Sunday, January 19, 2014

Rational Agents: Irrational Markets



I am going to stake out a position that Amartya Sen, in his lovely article on rational fools, ascribes to Edgeworth in his book, Mathematical Psychics: namely, that agents are rational in a narrowly defined sense. I am willing to make that assumption because, as I will argue, the financial markets would go very badly wrong most of the time even if agents were fully rational in the sense in which economists define rationality.

Edgeworth introduced what he called his first principle of economics which is that "every agent is actuated only by self interest." As Sen points out, Edgeworth was not naive enough to think that people behave exactly in the way he portrays them. In Sens's words,
... Edgeworth himself was quite aware that [his] first principle of Economics was not a particularly realistic one. Indeed, he felt that "the concrete nineteenth century man is for the most part an impure egoist, a mixed utilitarian." This raises the interesting question as to why Edgeworth spent so much of his time and talent in developing a line of inquiry the first principle of which he believed to be false.
Sen goes on to provide an answer to his own question, arguing that
Edgeworth, did not think the assumption to be fundamentally mistaken in the particular types of activities to which he applied what he called "economical calculus": (i) war and (ii) contract.
Like Edgeworth, I believe that the rationality assumption is useful to describe much of economic behavior. Unlike Shiller, I do not think we need to move beyond that assumption to explain asset market fluctuations.

In my own work, I have shown that the labor market can go very badly wrong even when everybody is rational.  My coauthors and I showed in a recent paper, that the same idea holds in financial markets. Even when individuals are assumed to be rational; the financial markets may function very badly.1

In my coauthored paper, we describe a world populated by rational utility maximizers. We make only two, reasonable, changes to the representative agent model. We allow for two kinds of agents instead of one, and unlike the standard model, our agents do not live forever; they are born and they die. Those assumptions turn out to be sufficient to cause huge inefficient swings in asset prices. Asset market fluctuations occur because agents are unable to insure against the state of the world into which they are born.

Figure 1: The Invariant Distribution of Human Wealth

Figure 1 is a plot, taken from the paper, that shows the distribution of the expected value of the earnings of a new born person. The figure illustrates the differing lifetime opportunities of being born into a boom or a recession. And since human wealth and stock market wealth move together in our model, the picture also illustrates the range of values that can be taken by the price earnings ratio.

Miles Kimball and I have both been arguing that stock market fluctuations are inefficient and we both think that government should act to stabilize the asset markets. Miles' position is much closer to that of Bob Shiller; he thinks that agents are not always rational in the sense of Edgeworth. Miles and Bob may well be right. But in my view, the argument for stabilizing asset markets is much stronger. Even if we accept that agents are rational, it does not follow that swings in asset prices are Pareto efficient. But whether the motive arises from irrational people, or irrational markets; Miles and I agree: We can, and should, design an institution that takes advantage of the government's ability to trade on behalf of the unborn. More on that in a future post.


1. Roger E. A. Farmer, Carine Nourry and Alain Venditti, "The Inefficient Markets Hypothesis; Why Financial Markets do not Work Well in the Real World. "NBER working paper 18647


  1. I wish I had a better intuition for what is going on in your model. Page 11 of the paper is helpful in this regard, but still unsatisfying. The best I can intuit is something like this: "High interest rates (i.e. high prospective asset returns and low current asset prices) are a self-fulfilling prophecy because they make older people rich (raise permanent income), which makes impatient older people want to borrow against future income, and this demand for borrowing results in the prophesied high interest rates." But this description is missing the stochastic aspect entirely, and it seems odd, because I would think that high interest rates would make impatient older people poor even if they make older people in general rich. And my mind gets lost when I try to think about whether there is some degree of impatience small enough to make a person prefer high interest rates but large enough to make them want to borrow.

  2. Professor Farmer,

    Your posts are very interesting - many thanks.

    Just want to remark on one point you made above, and what Keynes thought of the Victorian (classical) economists:

    You write:


    "I am not convinced that we need to go much beyond the rationality assumption"

    Keynes himself, however, I feel thought that that particular form critical enquiry WAS important:

    He writes:


    In this sense how preferences are formed are important. Are they genetic and innate? Or are they formed more in line with what I think would be a Marxian interpretation which says that they become exogenously shaped by capitalism (granted that Keynes himself was as critical of Marx as he was the Classicals).

    Is there a danger in abstracting from deeper philosophical questions about humanity (or empirical evidence about human behaviour) and assuming rationality and basing analysis on micro-economic foundations which assume unlimited wants and limited resources (greed) - I am assuming these are the micro-foundations - eg budget lines and indifferent curves - that the whole theoretical edifice is subject to "marketplace idols"?

    You say it is time to think outside the box. Does that include the Edgeworth Box?

    1. ssmathhews
      Preferences are clearly shaped by society.

      Does that include the Edgeworth Box?

      YES: most certainly.

  3. Brad DeLong posted a long time ago, a paper of even longer ago by today's US Fed Chair, and George Akerlof -- showing this result with the envelope theorem.

    1. Do you mean the Akerlof and Yellen paper on menu costs?

