Directional distance function DEA estimators for evaluating efficiency gains from possible mergers and acquisitions

A modified generalised directional distance function data envelopment analysis model is introduced into the smoothed bootstrap context. The new model handles asymmetrically desirable and undesirable outputs and deals with positive and negative values, while the bias-corrected estimators are independent of the length of the direction vector. The reason for the development of this new efficiency assessment model is the estimation of the degree of operating efficiency gains from possible mergers and acquisitions (M&A) between banks. Our estimations are regarded as more realistic compared to those found in the extant literature, as they consider not only desirable but also undesirable variables and negative values that are crucial to the evaluation of firm performance. The new model is not only applicable to the banking sector but also in any industry. We use two data samples, one consisting of 86 conventional and a second consisting of 21 Islamic banks. Among the findings of this study is the convergence of the conventional and Islamic banks’ efficiencies over the period 2014–2016. Moreover, consolidations only between efficient and inefficient conventional banks lead to higher operating efficiency, while M&A between efficient only or inefficient only conventional banks and between Islamic banks are likely to be undesirable.