Microfoundations -- fact and fiction

UPDATE AT THE END

I generally try not to write about things I know almost nothing about, but here goes. Take everything that follows here as a kind of "thinking out loud" -- a struggle to put into words my thoughts about some apparently odd ideas in macroeconomics. I say "apparently" because I don't know enough to be sure. Maybe they are all very sensible. I would greatly appreciate any further insight from anyone out there who knows.

The idea puzzling me is "microfoundations." As I understand it, the rational expectations revolution in macroeconomics, linked to the names Robert Lucas, Edward Prescott, Thomas Sargent and others, demanded that macroeconomic theories shouldn't just be built as coarse-grained effective theories operating at the macroscale and written in terms of macroscopic variables such as inflation, unemployment, etc. Rather, a good theory henceforth was to link macroeconomic outcomes back to the behaviour of the individual agents in an economy, i.e. to their microeconomics behaviour. Such as theory would have "microfoundations."

To my physicist mind, this seems entirely sensible, so far. A difficult project, no doubt but sensible. By analogy, of course, this just seems like the effort to derive thermodynamics (a macroscopic theory) from the underlying behaviours of individual particles, which is the project of statistical mechanics. Deriving theories at higher levels from behaviours at lower levels is, when possible, a natural scientific project -- it offers unification or, if it can't be carried through, points to problem areas from which new ideas are likely to come.

Now, I have also read that much of the impetus for the rational expectations movement was the famous Lucas Critique which, if I understand it correctly, says that you can't reliably base policy interventions on simple regularities observed in macroeconomic data (a historically observed tradeoff between unemployment and inflation, for example). That regularity existed, after all, in the context of the policies prevailing in the past. Change the policies and those changes, by influencing the way people act and anticipate the future, may well strongly change or destroy the regularity on which you had based your plans. Again, plausible and sensible, it seems to me.

So, I can see the attraction of theories with microfoundations -- theories, that is, giving a plausible account of how macroeconomic reality emerges out of the micro reality and actual behaviour of millions of people and firms in interaction.

Now my puzzlement. As far as can tell, the idea of "microfoundations" as actually used in macroeconomics isn't quite how I described it above, i.e. seeking to base macro theory on a plausible account of the behaviour of individuals. Rather, in economics (through the work of Lucas) it has come to mean theories in which individuals and firms are hyperrational optimizers of their utility over a span of time (they solve a complicated optimization problem over their lifetime). This no longer seems so plausible, and on this point, a commenter from Mark Thoma's blog captures my feelings on this quite clearly:

hrsaccount said...

Microfoundations would be important if there were clear evidence that they represented the truth. For example, if there had been a series of experiments demonstrating that individuals are rational and make decisions so as to maximize some measurable quantity called utility, it would be important that macro models were consistent with this and the most direct way of ensuring that would be to incorporate rational utility-maximizing households into the model.

The fact is that there is no such evidence. Microeconomics is not based on empirical evidence, and the approach used in microeconomics has no special claim to the truth. So, leaving aside the fact that the way macroeconomics uses micro (i.e., in a way that many microeconomists don't approve, ignoring aggregation issues) there's no logical reason why macro needs to even be consistent with micro.

His point seems to me very well put -- if "microfoundations" as currently interpreted don't give foundations to anything, then a theory having them has no advantage. Theories with microfoundations (as interpreted in this odd sense) have no more claim to relevance than anything else. Indeed, we might say they are even worse as they are almost certainly demonstrably inconsistent with real behaviour at the micro level.

Again, I'm not an expert on this. But I see this kind of argument breaking out over and over among economists. I often think I must have it wrong, so please if I do, someone let me know.

UPDATE

While writing the above, I happened to find and read a couple of things that clarified matters quite a bit for me. My take seems to be shared by economists as well, although I'm not sure the few things I read are representative. First, Maarten Janssen of the Tinbergen Institute published an excellent short review of the idea of microfoundations in 2008. He describes the history, but notes that key criticisms of the idea do center in the "plausibility" of the rational expectations approach. That is, including expectations in macromodels is sensible, but everything depends on how you include them:

The approaches discussed so far... all postulate rational behavior on the part of economic agents and some notion of equilibrium. If expectations are important, it is postulated that agents’ expectations concerning important variables coincide with the model’s predicted values concerning these same variables.

And he mentions several branches of research criticizing this view and testing it, in particular, testing whether in a decentralized economy economic agents may learn over time to have expectations that are consistent with those that are assumed by the rational expectations hypothesis:

The general conclusion of this literature is that due to the feedback from expectations to economic behavior, the outcomes of an economic model with learning agents do not converge to the rational expectations solution. It then follows that the microfoundations literature mentioned so far has not really succeeded in deriving all macroeconomic propositions from fundamental hypotheses on the behavior of individual agents. The requirements of methodological individualism have thus not been satisfied by the microfoundations literature that has pre-dominantly presumed that individuals behave rationally...

