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.
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. JJP initiated the research, developed the general idea for the empirical analysis, collected the data, built the data set, and conducted most of the literature review. AH suggested to derive a ray-based input distance function in order to deal with zero-valued outputs in the empirical analysis. The mathematical derivations and the coding of the derived model specification was done by JJP with guidance and help from AH. JJP drafted the first version of the article, while AH revised some of its parts. Both authors participated in the revisions of the article.
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
UR - http://www.scopus.com/inward/record.url?scp=85161354261&partnerID=8YFLogxK
U2 - 10.1007/s11123-023-00684-1
DO - 10.1007/s11123-023-00684-1
M3 - Article
AN - SCOPUS:85161354261
SN - 0895-562X
VL - 60
SP - 179
EP - 188
JO - Journal of Productivity Analysis
JF - Journal of Productivity Analysis
IS - 2
ER -