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題名 運用新共同邊界函數探討多重產出下聯立估計銀行競爭度與成本效率之影響
A New Approach to Jointly Estimating the Lerner Index and Cost Efficiency for Multi-output Banks under a Meta-Frontier Framework
作者 江典霖
Chiang, Dien Lin
貢獻者 黃台心
Huang, Tai Hsin
江典霖
Chiang, Dien Lin
關鍵詞 Lerner指數
成本效率
產出價格邊界
共同邊界
關聯結構函數
Lerner index
cost efficiency
output price frontier
meta-frontier
copula methods
日期 2014
上傳時間 1-Jul-2015 14:46:33 (UTC+8)
摘要 過去文獻大多使用Lerner指數來衡量銀行業之市場競爭度，但在計算過程中有可能出現其值為負之問題。為解決上述問題，本文運用關聯結構函數建立聯立隨機邊界模型，它由銀行成本邊界與兩條產出價格邊界所組成，可以同時衡量放款市場及投資市場之市場競爭度與成本效率。另外，為比較西歐五個國家的銀行市場競爭度與成本效率，本文進一步採用Huang et al. (2014)所提出的新隨機共同邊界模型，此模型除使用共同成本邊界計算技術缺口比率外，還透過產出價格共同邊界衡量潛在Lerner指數，進一步拆解成Lerner指數與MC gap ratio (MCGR)兩部分，可以比較不同國家間的市場競爭程度。
This paper proposes the copula-based simultaneous stochastic frontier model (CSSFM), 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 index can be estimated by relying on the simultaneous equations model, consisting of three frontier equations, which avoids obtaining negative measures of the Lerner index. We then apply the new meta-frontier model to simultaneously estimate and compare cost efficiency and market power across five countries over the period 1998-2010. The salient feature of our proposed approach is that it allows for calculating the technology gap ratio on the basis of the cost frontier, as well as evaluating the potential Lerner index from price frontiers, which can be decomposed into the country-specific Lerner index and marginal cost gap ratio.
參考文獻 Aigner, D., C.A.K. Lovell, and P. Schmidt (1977), “Formulation and Estimation of Stochastic Frontier Production Function Models,” Journal of Econometrics, 6, 21-37.
Akhigbe, A. and B.A. Stevenson (2010), “Profit efficiency in U.S. BHCs: Effects of increasing non-traditional revenue sources,” Quarterly Review of Economics and Finance, 50, 132-40.
Alegria, C. and K. Schaeck (2008), “On Measuring Concentration in Banking Systems,” Finance Research Letters, 5, 59-67.
Altunbas, Y., E.P.M. Gardener, P. Molyneux, and B. Moore (2001), “Efficiency in European banking,” European Economic Review, 45, 1931-1955.
Angelini, P. and N. Cetorelli (2003), “The Effects of Regulatory Reform on Competition in the Banking Industry,” Journal of Money, Credit, and Banking, 35, 663-684.
Banker, R. D., A. Charnes, and W.W. Cooper (1984), “Some models for estimating technical and scale inefficiencies in Data Envelopment Analysis,” Management Science, 30, 1078-1092.
Battese, G.E., D.S.P. Rao, and C.J. O’Donnell (2004), “A metafrontier production function for estimation of technical efficiencies and technology gaps for firms operating under different technologies,” Journal of Productivity Analysis, 21, 91-103.
Beck, T., A. Demirgüç-Kunt, and R. Levine (2006), “Bank Concentration, Competition, and Crisis: First Results,” Journal of Banking and Finance, 30, 1581-1603.
Berg, S.A. and M. Kim (1998), “Bank as Multioutput Oligopolies: An Empirical Evaluation of the Retail and Corporate Banking Markets,” Journal of Money, Credit, and Banking, 30, 135-153.
Berger, A.N., A. Demirgüç-Kunt, R. Levine, and J.G. Haubrich (2004), “Bank Concentration and Competition: An Evolution in the Making,” Journal of Money, Credit, and Banking, 36, 433-451.
Berger, A.N., L.F. Klapper, and R. Turk-Ariss (2009), “Bank Competition and Financial Stability,” Journal of Financial Services Research, 35, 99-118.
