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Tuesday, July 25, 2006

Adaptive Expectations, Rational Expectations, and Learning in Macroeconomic Models

This commentary says models of expectations in economics are like porridge in the story of Goldilocks, but there is no 'just right' -- agents are either too smart, or too dumb, and he calls for more realistic models somewhere in the middle:

Central banking model for neither gods nor monkeys, by Paul de Grauwe, Commentary, Financial Times: The quest for a scientific foundation for central banking has been going on for a long time. This quest led in the 1960s and 1970s to large-scale econometric models with hundreds of equations describing the economy in much detail. Central banks used them to predict how interest rate movements would affect the economy and to discover the best way to react to shocks like the oil price increases of the 1970s.

It quickly turned out that these large models led to unreliable predictions. ... The diagnosis of this failure was given by Robert Lucas, Nobel Prize winner in economics. The old models considered individual agents (consumers and producers) as passive... Prof Lucas stressed that these agents are human beings endowed with intelligence and a desire to look for the best possible outcome. In such an environment, he argued, the [agents] should be modelled as active ... trying to anticipate what the central bank would do.

This criticism led to the rational expectations revolution in economics. New models were built in which a new assumption was introduced. Individual agents now were assumed to understand the complexity of the world in which they live and to continuously compute the implications of central bank actions for their present and future welfare.

The earlier extreme assumption of complete stupidity of individual agents was replaced by another extreme assumption of supreme understanding of the intricacies of the economy. In the old models, agents were assumed to have the brains of monkeys. In the new “rational expectations models”, agents were given god-like features allowing them to see through the complexities of the world. Milton Friedman reminded us a long time ago that even if the underlying assumptions of a model seem implausible, its power depends on how well it performs in making predictions. ... They failed, so much so that they had to be brought back to the repair shops almost immediately. There, ad-hoc features that had little to do with rational agents were added until the model ran better.

In spite of this empirical failure, many central banks today use versions of this model. The model is inhabited by super-rational agents for whom the complexity of the world has few secrets. They continuously optimise their present and future consumption plans and are capable of calculating with great precision what the effects will be of interest rate changes implemented by the central bank. This is a fairytale world.

It is quite paradoxical that macroeconomics has arrived at such an extreme view now that we start to learn from psychology and brain sciences that the economic paradigm of perfectly informed optimisers may not be the correct way to model individual decision-making. We learn from these other sciences that individuals experience great problems when they try to understand the world in which they live. They find it difficult to collect and to process the complex information with which they are confronted.

Since they cannot see the whole picture, they use simple rules (“rules of thumb”) and partial information to guide their decisions. They are not fools though. They regularly subject these simple rules to profitability tests and only keep those rules that keep their profits at reasonable levels. ... There is a need to move away from extreme assumptions when modelling human behaviour. Human beings are neither the dumb automatons of the old models nor the supreme creatures of knowledge and understanding of the new models.

There is good news though. Increasingly, academic researchers are trying to model the economy assuming that agents with imperfect knowledge are learning and revising their knowledge about the workings of the economy. This approach is still in its infancy but is full of promise for a scientific foundation of central banking. In the meantime, until these new insights mature, central banking will continue to be more art than science.

A colleague just returned from a week long conference at the St. Louis Fed where they went through 60 papers on learning models in economics, and there have been many such conferences in recent years. These papers do exactly what the author calls for, and the Fed is very interested in learning as evidenced by the fact that some of the best researchers in this area have Fed appointments. How the public learns about policy, how the Fed itself learns about economic modeling and policy, how the two interact, and so on, are of primary interest to Fed policymakers. This work has been going on for a long time so I would not characterize this research as "still in its infancy." Here's part of the introduction to Learning and Expectations in Macroeconomics, by George W. Evans, who is just down the hall, and Seppo Honkapohja:

1.1 Expectations in Macroeconomics Modern economic theory recognizes that the central difference between economics and natural sciences lies in the forward-looking decisions made by economic agents. In every segment of macroeconomics expectations play a key role. ...

Contemporary macroeconomics gives due weight to the role of expectations. A central aspect is that expectations influence the time path of the economy, and one might reasonably hypothesize that the time path of the economy influences expectations. The current standard methodology for modeling expectations is to assume rational expectations (RE)... Formally, in dynamic stochastic models, RE is usually defined as the mathematical conditional expectation of the relevant variables. The expectations are conditioned on all of the information available to the decision makers. For reasons that are well known, and which we will later explain, RE implicitly makes some rather strong assumptions.

