Estimation of a Non-Parametric Principal-Agent Model with Hidden Actions

Principal-agent models are essential to the analysis of incentive contracts. Despite their prevalence, existing work on estimating principal-agent models from contract data – which can be valuable for evaluating counterfactuals and designing incentives in practice – is limited. In this paper, we propose an estimator for a non-parametric principal-agent model where agent actions are hidden. We show the estimator to be statistically consistent, and show that the unobservability of agent actions can make the estimation problem NP-hard. While the estimator can be expressed exactly as an integer program, the resulting formulation scales poorly in the size of the data due to weak linear programming relaxations. To bypass this deficiency, we present an approximate estimator, also formulated as an integer program, along with a “statistical” column generation algorithm that relies on using hypothesis tests to identify variables to introduce into the model. We show that our solution algorithm preserves statistical consistency, and present a bound on the expected iteration count as a function of the Type I error rate. Numerical results show that our statistical column generation algorithm dramatically reduces the computational time required to obtain competitive parameter estimates compared to off-the-shelf solvers. Lastly, we apply our estimation procedure to a dataset from a large Medicare program, and derive associated policy recommendations