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Optimal sickness benefits in a principal–agent model

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Abstract

This paper studies the optimal design of sickness benefits in a repeated principal–agent model, where the fraudsters are not observed by the principal. Sickness compensation protects workers against the income fluctuations implied by the risk of illness and its provision is limited by the presence of fraudsters using this protection to temporarily adjust their labour supply. We show that the slope of the optimal contract depends on the dynamics of the rate of fraudsters over time. When the duration of temporary shocks on the disutility of work is shorter than the average duration of diseases, the sickness benefits must increase over time. In addition, A tax dependent on the length of the sick leave makes it possible to minimise the cost for a given promise-keeping constraint. Contrary to intuition, this tax must be decreasing because the necessity to penalise the shortest sick leave to deter agents from cheating.

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Notes

  1. If a pathology is perfectly observable by the principal, there is no moral hazard and the result is trivial: the replacement ratio is constant over time.

  2. The counterpart of the full wage continuation can be the annualization of the working time, ie the obligation to recover later the hours not made during the days of absence. Another justification is precisely to reduce absenteeism by avoiding the spread of contagious illness within the firm. In Italia, there is no waiting period for tuberculosis (MISSOC).

  3. We make a sensitivity test taking into account precautionary savings. However, this does not modify the result according to which the dynamics of the total consumption depends on the dynamics of the fraud rate.

  4. This is the reason why we can assume that the probability to take a sickness absence \(\pi \) is exogenous.

  5. French Ministry of Labour.

  6. This calls for compensation profiles adapted to the illness declared by the patient: When it is easy for the principal to check ex-post the reality of pathology, the waiting days are no longer necessary.

  7. The principal observes the agents perfectly and can use all the tools (b and \(\theta \)) without constraint.

  8. This is a partial equilibrium enabling an analysis of the effects of wealth on the optimal sickness benefits profile. But, we do not explain the effects of the optimal contract on the distribution of wealth.

  9. In this exercise, the difference in welfare comes from the fact that employment is permanent state after a sick leave. Therefore, the agent has at most one episode of sickness.

  10. For our calibration, the average sick leave duration for type h agents is 2 days.

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  1. GAINS-TEPP and IRA (University of Le Mans), Avenue Olivier Messiaen, 72000, Le Mans, France

    Sebastien Menard

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  1. Sebastien Menard
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Menard, S. Optimal sickness benefits in a principal–agent model. Soc Choice Welf 57, 5–33 (2021). https://doi.org/10.1007/s00355-020-01307-6

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