Assessing competition in the banking industry: A multi-product approach

Journal of Banking & Finance xxx (2014) xxx–xxx

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Journal of Banking & Finance journal homepage: www.elsevier.com/locate/jbf

Assessing competition in the banking industry: A multi-product approach q Klenio Barbosa a,⇑, Bruno de Paula Rocha b, Fernando Salazar c a

Sao Paulo School of Economics - FGV, Brazil Federal University of Minas Gerais, Brazil c Votorantim Bank, Brazil b

a r t i c l e

i n f o

Article history: Received 14 September 2013 Accepted 5 May 2014 Available online xxxx JEL classification: L11 G21 Keywords: Bank competition Panzar and Rosse Multi-product banks

a b s t r a c t This paper investigates the competitive aspects of multi-product banking operations. Extending Panzar and Rosse’s (1987) model to the case of a multi-product banking firm, we show that higher economies of scope in multi-product banking are associated with lower Panzar–Rosse measures of competition in the banking sector. To test this empirical implication and determine the impact of multi-production on market power, we use a new dataset on the Brazilian banking industry. Consistent with our theoretical prediction, we find that banks that offer classic banking products (i.e., loans and credit cards) and other banking products (i.e., brokerage services, insurance and capitalization bonds) have substantially higher market power than banks that offer only classic products. These results suggest a positive bias in the traditional estimates of competition in which multi-output actions are not considered. Ó 2014 Elsevier B.V. All rights reserved.

1. Introduction The global banking sector has experienced enormous changes in recent decades. Marked growth in technological and financial innovation and strong deregulation in the sector have led to increased banking concentration and to the creation of large financial conglomerates (Bikker and Haaf, 2002). Curiously, the theoretical and applied literature has paid little attention to the competitive effects of multi-product operations in banking conglomerates. These institutions may be defined as entities that offer financial, banking and insurance services using the same corporative structure (Freixas et al., 2007). Possession of a multi-product structure allows these companies to benefit from economies of scale and scope and provides greater opportunities for risk diversification when supplying this range of services as a package.1 Indeed, conglomerations and multi-product q We would like to thank Claudio Lucinda for his insightful suggestions. We are also grateful to the seminar participants at Insper Business School (Sao Paulo), Sao Paulo School of Business – FGV (Sao Paulo), 2013 LACEA/LAMES Meeting (Mexico), and 2013 ANPEC Meeting (Foz do Iguaçu) for their helpful comments. The usual disclaimer applies. ⇑ Corresponding author. Tel.: +55 1137993244. E-mail addresses: [email protected] (K. Barbosa), [email protected] (B. de Paula Rocha), [email protected] (F. Salazar). 1 A more detailed discussion of the economic justification for the development of conglomerates may be found in studies by Milbourn et al. (1999) and Dierick (2004).

operations have become a characteristic feature of the banking sector in recent years and have even received special attention in the new banking regulations drafted in the aftermath of the recent international financial crisis (see for example Levine (2012)). Some studies in the literature have analyzed the cost efficiency of financial conglomerates and universal banks vis-à-vis commercial banks. Allen and Rai (1996), for instance, estimate economies of scale and scope in financial conglomerates by investigating countries with and without universal banks. Vander Vennet (2002) empirically analyzes the cost and profit efficiency of European financial conglomerates and universal banks. However, the only research that has addressed the effects of multi-product operations on banking competition is that of Berg and Kim (1998). Berger and Kim analyze the behavior of banks operating simultaneously in the retail and corporate banking loan segments. The results revealed asymmetries in the degree of competition, which may be related to the characteristics of the consumers in each of these segments. Although important, Berger and Kim’s article is essentially descriptive and does not investigate the possible relationship between multi-production operations and competition in the banking industry. This article aims to theoretically and empirically fill the gap in the literature on the relationship between multi-production operations and competition by studying the effects of a multi-product structure on the patterns of competition in the banking sector. The operating costs of multi-product banks should be lower than

http://dx.doi.org/10.1016/j.jbankfin.2014.05.003 0378-4266/Ó 2014 Elsevier B.V. All rights reserved.

