Using Two-Part Contracts to Identify Complementarities Across Tasks: An Application to Family Doctors
Whether tasks are cost complement or subsitutes is crucial for the optimal design and ultimate success of any pay-for-perfomance scheme. We propose an empirical test for determining if tasks are cost complements or substitutes. The test requires that the reward scheme is piece-wise linear, and that that there are changes over time on the rewards of some tasks. However, the reward scheme does not need to vary across agents, making it applicable to nationwide pay-for-performance programmes. The test is based on the insensitivity of effort on a particular task to variations in the price of other tasks for agents who are bunched at the kinks. We apply our new test to The Quality and Outcomes Framework in the UK, which is the largest pay-for-performance programme for primary care services in the world. We find that seven tasks are complements and one is substitute. Overall, our results indicate that pay-for-performance schemes should be successful because increasing the effort exerted in most tasks decreases the marginal cost of effort on other tasks, and consequently effort diversion does not take place. The results also has implications on how to design an efficient primary care system: one based on family doctors rather than specialists groups together tasks, which are complements in the cost function, and hence improves efficiency.