Competition and efficiency in the mexican banking industry theory and empirical evidence

Jes ú s has studied the relationship between market structure and efficiency with bank performance and competition in the Latin American banking industry since his doctoral dissertation.

the Mexican Banking Industry

Competition and Efficiency in the Mexican Banking Industry

Theory and Empirical Evidence

Sara G Castellanos , Gustavo A Del Á ngel , and Jes ú s G Garza-Garc í a

Palgrave

macmillan

Copyright © Sara G Castellanos, Gustavo A Del Ángel, and Jesús G Garza-García 2016

Softcover reprint of the hardcover 1st edition 2016 978-1-137-46528-3 All rights reserved No reproduction, copy or transmission of this publication may be made without written permission No portion of this publication may be reproduced, copied or transmitted save with written permission In accordance with the provisions of the Copyright, Designs and Patents Act

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ISBN 978-1-349-55677-9

E-PDF ISBN: 978–1–137–51841–5

DOI: 10.1057/9781137518415

Library of Congress Cataloging-in-Publication Data

Castellanos, Sara G (Sara Gabriela), 1968–

Competition and effi ciency in the Mexican banking industry : theory and empirical evidence / by Sara G Castellanos, Gustavo A Del Ángel and Jesús G Garza-García

pages cm

Includes bibliographical references and index

1 Banks and banking—Mexico 2 Competition I Angel, Gustavo A del

II Garza-García, Jesús Gustavo III Title

HG2714.C37 2015

A catalogue record for the book is available from the British Library

SGC, GD, JGGG

List of Figures and Tables ix

5 Analysis of Competition and Efficiency in the Mexican

Figures

Tables

A.3.1 Authorization to new commercial banks after the 1995 crisis 67

5.4 Major changes to Mexico’s banking institutional framework 99

Reform to the Law for Transparent and Ordered

A.6.2 ROA of development banks and commercial banks,

A.6.3 Delinquency index of the credit portfolio of

Competition in economic activities is relevant for any economy since greater competition improves the efficient allocation of resources enhancing social welfare Mexico is a particularly representative case The lack of competition is visible in various sectors of the Mexican economy, among them telecommunications, aircraft, media, food and agro-industrial goods, and mining In fact, some of the most dynamic sectors of the Mexican economy are considered highly concentrated and show low lev-els of competition There are consequently effects in the efficiency of markets

Since several years ago, competition in the banking industry has been

at the center of the public debate and has caught the attention of the Mexican financial authorities Likewise, competition in the financial sector has drawn regulator’s attention in most of the world This is not accidental The nature of the financial activities is prone to market failures: presence of multiproduct firms, a production function with scale and scope economies, high entry costs, firms that manage risk and information of economic agents, high regulation and entry barriers, among others It is not surpris-ing that credit to GDP in Mexico shows very low levels compared to its peer economies; net interest margins have remained high and financial inclusion is low

The financial sector is particularly special because of the well-known functions that it performs in the economy, its unmistakable effect on eco-nomic growth and its fiduciary role in society Hence, obstacles to competi-tion that affect efficiency have ramifications in all the economy In fact, the expansion of financial services would further enhance growth since lack of financing is one of the main constraints for firms in Mexico

Our aim in writing this book is twofold We are interested in ing the general question of the importance of competition and efficiency

answer-in bankanswer-ing And second, we are answer-interested answer-in havanswer-ing a precise evaluation

of competition and efficiency of banks in Mexico, and to document a clear view of the status of competition in the financial industry of that

country Overall, our aim is to better understand how policies that have been implemented during the last decade are framed to promote com-petition in the Mexican banking industry It also helps to establish a cor-respondence between academic studies, policy assessments and current policies A recently enacted financial reform in Mexico aims to foster the competitive conditions of the banking industry and this is discussed in the book

The writing of this book started in 2012 as a working paper written

by Jes ú s and Sara, “Competition and Efficiency in the Mexican Banking Sector.” This paper was presented at the Latin American Meetings of the Econometric Society (Mexico City, November 2013), where it grabbed the attention of editorial staff of Palgrave Macmillan who contacted Sara and proposed to her writing this book As Sara and Jes ú s realized that their research might spinoff to a broader work it became evident the need to bring on board a third author, Gustavo, who has expertise in the evolution and structure of the Mexican banking system

Jes ú s has studied the relationship between market structure and efficiency with bank performance and competition in the Latin American banking industry since his doctoral dissertation In addition, he has published sev-eral papers about market power, efficiency, productivity, and competition

in Latin American banking and more recently focusing on the Mexican banking industry Among his most recent studies regarding Mexican bank-ing, Jes ú s has studied the influence of market power on bank profits, the determinants and evolution of bank efficiency, and the relationship between bank competition and financial stability

Sara, who has worked as economist in the banking industry and in the central bank, has several contributions to the banking literature that explain the effect of regulations and policy in the activity of the Mexican financial markets As the chief economist of the Mexican antitrust author-ity, Sara headed the efforts to produce the document “Research and Recommendations on Competition Conditions in the Financial Sector and its Markets,” which that authority published in 2014, to fulfill that author-ity’s mandate according to the financial reform to assess the conditions of competition in the financial markets and, formulate recommendations to financial authorities to enhance competition in the system and its markets

as well as exercise its powers to sanction monopolistic practices and other restrictions to the efficient functioning of the markets in this system Gustavo has published several books and papers about the history and structural evolution of Mexican banks during the last century The waves of consolidation of financial intermediaries and the persistent concentration of the banking system have been always present in his work, as well as the epi-sodes when the industry has opened This is essential to explaining some of

the sources of concentration in the Mexican banking industry, and to have a long term view of the structural changes until the most recent events The writing of the book presented challenges Although all of the authors study the banking industry, the areas of expertise are different and

a clearer structure and framework of the contents was needed to enrich the book Comprehensive literature reviews on the analysis of competition and efficiency in the banking industry generally and in Mexico’s banking

in particular were natural extensions of the seminal article Also, because

of the ebb and flow observed in the consolidation of this system through time and the importance attached to concentration as a potential source

of market power, we decided to provide the reader with the background that allows a better understanding of Mexico’s banking industry develop-ment and challenges Lastly, since an ambitious financial reform that modi-fied 34 laws and codes took place in 2014, with an important emphasis

in competition issues, we decided that our book would not be complete without offering the readers a general view of this reform and its possible consequences

Notwithstanding the technical work, the framing of aspects related to policy always poses a challenge The development of a policy to foster com-petition in the financial system, from the reduction of entry barriers to the enactment of the 2014 financial reform, is still work in progress and thus it

is relatively early to assess some of its results, and consequently to have an adequate analytical frame Regarding the role of the regulators in competi-tion, there is not a last word about the role of different regulators to assess, prevent and enforce the law in anticompetitive practices; nevertheless the authors agreed to take a stance in this matter A further challenge was that there is not a vast number of studies about competition in the Mexican financial system, so there are not many points of reference in the literature for every topic discussed in the book However, there is a critical mass of papers, books and policy reports published that preceded this book and allow having a solid base for the analysis

