Orthogonality Conditions for Identification of Joint Production Technologies: Axiomatic Nonparametric Approach to the Estimation of Stochastic Distance Functions

38 Pages Posted: 5 May 2015

See all articles by Timo Kuosmanen

Timo Kuosmanen

Aalto University School of Business

Andrew L Johnson

Texas A&M University

Christopher Parmeter

University of Miami

Date Written: May 4, 2015

Abstract

The regression residual is commonly used as a productivity indicator. However, the observed input demands are endogenous if rational managers adjust their input use for inefficiency. A large stream of studies considers possible solutions to the endogeneity problem that require as little external information for instrumental variables as possible. This paper pursues the distance function approach to address the endogeneity problem. We first establish probabilistic duality results for deterministic input and output distance functions evaluated at input-output vectors that contain inefficiency and noise. We then resort to the directional distance function (DDF) as a functional representation of technology, and show that it is possible to use the direction vector of the DDF as an internal instrument to cancel out the effects of inefficiency and noise from the observed input-output data. Our main result is to establish orthogonality conditions for econometric identification of the DDF in the case where the direction vector governing the data generating process is known to the econometrician. We also examine possible endogeneity caused by the use of imperfect proxy direction vectors. Building on these insights, an axiomatic, fully nonparametric step-wise approach to estimate the DDF representation of technology is outlined.

Keywords: Economies of scope, Efficiency analysis, Endogeneity, Frontier estimation, Simultaneity bias, Productivity measurement

JEL Classification: C14, C21, C51, D24

Suggested Citation

Kuosmanen, Timo and Johnson, Andrew L and Parmeter, Christopher, Orthogonality Conditions for Identification of Joint Production Technologies: Axiomatic Nonparametric Approach to the Estimation of Stochastic Distance Functions (May 4, 2015). Available at SSRN: https://ssrn.com/abstract=2602340 or http://dx.doi.org/10.2139/ssrn.2602340

Timo Kuosmanen

Aalto University School of Business ( email )

P.O. Box 1210
Runeberginkatu 22-24
Helsinki, Finland 00101
Finland

HOME PAGE: http://www.aalto.fi

Andrew L Johnson (Contact Author)

Texas A&M University ( email )

4033 Emerging Technologies Building
College Station, Texas 77843-3131
College Station, TX 77843-4353
United States

HOME PAGE: http://www.andyjohnson.guru

Christopher Parmeter

University of Miami ( email )

Coral Gables, FL 33124
United States

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