Bikker, J.A. and K. Haaf (2002), “Competition, Concentration and Their Relationship: An Empirical Analysis of the Banking Industry,” Journal of Banking and Finance, 26, 2191-2214.
Bikker, J.A., S. Shaffer, and L. Spierdijk (2012), “Assessing competition with the Panzar-Rosse model: the role of scale, costs, and equilibrium,” Review of Economics and Statistics, 94, 1025-1044.
Bresnahan, T. (1982), “The oligopoly solution identified,” Economics Letters, 10, 19-27.
Boone, J., J.C. van Ours, and H. van der Wiel (2007), “How (not) to measure competition,” TILEC discussion paper, DP 2007-014, Tilburg University.
Bos, J.W.B. and H. Schmiedel (2007), “Is there a single frontier in a single European banking market?,” Journal of Banking and Finance, 31(7), 2081-2102.
Carbó, S., D. Humphrey, J. Maudos, and P. Molyneux (2009), “Cross-country Comparisons of Competition and Pricing Power in European Banking,” Journal of International Money and Finance, 28, 115-134.
Charnes, A., W.W. Cooper, E. Rhodes (1978), “Measuring the efficiency of decision making units,” European Journal of Operations Research, 2, 429-444.
Casu, B. and C. Girardone (2006), “Bank Competition, Concentration and Efficiency in the Single European Market,” Manchester School, 74, 441-468.
Chen, K.H. and H.Y. Yang (2011), “A Cross-country comparison of productivity growth using the generalized meta-frontier Malmquist productivity index: With application to banking industries in Taiwan and China,” Journal of Productivity Analysis, 35(3), 197-212.
De Bandt, O. and E.P. Davis (2000), “Competition, Contestability and Market Structure in European Banking Sectors on the Eve of EMU,” Journal of Banking and Finance, 24, 1045-1066.
Delis, M.D. and E.G. Tsionas (2009), “The Joint Estimation of Bank-level Market Power and Efficiency,” Journal of Banking and Finance, 33, 1842-1850.
Fitzpatrick, T. and McQuinn, K. (2008), “Measuring bank profit efficiency,” Applied Financial Economics, 18, 1-8.
Greene, W.H. (2003), “Simulated likelihood estimation of the normal-gamma stochastic frontier function,” Journal of Productivity Analysis, 19, 179-190.
Greene, W.H. (2010), “A stochastic frontier model with correction for sample selection,” Journal of Productivity Analysis, 34, 15-24.
Huang, C.J., T.H. Huang, and N.H. Liu (2014), “A New Approach to Estimating the Metafrontier Production Function Based on a Stochastic Frontier Framework,” Journal of Productivity Analysis, 42, 241-254.
Huang, T.H., and N.H. Liu (2013), “Formulation and joint estimation of the Lerner index and cost efficiency for banks using copula methods,” manuscript.
Huang, T.H. (2000), “Estimating X-efficiency in Taiwanese banking using a translog shadow profit function,” Journal of Productivity Analysis, 14, 225-245.
Huang, T.H., L.C. Chiang, K.C. Chen, and P.H. Chiu (2010), “An application of the meta-frontier cost function to the study of bank efficiencies and technology gaps in 16 European countries,” Management Review, 29, 25-43.
Kasman, A. and C. Yildirim (2006), “Cost and profit efficiencies in transition banking: the case of new EU members,” Applied Economics, 38, 1079-90.
Koetter, M., J. Kolari, and L. Spierdijk (2012), “Enjoying the Quiet Life under Deregulation? Evidence from Adjusted Lerner Indices for U.S. Banks,” Review of Economics and Statistics, 94, 462-480.
Koetter, M. and T. Poghosyan (2009), “The Identification of Technology Regimes in Banking: Implications for the Marker Power-fragility Nexus,” Journal of Banking and Finance, 33, 1413-1422.
Koutsomanoli-Filippaki, A., E. Mamatzakis, and C. Staikouras (2009), “Structural reforms and banking efficiency in the new EU States,” Journal of Policy Modeling, 31, 17-21.
Lai, H.P. and C.J. Huang (2013), “Maximum Likelihood Estimation of Seemingly Unrelated Stochastic Frontier Regressions,” Journal of Productivity Analysis, 40, 1-14.
