Workhorse search and matching models assume constant bargaining weights, while recent evidence indicates that weights vary across time and in cross section. We endogenize bargaining weights in a life-cycle search and matching model by replacing a standard Cobb-Douglas (CD) matching function with a general constant elasticity of substitution (CES) matching function and study the implications for the long-term labor share and bargaining power in the U.S. The CES model explains 64 percent of the reported decline in the labor share since 1980, while the CD model explains only 28 percent of the decline.

We then use the model to recover changes in bargaining power and find that workers bargaining power has declined 11 percent between 1980 and 2007 because of a decline in tightness.