Please cite this article in press as: Barbosa, K., et al. Assessing competition in the banking industry: A multi-product approach. J. Bank Finance (2014), http://dx.doi.org/10.1016/j.jbankfin.2014.05.003

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K. Barbosa et al. / Journal of Banking & Finance xxx (2014) xxx–xxx

those of specialized banks if integration allows for the realization of operational synergy. In addition, these institutions may exhibit superior performance if informational or other advantages produce positive spillovers to the traditional and non-traditional banking activities that these banks undertake. Because multiproduct operations can significantly change a bank’s cost structure, it may also have a significant effect on banking competition. In this paper, we examine the behavior and conduct of multiproduct banks that supply classic bank products (i.e., loans and credit cards) and other bank products (i.e., brokerage services, insurance and capitalization bonds) compared to those of banks that offer only classic bank products. Multi-product banks that jointly offer classic and other bank products may benefit from economies of scope and may therefore be more efficient than two separate entities that specialize in offering either classic or other banking products. The sharing of inputs such as labor, technology and information across multiple outputs constitutes the major source of such potential cost savings. As documented by Vander Vennet (2002), multi-product banks are more revenue-efficient than their specialized competitors, and the degree of both cost and profit efficiency is higher for universal banks than for non-universal banks. As Vander Vennet shows, economies of scope in multi-product banks are one of the main forces driving improvements in measures of cost efficiency. This paper departs from Panzar and Rosse’s (1987) model to derive a theoretical model that explicitly analyzes the behavior and conduct of a representative multi-product bank that enjoys economies of scope in supplying classic and other banking products. Panzar and Rosse (1987) develop a model that allows for a distinction between perfect competition, monopolistic competition and monopoly. Panzar and Rosse’s test procedure became prevalent in the literature largely due to the low level of information required about the sector under investigation. The level of market competition may be inferred using simple restrictions on the values of input price elasticity in the revenue equation. Panzar and Rosse show how the effects of variations in input prices on revenues in the banking sector are influenced by market power. The test statistic (H) for the level of competition is given by the sum of the elasticities of revenue in relation to input prices. A monopoly situation would be consistent with an H value less than or equal to 0 because the company would always operate in the elastic part of the demand curve. However, equilibrium with perfect competition would mean that H is equal to 1. In this market environment, a rise in input prices would lead to a proportional increase in both marginal costs and income within the sector. Finally, intermediate values of H that lie between 0 and 1 would be typical of monopolistic competition.2 We begin by extending the original Panzar and Rosse (1987) model to the case of a multi-product bank with economies of scope and computing the multi-product Panzar–Rosse H-Statistic. Second, we show how economies of scope at multi-product banks affect the H-Statistic. In particular, we find that greater economies of scope at multi-product banks are associated with a lower Panzar–Rosse H-Statistic. This relationship exists because a multi-product bank that supplies classic and other banking products benefits from economies of scope. Economies of scope reduce a bank’s marginal costs for every product and therefore increase its price–cost margin (i.e., mark-up) in the banking and non-banking markets. Consequently, a multi-product bank will have a higher

2 Shaffer (1982, 1983) explores the relationship between the H-statistic, the conduct parameter proposed by Bresnahan (1982) and a firm’s demand elasticity. In a recent paper, Bikker et al. (2012) show the implications of Panzar and Rosse’s (1987) interpretation of the test, which uses specifications with price equations and includes firm scale controls.