I cannot say I'm surprised. So we're left with theories that only go one short step toward the idea of microfoundations, and, in my view, can't claim they have given microfoundations to anything -- the use of the word in these models is totally unwarranted, and I think way overstates what they achieve.

I think much the same point of view is expressed by Michael Woodford, himself a big name in macro modelling. In a response to an essay by John Kay critical of modern macroeconomics and its unrealistic assumptions, Woodford in a roundabout way eventually says, well, yes, I agree:

 

It has been standard for at least the past three decades to use models in which not only does the model give a complete description of a hypothetical world, and not only is this description one in which outcomes follow from rational behavior on the part of the decision makers in the model, but the decision makers in the model are assumed to understand the world in exactly the way it is represented in the model. More precisely, in making predictions about the consequences of their actions (a necessary component of an accounting for their behavior in terms of rational choice), they are assumed to make exactly the predictions that the model implies are correct (conditional on the information available to them in their personal situation).

This postulate of “rational expectations,” as it is commonly though rather misleadingly known, is the crucial theoretical assumption behind such doctrines as “efficient markets” in asset pricing theory and “Ricardian equivalence” in macroeconomics. It is often presented as if it were a simple consequence of an aspiration to internal consistency in one’s model and/or explanation of people’s choices in terms of individual rationality, but in fact it is not a necessary implication of these methodological commitments. It does not follow from the fact that one believes in the validity of one’s own model and that one believes that people can be assumed to make rational choices that they must be assumed to make the choices that would be seen to be correct by someone who (like the economist) believes in the validity of the predictions of that model. Still less would it follow, if the economist herself accepts the necessity of entertaining the possibility of a variety of possible models, that the only models that she should consider are ones in each of which everyone in the economy is assumed to understand the correctness of that particular model, rather than entertaining beliefs that might (for example) be consistent with one of the other models in the set that she herself regards as possibly correct.

So I feel that my suspicions and objections aren't misplaced, despite my vast ignorance. One other excellent article I recommend is this one from 2011 in which Woodford details the history of modern macroeconomics over the past century. Nothing I've read has given such a complete and clearly explained exposition, while it seems being balanced along the way (or so it seems, to my physicist's eyes).

UPDATE

Ole Rogeberg kindly let pointed me to this post by economist Noah Smith who makes some of the same points -- but from the position of someone with far economics domain knowledge than myself.

Learning in macroeconomics...

I've posted before on macroeconomic models that try to go beyond the "rational expectations" framework by assuming that the agents in an economy are different (they have heterogeneous expectations) and are also not necessarily rational. This approach seems wholly more realistic and believable to me.

In a recent comment, however, ivansml pointed me to this very interesting paper from 2009, which I've enjoyed reading. What the paper does is explore what happens in some of the common rational expectations models if you suppose that agents' expectations aren't formed rationally but rather on the basis of some learning algorithm. The paper shows that learning algorithms of a certain kind lead to the same equilibrium outcome as the rational expectations viewpoint. This IS interesting and seems very impressive. However, I'm not sure it's as interesting as it seems at first.

The reason is that the learning algorithm is indeed of a rather special kind. Most of the models studied in the paper, if I understand correctly, suppose that agents in the market already know the right mathematical form they should use to form expectations about prices in the future. All they lack is knowledge of the values of some parameters in the equation. This is a little like assuming that people who start out trying to learn the equations for, say, electricity and magnetism, already know the right form of Maxwell's equations, with all the right space and time derivatives, though they are ignorant of the correct coefficients. The paper shows that, given this assumption in which the form of the expectations equation is already known, agents soon evolve to the correct rational expectations solution. In this sense, rational expectations emerges from adaptive behaviour.

I don't find this very convincing as it makes the problem far too easy. More plausible, it seems to me, would be to assume that people start out with not much knowledge at all of how future prices will most likely be linked by inflation to current prices, make guesses with all kinds of crazy ideas, and learn by trial and error. Given the difficulty of this problem, and the lack even among economists themselves of great predictive success, this would seem more reasonable. However, it is also likely to lead to far more complexity in the economy itself, because a broader class of expectations will lead to a broader class of dynamics for future prices. In this sense, the models in this paper assume away any kind of complexity from a diversity of views.

To be fair to the authors of the paper, they do spell out their assumptions clearly. They state in fact that they assume that people in their economy form views on likely future prices in the same way modern econometricians do (i.e. using the very same mathematical models). So the gist seems to be that in a world in which all people think like economists and use the equations of modern econometrics to form their expectations, then, even if they start out with some of the coefficients "mis-specified," their ability to learn to use the right coefficients can drive the economy to a rational expectations equilibrium. Does this tell us much?

