Archive for November, 2016

Making Sense of Rational Expectations

Almost two months ago I wrote a provocatively titled post about rational expectations, in which I argued against the idea that it is useful to make the rational-expectations assumption in developing a theory of business cycles. The title of the post was probably what led to the start of a thread about my post on the econjobrumors blog, the tenor of which  can be divined from the contribution of one commenter: “Who on earth is Glasner?” But, aside from the attention I received on econjobrumors, I also elicited a response from Scott Sumner

David Glasner has a post criticizing the rational expectations modeling assumption in economics:

What this means is that expectations can be rational only when everyone has identical expectations. If people have divergent expectations, then the expectations of at least some people will necessarily be disappointed — the expectations of both people with differing expectations cannot be simultaneously realized — and those individuals whose expectations have been disappointed will have to revise their plans. But that means that the expectations of those people who were correct were also not rational, because the prices that they expected were not equilibrium prices. So unless all agents have the same expectations about the future, the expectations of no one are rational. Rational expectations are a fixed point, and that fixed point cannot be attained unless everyone shares those expectations.

Beyond that little problem, Mason raises the further problem that, in a rational-expectations equilibrium, it makes no sense to speak of a shock, because the only possible meaning of “shock” in the context of a full intertemporal (aka rational-expectations) equilibrium is a failure of expectations to be realized. But if expectations are not realized, expectations were not rational.

I see two mistakes here. Not everyone must have identical expectations in a world of rational expectations. Now it’s true that there are ratex models where people are simply assumed to have identical expectations, such as representative agent models, but that modeling assumption has nothing to do with rational expectations, per se.

In fact, the rational expectations hypothesis suggests that people form optimal forecasts based on all publicly available information. One of the most famous rational expectations models was Robert Lucas’s model of monetary misperceptions, where people observed local conditions before national data was available. In that model, each agent sees different local prices, and thus forms different expectations about aggregate demand at the national level.

It is true that not all expectations must be identical in a world of rational expectations. The question is whether those expectations are compatible with the equilibrium of the model in which those expectations are embedded. If any of those expectations are incompatible with the equilibrium of the model, then, if agents’ decision are based on their expectations, the model will not arrive at an equilibrium solution. Lucas’s monetary misperception model was a clever effort to tweak the rational-expectations assumption just enough to allow for a temporary disequilibrium. But the attempt was a failure, because Lucas could only generate a one-period deviation from equilibrium, which was too little for the model to pose as a plausible account of a business cycle. That provided Kydland and Prescott the idea to discard Lucas’s monetary misperceptions idea and write their paper on real business cycles without adulterating the rational expectations assumption.

Here’s what Muth said about the rational expectations assumption in the paper in which he introduced “rational expectations” as a modeling strategy.

In order to explain these phenomena, I should like to suggest that expectations, since they are informed predictions of future events, are essentially the same as the predictions of the relevant economic theory. At the risk of confusing this purely descriptive hypothesis with a pronouncement as to what firms ought to do, we call such expectations “rational.”

The hypothesis can be rephrased a little more precisely as follows: that expectations of firms (or, more generally, the subjective probability distribution of outcomes) tend to be distributed, for the same information set, about the prediction of the theory (or the “objective” probability distributions of outcomes).

The hypothesis asserts three things: (1) Information is scarce, and the economic system generally does not waste it. (2) The way expectations are formed depends specifically on the structure of the relevant system describing the economy. (3) A “public prediction,” in the sense of Grunberg and Modigliani, will have no substantial effect on the operation of the economic system (unless it is based on inside information).

It does not assert that the scratch work of entrepreneurs resembles the system of equations in any way; nor does it state that predictions of entrepreneurs are perfect or that their expectations are all the same. For purposes of analysis, we shall use a specialized form of the hypothesis. In particular, we assume: 1. The random disturbances are normally distributed. 2. Certainty equivalents exist for the variables to be predicted. 3. The equations of the system, including the expectations formulas, are linear. These assumptions are not quite so strong as may appear at first because any one of them virtually implies the other two.