Rational expectations modeling has been the latest step in a very long line of dynamic theories which have emphasized the role of expectations. The earliest references to economic expectations or forecasts date to the ancient Greek philosophers. In Politics (1259a), Aristotle recounts an anecdote concerning the pre-Socratic philosopher Thales of Miletus (c. 636–c. 546 B . C .). Forecasting one winter that there would be a great olive harvest in the coming year, Thales placed deposits for the use of all the olive presses in Chios and Miletus. He then made a large amount of money letting out the presses at high rates when the harvest time arrived.[1] Stories illustrating the importance of expectations in economic decision making can also be found in the Old Testament. In Genesis 41–47 we are told that Joseph (on behalf of the Pharaoh) took actions to store grain from years of good harvest in advance of years in which he forecasted famine. He was then able to sell the stored grains back during the famine years, eventually trading for livestock when the farmers’ money ran out.[2]

Systematic economic theories or analyses in which expectations play a major role began as early as Henry Thornton’s treatment of paper credit, published in 1802, and Émile Cheysson’s 1887 formulation of a framework which had features of the “cobweb” cycle.[3] There is also some discussion of the role of expectations by the Classical Economists, but while they were interested in dynamic issues such as capital accumulation and growth, their method of analysis was essentially static. The economy was thought to be in a stationary state which can be seen as a sequence of static equilibria. A part of this interpretation was the notion of perfect foresight, so that expectations were equated with actual outcomes. This downplayed the significance of expectations.

Alfred Marshall extended the classical approach to incorporate the distinction between the short and the long run. He did not have a full dynamic theory, but he is credited with the notion of “static expectations” of prices. The first explicit analysis of stability in the cobweb model was made by Ezekiel (1938). Hicks (1939) is considered to be the key systematic exposition of the temporary equilibrium approach, initiated by the Stockholm school, in which expectations of future prices influence demands and supplies in a general equilibrium context.[4] Finally, Muth (1961) was the first to formulate explicitly the notion of rational expectations and did so in the context of the cobweb model.[5]

In macroeconomic contexts the importance of the state of long-term expectations of prospective yields for investment and asset prices was emphasized by Keynes in his General Theory.[6] Keynes emphasized the central role of expectations for the determination of investment, output, and employment. However, he often stressed the subjective basis for the state of confidence and did not provide an explicit model of how expectations are formed.[7] In the 1950s and 1960s expectations were introduced into almost every area of macroeconomics, including consumption, investment, money demand, and inflation. Typically, expectations were mechanically incorporated in macroeconomic modeling using adaptive expectations or related lag schemes. Rational expectations then made the decisive appearance in macroeconomics in the papers of Lucas (1972) and Sargent (1973).[8]

We will now illustrate some of these ways of modeling expectations with the aid of two well-known models. ... These two examples are chosen for their familiarity and simplicity. This book will analyze a large number of macroeconomic models, including linear as well as nonlinear expectations models and univariate as well as multivariate models. Recent developments in modeling expectations have gone beyond rational expectations in specifying learning mechanisms which describe the evolution of expectation rules over time. The aim of this book is to develop systematically this new view of expectations formation and its implications for macroeconomic theory.


1 In giving this story, as well as another about a Sicilian who bought up all the iron from the iron mines, Aristotle also emphasized the advantage of creating a monopoly.
2 The forecasting methods used in these stories provide an interesting contrast with those analyzed in this book. Thales is said to have relied on his skill in the stars, and Joseph’s forecasts were based on the divine interpretation of dreams.
3 This is pointed out in Schumpeter (1954, pp. 720 and 842, respectively). Hebert (1973) discusses Cheysson’s formulation. The bibliographical references are Cheysson (1887) and Thornton (1939).
4 Lindahl (1939) is perhaps the clearest discussion of the approach of the Stockholm school. Hicks (1965) has a discussion of the methods of dynamic analysis in the context of capital accumulation and growth. However, Hicks does not consider rational expectations.
5 Sargent (1993) cites Hurwicz (1946) for the first use of the term “rational expectations.”
6 See Keynes (1936, Chapter 12).
7 Some passages, particularly in Keynes (1937), suggest that attempting to forecast very distant future events can almost overwhelm rational calculation. For a forceful presentation of this view, see Loasby (1976, Chapter 9).
8 Most of the early literature on rational expectations is collected in the volumes Lucas and Sargent (1981) and Lucas (1981).

    Posted by on Tuesday, July 25, 2006 at 01:18 PM in Economics, Macroeconomics, Methodology | Permalink  TrackBack (0)  Comments (2)

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