Bank branch efficiency with a Bayesian lens on technological heterogeneity

Although technological heterogeneity between banks has been previously considered in the literature, less attention has been given to technological heterogeneity between branches of the same bank. This paper analyses the efficiency, returns to scale (RTS) and productivity growth of bank branches considering a stochastic frontier approach that includes unobserved technological heterogeneity between branches and time-varying efficiencies. Specifically, we propose a random parameters stochastic distance frontier model that includes multiple inputs and outputs. We assume a translog output distance function estimated in an objective Bayesian framework. The empirical analysis was carried out using data from 2011 to 2017 from a large Spanish commercial bank with 122 branches. The random parameters model adds, in general, flexibility to the estimates, allowing for the identification of periods with more extreme efficiencies, both high and low, which the fixed parameters model is unable to capture. The random parameters model also detects an increase in efficiency over time that the fixed parameters model fails to identify. The differences between the two models are sufficient to drastically modify the efficiency ranking of the branches. The random parameters model also found greater dispersion than the fixed parameters model in estimation of the RTS and productivity growth.