Self-Enforcing Wage Contracts

A duality approach to continuous-time contracting problems with limited commitment

“…The main contribution of this paper is to propose a duality approach in a continuous-time setup, which permits analytical solutions. We consider a consumption insurance problem between a principal and an agent analogous to the problems analyzed by Thomas and Worrall (1988), Kocherlakota (1996), Alvarez and Jermann (2000), Ligon, Thomas, and Worrall (2002), and Ljungqvist and Sargent (2004). 2 The continuous-time setup is analytically convenient and allows us to derive sharp and transparent results.…”

“…We study the link between the dual and primal problems and establish the weak and strong 1 Other examples include applications to wage contracts by Thomas and Worrall (1988), sovereign debt by Bulow and Rogoff (1989), Kletzer and Wright (2000), and Hellwig and Lorenzoni (2009), asset markets by Kehoe and Levine (1993) and Jermann (2000, 2001), optimal taxation by Chari and Kehoe (1993), business cycles by Cooley, Marimon, and Quadrini (2004), international business cycles by Kehoe and Perri (2002), consumption inequality by Krueger and Uhlig (2006) and Krueger and Perri (2006), the welfare effects of a progressive tax by Krueger and Perri (2011), political economy by Acemoglu, Golosov, and Tsyvinski (2011), and asset bubbles by Kocherlakota (2008) and Wang (2011, 2012).…”

“…The first example is a continuous-time version of the discrete-time models analyzed in Thomas and Worrall (1988), Krueger and Uhlig (2006), and in Chapter 19 of Ljungqvist and Sargent (2004). In this example, the principal is a risk-neutral planner and the agent is a household with a constant relative risk aversion utility function.…”

When can we do better than autarky?

“…Following Thomas and Worrall (1988) and Ligon et al (2002), this subsection considers a model with utilities linearized around autarkic endowment. We show below that the linearized model not only is analytically more tractable, it also offers clear intuition about the cost and the benefit of participating in this long-term contract.…”

“…Kocherlakota (1996) and Ligon et al (2002)), and wage contracts (cf. Thomas and Worrall (1988)). In this theory, a commonly made assumption is that some nonautarkic risk sharing arrangement is sustainable (in the sense that no one would leave the contract).…”