In its origin this book would not have been written without the agement and support of the heads of BBVA Research, Jorge Sicilia, Alicia Garc í a-Herrero, and Carlos Serrano Valuable comments to a draft of chapter 5

encour-in its article form were provided by various participants at workshops at BBVA Bancomer, Banco de M é xico (Central Bank of Mexico) and the Latin American Meetings of the Econometric Society of 2013 Gustavo’s

about the structure of the Mexican banking system and the recent ments Sara benefited from multiple conversations with Biliana Alexandrova, Rafael Del Villar, Blanca Nelly Flores, Lorenza Mart í nez, Alberto Mendoza,

develop-and Francisco Sol í s to understdevelop-and payment systems develop-and instruments for the writing of those sections of the book Valuable guidance throughout the editorial process was provided by Leila Campoli and Sarah Lawrence, from Palgrave Macmillan We thank very much all of them

The views expressed in this book represent those of the authors and do not necessarily those of the institutions where they work at present or have worked in the past

INTRODUCTION

increas-ing attention of policymakers and researchers The structure of the financial industry and the interaction among its players has changed sub-stantially in the preceding years, particularly after the 2008 global economic crisis However, scholars have not been able to agree so far on, or resolve how, to accurately analyze competition in the banking system and how the state of competition relates to the efficiency and overall stability of the banking system All these questions are relevant for the implementation

of competition policy and to clarify key theoretical aspects of tion in the financial markets In this book, our analysis of competition in the Mexican financial system provides some answers to these important questions

The central finding of this book is that competition enhances the ciency of the Mexican banking sector We show that the level of competi-tion of Mexican banks increased from 2002 to 2005, achieving its highest level in 2008 It is important to mention that during the period 2006–2008,

effi-16 commercial banks entered the market, which could explain the ment in the competitive levels in that period Afterward, and probably due

improve-to the financial crisis, there was a decline in the competition levels, larly in 2009, and a weak recovery thereafter

We find that besides competition, other variables that increase Mexican banks’ efficiency are the level of capitalization and loan intensity Noninterest rate expenses and nonperforming loans, on the other hand, decrease bank efficiency, as also do higher inflation rates The results suggest that overall efficiency of Mexican banks increased during the last decade until 2008, once the global financial crisis started, when efficiency declined noticeably and has gradually improved since then However, it has not recovered the levels observed before the crisis Regarding the relative efficiency of local

or foreign ownership of banks, we show that the system’s trend is a shared

characteristic among both local and foreign banks However, local banks are more efficient Banks that became foreign through a merger or acquisition are more efficient than de novo banks, and the Spanish banks display higher efficiency indexes than those of other nationalities

This book also shows that designing a competition policy for the cial industry requires an in-depth analysis of the conditions of the mar-ket This is because it needs to be effective and at the same time it may increase the regulatory burden on financial institutions Mexico’s banking system constitutes an interesting case study for various reasons Mexico is a developing country with a well-regulated and sound banking system, and

finan-an industry with a strong participation of global systemic bfinan-anks However,

it continues to be a financial system with low financial deepening in the economy This is the result of the changes experienced by the Mexican financial system over the last 30 years, which have completely transformed the architecture, the structure of ownership and control, as well as the com-petitive conditions of the financial system

In spite of the growing literature about the Mexican banking sector, in general, and competition conditions, in particular, the analysis of competi-tion in the emerging financial markets is still scarce, although the literature and financial press make a constant reference to the Mexican banking sector’s competition conditions and well functioning An ongoing argument about the Mexican financial system is that the banking system experiences low levels of competition, thus undermining its role as a catalyst in the poten-tial growth of the economy (Haber 2005; Hanson 2010) This argument

is usually based on the high concentration ratios that have been persistent throughout the history of the Mexican banking system It is important to note that a highly concentrated banking sector does not necessarily imply low levels of competition Thus, other elements such as profit margins and prices must be taken into account when analyzing the competition condi-tions in the banking system

We seek to contribute to the understanding of competition policy in the banking system and to explain how levels of competition relate to the efficiency of banks The rest of the book is organized into five chapters that provide summaries of the theoretical literature on competition, efficiency and productivity in the banking sector, and the relevant applications of such models for the Mexican banking system

throughout the book as well as a review of the main banking literature on market power, efficiency, and competition The chapter commences with

a discussion of the market power and efficiency hypotheses of industrial organization, which posit contrasting views about the relationship between market power and profitability

The traditional structure-conduct performance (SCP) hypothesis poses that market power has a direct relationship with profitability, in which firms can set less favorable prices to consumers in more concentrated mar-kets as a result of anticompetitive behavior In this framework, the char-acteristics of the structure of the market, such as the number and types of firms in a market, entry barriers, market share and market concentration, competition and regulatory policies, are relevant to determine the conduct

pro-of the main market participants A related theory is the so-called market power hypothesis (RMP), in which firms with large market shares and well-differentiated products exert pricing advantages and earn profits above competitive levels (Berger 1995) The first studies that investigated these hypotheses found a positive relationship between concentration and profits, conducive of collusion (see Gilbert 1984; Rhoades 1977, 1982, among others)

The alternative efficient-structure (ES) hypothesis challenges this view

by arguing that higher concentration is often derived from greater market share of more efficient firms That is, higher levels of concentration are often the result of greater market shares of firms that achieve lower costs than others Berger (1995) elaborated further and suggested that there are two distinct ES hypotheses: (a) X-efficiency, in which firms with greater management skills and better technologies have lower costs and therefore higher profits; and (b) scale-efficiency, where firms produce at more effi-cient scales than others lowering their unit costs and boosting profits Hence, while the market power hypotheses postulate that market power has a direct relationship with profitability, in which firms set less favorable prices to consumers in more concentrated markets as a result of anticom-petitive behavior, the efficiency hypothesis proposes that higher levels of concentration are often the result of higher market shares of firms that are more efficient than others These hypotheses have been thoroughly debated

in the academic circles, and although empirical evidence testing the market power and efficient-structure hypotheses has found similar results, there are distinct interpretations The different interpretations of the aforementioned relationship as well as the empirical evidence are analyzed in this section While the majority of the original studies focused on the banking system of the United States and found support for the market power hypothesis, other studies have extended the time period of study, adding different geographi-cal locations, and have found contrasting results

