Friday, April 24, 2015

Beyond 1950's Economic Theory: Nonlinearity, Multiple Equilibria and Sticky Prices

David Glasner has a very nice post on Price Stickiness and Economics with great comments from Rajiv Sethi,  Richard Lipsey and Kevin Donoghue among others. David reacts to a post from Noah Smith: this is all classic stuff

Here is David
While I am not hostile to the idea of price stickiness — one of the most popular posts I have written being an attempt to provide a rationale for the stylized (though controversial) fact that wages are stickier than other input, and most output, prices — it does seem to me that there is something ad hoc and superficial about the idea of price stickiness and about many explanations, including those offered by Ball and Mankiw, for price stickiness. I think that the negative reactions that price stickiness elicits from a lot of economists — and not only from Lucas and Williamson — reflect a feeling that price stickiness is not well grounded in any economic theory.
 Let me offer a slightly different criticism of price stickiness as a feature of macroeconomic models, which is simply that although price stickiness is a sufficient condition for inefficient macroeconomic fluctuations, it is not a necessary condition. It is entirely possible that even with highly flexible prices, there would still be inefficient macroeconomic fluctuations. And the reason why price flexibility, by itself, is no guarantee against macroeconomic contractions is that macroeconomic contractions are caused by disequilibrium prices, and disequilibrium prices can prevail regardless of how flexible prices are.
This is my response, first posted as a comment on David's blog,
I have a somewhat different take. I like Lucas’ insistence on equilibrium at every point in time as long as we recognize two facts. 1. There is a continuum of equilibria, both dynamic and steady state and 2. Almost all of them are Pareto suboptimal.
The Arrow-Hahn distaste for RBC models was as much a distaste for the policy implication as it was for the method. At least that’s what I gleaned from conversations with Frank. Perhaps Ken Arrow reads blogs and will jump in and prove me wrong.
David replies...
Roger, I think equilibrium at every point in time is ok if we distinguish between temporary and full equilibrium, but I don’t see how there can be a continuum of full equilibria when agents are making all kinds of long-term commitments by investing in specific capital. Having said that, I certainly agree with you that expectational shifts are very important in determining which equilibrium the economy winds up at. I would certainly be curious to know what Arrow makes of RBC theory, but it would be shocking to me if he had anything positive to say about it. I thought that he always tried to emphasize the ways in which the assumptions of the Arrow-Debreu model deviated from real world conditions.
I agree with much of this. My response to David, which I have also posted on Uneasymoney....
I am comfortable with temporary equilibrium as the guiding principle, as long as the equilibrium in each period is well defined. By that, I mean that, taking expectations as given in each period, each market clears according to some well defined principle. In classical models, that principle is the equality of demand and supply in a Walrasian auction. I do not think that is the right equilibrium concept.
Hicks wanted to separate ‘fix price markets’ from ‘flex price markets’. I don't think that is the right equilibrium concept either. I prefer to use competitive search equilibrium for the labor market. Search equilibrium leads to indeterminacy because there are not enough prices for the inputs to the search process. Classical search theory closes that gap with an arbitrary Nash bargaining weight. I prefer to close it by making expectations fundamental.
Once one treats expectations as fundamental, there is no longer a multiplicity of equilibria. People act in a well defined way and prices clear markets. Of course ‘market clearing’ in a search market may involve unemployment that is considerably higher than the unemployment rate that would be chosen by a social planner. And when there is steady state indeterminacy, as there is in my work, shocks to beliefs may lead the economy to one of a continuum of steady state equilibria.
That brings me to the second part of an equilibrium concept. Are expectations rational in the sense that subjective probability measures over future outcomes coincide with realized probability measures? That is not a property of the real world. It is a consistency property for a model. And yes: if we plop our agents down into a stationary environment, their beliefs should eventually coincide with reality. If the environment changes in an unpredictable way, it is the belief function, a primitive of the model, that guides the economy to a new steady state. And I can envision models where expectations on the transition path are systematically wrong.
The recent ‘nonlinearity debate’ on the blogs confuses the existence of multiple steady states in a dynamic model with the existence of multiple rational expectations equilibria. Nonlinearity is neither necessary nor sufficient for the existence of multiplicity. A linear model can have a unique indeterminate steady state associated with an infinite dimensional continuum of locally stable rational expectations equilibria. A linear model can also have a continuum of attracting points, each of which is an equilibrium. These are not just curiosities. Both of these properties characterize modern dynamic equilibrium models of the real economy.
There are still a number of self-professed Keynesian bloggers out there who see the world through the lens of 1950s theory. They have some catching up to do with the literature.


