Persistence of labor share fluctuations and overshooting

Workhorse business cycle models struggle to explain the magnitude and persistence of cyclical fluctuations in the labor share of output and employment in the United States. A model with search frictions in the labor market and a technology choice addresses this shortcoming. In this model, the production technology is a constant elasticity of substitution (CES) in the short run, while it converges to Cobb-Douglas in the long run. We calibrate the model using U.S. data and find that the inclusion of a technology choice with adjustment costs significantly enhances the model's ability to propagate productivity shocks, compared to a model with a fixed Cobb-Douglas technology. The calibrated model successfully replicates the overshooting of the labor share in the data.