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 the outcome of wage bargaining. Instead workers use a recursive OLS learning mechanism and base their forecasts on the linear wage regression with the firm's productivity and worker's current wage as regressors. For a restricted set of parameters we show analytically that the Nash bargaining solution in this setting is unique. We embed this solution into the agentbased simulation and provide a numerical characterization of the Restricted Perceptions Equilibrium. The simulation allows us to collect data on productivities and wages which is used for updating workers' expectations. The estimated regression coefficient on productivity is always higher than the bargaining power of workers, but the difference between the two is decreasing as the bargaining power becomes larger and vanishes when workers are paid their full productivity. In the equilibrium a higher bargaining power is associated with higher wages and larger wage dispersion, in addition, the earnings distribution becomes more skewed. Moreover, our results indicate that a higher bargaining power is associated with a lower overall frequency of job-to-job transitions and a lower fraction of inefficient transitions among them. Our results are robust to the shifts of the productivity distribution.