Proxy Variable Estimation of Multi-Product Production Functions

37 Pages Posted: 6 Nov 2017 Last revised: 30 Jul 2020

See all articles by Emir Malikov

Emir Malikov

University of Nevada, Las Vegas

Gudbrand Lien

Norwegian Agricultural Economics Research Institute

Date Written: June 17, 2020


Most empirical studies seeking to estimate firm-level production technologies via proxy variable estimators focus on single-output production functions despite that, in practice, the majority of firms produce multiple outputs. Arguably, the primary reason for vast popularity of a single-product model is the systematic lack of data on input usage by products. While one can always employ such a model by defining the firm's "output" as an aggregate of its multiple outputs in the form of deflated total revenue as customarily done in the literature, such a formulation rarely provides an adequate representation of the multi-product firm's technology: (i) it does not allow identification of technological trade-offs between outputs along the firm's production possibilities frontier, and (ii) it unrealistically assumes perfect substitutability of outputs effectively embedded in a linearly additive revenue-based output aggregator which, if misspecified, would produce biased estimates of the firm's production technology and productivity. This paper provides a new methodology for the proxy variable identification of multi-product production technology which not only does not require the access to information beyond that available in most datasets but also successfully identifies the cross-output technological relationship within the firm by not a priori aggregating outputs. We operationalize the model nonparametrically using B-spline sieves and showcase it using data on Norwegian dairy-and-beef farms.

Keywords: multiple outputs, production function, proxy variable, control function, structural identification, endogeneity, sieve estimation, dairy

JEL Classification: C14, D24, L10, Q12

Suggested Citation

Malikov, Emir and Lien, Gudbrand, Proxy Variable Estimation of Multi-Product Production Functions (June 17, 2020). Available at SSRN: or

Emir Malikov (Contact Author)

University of Nevada, Las Vegas ( email )

4505 S. Maryland Parkway
Las Vegas, NV 89154
United States

Gudbrand Lien

Norwegian Agricultural Economics Research Institute ( email )

PO Box 8024 Dep.
NO-0030 Oslo
+47 22 36 72 90 (Phone)
+47 22 36 72 99 (Fax)

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