  1. Hi Roger,

    You write, “There are still a number of self-professed Keynesian bloggers out there who see the world through the lens of 1950s theory. They have some catching up to do with the literature.”

    Ouch! I’m trying to catch up, but in the meantime . . . I’m having a hard time trying to figure out what you’re trying to achieve with these models. On the one hand, several model-builders seem to adopt, implicitly at least, Milton Friedman’s “instrumentalism,” i.e., ignore a model’s assumptions, focus on its predictions. On the other hand, most advocates of the “Lucas-Sargent-Farmer (?) approach” insist that models which don’t assume rational agents and some kind of market-clearing equilibrium are worthless. Which is it, do the assumptions matter or not?

    Somewhere in between the assumptions and the macro states/paths that are deduced from the assumptions there’s a lot of “mid-level” things that cannot be derived from these assumptions. For example, if everyone shares the same expectations, rational or not, it’s hard to make sense of trading in financial assets – the bulls and the bears and whatnot. In a similar fashion, we know that decision makers who control lots of resources, real and financial, view “the news” through some theoretical lens even if it’s only a cloudy one. (We do know this don’t we?) Let’s call these “theories” New Classical, Old Keynesian, Austrian, etc. Surely, the effects of a change in monetary or fiscal policy will depend on the distribution of these theories, or views, across the many organizations that will act in response to these policy changes.

    In an interview with the Minnesota Fed, Kenneth Arrow said he thought of macro as a “disequilibrium” phenomenon. Later, he mocked New Classical explanations of unemployment. Most recently (at least as far as I know), he said the economy is chaotic and praised the agent-based modeling being done at the Santa Fe Institute.

    You have an advantage in having talked with Frank Hahn, who told you he was concerned with the policy implications of the New Classical economics. OK, but his books and papers are filled with critical analyses of New Classical economics, and he did, after all, write a book in 1995 (45 years after 1950) with Robert Solow entitled “A Critical Essay on Modern Macroeconomic Theory.”

    From the back cover:

    “In the early 1980s, rational expectations and new classical economics dominated macroeconomic theory. This essay evolved from the authors’ profound disagreement with that trend. It demonstrates not only how the new classical view got macroeconomics wrong, but also how to go about doing macroeconomics the right way.”

    1. Greg
      I don't have a strong take on this. I'm certainly not an instrumentalist. I'm closer to Feyerabend. Whatever works, works. What am I trying to achieve? A policy consensus to actively stabilize the stock market.

    2. Roger

      Thanks again responding. I share your view of Feyerabend and his affirmation of methodological diversity. There’s no point in putting all your theoretical eggs in one basket, unless, of course, you’re absolutely certain its payoff will trump all others.

  2. "There are still a number of self-professed Keynesian bloggers out there who see the world through the lens of 1950s theory. They have some catching up to do with the literature."

    That's an understatement, and you can see the problems above. Greg claims he's trying to "catch up," but I think he's actually dug in, and just wants to argue with you. One doesn't have to look hard for critics of modern macro, many of whom don't actually understand what it is. Probably the most bizarre of these critics are the people who wrote down aggregative constructs in the 1950s that form the basis of what many macroeconomists currently do - here I'm talking about Arrow and Solow in particular - but fail to understand the power of the work they did. Quite weird, if you ask me.

    1. Thanks Steve.
      You can lead a philosopher to water....
      As for Bob and Ken... If I can contribute a small fraction of what either of them has given to us all I will leave this world a happy man��

  3. The best I can tell is that expectations = phlogiston. I can accept goals or decision points, but expectations are way too mystical for any realistic use in a model. The whole discussion of equilibrium here seems to be a-mathematical. In mathematics, there are equilibrium points and their are attractors. There is no such thing as a temporary equilibrium. Someone needs to do some serious foundations work to get this kind of theorizing consistent with mathematics.

    1. In physics there are things called metastable states that would be analogous to what is being referred to as a temporary equilibrium. But I could be wrong about that being what Glasner and Farmer mean.

      Although I agree with expectations = phlogiston ... and TFP = phlogiston, too.

    2. Physics is not much help here. But yes, TFP = phlogiston.

  4. Roger,

    In this continuum of equilibria or linear attractors, does this mean you are abandoning Arrow-Debreu? The multiple equilibria (via the SMD theorem) are locally unique in that framework (they represent a countable subset of zeros in the excess demand vector field).

    Just a question as I have no particular attachment to Arrow-Debreu ...



    1. Yes. I'm abandoning Arrow Debreu and replacing it with competitive search (with a Keynesian twist).

  5. Roger, Thanks so much for this post. I have posted a reply of sorts along with some questions on my blog


Note: Only a member of this blog may post a comment.