TY - JOUR

T1 - Robust Semi-Parametric Inference for Two-Stage Production Models

T2 - A Beta Regression Approach

AU - Ospina, Raydonal

AU - Baltazar, Samuel G.F.

AU - Leiva, Víctor

AU - Figueroa-Zúñiga, Jorge

AU - Castro, Cecilia

N1 - Publisher Copyright:
© 2023 by the authors.

PY - 2023/7

Y1 - 2023/7

N2 - The data envelopment analysis is related to a non-parametric mathematical tool used to assess the relative efficiency of productive units. In different studies on productive efficiency, it is common to employ semi-parametric procedures in two stages to determine whether any exogenous factors of interest affect the performance of productive units. However, some of these procedures, particularly those based on conventional statistical inference, generate inconsistent estimates when dealing with incoherent data-generating processes. This inconsistency arises due to the efficiency scores being limited to the unit interval, and the estimated scores often exhibit serial correlation and have limited observations. To address such inconsistency, several strategies have been suggested, with the most well-known being an algorithm based on a parametric bootstrap procedure using the truncated normal distribution and its regression model. In this work, we present a modification of this algorithm that utilizes the beta distribution and its regression structure. The beta model allows for better accommodation of asymmetry in the data distribution. Our proposed algorithm introduces inferential characteristics that are superior to the original algorithm, resulting in a more statistically coherent data-generating process and improving the consistency property. We have conducted computational experiments that demonstrate the improved results achieved by our proposal.

AB - The data envelopment analysis is related to a non-parametric mathematical tool used to assess the relative efficiency of productive units. In different studies on productive efficiency, it is common to employ semi-parametric procedures in two stages to determine whether any exogenous factors of interest affect the performance of productive units. However, some of these procedures, particularly those based on conventional statistical inference, generate inconsistent estimates when dealing with incoherent data-generating processes. This inconsistency arises due to the efficiency scores being limited to the unit interval, and the estimated scores often exhibit serial correlation and have limited observations. To address such inconsistency, several strategies have been suggested, with the most well-known being an algorithm based on a parametric bootstrap procedure using the truncated normal distribution and its regression model. In this work, we present a modification of this algorithm that utilizes the beta distribution and its regression structure. The beta model allows for better accommodation of asymmetry in the data distribution. Our proposed algorithm introduces inferential characteristics that are superior to the original algorithm, resulting in a more statistically coherent data-generating process and improving the consistency property. We have conducted computational experiments that demonstrate the improved results achieved by our proposal.

KW - R software

KW - Simar and Wilson algorithm

KW - asymmetry

KW - bootstrapping

KW - data envelopment analysis

KW - decision-making units

KW - efficiency

KW - optimization methods

KW - statistical consistency

UR - http://www.scopus.com/inward/record.url?scp=85166315383&partnerID=8YFLogxK

U2 - 10.3390/sym15071362

DO - 10.3390/sym15071362

M3 - Article

AN - SCOPUS:85166315383

SN - 2073-8994

VL - 15

JO - Symmetry

JF - Symmetry

IS - 7

M1 - 1362

ER -