Some Unpleasant Markup Arithmetic: Production Function Elasticities and their Estimation from Production Data

The ratio estimator of a firm’s markup is the ratio of the output elasticity ofThe ratio estimator of a firm’s markup is the ratio of the output elasticity ofa variable input to that input’s cost share in revenue. This note raises issues thatconcern identification and estimation of markups using the ratio estimator. Concerningidentification: (i) if the revenue elasticity is used in place of the output elasticity, thenthe estimand underlying the ratio estimator does not contain any information aboutthe markup; (ii) if any part of the input bundle is either used to influence demand, or isneither fully fixed nor fully flexible, then the estimand underlying the ratio estimatoris not equal to the markup. Concerning estimation: (i) even with data on outputquantities, it is challenging to obtain consistent estimates of output elasticities whenfirms have market power; (ii) without data on output quantities, as is typically thecase, it is not possible to obtain consistent estimates of output elasticities when firmshave market power and markups are heterogeneous. These issues cast doubt overwhether anything useful can be learned about heterogeneity or trends in markups,from recent attempts to apply the ratio estimator in settings without output quantitydata.