Sequential Malmquist-Luenberger productivity index for interval data envelopment analysis

Abstract

<p style='text-indent:20px;'>Data envelopment analysis (DEA) based productivity indexes models are widely applied to evaluate the productivity of decision-making units over a period. This study proposes a productivity index for evaluating environmentally sensitive productivity growth while excluding the possibility of spurious technical regress. This innovative index has been created by combining directional distance functions, sequential DEA, undesirable data, and the concept of interval DEA. With this combination, the traditional sequential Malmquist-Luenberger productivity index (SMLPI) has been reformulated as an interval DEA problem to present a novel productivity index named interval SMLPI. We propose a decomposition of the developed index utilizing both constant returns to scale and variable returns to scale frontiers as the benchmark, which allows us to quantify scale efficiency change with interval data. To exhibit the capability of the proposed extension of SMLPI, we model a framework for Indian commercial banks and measure productivity change intervals for twenty-one banks from 2011 to 2018. The empirical findings elucidate that the scale efficiency change plays an essential role in driving productivity change. ICICI Bank had the highest average marginal productivity gain of 1.5007 between 2011 and 2018, whereas Karur Vysya bank had the highest average marginal productivity decline of 0.9411.</p>