq is uncomfortable with.

      The assumption of common priors is indeed a very strong assumption and one that I think it worth relaxing.

      There is a growing acceptance in the research community of models that drop the strong form of rational expectations; but no agreement yet of what to replace it with.


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