Estimation, Data Generators, and Optimal Contract, A Robust Approach

Abstract

This paper considers the problem of using monetary transfers to incentivize data generation in data markets. A principal who collects multiple agents' (data generators') data to estimate the unknown state by a fixed estimator attempts to use a data-dependent transfer to incentivize high-quality data generation. The fact that the outcome of the estimation, the prediction error, is not contractable creates difficulty for incentive control even if there is unlimited liability. I propose a contract using subsample estimation to discipline agents' behavior that can implement the first-best actions under mild conditions, for example, if the principal uses a linear unbiased estimator. The implementation result is robust even if the principal has no knowledge about agents' belief structures and worries about strategic uncertainty. The informational robustness makes it possible to apply the result in the joint design problem, where the estimator is endogenously chosen, under a Bayesian or minimax objective.