Procedures are presented that allow the empiricist to estimate and test asset pricing models on limited-liability securities without the assumption that thehistorical payoff distribution provides a consistent estimate of the market's priorbeliefs. The procedures effectively filter return data for unspecified historical biases in the market's priors. They do not involve explicit estimation of the market's priors, and hence, economize on parameters. The procedures derive from a new but simple property of Bayesian learning, namely: if the correct likelihood is used, the inverse posterior at the true parameter value forms a martingale process relative to the learner's information filtration augmented with the true parameter value. Application of this central result to tests of asset pricing models requires a deliberate selection bias. Hence, as a by-product, the article establishes that biased samples contain information with which to falsify an asset pricing model or estimate its parameters. These include samples subject to, "e.g." survivorship bias or Peso problems. Copyright The Review of Economic Studies Limited, 2004.

We report on two sets of large-scale financial markets experiments that were designed to test the central proposition of modern asset pricing theory, namely, that risk premia are solely determined by covariance with aggregate risk. We analyze the pricing within the framework suggested by two theoretical models, namely, the (general) Arrow and Debreu's complete-markets model, and the (more specific) Sharpe-Lintner-Mossin Capital Asset Pricing Model (CAPM). Completeness of the asset payoff structure justifies the former; the small (albeit non-negligible) risks justifies the latter. We observe swift convergence towards price patterns predicted in the Arrow and Debreu and CAPM models. This observation is significant, because subjects always lack the information to deliberately set asset prices using either model. In the first set of experiments, however, equilibration is not always robust, with markets temporarily veering away. We conjecture that this reflects our failure to control subject' beliefs about the temporal independence of the payouts. Confirming this conjecture, the anomaly disappears in a second set of experiments, where states were drawn without replacement. We formally test whether CAPM and Arrow–Debreu equilibrium can be used to predict price movements in our experiments and confirm the hypothesis. When multiplying the subject payout tenfold (in real terms), to US $ 500 on average for a 3-h experiment, the results are unaltered, except for an increase in the recorded risk premia.