mark-up than banks that supply only classic bank products. Finally, we develop an econometric strategy that allows us to test those theoretical predictions. To test for such empirical implications, we must consider the multi-product dimension intended in our empirical analysis. Therefore, the dataset must be adjusted to include the accounting information of banking conglomerates instead of single institutions in some cases. This strategy is data-heavy because we must identify the final products and the individual institutions that compose a given banking conglomerate. In our empirical analysis, we used information on the Brazilian banking industry. Brazil is an ideal testing ground for the effects of multi-product banking using Panzar and Rosse’s (1987) measure of competition for several reasons. First, Brazilian regulatory authorities release accounting statements that include information for every banking conglomerate and the individual institutions that compose each banking conglomerate in Brazil. This fact is important in the present context because attempting to build accounting statements by simply aggregating individual records will produce misleading results. For example, intra-group credit operations, which could be miscalculated in an aggregation procedure, are already considered in the consolidated statements. In addition, regulatory authorities provide information on the final products offered by each individual institution. This information allows us to identify which bank products are supplied by which banking conglomerates and which accounting statements come from which banking conglomerates. These findings are crucial for testing the empirical implications described above and enable us to generate a new and complete dataset using account data for Brazilian individual banking institutions and banking conglomerates from 2001Q1 to 2012Q4. We begin by estimating a cost function to evaluate the existence of global economies of scope in Brazilian banking system. The results suggest the occurrence of economies of scope, supporting the theoretical channel proposed in this article and the subsequent empirical analysis. Moreover, an individual banking-level measure of economies of scope is created and included in Panzar and Rosse’s (1987) test. The results support the theoretical model’s suggestion that economies of scope increase multi-product banks’ market power. Based on the extension of Panzar and Rosse’s (1987) empirical test to the case of a multi-product banking firm, we infer the impact of multi-production operations in the banking sector on market power. We find that banks that offer classic products (e.g., loans and credit cards) and other products (e.g., brokerage services, insurance and capitalization bonds) have substantially greater market power than banks that offer classic products only. Therefore, Panzar and Rosse’s (1987) test reveals that market power is underestimated when multi-product information is not considered. To identify which of these other banks acquire increases in market power through multi-product banking, we estimate the market power of banks that offer the following products: (i) classic and other financial banking products (such as brokerage and currency exchange services), (ii) classic and other non-financial banking products (such as insurance, life insurance, capitalization bonds and reinsurance) and (iii) classic, financial and nonfinancial products with the banks that offer classic products only. Our estimates show that banks that offer any of these three product profiles enjoy greater market power than banks that offer only classic products. These results indicate that either financial or non-financial banking products may increase a bank’s market power. To summarize, our theoretical and empirical results suggest that empirical models that do not consider the multi-product

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nature of banking operations underestimate multi-product firms’ market power in the banking markets. This paper is organized as follows. Section 2 presents a theoretical discussion that extends Panzar and Rosse’s original (1987) model to the case of a multi-product firm that enjoys economies of scope by supplying classic and other banking products. That section also discusses the effect of economies of scope in multi-product banks on Panzar and Rosse’s (1987) measure of competition. In Section 3, we briefly present the major features of the Brazilian banking system, explaining why Brazil is an ideal testing ground for the effects of multi-product banking on competition. In Section 4, we present the data and empirical procedures used in this study along with its main econometric results. Finally, Section 5 presents our conclusions. The proofs, figures and tables are found in the appendix.

2.1. The model Consider a representative multi-product bank that faces a downward-sloping demand curve for classic bank products (i.e., loans and credit cards), qc ðpc Þ and other bank products (i.e., brokerage services, insurance and capitalization bonds), qo ðpo Þ. For the sake of convenience, these demand curves will be represented by the following demand functions, respectively: pc ðqc Þ and po ðqo Þ, which relate prices pi to output qi , for i ¼ c; o. We note that the bank elasticity of demand in the market for classic bank products @qc pc o po and eo ¼  @q , and other bank products is given by ec ¼  @p q @p q o

o

respectively. Banking technology is represented by a cost function Cðqc ; qo ; w1 ; w2 ; cÞ, interpreted as the function of managing a volume qc of classic banking products and a volume qo of other banking products. For the sake of simplicity, we assume that the bank uses only two inputs (e.g., capital and labor) to produce outputs such that w1 and w2 are input prices. We also assume that Cð:Þ is an increasing, convex and twice continuously differentiable function in ðqc ; qo Þ. This assumption suggests that (i) @Cð:Þ P 0; 8i, (ii) @qi h 2 i2 @ 2 Cð:Þ @ 2 Cð:Þ @ Cð:Þ @ 2 Cð:Þ  @qc qo P 0, and (iii) @q2 P 0; 8i. Note also that the cost @q2 @q2 c

o

i

function depends on a parameter c. The parameter c captures the economies of scope in multi-product banks for supplying classic and other banking products. In the following paragraphs, we explain in detail how economies of scope emerge in multi-product banks and the role of the parameter c in multi-product banking technologies. We assume that banking technology exhibits economies of scope between classic and non-classic banking products. Therefore, 2

