Carryover Effect and Risk Aversion: Dynamic Incentives in Sales Force Compensation

Abstract

I solve the discrete dynamic decision of sales agents effort allocation under a quota bonus compensation when the carryover from the past period is introduced in sales. With the solution of dynamic programming, I generate the sales data from two segments of sales agents: one with high risk-aversion and the other with low risk-aversion. As the carryover in sales increases both the expected mean and variance of sales in the next period, the sales agents optimal effort allocation and thus the realized sales pattern vary according to his degree of risk aversion. The highly risk-averse set the baseline of performance while the less risk averse fluctuate their sales above the highly risk-averse. Also, the frequency of achieving quotas is higher in the less risk averse group compared to the highly risk-averse group. These different patterns could be interpreted as that the highly risk averse try not to exert more effort to avoid the uncertainty from the increased sales. Following Arcidiacono and Miller (2011), I estimate the segment-wise optimal effort functions and utility functions in two steps: calculating the conditional choice probability with nonparametric functions and then searching for parameters with EM algorithm. The estimation result shows that ignoring the carryover when it exists gives out poor estimates of the number and even the size of segments. This is because ignoring carryover results in the wrong segmenting of the sales agents from the first stage estimation and thus affects the second stage estimation subsequently. The result highlights the necessity of considering carryover when understanding sales forces performance history from the sales data if carryover exists. Neglecting carryover might lead to wrong segmentation of sales force and thus the inefficient design of segment-wise compensation plans.