Proxy Variable Estimation of Multi-Product Production Functions

Productivity studies that use proxy variable estimators routinely specify single-output production functions despite most firms producing multiple outputs. This is usually accomplished by aggregating the firm's outputs using total revenue. Such a formulation rarely provides an adequate representation of the multi-product firm's production: (i) it cannot identify technological cross-output trade-offs along the production possibilities frontier, (ii) it unrealistically assumes perfect output substitutability which, if misspecified, produces biased estimates. We develop a new methodology for estimating multi-product production functions that addresses these limitations without requiring information beyond that which is available in most datasets and showcase it on Norwegian dairy-and-beef farming