Expectation formation and learning in the labour market with on-the-job search and Nash bargaining

This paper develops a search and matching model with heterogeneous firms, on-the-job search by workers, Nash bargaining over wages and adaptive learning. We assume that workers are boundedly rational in the sense that they do not have perfect foresight about future bargaining outcomes. Instead workers rely on a recursive OLS learning mechanism and base their forecasts on a linear wage regression. We apply adaptive learning to a setting with generalized Nash bargaining and show analytically that the bargaining solution is unique. We use this solution to simulate the model and provide a numerical characterization of the Restricted Perceptions Equilibrium. We show that some job-to-job transitions are socially inefficient since workers can move to less productive employers. Output losses from these transitions decrease with workers’ bargaining power due to a more efficient allocation of workers to jobs. Finally, we find that bounded rationality taking form of adaptive learning can reduce wage inequality among heterogeneous worker groups if workers’ expectations are based on pooled statistical information.