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.

加价率估计值是灵活投入的产出弹性与该投入在总收入中的成本份额之比。当没有观察到公司水平的产出价格时，我们强调与这个比率估计器有关的识别和估计问题。如果使用灵活投入的收入弹性代替产出弹性，那么利润最大化意味着比率估计量等于 1，因此无法提供关于加价的信息。关于产出弹性的估计：只有收入数据，利润最大化还意味着，如果企业具有市场支配力，则不能从收入生产函数的估计中非参数地确定产出弹性。即使有单独的输出价格和数量数据，