I'd be very interested in others' reactions to this. I do not claim to know much of anything about macroeconomics. Indeed, one of the nice things about this paper is its clear introduction to some of the standard models. This in itself is quite illuminating. I hadn't realized that the standard models are not any more complex than linear first-order time difference equations (if I have this right) with some terms including expectations. I had seen these equations before and always thought they must be toy models just meant to illustrate the far more complex and detailed models used in real calculations and located in some deep economic book I haven't yet seen, but now I'm not so sure.

Crazy economic models

**UPDATED AT END OF POST**

In a recent post I commented on the "fetish of rationality" present in a great deal of mathematical economic theory. Agents in the theories are often assumed to have super-human reasoning abilities and to determine their behaviour and expectations solely through completely rational calculation. In comments, Relja suggested that maybe I'd gone too far and that economists version of rationality isn't all that extreme:

I think critiques like this about rationality in economics miss the point. The rationality assumed in economics is concerned with general trends; generally people pursue pleasure, not pain (according to their own utility functions), they prefer more money to less (an expanded budget constraint leaves them on a higher indifference curve, thus better off), they have consistent preferences (when they're in the mood for chocolate, they're not going to choose vanilla). Correspondingly, firms have the goal of profit maximization - they produce products that somebody will want to buy or they go out of business. Taking the rationality assumption to its "umpteenth" iteration is really quite irrational in itself. A consumer knows that spending 6 years to calculate the mathematically optimal choice of ice-cream is irrational. An economist accordingly knows the same thing. And although assumptions are required for modelling economic scenarios (micro or macro), I seriously doubt that any serious economist would make assumptions that infer such irrationality. :).

I think Relja expressed a well-balanced perspective, has learned some economics in detail, and has taken away from it some conclusions that are, all in all, pretty sound. Indeed, people are goal oriented, don't (usually) prefer pain, and businesses do try to make profits (although whether they try to 'maximize' is an open question). If economists were really just following these reasonable ideas, I would have no problem.

But I also think the problem is worse than Relja may realize. The use of rationality assumptions is more extreme than this, and also decisive in some of the most important areas of economic theory, especially in macroeconomics. A few days ago, John Kay offered this very long and critical essay on the form of modern economic theory. It's worth a read all the way through, but in essence, Kay argues that economics is excessively based on logical deduction of theories from a set of axioms, one of which (usually) is the complete rationality of economic agents:

Rigour and consistency are the two most powerful words in economics today.... They have undeniable virtues, but for economists they have particular interpretations.  Consistency means that any statement about the world must be made in the light of a comprehensive descriptive theory of the world.  Rigour means that the only valid claims are logical deductions from specified assumptions.  Consistency is therefore an invitation to ideology, rigour an invitation to mathematics.  This curious combination of ideology and mathematics is the hallmark of what is often called ‘freshwater economics’ – the name reflecting the proximity of Chicago, and other centres such as Minneapolis and Rochester, to the Great Lakes.

Consistency and rigour are features of a deductive approach, which draws conclusions from a group of axioms – and whose empirical relevance depends entirely on the universal validity of the axioms.

Kay isn't quite as explicit as he might have been, but economist Michael Woodford, in a comment on Kay's argument, goes further in spelling out what Key finds most objectionable -- the so-called rational expectations framework, originally proposed by Robert Lucas, which forms the foundations of today's DGSE (dynamic stochastic equilibrium models). A core assumption of such models is that all individuals in the economy have rational expectations about the future, and that such expectations affect their current behaviour.

Now, if this meant something like Relja's comment suggests it might -- that people are simply forward looking, as we know they are -- this would be fine. But it's not. The form this assumption ultimately takes in these models is to assume that everyone in the economy has fully rational expectations, in that they form their expectations in accordance with the conceivably best and most accurate economic models, even if solving those models might require considerable mathematics and computation (and knowledge of everyones' expectations). As Woodford puts it in his comment,

It has been standard for at least the past three decades to use models in which not only does the model give a complete description of a hypothetical world, and not only is this description one in which outcomes follow from rational behavior on the part of the decision makers in the model, but the decision makers in the model are assumed to understand the world in exactly the way it is represented in the model. More precisely, in making predictions about the consequences of their actions (a necessary component of an accounting for their behavior in terms of rational choice), they are assumed to make exactly the predictions that the model implies are correct (conditional on the information available to them in their personal situation).
                 
This postulate of “rational expectations,” as it is commonly though rather misleadingly known, is the crucial theoretical assumption behind such doctrines as “efficient markets” in asset pricing theory and “Ricardian equivalence” in macroeconomics.  

