The objective of this study is to demonstrate that the recently developed stochastic frontier (SFA) estimator of market power measures mark{ups in the output market, as the seminal paper demonstrates, only under a specic market structure. The measurement of market power along the food market- ing channel is employed in order to derive our theoretical ndings. The results indicate that, without prior knowledge of the structure of the market under investigation, it is only safe to say that the SFA estimator of market power measures the sum of oligopolistic and oligopsonistic distortions.