Exploring the Optimal Design of an Employer-Sponsored Sickness-Disability Compensation Insurance Plan When Sickness Presenteeism Is Penalized

Colin M. Ramsay, Victor I. Oguledo and Annika Krutto

North American Actuarial Journal, 2018, vol. 22, issue 3, 426-457

Abstract: We explore the impact of presenteeism, absenteeism, and shirking on the optimal design of an employer-sponsored sickness-disability compensation insurance plan when the employer penalizes sickness presenteeism. We assume an employee's health follows a simple multistate model with a “severely ill” sickness state. To combat absenteeism, the employer randomly verifies an employee's claim of sickness. However, to combat presenteeism, we also introduce the new concept of a presenteeism penalty whereby employees who are found to be at work in the “severely ill” sickness state are sent home and receive a penalized sick pay that is lower than the normal sick pay. Thus sick employees must decide whether to stay at home and receive a sick pay or go to work sick and run the risk of being sent home and penalized. We further assume (1) employees are risk-averse utility maximizers, (2) each employee has a strategy for staying home or working while sick that maximizes his or her lifetime expected discounted utility, and (3) an employee's strategy is unknown to the employer. The primary plan design factors that affect an employee's lifetime expected discounted utility and the employer's discounted expected accounting profits over an employee's working lifetime are the sick pay, the presenteeism penalty, and two health check probabilities. Volterra integral equations are used to derive expressions for an employee's lifetime expected discounted utility and the employer's expected discounted accounting profits over an employee's lifetime under various employee strategies. Laplace transforms are used to derive asymptotic expressions for the solutions to these integral equations. These asymptotic solutions are used to explore the impact of these factors on the optimal sickness compensation insurance plan design.

Date: 2018
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DOI: 10.1080/10920277.2018.1435287

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