We consider a general social choice environment that has multiple agents, a finite set of alternatives, independent types, and atomless type distribution. We show that for any Bayesian incentive compatible mechanism, there exists an equivalent deterministic mechanism that (1) is Bayesian incentive compatible; (2) delivers the same interim expected allocation probabilities and the same interim expected utilities for all agents; and (3) delivers the same ex ante expected social surplus. This result holds in settings with a rich class of utility functions, multidimensional types, interdependent valuations, and in settings without monetary transfers. To prove our result, we develop a novel methodology of mutual purification, and establish its link with the mechanism design literature.

We provide causal evidence on the value of asset pledgeability by exploiting a unique feature of Chinese corporate bond markets: bonds with identical fundamentals are traded on two segmented markets with different rules for repo transactions. Using a policy shock that rendered AA+ and AA bonds ineligible for repo on one market only, we compare how bond prices changed across markets and rating classes around this event. When the haircut increases from 0% to 100%, bond yields increase by 39 bps to 85 bps. These estimates help us infer the magnitude of the shadow cost of capital in China.