A new approach to jointly estimating the Lerner index and cost efficiency for multi-output banks under a stochastic meta-frontier framework

This paper proposes the copula-based simultaneous stochastic frontier model, composed of a cost frontier and two output price frontiers, for the banking sector in order to measure cost efficiency and market power in the markets of loans and investments. The new Lerner indices are estimated by the simultaneous equations model, consisting of three frontier equations, thus avoiding obtaining negative measures of the Lerner index. We apply the stochastic meta-frontier model of Huang et al. (2014) to estimate and compare cost efficiency and market power across five European countries over the period 1998–2010. Our approach allows for calculating the technology gap ratio and evaluating the potential Lerner indices, which consist of the Lerner index and marginal cost gap ratio. Empirical results suggest that banks reallocate their output quantities toward the one with a higher measure of the potential Lerner index in order to promote profits. Adopting advanced technology and conducting merger and acquisitions are effective ways to achieve this goal.