We develop a theory on the joint dynamics of labor share and technology at the business cycle frequency. Our main motivating fact is the overshooting property of the labor share: After a positive technology shock, the share of output that corresponds to labor falls temporarily but it quickly rises, at a higher level (in absolute terms) than the initial drop. We propose a framework where firms own heterogeneous production units (putty clay technology) and the labor market functions as in the search and matching literature. The model is capable of reproducing the business cycle facts of labor share and its components and also provides a framework in which sticky wages do not solve the unemployment-productivity correlation (the so called Shimer) puzzle.
