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 classicalassumption 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 wouldnot 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!

 

 

 

Download my Data on the Stock Market and Unemployment

The recent drop in the stock market, if it persists, will present serious challenges for the Yellen Fed.


In a couple of recent academic papers, The Stock Market Crash of 2008 caused the Great Recession: Theory and Evidence here and The Stock Market Crash Really Did Cause the Great Recession here I showed that changes in the value of the stock market cause changes in the unemployment rate three months later. Here is a link to a Freakonomics post that features my work.
I continue to receive requests for the data that I used in those studies. That data is available here. These are important empirical findings that establish a strong and stable relationship between changes in the value of the S&P and changes in the U.S. unemployment rate.

Quote of the Day

This piece is widely known, but I never tire of reading it. It comes from a 1906 letter by Alfred Marshall to his student Arthur Bowley (of the Edgworth-Bowley Box)
  1. Use mathematics as shorthand language, rather than as an engine of inquiry. 
  2. Keep to them till you have done. 
  3. Translate into English. 
  4. Then illustrate by examples that are important in real life.  
  5. Burn the mathematics. 
  6. If you can’t succeed in 4, burn 3. This I do often.

Old Keynesian Economics and Equilibrium Theory

Noah Smith refers to a vintage piece by Robert Barro that pours scorn on the New Keynesian agenda. I am grateful to Noah for drawing our attention to it. I find much to agree with in Barro’s critique of the New Keynesians and those who would attack his position would be wise to heed the proverb: those who live in glass houses should not throw stones.

Much of the modern debate between classical and Keynesian economics is framed around equilibrium theory. In the red corner is a class of reactionary equilibrium theorists who are blind to the reality of mass unemployment. In the blue corner, is a class of enlightened new Keynesians who are champions of the unemployed. These progressives recognize that nominal rigidities prevent the labor market from equating demand and supply and the obvious remedy is large-scale fiscal expansion. The failure of the reactionaries to recognize the obvious merits of this argument must be due to their political motivation.

This is a simplistic description of reality, not just because both new-Keynesian and new classical economists span both sides of the political aisle. It is also simplistic because it misunderstands the modern meaning of the equilibrium assumption. Using general equilibrium theory, broadly defined, one can build sensible equilibrium models where high unemployment exists as one of many possible labor market equilibria.

Most of the macro-economists I know, and all of the macro-economists I respect, learned a huge amount from the rational expectations revolution, initiated by Robert Lucas. Drawing on Chapter 7 of Gerard Debreu’s Theory of Value, Lucas taught us to assume that markets are always in equilibrium. That observation was a game changer that is still playing out in the research community and its implications were not, in my view, fully understood by early adopters of classical economic models.

Most modern macroeconomic theorists use dynamic stochastic general equilibrium models, DSGE, for short. These models are direct descendants of John Hicks' classic book, Value and Capital, which developed the idea that economies evolve as a series of ‘weeks’, each of which is characterized by markets that are in what Hicks called a ‘temporary equilibrium’.

After reading Keynes’ General Theory, Hicks renounced the equilibrium assumption (see Michel De Vroey) and argued instead, that for some commodities, demand may not equal supply in any given week. That ‘disequilibrium’ assumption, came to dominate the subsequent development of macroeconomics and it manifests itself today in new-Keynesian models of sticky prices.

The disequilibrium assumption favored by Hicks came under attack in the 1970s because simple models of that era could not account for the simultaneous occurrence of inflation and unemployment.

The main tool used to understand macroeconomics in 1970 was the IS-LM model. That model was widely perceived to be unsatisfactory, in part, because it is purely static. The IS-LM model does not explain the interaction of prices and expectations and, for that reason, it is an unsatisfactory model if one is interested in understanding inflation, which is an inherently dynamic process. That problem was solved by the introduction of mathematical techniques that were unavailable to previous generations of theorists. Those techniques were introduced to macroeconomics in the rational expectations revolution.

