Accounting for Productivity Dispersion Over the Business Cycle

Abstract

We present model-free decompositions of changes in aggregate labor and capital productivity. Our decompositions are a useful accounting tool for researchers looking to assess the role of distortions to the distribution of labor or capital across firms in driving the dynamics of productivity and other aggregates over the business cycle. Our decompositions can be used to test whether firm-level behavior in models with frictions is consistent with firm-level behavior in data, or to help guide model selection. Our simplest decomposition breaks changes in an aggregate factor 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 higher order moments of the distribution of firm factor productivity ratios. We demonstrate analytically in a model of frictions to firm labor and capital choices that the dispersion component reflects changes in the extent of distortions to firm factor input allocations across firms. We then present results on our decomposition using data on non-financial public firms from the United States and Japan. For aggregate productivity, we find the dispersion component is relatively constant over the business cycle, but the mean component moves closely with movements in aggregate productivity.