¼ c; c P 0, where the parameter c measures the economies

of scope in banking technology. This assumption allows us to evaluate the effect of the change in economies of scope c on Panzar and Rosse’s measure of competition, which will be computed in the next subsection. Under the aforementioned assumptions, a bank’s profit may be expressed using the following equation:

¼ pc ðqc Þqc þ po ðqo Þqo  Cðqc ; qo ; w1 ; w2 ; cÞ;

In this section, we derive a theoretical model that explicitly analyzes the behavior and conduct of a representative multi-product bank that enjoys economies of scope in supplying classic and other banking products. We begin by extending Panzar and Rosse’s (1987) original model to the case of a multi-product bank with economies of scope, computing the multi-product Panzar–Rosse H-Statistic. Next, we show how economies of scope in multi-product banks affect H-Statistics in the market for classical banking products. More specifically, we demonstrate that a multi-product bank with a greater economy of scope is associated with a lower Panzar–Rosse H-Statistic. This empirical implication will be tested in the remaining sections of the paper.

c

@ 2 Cð:Þ @qc @qo

P ¼ Pðqc ; qo ; w1 ; w2 ; cÞ

2. Panzar and Rosse’s test and economies of scope in a multiproduct bank: theoretical framework

c

qc decreases the marginal cost of qo and vice versa. Baumol et al. (1982) define this expression as a weak cost complementarity condition and show that this particular case of economies of scope implies that a multi-product bank that jointly offers classic and other banking products is more efficient than two separate entities that specialize in classic and other banking products, respectively. For the sake of simplicity, we suppose that banking technology has constant economies of scope. Formally, we assume that

@ Cð:Þ 6 0. This condition means that an increase in we suppose that @q c @qo

ð1Þ

where the first two terms correspond to the revenue from classic banking products and other banking products, respectively, and where the third term corresponds to management costs. Note that the economies of scope between classic and other banking products, represented by the parameter c in Eq. (1), affect a bank’s profit through the cost function by making an multi-product bank more efficient than a single-product bank. The bank’s decision variables are qc (the amount of classic bank products) and qo (the amount of other bank products), and the bank chooses qc and qo such that it maximizes the profit function in Eq. (1). The first-order conditions that equate the marginal revenue and marginal cost in each product market are as follows:

  @P ec  1 @Cð:Þ  ¼ pc ¼ 0; ec @qc @qc   @P eo  1 @Cð:Þ  ¼ po ¼ 0: eo @qo @qo

ð2Þ ð3Þ

The second-order conditions associated with the bank’s profit maximization problem are

  @ 2 P pc 1  ec p @ec @ 2 Cð:Þ þ 2c ¼  6 0; ð4Þ 2 2 @q2c @q q ec ec @qc " c  c #" #    pc ec  1 pc @ec @ 2 Cð:Þ po eo  1 po @eo @ 2 Cð:Þ  þ 2 þ 2    e2c @q2c e2o @q2o qc ec @qc qo eo @qo " #2 @ 2 Cð:Þ P 0: ð5Þ  @qc @qo Note that the left-hand side of Eq. (5) corresponds to the determinant of the Hessian matrix of the second-order partial derivatives of the profit function defined in Eq. (1). As in the study by Shaffer (1982), we assume that the elasticity   @ei of demand in both markets is locally constant @q ¼ 0; 8i and that i the bank’s cost function is locally linear in every output   @ 2 Cð:Þ @ 2 Cð:Þ ¼ 0; 8i . Because we have supposed that @q ¼ c, we are @q @q2 i

c

o

able to replace the square of the cross-derivative in the last term of Eq. (5) by c2 . After introducing all these assumptions in Eqs. (4) and (5), we may write the second-order conditions as follows:

