This study discusses two widely used approaches in the New Empirical Industrial Organization (NEIO) literature and examines the strengths and weaknesses of the Production‐Theoretic Approach (PTA) and the General Identification Method (GIM) for the econometric analysis of market power in agricultural and food markets. We provide a framework that may help researchers to evaluate and improve structural models of market power. Starting with the specification of the approaches in question, we compare published empirical studies of market power with respect to the choice of the applied approach, functional forms, estimation methods and derived estimates of the degree of market power. Thereafter, we use our framework to evaluate several structural models based on PTA and GIM to measure oligopsony power in the Ukrainian dairy industry. The PTA‐based results suggest that the estimated parameters of oligopsony power are significantly different from zero, while GIM‐based results do not indicate any evidence of oligopsony market power in the Ukrainian dairy industry. Moreover, estimations results vary substantially due to the employed estimation procedure.