Lau, L. (1982), “On identifying the degree of competitiveness from industry price and output data,” Economics Letters, 10, 93-99.
Lerner, A.P. (1934), “The Concept of Monopoly and the Measurement of Monopoly Power,” Review of Economic Studies, 1, 157-175.
Maudos, J. and J. Fernández de Guevara (2004), “Factors Explaining the Interest Margin in the Banking Sectors of the European Union,” Journal of Banking and Finance, 28, 2259-2281.
Maudos, J. and J. Fernández de Guevara (2007), “The Cost of Market Power in Banking: Social Welfare Loss vs. Cost Inefficiency,” Journal of Banking and Finance, 31, 2103-2125.
Meeusen, W. and J. van den Broeck (1977), “Efficiency Estimation from Cobb-Douglas Production Functions with Composed Error,” International Economic Review, 18, 435-444.
Molyneux, P., D.M. Lloyd-Williams, and J. Thornton (1994), “Competitive conditions in European banking,” Journal of Banking and Finance, 18, 445-459.
Molyneux, P., J. Thornton, and D.M. Lloyd-Williams (1996), “Competition and market contestability in Japanese commercial banking,” Journal of Economics and Business, 48, 33-45.
Panzar, J.C. and J.N. Rosse (1987), “Testing for Monopoly Equilibrium,” Journal of Industrial Economics, 35, 443-456.
O’Donnell, C.J., D.S.P. Rao, and G.E. Battese (2008), “Metafrontier Frameworks for the Study of Firm-Level Efficiencies and Technology Ratios,” Empirical Economics, 34, 231-255.
Sklar, A. (1959), “Functions de Répartition àn Dimensions et Leurs Marges,” Publications de l’Institut de Statistique de L’Université de Paris, 8, 229-231.
Tsay, W.J., C.J. Huang, T.T. Fu, and I.L. Ho (2013), “A simple closed-form approximation for the cumulative distribution function of the composite error of stochastic frontier models,” Journal of Productivity Analysis, 39, 259-269.
Turk-Ariss, R. (2009), “Competitive Behavior in Middle East and North Africa Banking Systems,” Quarterly Review of Economics and Finance, 49, 693-710.
Turk-Ariss, R. (2010), “On the Implications of Market Power in Banking: Evidence from Developing Countries,” Journal of Banking and Finance, 34, 765-775.
Van Leuvensteijn, M., J.A. Bikker, Adrian A.R.J.M. van Rixtel, and C.K. Sorensen (2011), “A new approach to measuring competition in the loan markets of the euro area,” Applied Economics, 43, 3155-3167.
Van Leuvensteijn, M., C.K. Sorensen, J.A. Bikker, Adrian A.R.J.M. van Rixtel (2013), “Impact of bank competition on the interest rate pass-through in the euro area,” Applied Economics, 45, 1359-1380.
Vennet, R.V. (2002), “Cost and profit efficiency of financial conglomerates and universal banks in Europe,” Journal of Money, Credit, and Banking, 34, 254-282.
Williams, J. (2012), “Efficiency and market power in Latin American banking,” Journal of Financial Stability, 8, 263-276.