It seems to me that Muth was confused about what the rational-expectations assumption entails. He asserts that the expectations of entrepreneurs — and presumably that applies to other economic agents as well insofar as their decisions are influenced by their expectations of the future – should be assumed to be exactly what the relevant economic model predicts the expected outcomes to be. If so, I don’t see how it can be maintained that expectations could diverge from each other. If what entrepreneurs produce next period depends on the price they expect next period, then how is it possible that the total supply produced next period is independent of the distribution of expectations as long as the errors are normally distributed and the mean of the distribution corresponds to the equilibrium of the model? This could only be true if the output produced by each entrepreneur was a linear function of the expected price and all entrepreneurs had identical marginal costs or if the distribution of marginal costs was uncorrelated with the distribution of expectations. The linearity assumption is hardly compelling unless you assume that the system is in equilibrium and all changes are small. But making that assumption is just another form of question begging.

It’s also wrong to say:

But if expectations are not realized, expectations were not rational.

Scott is right. What I said was wrong. What I ought to have said is: “But if expectations (being divergent) could not have been realized, those expectations were not rational.”

Suppose I am watching the game of roulette. I form the expectation that the ball will not land on one of the two green squares. Now suppose it does. Was my expectation rational? I’d say yes—there was only a 2/38 chance of the ball landing on a green square. It’s true that I lacked perfect foresight, but my expectation was rational, given what I knew at the time.

I don’t think that Scott’s response is compelling, because you can’t judge the rationality of an expectation in isolation, it has to be judged in a broader context. If you are forming your expectation about where the ball will fall in a game of roulette, the rationality of that expectation can only be evaluated in the context of how much you should be willing to bet that the ball will fall on one of the two green squares and that requires knowledge of what the payoff would be if the ball did fall on one of those two squares. And that would mean that someone else is involved in the game and would be taking an opposite position. The rationality of expectations could only be judged in the context of what everyone participating in the game was expecting and what the payoffs and penalties were for each participant.

In 2006, it might have been rational to forecast that housing prices would not crash. If you lived in many countries, your forecast would have been correct. If you happened to live in Ireland or the US, your forecast would have been incorrect. But it might well have been a rational forecast in all countries.

The rationality of a forecast can’t be assessed in isolation. A forecast is rational if it is consistent with other forecasts, so that it, along with the other forecasts, could potentially be realized. As a commenter on Scott’s blog observed, a rational expectation is an expectation that, at the time the forecast is made, is consistent with the relevant model. The forecast of housing prices may turn out to be incorrect, but the forecast might still have been rational when it was made if the forecast of prices was consistent with what the relevant model would have predicted. The failure of the forecast to be realized could mean either that forecast was not consistent with the model, or that between the time of the forecast and the time of its realization, new information,  not available at the time of the forecast, came to light and changed the the prediction of the relevant model.

The need for context in assessing the rationality of expectations was wonderfully described by Thomas Schelling in his classic analysis of cooperative games.

One may or may not agree with any particular hypothesis as to how a bargainer’s expectations are formed either in the bargaining process or before it and either by the bargaining itself or by other forces. But it does seem clear that the outcome of a bargaining process is to be described most immediately, most straightforwardly, and most empirically, in terms of some phenomenon of stable and convergent expectations. Whether one agrees explicitly to a bargain, or agrees tacitly, or accepts by default, he must if he has his wits about him, expect that he could do no better and recognize that the other party must reciprocate the feeling. Thus, the fact of an outcome, which is simply a coordinated choice, should be analytically characterized by the notion of convergent expectations.

