On the Relative Performance of Linear vs. Piecewise-Linear-Threshold Intertemporal Incentives
通过数值模拟比较线性合同与分段线性阈值合同在代理人跨期选择行动时的表现，发现当代理人效用函数为指数型且产出仅定期更新时，线性合同已足够；但若效用函数为幂函数，则分段线性阈值合同显著更优。
This paper employs numerical simulations to compare the relative performance of linear contracts with piecewise-linear-threshold contracts in the case where the agent chooses actions over time. These contracts are restricted to be functions of the ending value of aggregate output. We find strong evidence that only linear contracts need be considered in comparison with piecewise-linear-threshold contracts in the situation where cumulative output is only updated periodically and the agent's utility function is exponential. This finding holds even when there are only two periods and hence one change of action by the agent. However, we find that the best piecewise-linear-threshold contract is significantly superior to the best linear contract when the agent has a power utility function. These numerical simulations also call into question the use of a cap when the agent's compensation is based on the ending value of aggregate output and the agent's effort takes place over time.