描述 博士
國立政治大學
金融研究所
97352508
103
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0973525082
資料類型 thesis
dc.contributor.advisor 黃台心zh_TW
dc.contributor.advisor Huang, Tai Hsinen_US
dc.contributor.author (Authors) 江典霖zh_TW
dc.contributor.author (Authors) Chiang, Dien Linen_US
dc.creator (作者) 江典霖zh_TW
dc.creator (作者) Chiang, Dien Linen_US
dc.date (日期) 2014en_US
dc.date.accessioned 1-Jul-2015 14:46:33 (UTC+8)-
dc.date.available 1-Jul-2015 14:46:33 (UTC+8)-
dc.date.issued (上傳時間) 1-Jul-2015 14:46:33 (UTC+8)-
dc.identifier (Other Identifiers) G0973525082en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/76179-
dc.description (描述) 博士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 金融研究所zh_TW
dc.description (描述) 97352508zh_TW
dc.description (描述) 103zh_TW
dc.description.abstract (摘要) 過去文獻大多使用Lerner指數來衡量銀行業之市場競爭度，但在計算過程中有可能出現其值為負之問題。為解決上述問題，本文運用關聯結構函數建立聯立隨機邊界模型，它由銀行成本邊界與兩條產出價格邊界所組成，可以同時衡量放款市場及投資市場之市場競爭度與成本效率。另外，為比較西歐五個國家的銀行市場競爭度與成本效率，本文進一步採用Huang et al. (2014)所提出的新隨機共同邊界模型，此模型除使用共同成本邊界計算技術缺口比率外，還透過產出價格共同邊界衡量潛在Lerner指數，進一步拆解成Lerner指數與MC gap ratio (MCGR)兩部分，可以比較不同國家間的市場競爭程度。zh_TW
dc.description.abstract (摘要) This paper proposes the copula-based simultaneous stochastic frontier model (CSSFM), 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 index can be estimated by relying on the simultaneous equations model, consisting of three frontier equations, which avoids obtaining negative measures of the Lerner index. We then apply the new meta-frontier model to simultaneously estimate and compare cost efficiency and market power across five countries over the period 1998-2010. The salient feature of our proposed approach is that it allows for calculating the technology gap ratio on the basis of the cost frontier, as well as evaluating the potential Lerner index from price frontiers, which can be decomposed into the country-specific Lerner index and marginal cost gap ratio.en_US
dc.description.tableofcontents 1. Introduction ……………………………………………………………………1
2. Literature review ………………………………………………………………4
2.1 Market competition ………………………………………………………4
2.2 A meta-frontier model ……………………………………………………6
3. Methodology ……………………………………………………………………8
3.1 Simultaneous equations model of the cost and price frontiers……………8
3.2 The copula-based joint PDF and the likelihood function…………………11
3.3 Meta-frontier cost function………………………………………………14
4. Data description ………………………………………………………………18
5. Empirical results ………………………………………………………………21
5.1 Parameter estimates ………………………………………………………21
5.2 Various efficiency scores…………………………………………………32
5.3 Lerner index ……………………………………………………………35
6. Conclusion …………………………………………………………………40
References ……………………………………………………………………42		zh_TW
dc.format.extent 1069080 bytes-
dc.format.mimetype application/pdf-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0973525082en_US
dc.subject (關鍵詞) Lerner指數zh_TW
dc.subject (關鍵詞) 成本效率zh_TW
dc.subject (關鍵詞) 產出價格邊界zh_TW
dc.subject (關鍵詞) 共同邊界zh_TW
dc.subject (關鍵詞) 關聯結構函數zh_TW
dc.subject (關鍵詞) Lerner indexen_US
dc.subject (關鍵詞) cost efficiencyen_US
dc.subject (關鍵詞) output price frontieren_US
dc.subject (關鍵詞) meta-frontieren_US
dc.subject (關鍵詞) copula methodsen_US
dc.title (題名) 運用新共同邊界函數探討多重產出下聯立估計銀行競爭度與成本效率之影響zh_TW
dc.title (題名) A New Approach to Jointly Estimating the Lerner Index and Cost Efficiency for Multi-output Banks under a Meta-Frontier Frameworken_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) Aigner, D., C.A.K. Lovell, and P. Schmidt (1977), “Formulation and Estimation of Stochastic Frontier Production Function Models,” Journal of Econometrics, 6, 21-37.
Akhigbe, A. and B.A. Stevenson (2010), “Profit efficiency in U.S. BHCs: Effects of increasing non-traditional revenue sources,” Quarterly Review of Economics and Finance, 50, 132-40.
Alegria, C. and K. Schaeck (2008), “On Measuring Concentration in Banking Systems,” Finance Research Letters, 5, 59-67.
Altunbas, Y., E.P.M. Gardener, P. Molyneux, and B. Moore (2001), “Efficiency in European banking,” European Economic Review, 45, 1931-1955.
Angelini, P. and N. Cetorelli (2003), “The Effects of Regulatory Reform on Competition in the Banking Industry,” Journal of Money, Credit, and Banking, 35, 663-684.
Banker, R. D., A. Charnes, and W.W. Cooper (1984), “Some models for estimating technical and scale inefficiencies in Data Envelopment Analysis,” Management Science, 30, 1078-1092.
