## A Ray-Based Input Distance Function to Model Zero-Valued Output Quantities: Derivation and an Empirical Application

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**A Ray-Based Input Distance Function to Model Zero-Valued Output Quantities : Derivation and an Empirical Application.** / Price, Juan José; Henningsen, Arne.

Publikation: Working paper

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*A Ray-Based Input Distance Function to Model Zero-Valued Output Quantities: Derivation and an Empirical Application*. Department of Food and Resource Economics, University of Copenhagen. IFRO Working Paper Nr. 2022/03

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TY - UNPB

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

PY - 2022

Y1 - 2022

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.

M3 - Working paper

T3 - IFRO Working Paper

BT - A Ray-Based Input Distance Function to Model Zero-Valued Output Quantities

PB - Department of Food and Resource Economics, University of Copenhagen

ER -

ID: 308552681