Aggregate behavior in matching markets with fl exible contracts and non-transferable representations of preferences

This paper modifies and extends the aggregate equilibrium models for matching markets developed earlier in the literature. Agents in the matching market search for a match among potential partners, including agreements about a flexible contract, such as hours and wage combinations in the labor market. Under general utility representations that are non-transferable and assuming the matching is stable, we derive a probabilistic framework for the probability of realizing a particular match, including the choice of contract. We also show that the popular transferable utility model with transferable utilities can be viewed as a limiting case within our modelling framework. The framework is practical to apply for empirical analysis and is at the same time sufficiently general to accommodate essential features of matching markets with heterogeneous agents