As for the developments for measuring efficiency and competition in the banking industry, we explain various approaches and methodologies to measure both efficiency and competition The assessment of efficiency has evolved from standard accounting ratios to best-practice frontiers, in which any deviations from the frontier are considered inefficiencies Two distinct

approaches to measure efficiency are addressed in this section: parametric and nonparametric Parametric methodologies, such as the stochastic fron-tier approach, are based on specific functional models for cost, profit or pro-duction relationships considering specific inputs, outputs, and other factors that rely on a theoretical hypothesis Nonparametric methodologies, such

as the data envelopment analysis (DEA), are based on a production or cost frontier Although these techniques rely on similar efficiency concepts, in sharp contrast with the parametric methodologies, they generate the func-tions of interest, for example, the production function, from the observed data instead of a specific functional form In the analysis of the distance to

a best-practice frontier in order to measure efficiency, the concept of the displacement of such frontier, from one period to another, hints at produc-tivity changes In theory, such displacement of the best-practice frontier alongside the changes in the distance from banks to the frontier denotes the level of productivity changes We discuss the nonparametric Malmquist index to measure productivity in this section

Moreover, following the new industrial organization theory, tural methodologies to measure competition are analyzed considering that the traditional structural approach does not take into consideration the revenue-cost structure of firms

The empirical evidence of some of the approaches and gies used are also mentioned in this section Although most of the original applications on both the market power and efficiency hypotheses and on bank efficiency focus on studying the US banking system up to date, there

methodolo-is an increasing number of applications of these models for the banking tors of other countries and regions This has been possible as data constraints have been relaxed as a result of new models or as more complete data sets about banks have become available

The last section of this chapter is dedicated to a more recent literature that examines the relationship between competition among banks and the stability of the financial system There are two contrasting views Some aca-demics have argued that more competition enhances the stability of the system, the so-called “competition-stability” view, while others suggest a negative relationship between bank competition and financial stability, sup-porting the “competition-fragility” view These views have initially been tested in a few studies for the banking system of the United States and, increasingly, for other countries, in both cases with mixed evidence Chapter 3 explains the evolution of the Mexican financial industry The goal of this chapter is to describe in detail the evolution of the Mexican banking sector and how it underwent cycles of consolidation This analysis addresses the structure of the industry: players, market shares, main market segments, and transformation in ownership In contrast to other recent

studies that focus in short periods of time, we elaborate in a more detailed, long-term view This is important because the Mexican banking sector has experienced many changes during the last 30 years, and the most sig-nificant have taken place over the last 15 years Particularly, in the last

30 years, the Mexican banking industry has changed from being a local industry, protected and established by specialized intermediaries, to a state-owned industry after an expropriation in 1982, to finally become a pri-vate industry, and more recently an industry made up of financial groups, many of them controlled by major international financial corporations This was not a smooth process; on the contrary, it was a complex devel-opment that generated high costs to the Mexican economy Events such

as the nationalization in 1982 and the crisis in 1995 changed the tion of this evolution irreversibly and triggered unexpected consequences Despite the internationalization of the Mexican banking system being part

direc-of an ongoing globalization process that has been direc-of particular relevance

in Latin America, the expansion of international banking in Mexico ally was accelerated by the crisis and was made possible due to the North American Free Trade Agreement (NAFTA) The last section of the chapter

actu-is a description of the situation of the banking sector and the changes in regulation—mostly to reduce entry barriers and stimulate credit growth—before the financial reform of 2014 This chapter highlights the driving forces for the consolidation of the banking system, and the process to improve the conditions of competition

Chapter 4 explains what is currently known about competition in the Mexican banking industry The goal of this chapter is to map the state of knowledge, contrast the studies about Mexico with studies in other econo-mies, and discuss the main limitations of the current studies First, this is important to dispel myths and platitudes about competition in the Mexican banking sector Second, it is also vital to assess the type of analysis needed

by authorities who implement competition policies and discern whether it differs from other views

As in other countries, the lack of detailed public data about the Mexican financial system has limited the analysis of these topics However, the avail-ability of such data since the beginning of the twenty-first century has allowed more quantitative research Most studies that measure competi-tion in Mexico’s banking sector rely on a combination of concentration indexes and regulation/institutional analysis of market contestability or on the estimation of the H-statistic proposed by Panzar and Rosse (1987), which is characterized by demanding less data in its estimation than other models like the one of Bresnahan (1982) and Lau (1982) Although most of the studies document an imperfectly competitive market, with competition problems in some segments like the credit card market, there are also some

studies that have documented episodes of fierce competition or competitive” behavior among Mexican banks In such a supercompetition, banks run at levels of output where the marginal cost exceeds the marginal revenue because they believe that by expanding their market shares, even

“super-by incurring losses, they obtain a positive present value of expected future returns Another finding of these studies is that the degree of competi-tion is not homogeneous across markets for different financial products Some markets that have experienced entry of nonbank intermediaries, like mortgages, or competition from foreign institutions or capital markets, like corporate credit, are found in empirical studies to be more competitive than the credit cards or deposits markets where banks predominate

Because of the empirical exercise that we undertake in the following chapter, measurements of banking sector’s efficiency using nonparametric techniques, such as DEA, are of special interest in the review of studies about the Mexican banking system In fact, these tools have been regularly employed in Mexico, particularly in light of the 1995 Tequila crisis and the liberalization that followed it The view that emerges from this set of studies

is that although the sector’s efficiency has increased overall since then, ciency differs among different groups or types of banks

By contrast, in regards to the stability” and fragility” views, it is found from the scant studies that are available for Mexico that they vary according to the period analyzed and whether the Mexican banking system is examined alone or with a set of other countries

Chapter 5 provides an estimation of efficiency indicators for Mexico’s banking system for the period 2002–2012 using the DEA technique Besides presenting estimations for the aftermath of the 2008 financial cri-sis that allow to examine its effect on the system’s efficiency compared with previous results, it tests through Tobit panel regressions the relevance

of several factors that affect efficiency, including bank characteristics, roeconomic and regulatory conditions, and market structure The most salient innovation with respect to previous studies is the estimation of the so-called Boone competition index (Boone, Griffith, and Harrison 2005) to assess competition and its inclusion as an explanatory variable

mac-in the model of bank efficiency determmac-inants But also of mac-interest mac-in view

of the local debates on the merits of the predominant presence of foreign banks in the system is the comparison of efficiency measures among the different groups of banks Our efficiency estimates allow us to look at this issue in a very detailed manner

