Dynamic Contracts and Equilibrium Unemployment

I construct a model of equilibrium unemployment where workers and firms enter into dynamic labor contracts. The model is in the spirit of the models of efficiency wages (e.g. Shapiro and Stiglitz (1984) in that I rely on moral hazard to give rise to involuntary unemployment. Compared the existing models of efficiency wages, my model offers several advantages. First, efficiency wage models are often criticised because the employment contracts are not optimal. In the existing efficiency wage models, because wage is constant, termination (lay-off) must be used to punish shirking. In my model, workers and firms enter into fully optimal dynamic contracts. Second, in the existing models of efficiency wages, in equilibrium $no$ workers are actually fired because of shirking (the contract makes effort-making incentive compatible), and the unemployed are a rotating pool of workers who quit for personal reasons. In my model, workers are actually fired, involuntarily, from their jobs, and firing is part of the optimal contract. Third, there is a single equilibrium wage in existing models of efficiency wages.Here, optimal contracting dicates that workers who have different histories earn different wages, and there is an non-degenerate distribution of wages in equilibrium. Finally, my model permits both involuntary and voluntariy unemployme