  @ 2 P pc 1  ec 6 0; ¼ @q2c q e2  c c  pc po ec  1 eo  1  c2 P 0: e2c e2o qc qo

ð6Þ ð7Þ

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Eqs. (6) and (7) imply that ec P 1 and eo P 1. This approach means that a multi-product bank that faces a downward-sloping demand curve for its products qc and qo will always choose to operate in the elastic region of the demand curve. For simplicity of notation, we hereafter define the left-hand side of Eq. (7), which is the determinant of the Hessian matrix of the profit function defined in Eq. (1), as equal to D. Therefore, we have

   p p ec  1 eo  1 : D c o e2c e2o qc qo

ð8Þ

The first order described by Eqs. (2) and (3) implicitly defines a bank’s optimal supply of classical and other banking products    qc ; qo . Note that the banking products are a function of the exogenous variable input prices w1 and w2 and the parameter of economies of scope c. The next proposition describes how the bank’s optimal supply of classical banking and other banking products varies when these exogenous variables change. Proposition 1. Let qc ¼ qc ðw1 ; w2 ; cÞ and qo ¼ qo ðw1 ; w2 ; cÞ be the bank’s optimal supply of classical and other banking products, respectively, defined implicitly by Eqs. (2) and (3). If the banking @ 2 Cð:Þ @qc qo

¼ c, the elasticity  of demand in both markets is locally constant ¼ 0; 8i and the   2 ¼ 0; 8i , bank’s cost function is locally linear in every output @ @qCð:Þ 2

technology has constant economies of scope,



@ei @qi

i

then the optimal bank’s supply of classical banking and other banking products changes when the input prices w1 and w2 and the parameter of economies of scope c changes according to the following expressions:

" ! # @qi 1 pj 1  ej @ 2 Cð:Þ @ 2 Cð:Þ ; i; j ¼ c; o; ¼  c @qi @w1 @qj @w1 @w1 D qj e2j " ! # @qi 1 pj 1  ej @ 2 Cð:Þ @ 2 Cð:Þ ; i; j ¼ c; o; ¼  c @qi @w2 @qj @w2 @w2 D qj e2j " ! # @qi 1 pj 1  ej @ 2 Cð:Þ @ 2 Cð:Þ ; i; j ¼ c; o: ¼  c @qi @ c @qj @ c @ c D qj e2j

ð9Þ

ð11Þ

Note that if we assume that the parameter for the economies of scope c reduces marginal costs such that

6 0; 8i, then the opti-

mal supply of classical and other banking products increases as the   i economies of scope increase @q P 0; 8i . @c 2.2. Economies of scope and Panzar–Rosse’s H-Statistic in the market for banking products Panzar and Rosse (1987) developed an empirical test that allows one to discriminate between perfect competition, monopolistic competition and monopoly using industry or bank-level data. For this test, Panzar and Rosse derived an H-Statistic, defined as the sum of revenue elasticities with respect to input prices. By using H-Statistics, it is possible to investigate the extent to which changes in factor input prices are reflected in equilibrium or bank-specific revenues and then to infer market competition. In the context of the model presented in the previous subsection, the H-Statistic of a multiproduct bank is defined as follows:

H¼

w1 @Rðw1 ; w2 Þ w2 @Rðw1 ; w2 Þ þ ; @w1 @w2 Rðw1 ; w2 Þ Rðw1 ; w2 Þ

@Rðw1 ; w2 Þ @Rð:Þ @qc ð:Þ @Rð:Þ @qo ð:Þ ¼ þ : @wi @qc @wi @qo @wi

ð12Þ

ð13Þ

By manipulating (12) and (13), we find that the H-Statistic of a multi-product bank is equal to

H ¼ hHc þ ð1  hÞHo ;

ð14Þ

pc qc , pc qc þpo qo

where h ¼ which is the fraction of the bank’s revenue that is derived from classic banking products, and where Hi is the bank’s H-Statistic in the market for the bank product i with i ¼ c; o. The expression (14) means that the multi-product bank’s H-Statistic is the sum of the bank’s H-Statistics for every product weighted by the share of each product in the bank’s total revenue. Because this paper assesses competition in the banking industry when banks exhibit economies of scope in a multi-product technology, we focus on Hc , which is the bank’s H-Statistic in the market for classical banking products. Hc is formally defined as

