Conflicting Markup Estimates and Cost Minimization

The production approach recovers markups from output elasticities of flexible inputs and their cost shares in revenue. Recent studies document that markups recovered from different flexible inputs systematically disagree, contradicting the maintained cost-minimization assumption. We show that such conflicting markups arise because standard estimation procedures do not fully exploit the implications of cost minimization. We develop a novel econometric framework that embeds cost-minimization conditions directly into estimation, through cost shares of flexible inputs, while retaining the common Hicks-neutral productivity process. The resulting estimating equation delivers markups that are invariant across flexible inputs by construction. Our findings imply that resolving the conflict in estimated markups across flexible inputs requires only that cost minimization enter the estimation procedure—whether directly, as in our framework, or indirectly via factor-augmenting productivity. These conclusions are illustrated empirically using the Colombian Annual Manufacturing Survey dataset.