Wage negotiations in multi-worker firms and stochastic bargaining powers of existing workers

This study develops a business cycle search and matching model in which the volatility of employment closely matches that of the U.S. data without wage rigidity and the labor share overshoots in response to productivity shocks. To this end, I introduce an alternative mechanism of wage negotiations and bargaining shocks in an environment wherein a firm hires more than one worker and faces diminishing marginal product of labor (MPL). When Nash bargaining with a marginal worker breaks down, a firm negotiates wages with existing workers and produces with them. The breakdown in the negotiation with the marginal worker negatively affects the bargaining position of the firm with existing workers (one fewer workers) due to diminishing MPL because MPL is higher with one fewer workers. How much the firm internalizes this negative effect depends on the stochastic bargaining powers of existing workers, which can be identified through labor share data. The stochastic bargaining power of existing workers provides an additional margin to increase the volatility of labor market variables, including wages.