Battese, G.E., D.S.P. Rao, and C.J. O’Donnell (2004), “A metafrontier production function for estimation of technical efficiencies and technology gaps for firms operating under different technologies,” Journal of Productivity Analysis, 21, 91-103.
Beck, T., A. Demirgüç-Kunt, and R. Levine (2006), “Bank Concentration, Competition, and Crisis: First Results,” Journal of Banking and Finance, 30, 1581-1603.
Berg, S.A. and M. Kim (1998), “Bank as Multioutput Oligopolies: An Empirical Evaluation of the Retail and Corporate Banking Markets,” Journal of Money, Credit, and Banking, 30, 135-153.
Berger, A.N., A. Demirgüç-Kunt, R. Levine, and J.G. Haubrich (2004), “Bank Concentration and Competition: An Evolution in the Making,” Journal of Money, Credit, and Banking, 36, 433-451.
Berger, A.N., L.F. Klapper, and R. Turk-Ariss (2009), “Bank Competition and Financial Stability,” Journal of Financial Services Research, 35, 99-118.
Bikker, J.A. and K. Haaf (2002), “Competition, Concentration and Their Relationship: An Empirical Analysis of the Banking Industry,” Journal of Banking and Finance, 26, 2191-2214.
Bikker, J.A., S. Shaffer, and L. Spierdijk (2012), “Assessing competition with the Panzar-Rosse model: the role of scale, costs, and equilibrium,” Review of Economics and Statistics, 94, 1025-1044.
Bresnahan, T. (1982), “The oligopoly solution identified,” Economics Letters, 10, 19-27.
Boone, J., J.C. van Ours, and H. van der Wiel (2007), “How (not) to measure competition,” TILEC discussion paper, DP 2007-014, Tilburg University.
Bos, J.W.B. and H. Schmiedel (2007), “Is there a single frontier in a single European banking market?,” Journal of Banking and Finance, 31(7), 2081-2102.
Carbó, S., D. Humphrey, J. Maudos, and P. Molyneux (2009), “Cross-country Comparisons of Competition and Pricing Power in European Banking,” Journal of International Money and Finance, 28, 115-134.
Charnes, A., W.W. Cooper, E. Rhodes (1978), “Measuring the efficiency of decision making units,” European Journal of Operations Research, 2, 429-444.
Casu, B. and C. Girardone (2006), “Bank Competition, Concentration and Efficiency in the Single European Market,” Manchester School, 74, 441-468.
Chen, K.H. and H.Y. Yang (2011), “A Cross-country comparison of productivity growth using the generalized meta-frontier Malmquist productivity index: With application to banking industries in Taiwan and China,” Journal of Productivity Analysis, 35(3), 197-212.
De Bandt, O. and E.P. Davis (2000), “Competition, Contestability and Market Structure in European Banking Sectors on the Eve of EMU,” Journal of Banking and Finance, 24, 1045-1066.
Delis, M.D. and E.G. Tsionas (2009), “The Joint Estimation of Bank-level Market Power and Efficiency,” Journal of Banking and Finance, 33, 1842-1850.
Fitzpatrick, T. and McQuinn, K. (2008), “Measuring bank profit efficiency,” Applied Financial Economics, 18, 1-8.
Greene, W.H. (2003), “Simulated likelihood estimation of the normal-gamma stochastic frontier function,” Journal of Productivity Analysis, 19, 179-190.
Greene, W.H. (2010), “A stochastic frontier model with correction for sample selection,” Journal of Productivity Analysis, 34, 15-24.
Huang, C.J., T.H. Huang, and N.H. Liu (2014), “A New Approach to Estimating the Metafrontier Production Function Based on a Stochastic Frontier Framework,” Journal of Productivity Analysis, 42, 241-254.
Huang, T.H., and N.H. Liu (2013), “Formulation and joint estimation of the Lerner index and cost efficiency for banks using copula methods,” manuscript.
Huang, T.H. (2000), “Estimating X-efficiency in Taiwanese banking using a translog shadow profit function,” Journal of Productivity Analysis, 14, 225-245.
Huang, T.H., L.C. Chiang, K.C. Chen, and P.H. Chiu (2010), “An application of the meta-frontier cost function to the study of bank efficiencies and technology gaps in 16 European countries,” Management Review, 29, 25-43.
