In models with search and matching, wages result from bilateral bargaining between employers and employees. Because workers and firms earn rents from the match (the surplus from employment relative to remaining unemployed or unfilled), there is room for negotiation. Wage dynamics reflect movements in unemployment, worker and firm outside options, and the value of the match. This framework explains why wages are sticky downward and respond sluggishly to labor market conditions, contributing to unemployment persistence.
In a frictionless labor market, wages adjust instantly to clear supply and demand — anyone willing to work at the going rate finds a job immediately. But real labor markets look nothing like this. It takes time and resources for workers to find jobs and for firms to fill vacancies. From your study of search and matching models, you know that this friction creates a match surplus: once a worker and firm find each other, the value of their relationship exceeds what either could get by returning to the search pool. The question of wage dynamics is essentially the question of how this surplus gets divided.
The standard approach is Nash bargaining, where the wage splits the match surplus according to the relative bargaining power of each side. The worker's outside option is the value of being unemployed — collecting unemployment benefits, enjoying leisure, and continuing to search. The firm's outside option is the value of an unfilled vacancy — paying recruiting costs while waiting for another applicant. The wage lands somewhere between these outside options, weighted by a bargaining power parameter. When the labor market tightens (low unemployment, many vacancies), workers' outside options improve because they can find alternative jobs more easily, and wages rise. When the market slackens, firms gain leverage and wages fall — but often slowly.
This framework explains a key empirical puzzle: wage stickiness. In a deep recession, unemployment spikes but wages barely fall. The search-and-matching model explains why. Even as unemployment rises and workers' outside options deteriorate, the wage is pinned partly by the worker's bargaining power parameter, by unemployment benefits that put a floor on the outside option, and by the fact that existing matches still generate positive surplus. Firms would rather keep workers at somewhat-above-market wages than destroy the match and incur future hiring costs. The result is that wages respond sluggishly to aggregate conditions, and unemployment adjustments happen primarily through quantities (hiring and firing rates) rather than prices.
The dynamics become richer when you allow for on-the-job search, where employed workers can look for better matches while working. This creates wage ladders: workers gradually move up to higher-paying jobs over time, and a recession destroys this job ladder by reducing the arrival rate of outside offers. Wage dynamics then reflect not just current bargaining but the entire distribution of match qualities and the rate at which workers climb or fall along the wage distribution. These models connect the microeconomic bargaining problem to macroeconomic phenomena like the Beveridge curve (the inverse relationship between vacancies and unemployment) and the persistence of unemployment after recessions.