The Non-Convexity Issues in a Limited-Commitment Economy

After reviewing some basic self-enforcing labour contracts models, we expose how self-enforcing labour market theory can help explain some important dynamic properties of key macroeconomic variables. Calmès (1999, 2003) detail how self-enforcing labour contracts improve the way macroeconomic models account for the response of the economy to external shocks. The introduction of a state-dependent outside opportunity for the manager is the first step in generalizing the theory (Calmès 2007, Thomas and Worrall 2007). In this paper, we discuss the next step, the endogenization of capital. Although desirable, this task is not straightforward as the contract set might no longer be compact in this case. Relatedly, we also discuss the introduction of a third agent (the financial intermediary) in the model. We also analyse the link between stationarity and set convexity when incorporating growth in the model. A stochastic trend may be considered but then the non-convexity issue arises again. The aggregation of heterogeneous individual contracts can also lead to the same problem.