Monetary Policy and Unemployment: A Matching Approach
Pascal Michaillat, Emmanuel Saez
This paper analyzes the interaction between monetary policy and unemployment using a matching model of the economy. By placing unemployment at the core of the analysis, this matching approach provides insights that complement those obtained with the traditional New Keynesian approach. We model the economy as a single matching market on which labor services are traded. Not all services are sold at all times so sellers of services are unemployed part of the time. Buyers direct their search towards sellers offering lower prices and shorter queues for their services; sellers set their price given this directed search and a price-adjustment cost. Unemployment and inflation are related by a Phillips curve because high unemployment pushes sellers to reduce their prices to attract customers, whereas low unemployment pushes them to increase their prices to take advantage of the long queues of customers. We obtain an optimal monetary policy formula expressed with estimable statistics and thus easy to implement: the gap between the optimal and current intercepts of the interest-rate rule equals the gap between the Hosios and current unemployment rates divided by the response of unemployment to the nominal interest rate. The formula is simple because the Hosios unemployment rate, which minimizes the resources wasted by matching, is also the unemployment rate maintaining inflation at its target level and therefore minimizing resources wasted by price changes. The Hosios unemployment rate is estimable with historical data because it is unaffected by aggregate demand or supply shocks. The formula maintains the unemployment rate at the Hosios level and the inflation rate at its target level.