Using Cost Minimization to Measure Markups

De Loecker and Warzynski's (2012) estimator produces exporters' markups greater, smaller or equal to those of non-exporters according to the variable employed (labor, materials or both). We remedy this adopting production elasticities that allow the relative first order conditions of cost minimization to hold up to an uncorrelated error. But then we still need to estimate the short-run elasticity of scale consistently. Imperfect competition makes the estimation dependent on the markup. Exporters and non-exporters' markups are basically the same. We detect a general upward bias in the elasticity of scale estimate when markup is not accounted for.