The intuitive formulation, or even a careful formulation in psychological terms, of what it is that a rational player expects in relation to another rational player in the “pure” bargaining game, poses a problem in sheer scientific description. Both players, being rational, must recognize that the only kind of “rational” expectation they can have is a fully shared expectation of an outcome. It is not quite accurate – as a description of a psychological phenomenon – to say that one expects the second to concede something; the second’s readiness to concede or to accept is only an expression of what he expects the first to accept or to concede, which in turn is what he expects the first to expect the second to expect the first to expect, and so on. To avoid an “ad infinitum” in the description process, we have to say that both sense a shared expectation of an outcome; one’s expectation is a belief that both identify the outcome as being indicated by the situation, hence as virtually inevitable. Both players, in effect, accept a common authority – the power of the game to dictate its own solution through their intellectual capacity to perceive it – and what they “expect” is that they both perceive the same solution.

Viewed in this way, the intellectual process of arriving at “rational expectations” in the full-communication “pure” bargaining game is virtually identical with the intellectual process of arriving at a coordinated choice in the tacit game. The actual solutions might be different because the game contexts might be different, with different suggestive details; but the intellectual nature of the two solutions seems virtually identical since both depend on an agreement that is reached by tacit consent. This is true because the explicit agreement that is reached in the full communication game corresponds to the a prioir expectations that were reached (or in theory could have been reached) jointly but independently by the two players before the bargaining started. And it is a tacit “agreement” in the sense that both can hold confident rational expectation only if both are aware that both accept the indicated solution in advance as the outcome that they both know they both expect.

So I agree that rational expectations can simply mean that agents are forming expectations about the future incorporating as best as they can all the knowledge available to them. This is a weak common sense interpretation of rational expectations that I think is what Scott Sumner has in mind when he uses the term “rational expectations.” But in the context of formal modelling, rational expectations has a more restrictive meaning, which is that given all the information available, the expectations of all agents in the model must correspond to what the model itself predicts given that information. Even though Muth himself and others have tried to avoid the inference that all agents must have expectations that match the solution of the model, given the information underlying the model, the assumptions under which agents could hold divergent expectations are, in their own way, just as restrictive as the assumption that agents hold convergent expectations.

In a way, the disconnect between a common-sense understanding of what “rational expectations” means and what “rational expectations” means in the context of formal macroeconomic models is analogous to the disconnect between what “competition” means in normal discourse and what “competition” (and especially “perfect competition”) means in the context of formal microeconomic models. Much of the rivalrous behavior between competitors that we think of as being essential aspects of competition and the competitive process is simply ruled out by the formal assumption of perfect competition.

OMG! The Age of Trump Is upon Us

UPDATE (11/11, 10:47 am EST): Clinton’s lead in the popular vote is now about 400,000 and according to David Leonhardt of the New York Times, the lead is likely to increase to as much as 2 million votes by the time all the votes are counted.

Here’s a little thought experiment for you to ponder. Suppose that the outcome of yesterday’s election had been reversed and Hillary Clinton emerged with 270+ electoral votes but trailed Donald Trump by 200,000 popular votes. What would the world be like today? What would we be hearing from Trump and his entourage about the outcome of the election? I daresay we would be hearing about “second amendment remedies” from many of the Trumpsters. I wonder how that would have played out.

(As I write this, I am hearing news reports about rowdy demonstrations in a number of locations against Trump’s election. Insofar as these demonstrations become violent, they are certainly deplorable, but nothing we have heard from Clinton and her campaign or from leaders of the Democratic Party would provide any encouragement for violent protests against the outcome of a free election.)

But enough of fantasies about an alternative universe; in the one that we happen to inhabit, the one in which Donald Trump is going to be sworn in as President of the United States in about ten weeks, we are faced with this stark reality. The American voters, in their wisdom, have elected a mountebank (OED: “A false pretender to skill or knowledge, a charlatan: a person incurring contempt or ridicule through efforts to acquire something, esp. social distinction or glamour.”), a narcissistic sociopath, as their chief executive and head of state. The success of Trump’s demagogic campaign – a campaign repackaging the repugnant themes of such successful 20th century American demagogues as Huey Long, Father Coughlin and George Wallace (not to mention not so successful ones like the deplorable Pat Buchanan) — is now being celebrated by Trump apologists and Banana Republican sycophants as evidence of his political genius in sensing and tapping into the anger and frustrations of the forgotten white working class, as if the anger and frustration of the white working class has not been the trump card that every two-bit demagogue and would-be despot of the last 150 has tried to play. Some genius.