Chapter 6 , starts with a brief discussion on the role of the government

in promoting competition in the financial system and a description of the regulatory framework and situation of the banking sector in place before the financial reform of 2014 Then it describes the comprehensive financial

reform that took place in Mexico in January 2014 as well as the key ings and recommendations of the study by Mexico’s antitrust authority

find-on the competitive cfind-onditifind-ons of the financial sector and its markets, with

an emphasis on those that pertain the banking system This chapter trays how competition policy in Mexico did not start from scratch, as the financial reforms of 2014 were preceded by various law reforms intended

por-to improve consumer protection, as a means por-to improve the conditions in which financial services were provided However, competition policy was an important ingredient of the financial reform reflected in both modifications

of various financial laws and as the mandate for undertaking a sive study that allowed to both propose further reforms to the regulators and to investigate anticompetitive practices The chapter concludes with a description of the effects of the reform so far and an assessment of whether

comprehen-we can expect a more efficient and competitive banking system in the future

as a result of these reforms

LITERATURE REVIEW OF BANKING STUDIES

2.1 Introduction

Banks are important in mobilizing and allocating savings in an economy and can solve important moral hazard and adverse selection problems by moni-toring and screening borrowers and depositors Besides, banks are important

in directing funds where they are most needed in an efficient manner and have direct implications on capital allocation, industrial expansion, and eco-nomic growth (Berger, Demirguc-Kunt, and Haubrich 2003; Levine 1997) Banks also play an important role in diminishing informational asymmetries and risks in the financial system Hence, the study of the banking industry and its impact on the economy is of the utmost importance The effects of concentration and competition on bank performance are pertinent since they have important policy implications A recent global trend of consolida-tion in the banking sector has intensified, generating important debates on its effects on the profitability of banks, consumer costs, the efficiency in allo-cating resources in an economy, and on overall financial stability

In this chapter we present and overview of this literature, starting with

a brief survey of the industrial organization theories of the market power and efficient-structure hypotheses that have been put forward to explain the relationship between the structure of the banking sector and its per-formance in section 2.2 Then, section 2.3 is dedicated to discussing the measurement of banks’ efficiency, which is key in the proper assessment

of the structure and profitability of the banking industry and, ultimately,

of competition conditions Two main methodologies, parametric and parametric, are discussed and analyzed as well as various examples of the empirical literature Furthermore, banking productivity is presented follow-ing the efficiency discussion The nonparametric Malmquist productivity index is detailed followed by some empirical evidence in the literature The discussion of the studies about competition in banking follows in section 2.4; here again two broad categories are distinguished; structural models

that follow the market power and efficient structure theories and structural models in line with the new industrial organization theory Some

non-of the latter models are discussed in this section Section 2.5 covers some non-of the most representative empirical studies of this vast and growing literature, which spans various time periods and geographical areas However, we defer the discussion of the studies for the Mexican banking sector to chapter 4 Section 2.6 deals with a more recent but growing literature strand on the relationship between bank competition and financial stability; akin to the market power and efficient structure models of the relationship between banking structure and profits, two opposing views of the effect of compe-tition among banks and stability of the banking system have been posed, namely the “competition-stability” and “competition-fragility” views, giv-ing place to growing academic discussions Some conclusions are presented

in the final section 2.7

2.2 Market Power versus Efficiency

Industrial organization studies have for long analyzed the concentration–profitability relationship in banking to assess if the structural features of a market influence the performance of banks in setting above-competitive prices, such as higher loan rates and lower deposit rates The traditional structure-conduct-performance (SCP) hypothesis, first proposed by Bain (1956), posits that market power has a direct relationship with profitability,

in which firms can set less favorable prices to consumers in more trated markets as a result of anti-competitive behavior (Berger and Hannan 1989) According to the SCP hypothesis, the characteristics of the structure

concen-of the market are relevant to determine the conduct concen-of the main market participants Therefore, the number and types of firms in a market, entry barriers, market share and market concentration, and competition and reg-ulatory policies become relevant to analyze the structure of the market According to the market power hypotheses a direct link between structure and conduct (profitability and performance) can be established The analysis

of bank performance has important social and economic impacts since the efficient and optimal allocation of resources through intermediation can produce welfare optimization (Dansby and Willig 1979)

A related theory is the so-called relative-market power hypothesis (RMP), in which firms with large market shares and well-differentiated products exert pricing advantages and earn profits above competitive levels (Berger 1995) The first studies that investigated these hypotheses found a positive relationship between concentration and profits, condu-cive of collusion (see Gilbert 1984; Rhoades 1977, 1982, among others) These studies often employed simple measures of concentration such as

the Herfindahl-Hirschman index (HHI) 1 or an n -firm concentration ratio

as exogenous indicators of market power and most of them were limited

to analyzing the US banking markets, and used cross-section static panels

As said before, there could be a direct relationship between the

struc-tural features of the industry with bank performance, producing collusion

effects in the market According to economic theory, the ability of a firm

i to increase prices above its marginal cost depends on the price-elasticity

( η ) of the industry, the market share of each firm ( MS i ), and the production

variation of the reaming firms participating in the industry Accordingly, the

following profit equation for firm i is (Rodríguez-Montemayor 2003):

the costs of firm i respectively, whereas Q is the total production of the

industry Next, by differentiating equation 1 by q we obtain the first-order

δ

the remaining terms represent the marginal revenue of firm i Therefore, the

marginal revenue can be defined as:

P⎡⎣⎡⎡1 (dP//dQ Q P q Q)( / )Q Q P P ( / q Q i i Q Q Q)⎤⎦ ⎤⎤⎤ P P−(P P P/ )s s i (3)

Substituting this equation in equation (2), we obtain the market

equilib-rium with marginal costs:

Multiplying equation (5) by the market share and summing for n firms we

obtain an equation related to average margins (prices minus costs) for the

industry with the HHI:

g

i

(P s i − CMg s CMg i i P) ) )=∑ ∑s s i i2/η ⇒ (((P P − CMg / CM / CMg g)))P P P =HHI HHI//η (6)

Now, allowing changes in production for all firms when firm i decides to

condi-tion equacondi-tion:

The marginal revenue is now transformed to obtain an expression in terms

of price elasticity and market share:

Finally, we establish an equation in terms of the market share, the price

elasticity of demand, and the variations in production of the competitive

firms (joint reaction):

The average margins of all the industry (profitability of the industry) is

obtained modeling for the interactions of firms when firm i decides to

change the production level If the changes in production are proportional

Multiplying equation (10) by market share and adding the n firms, the

industry profitability is obtained in terms of the HHI:

When A = 0, the industry follows a Cournot approach in which the

expectation is that competitors do not react; on the other hand, if A = 1

every firm supposes a complete compensation from its competitors, which

would establish a state of monopoly In fact, the equation above defines

the well-known Lerner index Depending on the range of decision

mak-ing of the firms, it can be said that the price can lie between the ranges

monopolic prices The theory suggests that the most influential variables

that affect the behavior of firms are the market structure and entry barriers

to industry j in which firm i operates, thus:

dQ i dddqddq q i i f CR E f ffff1C j E E j j,X ij) (12)

