TY - GEN

T1 - Applying Statistical Methods to Compare Frontiers

T2 - 10th North American Productivity Workshop, NAPW 2018

AU - Asmild, Mette

AU - Kronborg, Dorte

AU - Rønn-Nielsen, Anders

N1 - Publisher Copyright: © 2021, Springer Nature Switzerland AG.

PY - 2021

Y1 - 2021

N2 - The Malmquist index is widely used in empirical studies of productivity change over time. The index is based on estimates of the frontier obtained from the convex envelopment of the data as in DEA. The statistical properties of the Malmquist index and its components, i.e. the frontier shift and the efficiency change, have until recently only been subject to a limited number of studies. The asymptotic properties of the geometric mean of the individual Malmquist indexes have been studied in the literature. Permutation tests for performing statistical inference in finite samples have recently been proposed and are easily performed. In the present paper we illustrate the permutation methods by an analysis of data comprising organic and conventional dairy farms in Denmark from 2011–2015. Further, differences between the frontiers of the production possibility sets for two separate samples are studied, specifically those of the organic and the conventional producers. We suggest to use jackknife methods when estimating the differences to ensure that these are not affected by the well-known bias originating from estimation of the frontier. In summary, the paper offers an illustration of how to analyse productivity data, in particular a comparison of two independent groups, and furthermore an analysis of how the separate groups evolve over time is provided.

AB - The Malmquist index is widely used in empirical studies of productivity change over time. The index is based on estimates of the frontier obtained from the convex envelopment of the data as in DEA. The statistical properties of the Malmquist index and its components, i.e. the frontier shift and the efficiency change, have until recently only been subject to a limited number of studies. The asymptotic properties of the geometric mean of the individual Malmquist indexes have been studied in the literature. Permutation tests for performing statistical inference in finite samples have recently been proposed and are easily performed. In the present paper we illustrate the permutation methods by an analysis of data comprising organic and conventional dairy farms in Denmark from 2011–2015. Further, differences between the frontiers of the production possibility sets for two separate samples are studied, specifically those of the organic and the conventional producers. We suggest to use jackknife methods when estimating the differences to ensure that these are not affected by the well-known bias originating from estimation of the frontier. In summary, the paper offers an illustration of how to analyse productivity data, in particular a comparison of two independent groups, and furthermore an analysis of how the separate groups evolve over time is provided.

KW - Data envelopment analysis (DEA)

KW - Frontier differences

KW - Independent samples

KW - Malmquist index

KW - Organic farming

KW - Permutation tests

U2 - 10.1007/978-3-030-47106-4_14

DO - 10.1007/978-3-030-47106-4_14

M3 - Article in proceedings

AN - SCOPUS:85126089539

SN - 9783030471057

T3 - Springer Proceedings in Business and Economics

SP - 335

EP - 348

BT - Advances in Efficiency and Productivity Analysis

A2 - Parmeter, Christopher F.

A2 - Sickles, Robin C.

PB - Springer

Y2 - 15 June 2018 through 18 June 2018

ER -