Traders' values and information typically consist of both private and common-value elements. In such environments, full allocative efficiency is impossible when the private rate of information substitution differs from the social rate (Jehiel and Moldovanu, 2001). We link this impossibility result to a failure of the efficient market hypothesis, which states that prices adequately reflect all available information (Fama, 1970, 1991). The intuition is that if prices were able to reveal all information then the common value would simply shift traders' private values by a known constant and full allocative efficiency would result. In a series of laboratory experiments we study price formation in markets with private and common values. Rational expectations, which form the basis for the efficient market hypothesis, predict that the introduction of common values has no adverse consequences for allocative and informational efficiency. In contrast, a "private" expectations model in which traders' optimal behavior depends on both their private and common-value information predicts that neither full allocative nor full informational efficiency is possible. We test these competing hypotheses and find that the introduction of common values lowers allocative efficiency by 28% on average, as predicted by the private expectations model, and that market prices differ significantly and substantially from their rational expectation levels. Finally, a comparison of observed and predicted payoffs suggests that observed behavior is close to the equilibrium predicted by the private expectations model.