Dynamic risk-sharing with two-sided moral hazard

Dynamic Principal-Agent Models

“…This makes a computational treatment using this formula difficult, if not impossible. Zhao (2007) considers a two-agent model with a resource constraint. He assumes separability of the utility functions in consumption and effort and concavity of the consumption function.…”

“…We use results from the mathematical programming literature, so these proofs can be easily extended to different settings with multiple agents with additional constraints as in Zhao (2007) or to cases where we have different preferences, for example, those of the Epstein-Zin type. The resulting DP reformulation, however, is still a rather daunting problem.…”

Repeated moral hazard and recursive Lagrangeans

“…This Pareto-Negishi weight 2 becomes the new state variable 1 Many contributions have focused on the case in which agent's consumption is observable (see for example Rogerson (1985b), Spear and Srivastava (1987), Thomas and Worrall (1990), Phelan and Townsend (1991), Fernandes and Phelan (2000)) and more recently on the case in which agents can secretly save and borrow (Abraham and Pavoni (2008)); other works have explored what happens in presence of more than one agent (see e.g. Zhao (2007) and Friedman (1998)), while few researchers have extended the setup to production economies with capital (Clementi, Cooley, and Giannatale (2010)). Among applications, a non-exhaustive list includes unemployment insurance (Hopenhayn and Nicolini (1997), Shimer and Werning (2008), Pavoni (2007), Pavoni (2009)), executive compensation (Clementi, Cooley, and Giannatale (2010), Clementi, Cooley, and Wang (2006), Atkeson and Cole (2005)), entrepreneurship Quadrini (2004), Paulson, Townsend, and Karaivanov (2006)), credit markets (Lehnert, Ligon, and Townsend (1999)), and many more.…”

Essays on private information

“…He finds that in such an environment, incomplete risk-sharing is an optimal response to this friction. Kocherlakota (1996) and Zhao (2007) are the two papers that are most related to our paper. However, there several differences between these papers and ours.…”

“…This implies that each agent can commit only to the contract that provides a consumption stream that is at least as good as the one he or she can get in autarky from tomorrow on. This is the type of commitment that is studied in Zhao (2007) in the model of double moral hazard. We call this model "ex-ante limited commitment model."…”