Abstract
The data envelopment analysis (DEA) technique is well known for computing the Malmquist-Luenberger productivity index (MLPI) in measuring productivity change in the decision-making units (DMUs) over two consecutive periods. In this research, we detect infeasibility of the directional distance function (DDF) based DEA model of MLPI under the variable returns to scale technology when data takes on negative values. We address this problem by developing a novel DDF-based DEA model that computes an improved MLPI. We extend the DDF approach to the dynamic network structure and introduce the dynamic MLPI for analyzing the performance of DMUs over time. We also develop the dynamic sequential MLPI to detect shifts in the efficient frontiers due to random shocks or technological advancements over time. The dynamic network structure in the two indexes comprises multiple divisions in DMUs connected vertically by intermediate productivity links and horizontally over time by carryovers. The proposed models are feasible and bounded with undesirable features and negative and non-negative data values. Real data of 39 Indian commercial public and private banks from 2008 to 2019 used to illustrate the two indexes.
Highlights
Among the later methodological innovations that enticed a large number of practical applications are Malmquist productivity index (MPI) and Malmquist-Luenberger productivity index (MLPI)
We introduce an enhanced ML productivity index (MLPI) to address the problem of infeasibility when evaluating cross-period directional distance function (DDF) in the presence of negative data
0.9757 0.9994 0.9972 0.9981 1.0013 0.9947 0.9991 1.0003 1.0038 1.0020 1.0010 1.0030 0.9944 1.0012 1.0097 0.9989 1.0011 0.9984 1.0018 1.0053 1.0000 1.0071 1.0022 0.9995 0.9968 0.9906 1.0032 1.0153 1.0000 0.9967 0.9974 1.0000 1.0039 1.0151 1.0150 0.9835 0.9997 1.0007 1.0004 1.0003 where multiple divisions are connected through intermediate products and multiple periods are linked through carryovers, the paper’s significant contribution is an extension of MLPI to the dynamic MLPI (DMLPI) and dynamic sequential MLPI (DSMLPI) involving undesirable outputs and real data values
Summary
Productivity improvement is essential for the long-run sustainability and well being of the firms. These indexes allow decomposing the productivity change into two distinct drivers: efficiency change (EC) and technical change (TC) Though both MPfI and MLPI have emerged as standard tools for computing productivity change, their computation using the non-parametric DEA-based framework attracted more attention both at methodological and application levels. Unlike parametric techniques, which require parameter estimation in the regression model of the explanatory variables and the probability distribution of the error measure (or noise), the non-parametric methodology of DEA is deterministic. To the best of our knowledge, there is no research reported in the literature to cognate DMLPI and DSMLPI in the dynamic network structure under the variable returns to scale (VRS) technology in the presence of negative data-values.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