Therefore, the profitability equation can be stated as:

term

The following equation is the traditional market power equation used to

test the SCP hypothesis:

the return on assets or return on equity, or sometimes a price-to-cost ratio

CR denotes the degree of concentration in the industry usually measured

with the HHI or an n -concentration ratio, Z ’s a vector of other

explana-tory exogenous variables in the model, and i ’s the firm or observation In

con-centration of the market has a direct influence on profitability, indicative of

collusion If, however, we include market share as an explanatory variable

alongside the level of concentration, addressing both the SCP and RMP

hypothesis holds in which firms with large market shares and

well-differen-tiated products exert pricing advantages and earn profits above competitive

levels (Berger 1995) In both cases the market power models suggest that

profitability is determined by the structural features of the market

However, Demsetz (1973) and Peltzman (1977), among others,

chal-lenged the market power views by arguing that higher concentration is

often derived from greater market share of more efficient firms, proposing

the alternative efficient-structure (ES) hypothesis Hence, under the ES

hypothesis higher levels of concentration are often the result of greater

market shares of firms that are more efficient (lower costs) than others

(Berger and Hannan 1989; Smirlock, Guilligan, and Marshall 1984) Berger (1995) elaborated further and suggested that there are two distinct ES hypotheses: X-efficiency, in which firms with greater management skills and better technologies have lower costs and therefore higher profits; and scale-efficiency, where firms produce at more efficient scales than others, lowering their unit costs and boosting profits Empirical evidence employ-ing the two market-power and two efficient-structure hypotheses have found similar results but have interpreted them differently Studies such as Kurtz and Rhoades (1991), Rhoades (1985) and Shepherd (1982) found a positive and significant relationship between market share and profitability, supporting the RMP hypothesis On the other hand, Evanoff and Fortier (1988), Smirlock (1985), and Smirlock et al (1984) argued that the same result is supportive of the ES hypothesis in the absence of direct measures

of efficiency, suggesting that more efficient banks normally obtain greater market share than otherwise Berger (1995) advanced the literature by test-ing the two market-power and efficient-structure hypotheses including direct measures of efficiency, namely for X- and scale-efficiencies He sug-gests a structural relationship for the ES and market-power (MP) hypoth-eses and then derives a single equation that involves both the market power and efficiency hypotheses:

CR j = f f MS for f M fffffff MS M MS M MS M MS M i ff for ff all i in j all i in j) e ij2 (18)

where EFF denotes the efficiency measure: either X-efficiency or scale efficiency, Z ’s a vector of explanatory variables, and e the random errors

(Berger 1995) In equation (16), greater efficiency should increase the degree of profitability In equation (17), more efficient firms are expected

to have larger market shares due to lower marginal costs (ES hypothesis) Equation (18) implies that greater market share results in higher levels of concentration

On the other hand, the structural market power model (which includes the SCP and RMP hypotheses) is defined:

π i = f f f4( (EFF Z EFF i i i Z ij ij4j) )+ +∈ ij4 (19)

P P P i f f ff ffffff5(STRUC Z S RUC STRUC Z STRUC i ij ij5j)+ +∈ ij5 (20)

MS

M

MS

where P is the vector of prices, STRUC is a measure of market structure (either concentration or market share) and CR is the measure of concentra-

tion Hence, in equation 19 profitability is determined by prices, in equation

20 prices are then determined by the structure of the market (indicative of collusion) and equation 21 suggests a positive correlation between market share and market concentration

By joining all equations in one, we obtain equation (22), which includes all the market power and efficiency hypotheses:

π i = f f (CR M C CR M C j j j M M MS M S X S X i i i i −EFF S F i i S − EFF Z EFF Z EFF F F F i i i i ij i ij i j)+e i (22) Under the SCP hypothesis, the degree of concentration is expected to be positive and significant while the efficiency and market share variables are not significant Following the same analysis, a positive and significant rela-tionship between market share and profits would be supportive of the RMP hypothesis Finally, a direct and significant relationship between either X-efficiency and/or scale efficiency would indicate that the ES hypothesis holds, when the market power variables are not significant

An important policy question arises if the market power models hold, then antitrust policies are desirable, but if the ES hypotheses are true, then these measures may be counterproductive In the market power models, further concentration through mergers and acquisitions may result in col-lusion effects such as less favorable prices to consumers, reducing total con-sumer surplus Some studies suggest that high concentration is usually a signal of an uncompetitive and inefficient market (Demirguc-Kunt, Laeven and Levine 2003) As an example, some authors argue that banks operat-ing in highly concentrated markets charge higher loan rates to consumers, pay lower rates to depositors, and react slowly to the central bank’s policy actions (Berger and Hannan 1989; Hannan and Berger 1991; Neumark and Sharpe 1992, among others) On the other hand, if the efficiency models stand, then total consumer surplus is enhanced (see Berger 1995), and under this perspective, competitive markets may be both concentrated and effi-cient banking systems (Demirguc-Kunt et al 2003) The empirical literature has tried to solve this problem by testing the market power and efficiency models in various markets for different time periods and in a diverse array

of geographical locations However, the results are not conclusive of either hypothesis and vary depending of the methodology employed, the variables used, the time period, and the country or countries under study

Most of the original studies on both the MP and ES hypotheses focused

on studying the US banking system and the majority was supportive of the market power models Berger and Hannan (1989) analyzed the price–concentration relationship to test the SCP hypothesis for 470 banks in 195

local US banking markets using quarterly data for 1983–1985 Their results were strongly consistent with the SCP hypothesis, since banks in more con-centrated markets pay less deposit rates than otherwise Calem and Carlino (1991) also analyze the SCP hypothesis by using monthly data for 466 com-mercial and federal saving banks in the United States in 1985 The empirical results suggest that banks behave in a non-competitive manner when set-ting deposit rates, although their findings are not limited to concentrated markets Other studies have tested both the market power and efficiency hypotheses to observe their relationship with profitability, controlling for direct measures of market power and efficiency in their models

Berger (1995) advanced the literature by testing the two market-power and efficient-structure hypotheses for the US banking markets employ-ing more than 2,000 observations over a period of 10 years in the 1980s The results find limited support for the two efficient-structure hypotheses X-efficiency is found to be consistently directly related to higher profits, although the findings also suggest that the RMP model could not be dis-carded Market share was almost always positively related to higher profits after controlling for efficiency and concentration

Other studies have extended the time period of study and added ent geographical locations finding contrasting results Lloyd-Williams and Molyneux (1994) study the two contrasting market power and efficiency hypotheses in the Spanish banking system for the period 1986–1988 The results are supportive of the SCP hypothesis and the authors argue that fur-ther concentration in the market should be carefully assessed since it could harm the degree of competition Molyneux and Forbes (1995) studied the European banking industry for the period 1986–1989, finding strong evi-dence supporting the SCP hypothesis Goldberg and Rai (1996) test both the SCP and ES hypotheses for a sample of European banks for the period 1988–1991 In order to measure efficiency the authors apply the stochas-tic frontier approach to derive direct measures of X- and scale efficien-cies The results do not find a positive and significant relationship between concentration and profitability and only find support for the X-efficiency hypothesis Maudos (1998) analyzes the relationship between market struc-ture, efficiency, and profitability in the Spanish banking industry for the period 1990–1993 His findings suggest that efficiency is the main driver

differ-of greater bank performance in Spain Punt and Van Rooij (2001) study the two market power and two efficient structure hypotheses for eight European countries for the period 1992–1997 Their results were support-ive of the X-efficiency hypothesis as the main determinant of greater prof-itability Vander Vennet (2002) also tests the MP and ES hypotheses in 17 European countries for the period 1995–1996, finding support mainly for the X-efficiency hypothesis

