This paper compares full-information insurance markets (a) with markets where accident-reducing effort levels are unverifiable but trades between every pair of agents are verifiable and (b) with markets where neither effort nor trades are verifiable. Markets are represented by a contracting game, with a solution concept allowing coordination among coalitions through information-constrained contracts. Each informational setting yields a correspondence between market outcomes and the appropriate notion of constrained efficiency in a social planner's problem. Although incentive externalities do not cause market outcomes to be constrained inefficient, they do imply a welfare gain from public verifiability of trades.