How Deeply Do We Understand the Mechanism of Expectations Formation?

Faculty Fellow, RIETI

The Bank of Japan's quantitative and qualitative easing is designed to create inflation by beating down deflationary expectations and generating inflationary expectations. However, it remains theoretically unclear as to how the central bank can control such expectations under the current situation where interest rates are already zero-bound and cannot be lowered further. To what extent can macroeconomics explain the formation of expectations?

The rational expectations hypothesis, which is the dominant theoretical framework, assumes that agents at the micro level�i.e., households and corporations�process information and make decisions in a rational manner, thereby theorizing how their behavior affects the macro economy. However, the essentiality of rational expectations lies in the fact that expectations are by nature self-referential, whereas rational decision making by corporations and households are not necessarily essential. "Self-referential" refers to the self-defining nature of expectations.

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The Lucas critique, a 1976 paper by University of Chicago Professor Robert Lucas, pointed out that expectations, or economic rules, are self-referential. For instance, suppose there is an expectation (or a rule) that inflation makes people feel wealthier as their wages go up and hence they will increase consumption. Here, if the government creates inflation in an attempt to stimulate the economy, those who already know this rule and are aware of the government's intention to give them an illusion would increase savings in preparation of larger expenditures in the future. This then creates a new rule: inflation does not necessarily increase consumption.

The self-referential nature of expectations, illustrated in the Lucas critique, represents the fact that the rules of an economic system (or expectations) may change when both consumers and the government within the economic system know and act in accordance with such rules. Economic rules are generated through the loop process of expectations formation as shown in the figure below. This, Lucas says, makes macroeconomic policy invalid. Since this loop is infinite, economic rules can, in principle, never be defined.

Figure: Loop of Expectations Formation

However, under certain conditions, there are cases where expectations remain unchanged even after passing through the loop. One such condition for expectations to be defined as a fixed point is rationality at the micro level, namely, the rational processing of information by households and corporations.

Fixed points in the process of expectations formation are stable and easy to analyze. If the expectations are not the fixed points, they cannot be analyzed in a meaningful way. Thus, modern macroeconomists have decided to call such fixed points "rational expectations," and, by taking them as expectations formed in the real economy, they have developed various economic models. The need to justify this has caused them to make too strong of an assumption that households and corporations are perfectly rational.

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However, rational expectations are no more than a theoretical approximation because perfect rationality at the micro level, a state in which all households and corporations act rationally, is hardly�if at all�possible to achieve in reality. What is important here is to put the self-referential nature of expectations at the heart of theories. This point cannot be overemphasized.

Let's compare the evolution of economic theories with that of physics. Albert Einstein's theory of general relativity overturned the concepts of space and time in classical mechanics. Yet, both are based on the premise that a physicist (observer) observes the object externally. In contrast, quantum mechanics has been developed by invalidating that premise and instead assuming the presence of a self-referential loop, where the observer of a physical system is inside the system. As such, the quantum mechanics view of the world is a complete departure from that of classical mechanics and relativity in terms of the presence or absence of self-reference.

The same can be said about economic theories, namely, between pre- and post-Lucas theories. Macroeconomists are quite conscious of this. For instance, the title of a book written by New York University Professor Thomas J. Sargent et al., which is popularly used as an advanced-level textbook for graduate students, is Recursive Macroeconomic Theory. The term "recursive" is synonymous to "self-referential."

A big difference from physics is that tools for dealing with self-reference in realistic settings have yet to be established in economics. Because of this, rational expectations, an unrealistic hypothesis that has been adopted as an approximation, are still being used today. However, it is undeniable that models based on the rational expectations hypothesis are inadequate as a foundation for policy making in the real world. Thus, various theoretical improvements have been proposed in an attempt to develop realistic macroeconomic theories.

One area of such efforts is econophysics. Research conducted to date includes some attempts to find regularities in stock price dynamics by applying statistical physics. For instance, in a paper written in 2005, Professor Didier Sornette of the Swiss Federal Institute of Technology in Zurich (ETHZ) predicted the burst of the U.S. housing bubble.

However, as a result of giving so much priority to taking a statistical physics approach, econophysicists are ignoring the self-referential concept that households and corporations act with the knowledge of economic rules and that their behavior generates new rules. This must be corrected because abandoning the idea of self-reference is tantamount to falling back from quantum mechanics to classical mechanics.

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What about dynamic stochastic general equilibrium (DSGE) modeling, which has been used as a standard approach over the past 10 years by central bank economists all around the world? DSGE models have been criticized for failing to predict the 2008 collapse of Lehman Brothers but remain the mainstream of economic theory.

DSGE models assume that all households and corporations are rational. Meanwhile, the business cycle in the real world is an inertial process in which the economy moves gradually toward either the peak or trough and then attenuates. Such rigidity and its amplifying effects cannot be reproduced by simple models. Standard models reproduce such rigidity and amplifying effects by assuming special functions describing the utility of households and/or adjustments costs for corporate capital investment. A 2005 paper written by Northwestern University Professor Lawrence Christiano et al. is a leading example.

This makes it possible to explain economic data observed. But then, in theory, the business cycle is defined to be the result of the optimal behavior of households and corporations, whereby their responses exhibit similar movements to those of the business cycle. Such standard models, if they are correct, would lead us to the conclusion that there is no need for the government to take stimulus measures even in times of recession because it is the "optimal" state for households and corporations. This defect is commonly observed in standard DSGE models. The purpose of economic policy, as defined in DSGE models, is to address inefficiencies caused by sticky prices, not to smooth out economic fluctuations.

In an attempt to overcome this defect, some researchers have been trying to construct a theoretical model for analyzing interactions between heterogeneous economic agents without changing the hypothesis of rational expectations, as exemplified by a 2012 paper by Princeton University Professor Nobuhiro Kiyotaki and London School of Economics Professor John Moore. Under this kind of model, the aggregation of individual optimal decisions does not result in the optimal outcome at the macro level, and hence stabilizing economic fluctuations can improve efficiency.

Also, various attempts have been made to find out a realistic�rather than hypothetical�mechanism for the formation of expectations, including those taking a behavioral economics approach or utilizing the notion of bounded rationality. For instance, in their 1999 paper, University of Chicago Professor Lars Hansen, the winner of this year's Nobel Prize in Economics, and others proposed a new theory to estimate economic rules under the condition that the government and consumers are unaware of the true structure of the economy. However, those attempts are no more than criticism of the unrealistic assumption of rationality at the micro level�i.e., corporations and households are perfectly rational�and have not overturned the essential part of the rational expectations hypothesis in that expectations at the macro level are a fixed point in the loop of expectations formation. How can we tame the self-referential nature of economic systems to analyze the reality? Macroeconomics has yet to find a definite solution to this question.

>> Original text in Japanese

* Translated by RIETI.

October 21, 2013 Nihon Keizai Shimbun

November 26, 2013

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