Demirguc-Kunt et al (2003) study how concentration affects net est rate margins for a sample of over 1,400 banks in 72 countries controlling for bank-specific characteristics The main findings suggest that while con-centration increases net interest margins, they lose explanatory power once introducing other independent variables such as tighter regulations, infla-tion, and other bank-specific variables Beck, Demirgu ç -Kunt, and Levine (2003) test the relationship between the structure of the banking system and bank fragility using data for 70 countries from 1980 to 1997 and find that crises are less probable in more concentrated markets, fewer regulatory restrictions and with national institutions that foster competition M ó r é and Nagy (2003) test the SCP and RMP hypotheses for Central and Eastern European banks for the period 1998–2001 The results reject the SCP hypothesis but find evidence supportive of the RMP hypothesis Martinez Peria and Mody (2004) analyze the impact of market concentration on interest rate spreads for a group of Latin American banks during the 1990s They find that higher concentration was directly related to larger spreads and higher costs They also find that foreign banks charged lower spreads than domestic banks Bos (2004) studies whether market power affects the performance of Dutch banks by testing the traditional SCP model and a simple Cournot model The author finds that the MP hypotheses cannot be rejected although its impact on performance is weak Hahn (2005) investi-gates the determinants of banking profitability market conditions in Austria for the period 1995–2002 including more than 700 banks The author ana-lyzes the SCP, RMP, and ES hypotheses and test whether Austrian banks are contestable The results indicate that banks on average observe a certain degree of local market power, although excessive profit gains are minor Athanasoglou, Brissimis, and Delis (2005) analyze the effect of bank-specific, industry-specific, and macroeconomic variables, testing the tradi-tional SCP hypothesis, on the profitability of Greek banks for the period 1985–2001 The authors also measure profit persistence by applying the general method of moments (GMM) econometric technique The results indicate that profitability persists moderately, hinting that deviations from perfect competition are low Moreover, they find no evidence supportive

inter-of the SCP hypothesis Yu and Neus (2005) study the largest 288 banks

in Germany from 1998 to 2002 They find evidence supporting both the SCP and scale-efficiency version of the ES hypothesis, suggesting that even though higher market concentration is responsible of greater profitabil-ity, any consolidation does not come from monopolistic power but from greater scale efficiencies Tabak, Fazio, and Cajueiro (2011) analyzed the concentration–performance relationship of 17 Latin American countries, studying 495 banks for the period 2001–2008 The authors employ the stochastic frontier analysis to measure bank efficiency and its evolution over

time The results indicate that banks are more inefficient in terms of profits than costs and that concentration hinders cost efficiency Chortareas, Garza-García, and Girardone (2011) study whether market power or efficiency influence bank profits in Latin American banks for the period 1997–2005 They use the data envelopment analysis (DEA) methodology to measure the efficiency scores and test both the market power and efficiency hypoth-eses The main findings are supportive of ES hypothesis They also find that capital ratios and bank size are among the most important determinants of bank profitability in the region Mirzaei, Moore, and Liu (2013) study the empirical effects of market structure on bank profitability and stability in 40 emerging and advanced economies over 1999–2008 The authors analyze the SCP and RMP hypotheses and find support for the latter in advanced economies but no relationship of either market structure model in emerg-ing economies They also find evidence that more concentrated markets lead to greater financial instability

In conclusion, the empirical literature of the market power and ciency literature is extensive and provides with contrasting results depend-ing on the countries or regions studied, the period of time of the analysis and the methodology used However, the analysis and study of the effects of the structure of the market on the performance of banks remains an impor-tant issue of discussion, since social welfare and economic optimization may

effi-be influenced by structural market features

2.3 Measuring Bank Efficiency

During the last couple of decades, the study of the efficiency of the ing system and financial institutions has been gaining ground The estima-tion of both relative efficiency (which allows measuring efficiency between observations through time) and scale economies, which are based on tech-nological improvements, has become relevant Traditionally, accounting and financial ratios were used to determine efficiency considerations (e.g., cost over income ratio, return-on-assets, return-on-equity, fixed costs to total costs) However, recently the main focus has been to measure the distance from an optimal frontier of efficiency

Efficiency can be measured by analyzing the cost-structure of a bank or its standard profitability, both of which are based on economic optimization (minimizing costs and/or maximizing profits), in reaction to market prices and the degree of competition in a certain market (Berger and Humphrey 1997) The cost efficiency allows us to observe the distance between a cer-tain bank’s cost to a frontier (best practice behavior) and any deviation would constitute inefficiencies Efficiency can be measured as the minimi-zation of input prices subject to a certain level of output (input-oriented

approach or cost efficiency), or as a maximization of profits given a certain level of input prices (output-oriented approach or profit efficiency) In the latter case, a profit efficiency model measures how close a bank is to the maximum profit possible given a certain level of input costs (Berger and Humphrey 1997) Although there is no consensus on the best approach

to measure efficiency, some studies argue that profit efficiency generates superior results since it accounts for errors on both inputs and outputs and

is based on a more accepted economic aim of profit maximization (Berger, Hancock, and Humphrey 1993; Berger and Humphrey 1997) However, the most common approach is cost efficiency since banks are intermediaries and costs are easier to control

The first step to measure the degree of efficiency is to determine its inputs and output sources (Berger and Humphrey 1997) In the inter-mediation approach output is normally measured as the total amount of bank’s assets and its variants Inputs, in contrast, are generally considered as total labor, physical capital, deposits and other borrowed funds and in some cases equity capital Important to note is the discussion of using deposits

as an input since some studies have argued that it should be considered as

an output since banks provide ultimately services for depositors (Hughes and Mester 2008) Besides the intermediation approach, there are other approaches such as the production approach, user-cost approach, and value added approach; however, the most commonly used are the intermediation and production approaches (see Berger and Humphrey 1990)

There are two main methodologies used to estimate efficiency: ric and nonparametric methodologies Academics have used these method-ologies to account for both technical and allocative efficiencies Technical efficiency refers to the maximum available output produced by a firm with

paramet-a certparamet-ain number of inputs while paramet-allocparamet-ative efficiency refers to the best use

of inputs to produce a certain level of output (Thanassoulis 2003) The most common nonparametric methodologies are two: data envelopment analysis (DEA) and the free disposal hull (FDH) while the most common parametric methodologies are three: stochastic frontier approach (SFA), dis-tribution-free approach (DFA), and thick frontier approach (TFA)