The rational expectations revolution made two changes to the temporary equilibrium agenda as it was understood in 1972. First, rational expectations theorists insisted that markets are in equilibrium every period. According to this approach, the demand equals the supply for every commodity; including labor. Second, rational expectations theorists insisted that expectations of future prices are correct in the sense that no agent is systematically fooled into making decisions that he subsequently regrets. Early versions of rational expectations models also assumed a single agent, perfect competition, linear technologies, etc., etc., etc.

These early equilibrium models, (the RBC model of Kydland and Prescott is a good example), carried with them a very strong implication. There is nothing that government can do to improve the welfare of the agents in the model. In the language of economics; these models have a unique equilibrium and that equilibrium is Pareto Optimal.1

Many economists have recognized for a long time that the RBC model of Kydland and Prescott is not a good description of the real world. Larry Summers, for example, tells us that the classical vision of economics is nonsense because it disregards some basic facts; primary among them is the existence of large-scale unemployment that persists for decades. I agree whole-heartedly. But accepting equilibrium theory as an organizing principle does not require that we accept all of the assumptions of the RBC model.

The problem with classical models is not the equilibrium assumption; it is the optimality implication. The idea that the current state of affairs is socially optimal is so obviously at odds with the existence of mass unemployment that it has given equilibrium theory a bad name. In very simple models, equilibrium and optimality are the same thing. But that conclusion is a very special implication of some equilibrium models. It does not hold in general. That idea is key to reconciling Keynesian economics with equilibrium theory.

The sceptical reader will reasonably ask how equilibrium can be consistent with unemployment. Surely the existence of unemployment requires us to assume that the demand and supply of labor are not equal to each other. Not so: By modelling the process by which unemployed workers are matched with jobs, we can use search theory (for which Dale Mortensen, Chris Pissarides and Peter Diamond were awarded the 2010 Nobel prize) to understand how unemployment varies over time.

To understand the persistence of high unemployment, we do not need to assume that prices are sticky or that markets are in disequilibrium. Mass unemployment does not occur because markets are in disequilibrium: Mass unemployment occurs because the market equilibrium is not socially optimal. Recognizing that simple fact has important implications for our understanding of the current state of the world economy.

This post would not be complete without commenting on a claim that Paul Krugman recently made on his blog in the New York Times. In Krugman’s view we should return to what he refers to as Neo-Paleo-Keynesianism which, according to Krugman, involves
…turning away from hard math back toward rough-and-ready assumptions based on empirical observation. Aspiring up-and-coming economists may be able to publish empirical papers in this vein, but theoretical analyses are likely to be met with giggles and whispers. Just because the stuff works doesn’t mean that it will be publishable.
I disagree and in a recent blog post I suggested a different definition of Neo-Paleo-Keynesianism from Krugman's initial use of that term.  In 2008 I defined a way of reconciling Keynesian economics with equilibrium theory that I called Old-Keynesian Economics. Both of these links describe ways of reconciling the essence of Old Keynesian economics with equilibrium theory that go well beyond “rough-and-ready assumptions based on empirical observation”.

The challenge for aspiring up-and-coming economists is to reconcile the observation of persistent mass unemployment with the tools of economics by building on the foundation provided by the recent work of DSGE theorists. Often, that will involve mastering ‘hard math’ because hard math offers the best way of consistently formalizing the logic that underlies economic theory. The combination of search theory with temporary equilibrium theory offers the tools to do just that. No-one would use an abacus when offered a computer. For the same reason, it would be unwise for an aspiring up-and-coming economist to cling to the static IS-LM model when there are alternative tools available that are better suited to the task of explaining financial crises.
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1. To the unsuspecting natural scientist reading this blog -- economists use the word equilibrium to mean that plans of agents are internally consistent. There is no implication in an ‘equilibrium’ that observable variables are constant through time. Instead, they are typically described by a stationary probability measure.

