Unemployment insurance with hidden savings

Abstract

This paper studies the design of unemployment insurance when neither the searching effort nor the savings of an unemployed agent can be monitored. If the principal could monitor the savings, the optimal policy would leave the agent savings-constrained. With a constant absolute risk-aversion (CARA) utility function, we obtain a closed form solution of the optimal contract. Under the optimal contract, the agent is neither saving nor borrowing constrained. Counter-intuitively, his consumption declines faster than implied by Hopenhayn and Nicolini [4]. The efficient allocation can be implemented by an increasing benefit during unemployment and a constant tax during employment. JEL Classification Numbers: D82, D86, J65.

A solvable continuous time dynamic principal–agent model

“…9 I also consider an extension with hidden savings, where the agent can save or borrow in a risk-free asset with a constant rate of return. In this case, my results are related to the discrete time model of 5 Also see Allen (1985), Cole and Kocherlakota (2001), Kocherlakota (2004a), Doepke and Townsend (2006), Mitchell and Zhang (2010), and Edmans, Gabaix, Sadzik, and Sannikov (2012) for some alternative formulations with hidden savings.…”

“…7 Mitchell and Zhang (2010) and Edmans, Gabaix, Sadzik, and Sannikov (2012) show that their contracts are incentive compatible with hidden savings via different methods.…”

“…In this environment with hidden savings, that shadow value of additional wealth is the agent's current marginal utility of consumption. Again I employ a first-order approach to contracting, which is similar to 1 In addition to Holmstrom and Milgrom (1987), other papers making use of the exponential-linear structure in related models include Fudenberg, Holmstrom, and Milgrom (1990), Mitchell and Zhang (2010), Cvitanic and Zhang (2012), and Williams (2011). In an earlier version of this paper, Williams (2008), I considered more general specifications.…”

A Solvable Dynamic Principal-Agent Model with Linear Marginal Productivity

“…Using the assumption of linear production and exponential utility, we study a continuous time contracting model with linear marginal productivity in which optimal contract can be solved in a closed form. In addition to the works of Holmstrom and Milgrom [1], the exponential-linear structure is used in Fudenberg et al [2], Mitchell and Zhang [3], Cvitanic and Zhang [4], and Williams [5]. The explicit solutions allow us to derive a simple implementable contract and illustrate the effects of information frictions.…”

“…Therefore, we derive a candidate optimal contract by solving the agent's optimality problem which provides necessary conditions for optimal contracts, and then verify ex post that the contract is indeed implementable. Applying different methods, Mitchell and Zhang [3] and Edmans et al [26] show that their contracts are incentive and compatible in hidden saving case.…”