Rational Expectations and the Theory of Price Movements

This 1961 Econometrica paper by John Muth proposes that economic expectations should be modeled as essentially the same as the predictions of the relevant economic theory itself – so that, for a given information set, people’s subjective probability distribution of outcomes is centered on the true, objective probability distribution implied by the structure of the market – and calls such expectations “rational.” Muth motivates the hypothesis by noting two stylized facts from expectations-survey data: aggregate expectations in an industry are about as accurate as elaborate equation systems despite considerable individual-level disagreement, and reported expectations tend to underestimate the extent of actual changes; he argues existing ad hoc expectations formulas (naive extrapolation, adaptive expectations) do not explain either fact well. He develops the hypothesis formally in an isolated single-commodity market with a fixed production lag, deriving the equilibrium price process and its associated rational price-expectation formula as a function of the history of observable shocks, under assumptions of normally distributed disturbances, linear market equations, and the existence of certainty equivalents. He extends the analysis to commodity speculation, deriving an individual’s optimal speculative inventory demand from expected-utility maximization and showing that speculation, when based on moderately well-informed price expectations, reduces the variance of prices by spreading a market disturbance’s effect over several periods, while remaining privately profitable in expectation even though no speculative opportunities exist “in the aggregate.” In the paper’s most cited empirical exercise, Muth compares the implications of rational expectations against the classical (Schultz-Tinbergen), extrapolative (Goodwin), and adaptive (Nerlove) cobweb theories, showing that survey evidence of a positive-but-less-than-one regression coefficient between actual and expected price changes, and the observed length of commodity price cycles (which tend to be longer than the classical cobweb theorem implies), are both consistent with rational expectations but not with the cobweb theories, which require a negative relation between expectational errors and subsequent price changes.

D40 | Macro Paper Warehouse

Rational Expectations and the Theory of Price Movements