Efficiency, Shadow Pricing and Regime Switching in Multi-Ware Technologies: Evidence From Regulated Livestock Farms

Abstract

We develop a framework for regulated production systems where output generation and pollution abatement impose competing technological demands. Using a multi-ware technology, we model the production set as the intersection of two input requirement frontiers, one for production and one for abatement, each reflecting distinct trade-offs. We characterise the efficient set using gaps in efficiency distances and recover shadow prices for smooth and non-smooth frontiers, clarifying how subdifferentials govern shadow prices at switching points. To address unobserved heterogeneity in technological orientation, we estimate a full-information maximum likelihood model with endogenous regime-switching. Applying the framework to Chinese livestock farms, we recover regime-specific land costs, identify drivers of regime assignment and quantify inefficiency using multi-ware distances. Results reveal sharp asymmetries in spatial burdens between production and abatement, and systematic switching behaviour driven by inputs and weather. Our framework offers a widely applicable, policy-relevant tool for evaluating environmental and economic performance.

JEL Classification: D24, Q12, Q52