Accounting for Productivity Dispersion Over the Business Cycle

This paper presents accounting decompositions of changes in aggregate labor and capital productivity. Our simplest decomposition breaks changes in an aggregate productivity ratio into two components: A mean component, which captures common changes to firm factor productivity ratios, and a dispersion component, which captures changes in the variance and higher order moments of their distribution. In standard models with heterogeneous firms and frictions to firm input decisions, the dispersion component is a function of changes in the second and higher moments of the log of marginal revenue factor productivities and reflects changes in the extent of distortions to firm factor input allocations across firms. We apply our decomposition to public firm data from the United States and Japan. We find that the mean component is responsible for most of the variation in aggregate productivity over the business cycle, while the dispersion component plays a modest role