[This article advocates a theory of expectation formation that incorporates many of the central motivations of behavioral finance theory while retaining much of the discipline of the rational expectations approach. We provide a framework in which agents, in an asset pricing model, underparameterize their forecasting model in a spirit similar to Hong, Stein, and Yu (2007) and Barberis, Shleifer, and Vishny (1998), except that the parameters of the forecasting model and the choice of predictor are determined jointly in equilibrium. We show that multiple equilibria can exist even if agents choose only models that maximize (risk-adjusted) expected profits. A real-time learning formulation yields endogenous switching between equilibria. We demonstrate that a real-time learning version of the model, calibrated to U. S. stock data, is capable of reproducing regime-switching returns and volatilities, as recently identified by Guidolin and Timmermann]

We establish a framework wherein agents make expectation-revision decisions subject to a specified calculation technology and preferences over forecast errors. The technology endows agents with correctly specified economic models, but the cost of expectation calculation using these models leads to gradual and incomplete adjustment to long-run rational-expectations equilibrium. The rational-expectations hypothesis emerges as a special case of the equilibrium paths obtained in our framework. In a natural-rate model of monetary policy, calculation technology gives rise to long-run nonneutrality and hysteresis effects, and incomplete adjustment of forecast rules causes output fluctuations to be amplified.

We construct a rational expectations model in which the economy switches stochastically between periods of low and high growth. When agents expect growth to be slow, the returns on investment are low and little investment takes place. But if agents expect fast growth, investment is high, returns are high, and growth is rapid. This expectational indeterminacy is induced by monopolistic competition and complementarity between different types of capital goods. Neither externalities nor increasing returns to scale are required. The equilibrium with growth cycles is stable under the dynamics implied by a simple learning rule.

A number of studies (e.g., Robert J. Shiller, 1981; Olivier J. Blanchard and Mark Watson, 1982; Kenneth D. West, 1988) have argued that dividend and stock price data are not consistent with hypothesis, in which prices are given by present discounted values of expected dividends. These results have often been construed as evidence for existence of bubbles or fads. (Related arguments have been made with respect to gold, bonds, and foreign exchange). A major problem with such arguments (e.g., James Hamilton and Charles Whiteman, 1985) is that apparent evidence for bubbles can be reinterpreted in terms of market fundamentals that are unobserved by researcher. Behzad T. Diba and Herschel I. Grossman (1984, 1988b) and Hamilton and Whiteman (1985) have recommended alternative strategy of testing for rational bubbles by investigating stationarity properties of asset prices and observable fundamentals.1 In essence, argument for equities is that if stock prices are not more explosive than dividends then it can be concluded that rational bubbles are not present, since they would generate an explosive component to stock prices.2 Using unit-root tests, autocorrelation patterns, and cointegration tests to implement this procedure, Diba and Grossman (1988b p. 529) state that the analysis supports conclusion that stock prices do not contain explosive rational This paper shows that above battery of tests is in fact unable to detect an important class of rational bubbles. The point is demonstrated by constructing rational bubbles that appear to be stationary when unitroot tests are applied, even though they are explosive in relevant sense. Simulations show that, when such bubbles are present, stock prices will not appear to be more explosive than dividends on basis of these tests, even though bubbles are substantial in magnitude and volatility. The presence of rational bubbles in actual stock prices thus remains an open question.

The U.S. dollar price of the U.K. pound sterling is tested for a speculative bubble, defined as a period with a nonzero median in excessreturns. A nonparametric procedure is developed, which controls for data mining over the period of flexible exchange rates, and finds a negative bubble in the excess return to holding sterling rather than dollar assets during the period 1981-84. Possible interpretations arebootstrap equilibria (rational bubbles), nonsym-metric fundamentals, and nonrational expectations.

The authors establish a framework wherein agents make expectation-revision decisions subject to a specified calculation technology and preferences over forecast errors. The technology endows agents with correctly specified economic models, but the cost of expectation calculation using these models leads to gradual and incomplete adjustment to long-run rational-expectation equilibrium. The rational-expectations hypothesis emerges as a special case of the equilibrium paths obtained in the authors' framework. In a natural-rate model of monetary policy, calculation technology gives rise to long-run nonneutrality and hysteresis effects, and incomplete adjustment of forecast rules causes output fluctuations to be amplified.

A fundamentals based monetary policy rule, which would be the optimal monetary policy without commitment when private agents have perfectly rational expectations, is unstable if in fact these agents follow standard adaptive learning rules. This problem can be overcome if private expectations are observed and suitably incorporated into the policy maker's optimal rule. These strong results extend to the case in which there is simultaneous learning by the policy maker and the private agents. Our findings show the importance of conditioning policy appropriately, not just on fundamentals, but also directly on observed household and firm expectations.

Drawing upon recent contributions in the statistical literature, we present new results on the convergence of recursive, stochastic algorithms which can be applied to economic models with learning and which generalize previous results. The formal results provide probability bounds for convergence which can be used to describe the local stability under learning of rational expectations equilibria in stochastic models. Economic examples include local stability in a multivariate linear model with multiple equilibria and global convergence in a model with a unique equilibrium.