Bounded Rationality in Macroeconomics.

Vaughan, Mark D.

When former communists denounce Lenin, it makes headlines. A public disavowal of rational expectations by Thomas Sargent would also make headlines. In his new book, Bounded Rationality in Macroeconomics, Sargent does not quite apostatize. Yet, he does concede that rational expectations modeling leaves important research and policy questions unanswered. To search for potential answers, Sargent surveys the literature on bounded rationality. He also advocates bounded rationality as a new approach to macroeconomic modeling. Though Sargent offers an effective literature survey and several interesting applications of bounded rationality, he fails to persuade the general reader to embrace the new approach. Indeed, Sargent's reliance on mathematics at the expense of intuition limits the audience of Bounded Rationality in Macroeconomics to economists with highly technical research tastes.

Sargent's literature survey is effective because it clearly contrasts modeling with bounded rationality and modeling with rational expectations. In a rational expectations model, agents optimize subject to constraints and hold mutually consistent views about the constraints. Mutual consistency of views implies that agents know a great deal about the environment. As Sargent puts it:

When implemented numerically or econometrically, rational expectations models impute much more knowledge to the agents within the model (who use the equilibrium probability distributions in evaluating their Euler equations) than is possessed by an econometrician, who faces estimation and inference problems that the agents in the model have somehow solved [p. 3].

In contrast, bounded rationality drops the assumption of mutually consistent perceptions. Dropping mutual consistency forces agents to act like econometricians; now agents in the model must use theory and statistics to learn about the environment. While more realistic as a working assumption than rational expectations, bounded rationality exacts a computational price. Again, in Sargent's words:

Ironically, when we economists make the people in our models more "bounded" in their rationality and more diverse in their understanding of the environment, we must be smarter, because our models become larger and more demanding mathematically and econometrically [p. 2].

Researchers will pay the computational price if bounded rationality promises a large return. Sargent sees large returns in three areas of research: multiple equilibria, regime changes, and transitional dynamics. One problem with rational expectations models is that they generate multiple equilibria; bounded rationality can help identify a subset of admissible equilibria. Another problem with rational expectations models arises when analyzing regime changes. Analyzing regime changes under rational expectations implies that agents immediately accept the permanence of any change in policy rules; analyzing regime changes under bounded rationality allows agents to learn slowly about the consequences of policy changes. A third problem is that rational expectations models can predict outcomes inconsistent with real-world observations; bounded rationality offers new sources of dynamics that better capture some real-world processes.

Sargent uses Jean Tirole's No-Trade theorem to demonstrate that modeling with bounded rationality captures real-world processes effectively. Under rational expectations, Tirole proved that equilibrium prices in financial markets completely reveal private information without trade. The zero-trading-volume implication of the theorem strains credulity, given the observed volume in real-world financial markets. Sargent shows that replacing Tirole's rational agents with adaptive agents generates frictions capable of explaining volume. Indeed, in simulations security prices with least squares learning diverge from rational expectations prices, thereby generating volume, for hundreds of periods.

The no-trade example ranks as Sargent's most interesting application of bounded rationality. Appreciating the no-trade application is difficult, however, because the exposition leans heavily on mathematics at the expense of intuition. Consider an example lifted from the section:

Since [z.sub.jt] is a subvector of [z.sub.t], system (24) can be used to deduce the projections

E([z.sub.jt] [where] [Z.sub.jt-1]) = [S.sub.j]([Beta])[Z.sub.jt-1],

where [S.sub.j]([Beta]) depends on (T([Beta]), V([Beta])) and the moments Eutu't. Thus, we have a mapping from a pair of perceived laws of motion [Beta] = ([[Beta].sub.a], [[Beta].sub.b]) to a pair of matrices ([S.sub.a]([Beta]), [S.sub.b]([Beta])) that determine optimal (linear least squares) predictors. A rational expectations equilibrium is a fixed point of this mapping [p. 117]. To be fair, a random passage plucked from any mathematical treatise could bewilder the casual reader. Still, the passage above proves difficult after reading the previous 116 pages carefully.

The entire middle section of Bounded Rationality proves equally difficult. In Chapter four, for example, Sargent divides the subject-networks and artificial intelligence - into seven daunting subheadings: the Perceptron, Feedforward Neural Networks with Hidden Units, Associative Memory, Stochastic Networks, Local and Global Methods, The Genetic Algorithm, and Classifier Systems. In the perceptron discussion, Sargent confronts the reader with Heaviside step functions and sigmoid functions. Later, in the associate memory discussion, the reader trips over Hopfield networks and Hebb's rule. The material under the other subheadings proves no easier. The difficulty of the exposition is puzzling since Sargent seems to want a wider audience than simply highly technical economists. Indeed, in the closing pages of the book, he complains that ". . . macroeconomists have shown very little interest in applying models of bounded rationality to data." To reach a wider audience, Sargent could have expanded the book, including enough intuition to allow macroeconomists of all stripes to grasp the argument. Instead, he choose to argue at a level that only a subset of macroeconomists can follow.

In Bounded Rationality in Macroeconomics, Thomas Sargent seeks to inform the reader about bounded rationality and, more importantly, to persuade him that bounded rationality is a valuable approach to macroeconomic problems. The bounded rationality approach, Sargent argues, makes agents in macroeconomic models behave more like econometricians. Grasping the argument in Bounded Rationality requires, unfortunately, that readers behave more like econometricians. The book reads more like Macroeconomic Theory, a compilation of Sargent's Ph.D. lecture notes, than Rational Expectations and Inflation, a collection of his policy essays. In the introduction to Rational Expectations and Inflation, Sargent observes:

One consequence of the highly technical orientation of early work on rational expectations in macroeconomics is that an appreciation has been slow to develop for the relevance of the ideas for the practice of day-to-day macroeconomics [p. ix].

If Sargent had recalled the observation, he would have produced a valuable introduction to bounded rationality modeling. But, by emphasizing mathematics over intuition, Sargent reduced the value of Bounded Rationality in Macroeconomics. Some future economist will complain that macroeconomists failed to appreciate the relevance of bounded rationality to practical problems. To express the complaint, the economist can use Sargent's observation, with "bounded rationality" in place of "rational expectations."

Mark D. Vaughan The Federal Reserve Rank of St. Louis