Matching labor’s share in a search and matching model

Labor’s share of income varies over the business cycle, and different theories of nominal rigidities predict different behaviors for labor’s share. Based on evidence from a VAR for the USA, labor’s share falls sharply after a positive productivity shock and does not necessarily “overshoot” its trend; labor’s share rises after a contractionary monetary policy shock; and labor’s share falls gradually after a positive shock to the unemployment rate. A search and matching model with sticky nominal wages but flexible prices can match all three facts. In contrast, a model with flexible nominal wages and flexible prices does not match the first two facts, and a model with flexible nominal wages but sticky prices does not match the second fact. Furthermore, it is difficult to distinguish between a model where the wages of new hires are sticky from one in which they are flexible based purely on macro data.