Uncertainty, Risk, and the Efficiencies of the Principal and the Agent: A Chance Constrained Data Envelopment Analysis Approach

In a principal-agent relationship, although the principal (e.g., the investor) can control the inputs and decide the motivated payments to the agent (e.g., the top management team), she cannot have the ability to decide how many outputs she can be rewarded. Since the motivated payments the agent gains from the principal are closely related to the uncertain outputs, they also have the characteristic of uncertainty. Furthermore, the attitudes and behaviors of both parties, such as risk attitude of the principal/agent on the uncertainty of outputs/motivated payments, can have significant influence on the efficiencies of two parties and consequently affect the enthusiasm and effort of the agent. To address this issue, chance constrained data envelopment analysis (DEA) approach is proposed. Based on this stochastic approach, the measures of the principal's efficiency, the agent's efficiency, and the agent's effort level are provided. A case study of 16 China listed real estate companies validates our models and shows that the uncertainties of outputs and payments have significant influences on the efficiencies of the principal and the agent and the effort of the agent as well.