**1. Introduction**

The financial system plays a vital role in the economic development of an economy. Financial intermediaries, particularly the banks, mobilize funds from a diverse set of savers to investors (Drigă and Dura 2014). Efficient intermediation contributes to growth (Saini and Sindhu 2014) and economic stability. On the other hand, crisis in the banking sector could lead to broader macroeconomic instability (Baily and Elliott 2009) and adversely impact growth (Moyo et al. 2014). Despite their crucial importance to the economy, banks are prone to agency problems that may induce some managers to take excessive risks (Acharya and Naqvi 2012), and potentially jeopardize bank solvency. According to one study, 73% of the 171 failed banks in the United States for the period of 1979–1987 engaged in aggressive risk-taking (Office of the Comptroller of the Currency 1988).

There is a voluminous body of literature on the efficiency of banks (Kumar and Gulati 2014). With a few exceptions, this literature did not take into account the excessive risk-taking, often manifested in the form of non-performing loans. Moreover, almost all previous studies employed a single-stage, black-box, conceptualization of banking operations (Färe and Grosskopf 2000).<sup>1</sup> From a risk-modeling perspective, this is an inadequate representation of the actual banking operations, which have two stylized stages—a deposit mobilization stage and a loan financing stage—with excessive risk-taking relevant to the latter stage only. The technologies used for converting productive inputs into outputs

<sup>1</sup> Most previous studies used either the production or the intermediation approach to model bank efficiency.

may vary across different stages of bank operations; therefore, single-stage efficiency measurement approaches may lead to serious misspecification of the efficient technological frontier, and the resulting efficiency measurements may be misleading. To the best of our knowledge, there are only two studies that incorporated risk-taking or credit quality into efficiency measurements, following Chung et al. (1997), while using a sufficiently flexible representation of the banking operations (Akther et al. 2013; Fukuyama and Weber 2010). These studies, however, considered banks in single countries. There is a need for applying these more robust measurement approaches for investigating bank efficiency in a multi-country, emerging economy setting over time. This would allow the efficiency patterns to be compared across countries and regions and also make it possible to investigate the impacts on bank efficiency of macroeconomic shocks such as the 2007–2008 financial crisis.

The present study attempted to fill this gap. It used a two-stage network data envelopment analysis (DEA), with separate specification of technologies for the deposit mobilization and the loan financing stages using a directional distance function. In line with the stylized banking operations, the loan financing stage in the study was modeled with an undesirable output (non-performing loans) along with a good output. The risk-adjusted efficiency scores were found to be markedly different from scores obtained without accounting for bad loans, and these differences were more pronounced in the loan financing stage, thus underscoring the restrictive nature of the common technology assumption across banking operations that was extensively used in the extant literature. A second contribution of the study is that it investigated the determinant of bank efficiency using non-parametric regression that does not rely on ad hoc assumptions. Finally, the significant differences in measured efficiency scores across regions and countries served to highlight the importance of a studying bank efficiency in a cross-country setting in the emerging economies. The regional and cross-country comparisons are important as they help answer the question how global economic shocks, such as the Asian financial crisis of 1997 and the global financial crisis of 2007–2008, impacted bank efficiency in individual countries and regions.
