Firm and Industry Level Profit Efficiency Analysis Under Incomplete Price Data: A Nonparametric Approach based on Absolute and Uniform Shadow Prices

We discuss the nonparametric approach to profit efficiency analysis at the firm and industry levels in the absence of complete price information, and propose two new insights. First, choosing one commodity (whose price is known) as a numeraire good enables us to measure profit inefficiency in absolute monetary terms. Second, imposing a ‘Law of One Price’ (LoOP) constraint that all firms should be evaluated in terms of the same input-output prices allows us to aggregate firm-level profit inefficiencies to the overall industry inefficiency. Moreover, the LoOP restrictions increase the discriminatory power of the method by better capturing firm-level allocative inefficiencies. Besides the measurement of profit losses, the presented approach enables one to recover absolute price information from quantity data. We conduct a series of Monte Carlo simulations to study the performance of the proposed approach in controlled production environments.