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立 政 治 大 學
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1. Introduction
Over the past two decades, banks in the member countries of the European Union (EU) have faced dramatic systematic changes aiming at liberalization of financial markets. The implementation of the Single Banking Market noticeably lowered barriers to competition among European banks, as mergers and acquisitions (M&As) decreased the number of banks, such as mutual savings, cooperative banks, and commercial banks.
The number of foreign banks in each country also increased due to the removal of restrictions to foreign bank entry. Whether these financial reforms intensified banking competition and improved banking performance in the EU has drawn much attention from researchers.
The conventional Lerner index (henceforth, the old Lerner index) is a popular indicator of market power, ranging between 0 (perfect competition) and 1 (pure monopoly). There are two potential problems associated with the measurement of it in existing studies. First, it may take a negative value for some observations, which lacks economic implications. This arises mainly from the fact that its calculation requires using output price and marginal cost (MC), but those variables are derived from two separate sources. One has to first estimate the standard translog cost function to derive MC by taking the partial derivative of the cost function with respect to output quantity.
Output price is directly computed as the ratio of total revenues to the corresponding output measure. Second, the estimation of market power usually fails to consider potential cost inefficiency, which is likely to severely bias the parameter estimates of the cost function and the subsequent calculation of MC. See, for example, Berg and Kim (1998), Delis and Tsionas (2009), and Koetter and Poghosyan (2009).
To our knowledge, no existing works address the correlation between market power and cost inefficiency, except for Huang and Liu (2013) who propose the use of the copula-based simultaneous stochastic frontier model (CSSFM), which is composed of
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立 政 治 大 學
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two equations, i.e., a cost frontier and a price frontier.1 The estimation of the cost frontier allows one to obtain consistent parameter estimates and assess the cost efficiency. Moreover, the estimation of the price equation leads to the evaluation of the Lerner index for each bank. The measures of cost efficiency and the Lerner index are yielded simultaneously. The salient feature of this procedure is that the resultant Lerner index measure will be non-negative for each bank, in addition to taking the possible cost inefficiency into account, which avoids causing inconsistent coefficient estimates of the cost function. Note that the adoption of the joint estimation procedure is able to improve the efficiency of the parameter estimates.
This paper extends Huang and Liu (2013) by allowing banks to produce multiple outputs, therefore escaping from the aggregation problem. Our model requires the joint estimation of a cost frontier with two output price frontiers, corresponding to the outputs of loans and investments, respectively. As a result, the market power of each output can be individually assessed for each bank. The new Lerner indices of loans and investments are also immune from getting negative values, since these two measures are internally built into the simultaneous equations model and treated as if they are inefficiency terms.
This paper also generalizes the three equations model for a single country to the stochastic meta-frontier framework of Huang et al. (2014), which can then be used for comparisons of bank efficiency and market power across countries. We estimate the stochastic meta-frontier cost and two MC functions, which allows us to evaluate TGRs and the two MC gaps for each bank. This study also employs the mixed approach of Battese et al. (2004) and O’Donnell et al. (2008) to assess TGRs for the purpose of a comparison.
1 Huang and Liu (2013) implicitly assume that each bank produces a single output, which may incur the aggregation problem and appears to be not consistent with reality.
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立 政 治 大 學
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Since our price frontiers relate output prices to the corresponding MCs, we can measure the gaps between MCs of the group frontiers and those of the meta-frontiers, which is analogous to TGR. The MC gap ratio (MCGR) of an output is thus defined as the ratio of the MC gap to the corresponding output price, which represents a bank’s potential profitability. An efficient bank operating under a superior production technology has a higher value of MCGR and can reduce its production cost and MC more than a less efficient bank that has a lower value of MCGR, so as to earn higher profit in a competitive market.
The purpose of this paper is three-fold. First, we estimate the Lerner index in the context of multiple outputs, together with the new approach to calculating that index.
This appears to be new in the literature. Second, a joint estimation procedure of market power and cost efficiency is applied to yield the Lerner indices of various outputs for individual banks, which solve the problem of a negative value in the Lerner index.
Finally, we employ a new two-step SFA to simultaneously estimate the meta-frontier cost function and two MC frontiers, allowing us to compare bank efficiency, market power of different outputs, and profitability across countries, respectively.
The rest of the paper is organized as follows. Section 2 briefly reviews some relevant studies. Section 3 formulates the simultaneous equations suitable for estimating the cost and price frontiers, followed by deriving their joint probability density function (PDF) using the copula method. We also introduce the meta-frontier cost function and MCGR.
Section 4 briefly describes the data and variable definitions. Section 5 conducts the empirical study, while the last section concludes the paper.
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立 政 治 大 學
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