On the first-order approach in principal–agent models with hidden borrowing and lending

Abstract

Moral hazard models with hidden asset markets are useful to study several interesting problems such as unemployment insurance, income taxation, executive compensation, or human capital policies. Without the use the first-order condition approach, these models easily become non-tractable.In this paper, we provide sufficient conditions for the validity of the first-order approach for twoperiod dynamic moral hazard problems where the agent can save and borrow secretly. To ensure that the agent's problem is jointly concave in effort and asset decisions when facing the optimal contract, we build on the concept of log-convexity. Since this property, unlike convexity, is preserved under multiplication, we are able to separate the assumptions on the distribution function from the assumptions on the agent's preferences, even though the interaction between these two is important for the agent's incentives. We show that the first-order approach is valid if the following conditions hold: i) the agent has nonincreasing absolute risk aversion utility (NIARA), ii) the output technology has monotone likelihood ratios (MLR), and iii) the distribution function of output is log-convex in effort (LCDF). Moreover, under the above three conditions, the optimal contract is monotone in output. We also investigate a few possibilities of relaxing these requirements.

Efficient Risk Sharing with Limited Commitment and Storage

“…With private information as the friction, a few papers (Allen, 1985;Cole and Kocherlakota, 2001;Ábrahám, Koehne, and Pavoni, 2011) have integrated these two strands of literature by introducing a storage technology. This paper considers limited commitment (Thomas and Worrall, 1988;Kocherlakota, 1996), LC hereafter, and makes a similar contribution by introducing both a public and a private storage technology.…”

On the validity of the first-order approach with moral hazard and hidden assets

“…The functional form restrictions of Ábrahám, Koehne and Pavoni (2011) establish validity of the first-order approach in a two-period economy with hidden effort and non-contingent savings. Bertola and Koeniger (2013) provide similarly plausible and appealing conditions for an economy with hidden insurance against a single contingency, as in Pauly (1974).…”

“…" Ábrahám, Koehne and Pavoni (2011) similarly establish that first-order conditions are necessary and sufficient, under sensible and interpretable functional restrictions, in an economy with exclusive formal insurance and a single hidden non-contingent asset.…”

“…As in Ábrahám, Koehne and Pavoni (2011) and Bertola and Koeniger (2013), a promising restriction for the distribution function is…”

Non-exclusive dynamic contracts, competition, and the limits of insurance

“…7 For a review, refer to Golosov et al (2006), Kocherlakota (2010) and Albanesi (2008). 8 See also, Golosov and Tsyvinski (2007), Abraham and Pavoni (2005) and Abraham et al (2011). 9 See also Farhi et al (2009) for a related environment.…”