It is precisely here that modern economics takes the assumption of rationality much too far merely for the sake of mathematical and theoretical rigour. Do economists really believe people form their expectations in this way? It's hard to imagine they could as the live the rest of their lives with people who do not do this. But the important question isn't what they really believe but on what do they base their theories which then get used by governments in policy making? Sadly, these unrealistic assumptions remain in the key models. But these assumptions really have zero plausibility. Woodford again,

[The rational expectations assumption] is often  presented as if it were a simple consequence of an aspiration to internal consistency in one’s model and/or explanation of people’s choices in terms of individual rationality, but in fact it is not a  necessary implication of these methodological commitments. It does not follow from the fact that one believes in the validity of one’s own  model and that one believes that people can be assumed to make rational  choices that they must be assumed to make the choices that would be seen  to be correct by someone who (like the economist) believes in the validity of the predictions of that model. Still less would it follow, if the economist herself accepts the necessity of entertaining the  possibility of a variety of possible models, that the only models that  she should consider are ones -- in each of which everyone in the economy is assumed to understand the correctness of that particular model, -- rather than entertaining beliefs that might (for example) be consistent with  one of the other models in the set that she herself regards as possibly  correct.

This is the sense in which hyper-rationality really does enter into economic theories. It's still pervasive, and still indefensible. It would be infinitely preferable if macro-economists such as Lucas and his followers (one of whom, Thomas Sargent, was perversely and outrageously just awarded the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel).

**UPDATE**

Blogger sometimes doesn't seem to register comments. Email alerted me to a sharp criticism by ivansml of some of the points I made, but the comment isn't, at least for my browser, yet showing up. Just so it doesn't get lost, ivansml said:

Every assumption is false when understood literally, including rational expectations. The important thing is whether people behave as if they had rational expectations - and answer to that will fortunately depend on particular model and data, not on emotional arguments and expressive vocabulary.

By the way, if you reject RE but accept that expectations matter and should be forward-looking, how do you actually propose to model them? One possible alternative is to have agents who estimate laws of motion from past data and continously update their estimates, which is something that macroeconomists have actually investigated before. And guess what - this process will often converge to rational expectations equilibrium.

Finally, the comment about Nobel Prize (yeah, it's not real Nobel, whatever) for Sargent is a sign of ignorance. Sargent has published a lot on generalizations or relaxations of RE, including the learning literature mentioned above, literature on robustness (where agents distrust their model and choose actions which are robust to model misspecifications) and even agent-based models. In addition to that, the prize citation focuses on his empirical contributions (i.e. testing theories against data). This does not seem like someone who is religiously devoted to "hyper-rationality" and ideology.

To points in response:

1. Yes, the point is precisely to include expectations but to model their formation in some more behaviourally realistic way, through learning algorithms as suggested. I am aware of such work and think it is very important. Indeed, the latter portion of this post from earlier this year looked precisely at this and considered a recent review of work in this area by Cars Hommes and others. The idea is not to assume that everyone forms their expectations identically, that learning is important, that their may be systematic biases and so on. As ivansml notes, there are circumstances in which the model may settle into a rational expectations equilibrium. But there are also many in which it does not. My hunch -- not backed by any evidence that I can point to readily -- is that the rational expectations equilibrium will be increasingly unlikely as the decisions faced by agents in the model become increasingly complex. Very possibly the system won't settle into any equilibrium at all.

But I think ivansml for pointing this out. It is certainly the case that expectations matter, and these should be brought into theory in some plausible and convincing way. Just to finish on this point, this is a quote from the Hommes review article, suggesting that the RE equilibrium doesn't come up very often:

Learning to forecast experiments are tailor-made to test the expectations hypothesis, with all other model assumptions computerized and under control of the experimenter. Different types of aggregate behavior have been observed in different market settings. To our best knowledge, no homogeneous expectations model [rational or irrational] fits the experimental data across different market settings. Quick convergence to the RE-benchmark only occurs in stable (i.e. stable under naive expectations) cobweb markets with negative expectations feedback, as in Muth's (1961) seminal rational expectations paper. In all other market settings persistent deviations from the RE fundamental benchmark seem to be the rule rather than the exception.

2. On his second point about Thomas Sargent, I plead guilty. ivansml is right -- his work is not as one dimensional as my comments made it seem. Indeed, I had been looking into his work over the past weekend for different reasons and had noticed that his work has been fairly wide ranging, and he does deserve credit for trying to relax RE assumptions. (Although he did seem a little snide in one interview I read, suggesting that mainstream macro-economists were not at all surprised by the recent financial crisis.)

So thanks also ivansml for setting me straight. I've changed the offending text above.