TY - JOUR

T1 - A ray-based input distance function to model zero-valued output quantities

T2 - Derivation and an empirical application

AU - Price, Juan José

AU - Henningsen, Arne

N1 - Funding Information: We are grateful to Mette Asmild, Peter Bogetoft, and Christopher O’Donnell as well as to two anonymous reviewers and an anonymous associate editor of the Journal of Productivity Analysis for their helpful comments on earlier versions of this article. We also appreciate the comments made by participants of the North American Productivity Workshop, NAPW 2021, and the European Workshop on Efficiency and Productivity Analysis, EWEPA 2022, particularly those of Robin Sickles and Subal Kumbhakar. Of course, the authors take full responsibility for any remaining errors. We thank Lucas Alexander Kock and Berit Fruelund Kjærside from the Danish Ministry of Culture and Monika Bille Nielsen from Statistics Denmark for providing the data. Juan José Price acknowledges financial support from Copenhagen Business School (CBS) and Macquarie University. Publisher Copyright: © 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

PY - 2023

Y1 - 2023

N2 - We derive and empirically apply an input-oriented distance function based on the stochastic ray production function suggested by Löthgren (1997, 2000). We show that the derived ray-based input distance function is suitable for modeling production technologies based on logarithmic functional forms (e.g., Cobb-Douglas and Translog) when control over inputs is greater than control over outputs and when some productive entities do not produce the entire set of outputs — two situations that are jointly present in various economic sectors. We also address a weakness of the stochastic ray function, namely its sensitivity to the outputs’ ordering, by using a model-selection approach and a model-averaging approach. We estimate a ray-based Translog input distance function with a data set of Danish museums. These museums have more control over their inputs than over their outputs, and many of them do not produce the entire set of outputs that is considered in our analysis. Given the importance of monotonicity conditions in efficiency analysis, we demonstrate how to impose monotonicity on ray-based input distance functions. As part of the empirical analysis, we estimate technical efficiencies, distance elasticities of the inputs and outputs, and scale elasticities and establish how the production frontier is affected by some environmental variables that are of interest to the museum sector.

AB - We derive and empirically apply an input-oriented distance function based on the stochastic ray production function suggested by Löthgren (1997, 2000). We show that the derived ray-based input distance function is suitable for modeling production technologies based on logarithmic functional forms (e.g., Cobb-Douglas and Translog) when control over inputs is greater than control over outputs and when some productive entities do not produce the entire set of outputs — two situations that are jointly present in various economic sectors. We also address a weakness of the stochastic ray function, namely its sensitivity to the outputs’ ordering, by using a model-selection approach and a model-averaging approach. We estimate a ray-based Translog input distance function with a data set of Danish museums. These museums have more control over their inputs than over their outputs, and many of them do not produce the entire set of outputs that is considered in our analysis. Given the importance of monotonicity conditions in efficiency analysis, we demonstrate how to impose monotonicity on ray-based input distance functions. As part of the empirical analysis, we estimate technical efficiencies, distance elasticities of the inputs and outputs, and scale elasticities and establish how the production frontier is affected by some environmental variables that are of interest to the museum sector.

KW - Distance function

KW - Input-oriented efficiency

KW - Model averaging

KW - Museums

KW - Stochastic ray production frontier

KW - Zero output quantities

U2 - 10.1007/s11123-023-00684-1

DO - 10.1007/s11123-023-00684-1

M3 - Journal article

AN - SCOPUS:85161354261

VL - 60

SP - 179

EP - 188

JO - Journal of Productivity Analysis

JF - Journal of Productivity Analysis

SN - 0895-562X

ER -