Concerning the average revenue, it is common to approximate it by the fraction of total
revenue to total assets. However, unlike most other approaches to studying the relationship
between bank competition and bank (in)stability, we explicitly allow for banks using
less-than-optimal production technology. As argued by Koetter, Kolari, and Spierdijk
(2012), ignoring possible inefficiencies in the production process might lead to biased estimates
for the Lerner Index. We follow Koetter, Kolari, and Spierdijk (2012) and use the
sum of the predicted values for total cost C from Equation (2) and the predicted profits
derived from the estimation of a profit function dual to the cost function depicted in
Equation (2). The estimation of the standard stochastic profit function delivers predicted
values of profits of bank i (see Berger and Mester (1997)). These predicted profit values,
as well as the predicted costs of the stochastic cost frontier, are net of any inefficiencies
and thus proxy the true average revenue more reliably. To be specific, the average revenue
arit in Equation (1) is computed as