The production approach recovers markups using the output elasticity for a variable and undistorted input. We show using the revenue elasticity for a variable input recovers that input’s wedge. Our result has two implications. First, in the canonical setting with CES demand and monopolistic competition, past research using the production approach with revenue data should be recast as evidence of input, rather than output, distortions. Second, future research can use the production approach with revenue data to study input distortions, provided researchers can measure inputs in physical units. A promising application pertains to labor market distortions.

The ratio estimator of the markup is the ratio of the output elasticity for a flexible input to that input’s cost share in total revenue. We highlight identification and estimation issues pertaining to this ratio estimator, when firm-level output prices are not observed. If the revenue elasticity for a flexible input is used in place of the output elasticity, then profit maximization implies that the ratio estimator is identically equal to one, and thus is uninformative about markups. Concerning estimation of output elasticities: with only revenue data, profit maximization also implies that the output elasticity is not identified non-parametrically from estimation of the revenue production function, if firms have market power. Even with separate output price and quantity data, it is challenging to estimate the output elasticity consistently if there are non-linear productivity dynamics and firms face heterogeneous demand schedules, with unobserved variation in a demand shifter.