Some unpleasant markup arithmetic: Production function elasticities and their estimation from production data

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