50 I James B. Bullard I James B. Bullard is an economist at the Federal Reserve Bank of St. Louis. David H. Kelly provided research assistance. 1 I Learning, Rational Expecta- I tions and Policy: A Summary I of Recent Research I I I N THE THREE DECADES since the publica- eliminated may have important implications for tion of the seminal work on rational expecta- macroeconomic policy. Researchers who focus tions, a steely consensus has been forged in the on this question are studying what is called I economics profession regarding acceptable “learning,” because any method of expectations modeling procedures.’ Simply stated, the con- formation is known as a learning mechanism.’ sensus is that economic actors do not persist in making foolish mistakes in forecasting over This paper provides a synopsis of some of the I time. People are presumed to be able to both recent research on learning. Three important detect past patterns in their prediction errors points are emphasized within the context of the and base their behavior on the “best possible” survey. The most salient point is the close rela- I forecast of future economic conditions. In the tionship between learning issues and macroeco- classic phrase of Robert Lucas, the predictions nomic policy. In fact, the topic attracts attention precisely because of its perceived policy implica- of individuals must be “. - free of systematic I and easily correctable biases.” The current tions. The second point is more subtle: learning wide acceptability of this notion is testament to is implicitly an integral part of rational expecta- the success of the rational expectations tions models, and current research only makes this fact explicit. There is little prospect that revolution. I one can avoid the study of learning by assuming Unfortunately, the consensus that in equilibri- rational expectations. The third point is that in- um systematic forecast errors should be elimi- cluding learning in macroeconomic models is I nated has been insufficient to end the debate in unlikely to either confirm or overturn completely macroeconomics over expectational assumptions. the results from rational expectations macro- In particular, some current research examines models. Instead, the concept of rational expecta- the idea that how systematic forecast errors are tions equilibrium seems to provide the appropri- I 1 The seminal work is Muth (1960, 1961). 2 for different readers. This terminology developed because Lucas (1977), p. 224. rational expectations is justified by the notion that people I eliminate systematic forecast errors over time, and the ‘The phrase “learning mechanism” is used in this paper in dynamic elimination of errors is a definition of learning. a broad way, even though it conjures up different images I FEDERAL RESERVE BANK OF St LOUIS a I 51 ate benchmark for the study of learning in that, model” and thus can predict as well as the I when systems converge under learning, they economist manipulating the model.’ These are typically converge to stationary rational expecta- the tenets of the theory and are often espoused tions equilibria. by its advocates. I The next section provides a non-technical in- The first tenet, the heuristic notion that in- troduction to learning and rational expectations. dividuals eliminate systematic forecast errors, is The subsequent section looks at the effects of the one most responsible for the rise of the ra- introducing learning through a simple example tional expectations hypothesis. In a deterministic I attributable to Albert Marcet and Thomas environment, this idea implies that, once learn- Sargent. Some interpretation and discussion ing is complete, people have perfect foresight. of the example is offered in the third section, In a stochastic environment, it means that the I along with a review of other attempts to intro- remaining forecast errors are white noise. duce learning into macroeconomic models. The Since the consensus is that the elimination of final section provides summary comments. systematic forecast errors is a sensible postu- I late, all reasonable long-run equilibria must be THE LEARNING IMPLICIT IN RA- rational expectations equilibria. Macroeconomists TIONAL EXPECTATIONS generally are interested in the effects of changes I in policy parameters at these steady-state equi- Why Study Learning? librium points.’ Given such equilibria, there is at least one reason why the explicit specification of Since decisions made today affecting produc- learning could matter: in a model with multiple I tive behavior are presumed to be based, in part, rational expectations equilibria, the learning on individual assessments of the future, macro- mechanism may serve to select the actual out- economic theories and models generally have come.7 The next section contains an example of I provided a role for expectations. Around 1970, learning as a selection mechanism. however, researchers began to realize that the policy implications of their models were often Representing Learning Via Econ” quite sensitive to the choice of expectational ometric Techniques I assumptions.4 This failure of robustness has been increasingly apparent in the last 20 years Macroeconomists generally have avoided speci- and has drawn increased attention to the prob- fying explicitly the optimal learning mechanism I lem of how expectations are formed. This line underlying rational expectations for a number of research constitutes what has been called the of reasons. First and foremost, they considered rational expectations revolution. rational expectations a shortcut in expectations modeling that made explicit specification un- I A capsule characterization of rational expecta- 8 necessary. Further, ascertaining the full im- tions contains the following themes: (1) In equi- plications of the rational expectations hypothesis librium (a steady state in dynamic terms), ex- turned out to be a difficult problem; presumably, I pectations are “correct” in the sense that in- these implications must be understood before dividuals make no systematic forecast errors; the issue of learning can be investigated. (2) Individuals use all available information (as defined by the researcher) in forming forecasts; There was, however, at least one additional I (3) Expectations vary with changes in govern- reason why learning was essentially ignored— ment policy; and (4) Individuals know “the explicit specifications of how agents form expec- I 4 Sargent (1987) has documented some of this early can be made. This is called global stability. Alternatively, research in rational expectations. one can define local stability, where a particular stationary ‘A more formal approach to defining rational expectations equilibrium is stable only if the initial conditions are near is pursued in the next section. that equilibrium. I 6 ‘Lucas’ comment, “ --take the rational expectations For a discussion of policy along the transition path, see Taylor (1975). equilibrium ---as the model to be tested and view [learn- ing] as -- .an adjunct to the theory that serves to lend it ‘This is the same as saying that learning provides a stabili- plausibility,” hints at this pragmatism. See Lucas (1987a), I ty theory for rational expectations equilibria. In the best p.231. case, given initial conditions and some parameter values, statements claiming that the dynamic evolution of the I economy always leads to a particular stationary equilibrium a JANUARY/FEBRUARy 1991 52 I tations have often been attacked. In particular, ‘the impetus for a detailed analysis of learning one key criticism of the adaptive expectations has come from both advances in research tech- I formulation was that it allowed systematic er- nology and one pressing problem: many rational rors to persist over time.’ expectations models are characterized by multi- ple equilibria. Moreover, these different equilib- The notion of adaptive expectations is essen- ria can have different policy implications, as the 1 tially that people predict the future value of a next section illustrates.” variable via a geometric distributed lag (or Koyck lag) of its past values. One of Muth’s results was that adaptive expectations is an optimal predic- LEARNING AND THE UNPLEAS- I tion method if the variable being forecast follows ANT MONETARIST ARITHMETIC a random walk.”’ Muth’s result makes it clear that, from the beginning, rational expectations This section examines a simple expository ex- I theorists had econometric techniques in mind ample of Marcet and Sargent;14 it is a simplified when thinking about ways to model optimal version of the “unpleasant monetarist arithmetic” forecasting. of Sargent and Neil Wallace.” The example is meant only to illustrate the types of issues that I The idea of looking to econometrics to model can arise; it is not intended as a definitive state- learning obviously can be extended, since the ment of the effects of including learning in eco- Koyck lag is only one of many available econ- nomic models. As the next section will discuss, I ometric techniques. In principle, it should be these effects are still uncertain. possible to take advantage of the developments The model’s most important feature is that in econometric theory to shed light on the prob- there are two steady states (high inflation and lem of how expectations are formed. Further- I low inflation) with differing policy implications. more, if econometric methods are to be applied At the low-inflation steady state, a permanent to solve the inference problem faced by individ- increase