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1 2025

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Deterministic vs. stochastic methods for frontier estimation : update and illustration

Weber William, Grosskopf Shawna, Hayes Kathy, Wetzel Heike

Operations Research and Decisions

2025

Vol. 35, No. 2

121--141

We estimate and compare a deterministic production frontier to a production frontier estimated using stochastic methods. This comparison is illustrated by estimating the Lerner index of monopoly power for a public sector producer. The Lerner index estimates the percentage markup of price over marginal cost. For the deterministic method, we use bootstrapping methods to construct confidence intervals for the Lerner index and its price and marginal cost components. Marginal cost estimates are derived from a translog cost function. Since market prices are usually not observed for public sector producers or are distorted because of subsidies, we use duality theory and derive prices from observed costs and an estimated translog input distance function. Data from German public theaters’ production of performances to attract spectators using artistic staff, administrative staff, and operating expenditures are used as an example. We find no evidence of monopoly power.