Parametric methodologies are based on specific functional models that rely on a theoretical hypothesis The stochastic frontier approach (Aigner, Knox Lovell and Schmidt 1977), sometimes also called the econometric frontier approach, specifies a functional form modeling the cost, profit, or production relationships considering specific inputs, outputs, and other fac-tors, and assuming a random error term This approach assumes a model where inefficiencies follow an asymmetric distribution, while random errors follow a symmetric distribution (Ferrier and Lovell 1990) The model leads

to a best-practice frontier, in which any deviation to such frontier denotes

inefficiencies The DFA also specifies a frontier but assumes that the ciency of each firm is stable over time and that the error term tends to aver-age zero (Berger 1993) The TFA assumes that any deviations from predicted costs are inefficiencies (Berger and Humphrey 1994) All these models rely

effi-on specifying a functieffi-onal form to the error and disturbance terms

In equation (23), we exemplify the stochastic frontier methodology calculating X-efficiency in which a bank’s observed total cost is modeled through a multiproduct translogarithmic cost function:

ilnQ k

jh h j

(23)

input prices The linear homogeneity restrictions include:

which normalizes total cost and input prices with a specific unit price Nonparametric techniques, such as the DEA, first developed by Charnes, Cooper, and Rhodes (1978) are based on a production or cost frontier Compared to the parametric methodologies, the DEA methodology is based

on a concept of efficiency similar to the microeconomic one, differing in that the DEA production frontier is generated by observed data and not

by a specific functional form The DEA follows a mathematical approach formed by best practice observations yielding a convex production possi-bility set (PPS) (Casu and Molyneux 2003) The efficiency of an observa-tion is measured as the relative distance to the best practice frontier In the DEA, resources are typically referred to as “inputs” and the outcomes as

“outputs” A decision-making unit (DMU) transforms inputs into outputs Inputs should, in general, capture all the resources that produce the output whilst outputs should reflect all the useful outcomes on which we wish to

There are two approaches when analyzing DEA The first approach is the input-oriented model in which the model assumes the minimization of inputs in order produce a constant amount of output Thanassoulis (2003) defines it as a DMU is Pareto-efficient if it is not possible to lower anyone

of its input levels without increasing at least another input level and/or without lowering at least one of its output levels The second approach is

the output-oriented approach in which the model assumes the tion of output subject to the amount of input available Thanassoulis (2003) defines a DMU as Pareto-efficient if it is not possible to raise anyone of its output levels without lowering at least another one of its output levels and/

maximiza-or without increasing at least one of its input levels Mmaximiza-oreover, there are two variants in both models: CRS (constant returns to scale) and VRS (variable returns to scale) The model considers CRS when the DMUs are operating efficiently and at an optimum level On the other hand VRS models have

a constraint and assume there are imperfections in information, tion, and finance There have been recent debates into which models to use Many studies have used the input-oriented model since the input measures seem to be the most controllable variables in any industry, although that

competi-is not general for all industries and sectors Ferrier and Valdmancompeti-is (1996) suggest that in industries where emphasis is on cost-control, the choice

of model should be input-orientation Berger, Hancock, and Humphrey (1993) nevertheless point out that the restriction of a particular orientation may result in the neglecting of major sources of technical efficiency in a different direction In banking, a most common approach towards DEA has been the input-oriented VRS model to measure technical efficiency This approach is usually selected since banks tend to minimize costs, whereas output is normally constrained by market demand and, therefore, cannot

be controlled for The VRS model yields what is known as pure (technical) efficiency scores, in contrast to the CRS model that yields global techni-

(Thanassoulis 2003) An important measure of efficiency is scale efficiency, which is defined by the ratio: SCALE = CRS/VRS This measure of effi-ciency calculates the scale size of the productivity of the DMU The value

model calculates the input-oriented VRS, CRS and SCALE efficiencies

example of the VRS input-oriented DEA model can be observed below: The DEA VRS linear programming model can be defined as:

λ

λ λ

1

(25)

number of DMUs ranges from i = 1, , n , x 0 is a vector of input of DMU 0 ,

the DMU lies on the efficient frontier and thus the observation is fully (i.e 100%) efficient

The empirical literature of bank efficiency is vast with contrasting results depending on the methodology of efficiency employed, the regions ana-lyzed and the periods of time studied Berger and Humphrey (1994) sum-marize the efficiency research on US bank cost and profit functions, finding that X-efficiency or the ability to control costs is important in US banking, and that mergers have no significant effects on increased efficiency On the other hand they find that market concentration results in slightly less favorable prices to consumers, but has little impact on bank performance Persitiani (1996) studied the impact of postmerger activity in the US bank-ing markets between 1980 and 1990 The results concluded that acquiring banks failed to enhance postmerger X-efficiency although they increased their profitability and scale efficiencies Bhattacharyya, Lovell, and Sahay (1997) examine the productive efficiency of 70 Indian commercial banks during the ongoing period of financial liberalization (1986–1991) They use the DEA methodology to calculate radial technical efficiency scores The authors also apply the stochastic frontier approach to identify three different components in efficiency variation: a temporal component, an ownership component, and a random noise component The results show that public-owned banks were the most efficient, followed by foreign-owned banks and private banks They also find a temporal improvement in the perfor-mance of foreign-owned banks and a decline in the performance of public banks They acknowledge that government regulatory policies were key in explaining these variations

Berger and Humphrey (1997) examine the possible sources of ing differences in efficiencies for the US banking markets during the period 1990–1995 They examine three different economic efficiency measure-ments: cost-efficiency, standard profit-efficiency, and alternate profit-effi-ciency The main findings indicate that cost efficiencies are not correlated with profit efficiencies, suggesting that the three measures may be used

explain-to account for a more accurate measurement of efficiency Lozano Vivas (1997) analyzed the profit efficiency of Spanish saving banks for the period 1986–1991 The author estimates profit efficiency by using the thick frontier approach and calculated both the alternative and profit function specifications to address the competitiveness of the market Using the alter-native profit function, profit inefficiency of Spanish saving banks averaged

28 percent, and fell by 40 percent in the period of study By applying the standard profit function, there were greater average inefficiencies Overall,

the results indicate that there was no significant shift in the profit frontier during the period of study