I recently overheard a conversation between a close friend of mine who is a Trump supporter and a non-Trump supporter. My friend is white, but is not one of the poorly educated of whom Trump is so fond, holding a Ph.D. in physics, and being well read and knowledgeable about many subjects. Although he doesn’t like Trump, he is very conservative and can’t stand Clinton, so he decided to vote for Trump without any apparent internal struggle or second thoughts. One of his reasons for favoring Trump is his opposition to Obamacare, which he blames for the very large increase in premiums he has to pay for the medical insurance he gets through his employer. When it was pointed out to him that it is unlikely that the increase in his insurance premiums was caused by Obamacare, his response was that Obamacare has added to the regulations that insurance companies must comply with, so that the cost of those regulations is ultimately borne by those buying insurance, which means that his insurance premiums must have gone up because of Obamacare.

Since I wasn’t part of the conversation, I didn’t interrupt to point out that the standard arguments about the costs of regulation being ultimately borne by consumers of the regulated product don’t necessarily apply to markets like health care in which customers don’t have good information about whether suppliers are providing them with the services that they need or are instead providing unnecessary services to enrich themselves. In such markets, third-parties (i.e., insurance companies) supposedly better informed than patients about whether the services provided to patients by their doctors are really serving the patients’ interests, and are really worth the cost of providing those services, can help protect the interests of patients. Of course, the interests of insurance companies aren’t necessarily aligned very well with the interests of their policyholders either, because insurance companies may prefer not to pay for treatments that it would be in the interests of patients to receive.

So in health markets there are doctors treating ill-informed patients whose bills are being paid by insurance companies that try to monitor doctors to make sure that doctors do not provide unnecessary services and treatments to patients. But since the interests of insurance companies may be not to pay doctors to provide services that would be beneficial to patients, who is going to protect policyholders from the insurance companies? Well, um, maybe the government should be involved. Yes, but how do we know if the government is doing a good job or bad job of looking out for the interests of patients? I don’t think that we know the answer to that question. But Obamacare, aside from making medical insurance more widely available to people who need it, is an attempt to try to make insurance companies more responsive to the interests of their policyholders. Perhaps not the smartest attempt, by any means, but given the system of health care delivery that has evolved in the United States over the past three quarters of a century, it is not obviously a step in the wrong direction.

But even if Obamacare is not working well, and I have no well thought out opinion about whether it is or isn’t, the kind of simple-minded critique that my friend was making seemed to me to be genuinely cringe-worthy. Here is a Ph.D. in physics making an argument that sounded as if it were coming straight out of the mouth of Sean Hannity. OMG! The dumbing down of America is being expertly engineered by Fox News, and, boy, are they succeeding. Geniuses, that’s what they are. Geniuses!

When I took my first economics course almost a half century ago and read the greatest economics textbook ever written, University Economics by Armen Alchian and William Allen, I was blown away by their ability to show how much sloppy and muddled thinking there was about how markets work and how controls that prevent prices from allocating resources don’t eliminate destructive or wasteful competition, but rather shift competition from relatively cheap modes like offering to pay a higher price or to accept a lower price to relatively costly forms like waiting in line or lobbying a regulator to gain access to a politically determined allocation system.

I have been a fan of free markets ever since. I oppose government intervention in the economy as a default position. But the lazy thinking that once led people to assume that government regulation is the cure for all problems now leads people to assume that government regulation is the cause of all problems. What a difference half a century makes.

About Me

David Glasner
Washington, DC

I am an economist in the Washington DC area. My research and writing has been mostly on monetary economics and policy and the history of economics. In my book Free Banking and Monetary Reform, I argued for a non-Monetarist non-Keynesian approach to monetary policy, based on a theory of a competitive supply of money. Over the years, I have become increasingly impressed by the similarities between my approach and that of R. G. Hawtrey and hope to bring Hawtrey's unduly neglected contributions to the attention of a wider audience.

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