LEARNING TO FORECAST PRICE

I. INTRODUCTION In recent years economists have begun to investigate how people might learn equilibrium behavior. Microeconomists following Binmore (1987) and Fudenberg and Kreps (1988) consider learning models with roots in Cournot (1838) and Brown (1951). Numerous laboratory studies test and refine the microeconomists' learning models; see Camerer (1998) for a recent survey. There is also a separate theoretical macroeconomics literature on learning following Marcet and Sargent (1989a, 1989b, 1989c) and Sargent (1994); see Evans and Honkapohja (1997) for a recent survey. The focus is on how people might learn to forecast relevant prices and whether the learning process permits convergence to rational expectations equilibrium. We are not aware of any laboratory work intended to test and refine the learning models favored by macroeconomists. (1) The current study is intended to fill that gap. We gather laboratory evidence on the most basic questions a macroeconomist might ask about learning: Can people learn to forecast prices rationally? If there are obstacles to learning, are they transient or innate characteristics of human behavior? What sorts of environments reduce or enlarge those obstacles? Additional questions might be asked about the effects of learning observable in the usual macroeconomic and financial field data and about forecasting in a self-referential macroeconomic setting. Our work does not address such questions directly, but it does lay a foundation for later investigations of these additional questions. Available evidence on the basic questions is rather disquieting. An extensive cognitive psychology literature, following Kahneman, Slovic, and Tversky (1973), finds that human forecasts are bedeviled by many systematic biases, such as the anchoring and adjustment heuristic, the availability and representativeness heuristics, base rate neglect, and confirmatory and hindsight biases; see Rabin (1998) and Camerer (1998) for recent surveys. There is also a small experimental economics literature on forecasting prices and rational expectations that reaches generally negative conclusions. Garner (1982) presents 12 subjects over 44 periods with a continuous forecasting task that implicitly requires the estimation of seven coefficients in a third-order autoregressive linear stochastic model. He rejects stronger versions of rational expectations but finds some predictive power in weaker versions. Williams (1987) find autocorrelated and adaptive forecast errors by traders in simple asset markets. However, the true data -generating process is not stationary in this task and is unknown even to the experimenter, which makes it difficult to identify individually rational behavior. Dwyer et al. (1993) test subjects' forecasts of an exogenous random walk. They find excess forecast variance but no systematic positive or negative forecast bias for this nonstationary task. A possible objection to both strands of the empirical literature is that neither provides good opportunities for learning. Most of the cognitive studies frame the tasks in ways that do not immediately engage subjects' forecasting experience, offer no salient reward, or provide little feedback that would allow subjects to improve performance. The three economics articles just cited have relatively few trials with complicated or nonstationary processes. Our study, by contrast, presents laboratory subjects with a moderately difficult forecasting task in several stationary learning environments. We examine human learning in an individual choice task called Orange Juice Futures price forecasting (OJF). The OJF task has a form and complexity similar to the forecasting tasks in macroeconomists' models: Subjects must implicitly learn the coefficients of two independent variables in a linear stochastic process. The task is based on the observation of Roll (1984) that the price of Florida orange juice futures depends systematically on only two exogenous variables: the local weather hazard and the competing supply from Brazil. …