We investigate, in an experimental setting, the effect of private information on the Coase theorem's predictions of efficiency and allocative neutrality. For a two-person bargaining game, we find significantly more inefficiency and allocative bias in the case of private information compared with the case of complete information. We also find substantial bargaining breakdown, which is not predicted by the Coase theorem. For the case of private information, we reject the Coase theorem in favor of the alternative of a generalized version of the Myerson- Satterthwaite theorem, which predicts inefficiency, allocative bias in the direction of the disagreement point, and some bargaining breakdown.