**1. Introduction**

Recently, Tsionas (2020, MT) made some remarks regarding the use of stochastic frontier-based measures of market power in a part of our empirical study (Karadima and Louri 2020, KL), which examines the evolution, as well as the fragmentation and convergence dynamics, of market power, concentration and credit risk in the euro area banking sector during 2005–2017. To facilitate the comparison of the arguments of both sides, our answers are provided below in the same order as MT's remarks.

The present reply is organized as follows. In Section 2, we describe the context in which the term "profit maximization" is used in our research. In Section 3, we show that the calculation of the Lerner index, following the Kumbhakar et al. (2012) stochastic frontier methodology, does not involve the direct estimation of a translog cost function per se, but only the estimation of its partial derivative with respect to output. In Section 4, we explain why our basic equation cannot be considered as equivalent to the equation proposed by MT. In response to a general comment on output price, we take the opportunity in Section 5 to underline, using our own equations, one of the biggest innovations from Kumbhakar et al. (2012). As some auxiliary calculations had not been included for brevity in our research, we illustrate in Section 6 how we arrived at our Equation (5), starting from our Equation (4). In Section 7, we provide our answers to the criticism on the use of a single-output cost function. Finally, we show in Section 8 that the MT's criticism on our convergence analysis has been based on the incorrect hypothesis of the use of individual-bank data. Since our analysis has actually been based on country-level aggregated data, we consider that the criticism at this point is not relevant.

#### **2. Calculation of a Lerner Index following a Stochastic Frontier Methodology**
