A firm-specifc malmquist productivity index model for stochastic data envelopment analysis : an application to commercial banks

In the data envelopment analysis (DEA) literature, productivity change captured by the Malmquist productivity index, especially in terms of a deterministic environment and stochastic variability in inputs and outputs, has been somewhat ignored. Therefore, this study developed a frm-specifc, DEA-based Malmquist index model to examine the efciency and productivity change of banks in a stochastic environment. First, in order to estimate bank-specifc efciency, we employed a two-stage double bootstrap DEA procedure. Specifcally, in the frst stage, the technical efciency scores of banks were calculated by the classic DEA model, while in the second stage, the double bootstrap DEA model was applied to determine the efect of the contextual variables on bank efciency. Second, we applied a two-stage procedure for measuring productivity change in which the frst stage included the estimation of stochastic technical efciency and the second stage included the regression of the estimated efciency scores on a set of explanatory variables that infuence relative performance. Finally, an empirical investigation of the Iranian banking sector, consisting of 120 bankyear observations of 15 banks from 2014 to 2021, was performed to measure their efciency and productivity change. Based on the fndings, the explanatory variables (i.e., the nonperforming loan ratio and the number of branches) indicated an inverse relationship with stochastic technical efciency and productivity change. The implication of the fndings is that, in order to improve the efciency and productivity of banks, it is important to optimize these factors.