Do Cost-of-Living Shocks Pass Through to Wages?

We develop a novel, tractable New Keynesian model where firms post wages and workers search on the job, motivated by microeconomic evidence on wage setting. Because firms set wages to avoid costly turnover, the rate that workers quit their jobs features prominently in the model’s wage Phillips curve, matching U.S. empirical evidence. We then examine the response of wages to cost-of-living shocks, i.e., shocks that raise the price of household’s consumption goods but do not affect the marginal product of labor. Such shocks pass through to wages only to the extent that higher cost of living improves workers’ outside options, such as competing jobs or unemployment, relative to their current job. However, higher cost of living lowers real wages at all jobs evenly, and unemployment is rarely a credible outside option. We conclude that wage posting and on-the-job search limit the scope for pass-through from prices to wages.