Kasman, A. and C. Yildirim (2006), “Cost and profit efficiencies in transition banking: the case of new EU members,” Applied Economics, 38, 1079-90.
Koetter, M., J. Kolari, and L. Spierdijk (2012), “Enjoying the Quiet Life under Deregulation? Evidence from Adjusted Lerner Indices for U.S. Banks,” Review of Economics and Statistics, 94, 462-480.
Koetter, M. and T. Poghosyan (2009), “The Identification of Technology Regimes in Banking: Implications for the Marker Power-fragility Nexus,” Journal of Banking and Finance, 33, 1413-1422.
Koutsomanoli-Filippaki, A., E. Mamatzakis, and C. Staikouras (2009), “Structural reforms and banking efficiency in the new EU States,” Journal of Policy Modeling, 31, 17-21.
Lai, H.P. and C.J. Huang (2013), “Maximum Likelihood Estimation of Seemingly Unrelated Stochastic Frontier Regressions,” Journal of Productivity Analysis, 40, 1-14.
Lau, L. (1982), “On identifying the degree of competitiveness from industry price and output data,” Economics Letters, 10, 93-99.
Lerner, A.P. (1934), “The Concept of Monopoly and the Measurement of Monopoly Power,” Review of Economic Studies, 1, 157-175.
Maudos, J. and J. Fernández de Guevara (2004), “Factors Explaining the Interest Margin in the Banking Sectors of the European Union,” Journal of Banking and Finance, 28, 2259-2281.
Maudos, J. and J. Fernández de Guevara (2007), “The Cost of Market Power in Banking: Social Welfare Loss vs. Cost Inefficiency,” Journal of Banking and Finance, 31, 2103-2125.
Meeusen, W. and J. van den Broeck (1977), “Efficiency Estimation from Cobb-Douglas Production Functions with Composed Error,” International Economic Review, 18, 435-444.
Molyneux, P., D.M. Lloyd-Williams, and J. Thornton (1994), “Competitive conditions in European banking,” Journal of Banking and Finance, 18, 445-459.
Molyneux, P., J. Thornton, and D.M. Lloyd-Williams (1996), “Competition and market contestability in Japanese commercial banking,” Journal of Economics and Business, 48, 33-45.
Panzar, J.C. and J.N. Rosse (1987), “Testing for Monopoly Equilibrium,” Journal of Industrial Economics, 35, 443-456.
O’Donnell, C.J., D.S.P. Rao, and G.E. Battese (2008), “Metafrontier Frameworks for the Study of Firm-Level Efficiencies and Technology Ratios,” Empirical Economics, 34, 231-255.
Sklar, A. (1959), “Functions de Répartition àn Dimensions et Leurs Marges,” Publications de l’Institut de Statistique de L’Université de Paris, 8, 229-231.
Tsay, W.J., C.J. Huang, T.T. Fu, and I.L. Ho (2013), “A simple closed-form approximation for the cumulative distribution function of the composite error of stochastic frontier models,” Journal of Productivity Analysis, 39, 259-269.
Turk-Ariss, R. (2009), “Competitive Behavior in Middle East and North Africa Banking Systems,” Quarterly Review of Economics and Finance, 49, 693-710.
Turk-Ariss, R. (2010), “On the Implications of Market Power in Banking: Evidence from Developing Countries,” Journal of Banking and Finance, 34, 765-775.
Van Leuvensteijn, M., J.A. Bikker, Adrian A.R.J.M. van Rixtel, and C.K. Sorensen (2011), “A new approach to measuring competition in the loan markets of the euro area,” Applied Economics, 43, 3155-3167.
Van Leuvensteijn, M., C.K. Sorensen, J.A. Bikker, Adrian A.R.J.M. van Rixtel (2013), “Impact of bank competition on the interest rate pass-through in the euro area,” Applied Economics, 45, 1359-1380.
Vennet, R.V. (2002), “Cost and profit efficiency of financial conglomerates and universal banks in Europe,” Journal of Money, Credit, and Banking, 34, 254-282.
Williams, J. (2012), “Efficiency and market power in Latin American banking,” Journal of Financial Stability, 8, 263-276.		zh_TW