In public goods environments, the threat to punish non-contributors may increase contributions. However, this threat may make players' contributions less informative about their true social preferences. This lack of information may lead to lower contributions after the threat disappears, as we show in a two stage model with selfish and conditionally cooperatives types. Under specified conditions welfare may be improved by committing not to punish or exclude. Our laboratory evidence supports this. Contributions under the threat of targeted punishment were less informative of subjects' later choices than contributions made anonymously. Subjects also <em>realised </em> that these were less informative, and their incentivized predictions reflected this understanding. We find evidence of conditional cooperation driven by beliefs over other's contributions. Overall, our anonymous treatment led to lower first-stage contributions but significantly higher second-stage contributions than our revealed treatment. Our model and evidence may help explain why anonymous contributions are often encouraged in the real world.
