Proxy Variable Estimation of Multiproduct Production Functions

Abstract

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 multiproduct firm's production: (a) it cannot identify technological cross‐output trade‐offs along the production possibilities frontier, and (b) it unrealistically assumes perfect output substitutability that, if misspecified, produces biased estimates. We develop a new methodology for estimating multiproduct 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.