The Nash Wage Elasticity and its Business Cycle Implications

We develop a new measure of wage rigidity, the Nash wage elasticity (NWE). The NWE is the percentage change in the actual wage rate when the wage that would occur under Nash bargaining changes by 1%. We show that the NWE can be measured from aggregate data under relatively weak assumptions which hold across a large class of search and matching models. The empirical value can then be compared with the values predicted by specific models in this class. In the US data, our estimates of the NWE are generally between 0 and 0.1, indicating that, for both continuing workers and new hires, (a) there is a high degree of wage rigidity and (b) Nash bargaining provides a poor description of wage setting. We show that our estimates imply that wage rigidity greatly amplifies business cycles: A simple SAM model suggests that, if workers were paid Nash-bargained wages rather than actual wages, then the cyclical volatility of unemployment would decrease to less than one seventh of what it is in the data. We compare our results to various models of rigid and flexible wages in the literature.