More on Rational Agents and Irrational Markets: A Wonkish Response to Andy Harless

In a comment on my most recent blog post, Andy Harless "[wishes he] had a better intuition for what is going on in [my] model." I took a stab at responding to Andy in the comment section, but my response became so long that I turned it into a post. Here is my answer to Andy. You can find additional comments over at Economist's View where Mark Thoma was kind enough to post an excerpt.

The model Andy is talking about (here) describes an endowment economy with no production. There are two types of people; patient and impatient. Impatient people have a higher rate of time preference than impatient people and, as a consequence, one group will become lenders and the other group will become borrowers. Both types die in any given period, with the same age-independent probability. They are replaced by new people so that the population of each type is stationary and there is an exponential age distribution for each type.

All asset market transactions occur through a zero profit financial intermediary. There are complete annuities markets and when a person dies, his wealth is returned to the financial intermediary. If a person borrows from the intermediary, he is required to take out life insurance.

In the special example in this post, there is no fundamental uncertainty. I will also assume, in this post, that there are only two shocks. Because of these special assumptions, I will need only two assets to complete the markets. These assets are short-term bonds and long-term bonds. The more general case, where long-term bonds and equity are different assets, is covered in the paper.

Short term bonds represent a claim to one unit of the endowment next period. Long term bonds represent a claim to one unit of the endowment in every period. The price of a long term bond is the same as the value of a new born agent’s human wealth because human wealth and long-bonds are claims to the same income streams.

When they are born, lenders sell a portion of their human wealth to borrowers: in return, they buy short-term debt. Lenders start out life as savers and in the early years of their life they consume less than their endowment in every period.

Borrowers, in contrast, sell sell short-term debt to lenders. In the early years of their life they consume more than their endowment in every period.

As lenders age, eventually they reap the benefits of their youthful choices and they begin to spend the interest on their asset portfolios. Lenders have an increasing consumption profile over time.

As borrowers age, eventually they reap the harvest of their youthful indiscretion and they begin to pay back the interest on their debts. Borrowers have a decreasing consumption profile over time.

So far so good. But what about uncertainty?

The trades I described above imply that a lender shorts long-term debt and goes long in short-term debt. A borrower takes the opposite side of these trades.

A long bond issued in period t is a claim to one unit of the endowment next period PLUS a claim to a long bond in period t+1. Just as in Keynes’ beauty contest example, the price of a long bond next period is worth what the market thinks it is worth. In the paper, we assume that there is a complete set of markets that are indexed to an observable ‘sunspot’ variable. That is simply a short cut for bringing ‘animal spirits’ or market sentiment into the pricing equation. The model displays what George Soros calls ‘reflexivity’.

Our model has many equilibria where a long-bond is worth exactly what the market thinks it is worth. If people think that long bonds are worth a lot; they WILL BE worth a lot. In that case, there will be a resource transfer from lenders to the new born agents and the borrowers. If people think that long bonds are worth less; they WILL BE worth less. In that case, there will be a resource transfer from the new born agents and the borrowers to the lenders.

Our model differs from a representative agent economy because, although borrowers and lenders each make trades that obey a transversality condition, there is no analog of these transversality conditions for the market as a whole. It is this feature that distinguishes our work from most other models. The trades that occur in our model are equilibrium trades in the sense in which that term is used in standard DSGE models.  But unlike most existing models; these trades are NOT Pareto optimal. We think that this is a useful way to understand why financial crises are so painful.

Why are equilibria not Pareto optimal? The answer comes from our assumption that demographics limit participation. If the unborn could participate in the asset markets that occur before they are born, they would eliminate the inefficient sunspot fluctuations. Because everyone is assumed to dislike risk, in the absence of prenatal financial markets; everyone is worse off. The model captures a lot of what appears to have happened in the financial markets, within a framework that is very neoclassical in its structure. For me, that is a virtue.