Allen and Liu (2005) measure the economies of scale and cost cies of Canada’s six largest banks from 1983 to 2003 In order to do so, the authors estimate a pooled translog cost function and derive measures

efficien-of scale economies and relative efficiency The results indicate that larger banks seem to be more efficient than smaller ones and that over time rela-tive efficiencies have changed and the dispersion of efficiency among banks has reduced Fiordelisi, M á rques-Ibanez, and Molyneux (2010) analyze the impact of efficiency on bank risks for a large sample of European commer-cial banks They apply the stochastic frontier approach in order to calculate both cost and revenue efficiencies The authors find that a reduction in cost and revenue efficiencies increases bank’s future risks supportive of the bad management and efficiency version of the moral hazard hypothesis Overall, the main findings argue that less efficient banks might expect greater risk and lower capital levels than otherwise Fang, Hasan, and M á rton (2011) examine the cost and profit efficiencies of the banking sectors in six southeastern European countries for the period 1998–2008 The authors apply the stochastic frontier approach and find average cost efficiencies of 68.59 percent and average profit efficiencies of 53.87 percent Moreover, they show that foreign banks are associated with higher profit efficiencies but lower cost efficiencies At the same time, the efficiency gap between for-eign banks, domestic banks and government banks has narrowed through time Finally, they show that the degree of competition is directly related to cost and profit efficiencies Barth, Lin, Ma, Seade, and Song (2013) analyze whether bank regulation, supervision, and monitoring enhance or impede bank operating efficiency They studied more than four thousand banks in

72 countries over the period 1999–2007 and calculate the efficiency scores using DEA They found that tighter restrictions on bank activities are nega-tively associated with bank efficiency On the contrary, capital regulation stringency is marginally related to greater bank efficiency

Research studies have frequently tried to analyze whether foreign banks

in developing countries are more efficient Many authors have found that foreign banks and the institutions they acquired are more efficient in a group

of Eastern European countries (see Bonin Hasan and Wachtel 2004; Fries and Taci 2004; Grigorian and Manole 2006, among others) Others, mean-while, find that foreign banks are not necessarily more efficient Drake, Hall, and Simper (2005) studied the relative technical efficiency using DEA for a group of banks in Hong Kong during the period 1995–2001 They found high levels of technical efficiency for many banks and different impacts of environmental factors They also observed that the accession of Hong Kong

to China did not affect the level of bank efficiency Kwan (2006) applied the

stochastic frontier approach to measure cost efficiency in the Hong Kong banking sector His findings show large inefficiencies (although declining)

in the banking sector and a direct relationship between the size of the bank and the level of efficiency Ariff and Can (2008) analyze the cost and profit efficiency of 28 Chinese banks for the period 1995–2004 using DEA The results indicate that joint-stock banks (national and city based) and mid-size banks are the most efficient on average Staub, da Silva, and Tabak (2009) studied the evolution of bank efficiency in Brazil for 2000–2007 elaborating cost, technical, and allocative efficiencies Their findings sug-gest that domestic banks are more efficient than their foreign counterparts Moreover, the level of nonperforming loans and market share are important determinants of bank efficiency Wezel (2010) investigated the efficiency

of Central American banks by disaggregating them between foreign and domestic for the period 2005–2007 He applied the SFA and DEA meth-odologies in order to obtain efficiency scores and found that foreign banks are not necessarily more efficient than the domestic banks He added that country-, sector-, and firm-specific factors are important in determining the level of bank efficiency

in productivity can be understood as the variation in the level of output for a given change in the level of input However, as the banking sector includes multiple inputs and outputs, the calculation of productivity is com-plex Following the nonparametric approach to measure efficiency, Caves, Christiansen, and Diewert (1982) presented the Malmquist index of produc-tivity, a model that measures productivity as the distance to the ratio of two functions Furthermore, Fare, Grosskopf, Norris, and Zhang (1994) provided

a decomposition of productivity change from the Malmquist index:

Productivity Change (PC) = Technical Change (TC)

where technical change refers to the shift in the best-practice frontier and efficiency change are the individual variations of observations relative to the best practice frontier In order to understand the Malmquist index a production technology function is first defined:

If we have a vector of x inputs and y outputs:

Then, the technology production function is the relationship between the

we obtain the value of the output distance function of the potential radial

index is the ratio between two distance functions corresponding to the

input and output vectors of firm i in two different periods ( t , t + 1)

i t ii

According to the Malmquist index, productivity grows if it is above unity

and declines if it falls below one Furthermore, the Malmquist index can be

decomposed as a product of two ratios:

1 i i t i t ,t t 1 i i t i, 1

EC * TC

(31)

where the first ratio represents the efficiency change (EC) and the second

ratio is the technical change (TC) Efficiency change above unity refers to

how firms are moving closer to a best practice frontier or falling behind if

they fall below one On the other hand, technical change above unity refers

to greater technological progress, meaning that the efficiency frontier has

shifted upward, while a value below one would indicate technical regress

The empirical literature analyzing bank productivity is also vast with interesting results for the banking sectors of various countries and periods

of analysis Sathye (2002) studies the productivity changes in the Australian banking industry for the period 1995–1999 for a panel of 17 banks The author applies the Malmquist productivity index calculated by the DEA nonparametric analysis The main results show a decline of 3.1 percent in technical efficiency over the period of study and of 3.5 percent in total factor productivity Additionally, the study finds that bank size does not affect changes in productivity and suggests to advance technological devel-opment in order to enhance productivity Mohan and Ray (2004) analyze the productivity growth and efficiency of Indian banking distinguishing between public, private, and foreign banks They employ two measures

of productivity, namely the Malmquist and Tornqvist indices, to measure total factor productivity growth over the period 1992–2000 Overall, pub-lic sector banks seem to do better than their private and foreign coun-terparts Casu, Girardone, and Molyneux (2004) compare parametric and nonparametric estimates of productivity variations in European banks for the period 1994 to 2000 Productivity is further decomposed into tech-nological change and efficiency change The results indicate that produc-tivity change has been lifted mainly by improvements in technological change and not by “catch-up” effects Andreis, Marius, and Cuza (2011) examined the determinants of efficiency and productivity of the bank-ing system of seven Eastern and Central European countries during the period 2004–2008 They followed two approaches to measure efficiency, namely the stochastic frontier analysis and data envelopment analysis The main results indicated that efficiency increased on average in the period

of study In order to assess the level of productivity, the authors calculated the Malmquist productivity index They found that productivity increased

by 24 percent in the period of study, mainly due to technological changes Chortareas, Garza-García and Girardone (2011b) examined the possible effects of financial deepening on bank productivity changes and also mea-sured a two-way causality The productivity measures are obtained from the nonparametric Malmquist productivity index The results indicated a virtuous circle between financial deepening and bank productivity in Latin American banks

Overall, the empirical literature has gained ground due to the relevance

to assess the level of efficiency and productivity in the banking system The parametric and nonparametric approaches used to measure efficiencies have their advantages and disadvantages although both are superior than the traditional accounting ratios The results, however, vary depending on the focus of study of efficiency: cost or profit efficiency And there is no clear consensus on the best methodology to use