Hc ¼

  @Rc ð:Þ w1 @qc ð:Þ w2 @qc ð:Þ ; þ @qc Rc @w1 Rc @w2

ð15Þ

where Rc ¼ pc qc is the total revenue from classical banking products. Note that the H-Statistic of a single-product bank that supplies only classical banking products is exactly the same as Hc when it is evaluated with c equal to 0. @qc @qc Replacing @w and @w defined in Proposition 1 into Eq. (15), we 1 2 obtain the following:

Hc ¼

ð10Þ

Eqs. (9)–(11) in Proposition 1 are key to computing a multiproduct bank’s measure of competition (the H-Statistic) in the market for classical banking products using Panzar and Rosse’s method. These equations are also important in evaluating the effect of economies of scope on the H-Statistic. @ 2 Cð:Þ @qi @ c

where Rðw1 ; w2 ; cÞ ¼ pc qc þ po qo is the multi-product bank’s total revenue and where qc ¼ qc ðw1 ; w2 ; cÞ and qo ¼ qo ðw1 ; w2 ; cÞ are the optimal bank’s supply of classical and other banking products, respectively. These terms are defined implicitly in Eqs. (2) and (3). Note also that

" "  ##  @Rc ð:Þ w1 1 po 1  eo @ 2 Cð:Þ @ 2 Cð:Þ þ  c @qc Rc D qo @qc @w1 @qo @w1 e2o " "  ##  @Rc ð:Þ w2 1 po 1  eo @ 2 Cð:Þ @ 2 Cð:Þ þ :  c @qc Rc D qo @qc @w2 @qo @w2 e2o

ð16Þ

Grouping common terms and factoring out the expression DR1 c @R@qc ð:Þ in c the equation above, we obtain the following expression for the H-Statistic in the market for classical banking products:

(  # " 1 @Rc ð:Þ po 1  eo @ 2 Cð:Þ @ 2 Cð:Þ w1 Hc ¼ þ w2 DRc @qc @qc @w1 @qc @w2 qo e2o " #) 2 2 @ Cð:Þ @ Cð:Þ : þ w2 c w1 @qo @w1 @qo @w2

ð17Þ

To move forward, we need an intermediary result, which is found in Lemma 1. Lemma 1. Assume that the multi-product bank is a price-taker in the market for inputs (x1 ; x2 ) and that the cost function Cðqc ; qo ; w1 ; w2 Þ is defined as

Cðqc ; qo ; w1 ; w2 Þ  minw1 x1 þ w2 x2 x1 ;x2

s:t:

ðqc ; qo ; x1 ; x2 Þ 2 Y; ð18Þ

where Y is a production set. Then,

"

# @ 2 Cð:Þ @ 2 Cð:Þ @Ri ð:Þ ¼ w1 þ w2 ; 8i: @qi @w1 @qi @w2 @qi

ð19Þ

Replacing Eq. (19) into Eq. (17), we have

Hc ¼

    1 @Rc ð:Þ po 1  eo @Rc ð:Þ @Ro ð:Þ :  c DRc @qc qo @qc @qo e2o

ð20Þ

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From the Eqs. (2) and (3) in the first-order conditions, we know that h i ; 8i. Replacing this result into the expression above, we ¼ pi eie1 i

@Ri ð:Þ @qi

find that

" # 1 pc po ðec  1Þ2 ðeo  1Þ po ðec  1Þ ðeo  1Þ Hc ¼  þc ; D qc qo e2o ec eo e2c qc

ð21Þ

where D is as defined in Eq. (8). Because we wish to show how economies of scope in a multiproduct bank affect the H-Statistic in the market for classical banking products, all we need to know is how Hc varies with the parameter c. Despite the closed-formulae solution for Hc in Eq. (21), the process of computing the derivative of Hc with respect to c is not straightforward. The fact that Hc -Statistic depends directly on c and indirectly on qc ; pc , qo ; po and D makes the computation complex.3 Fortunately, we are able to show that Hc decreases with c, as stated in Proposition 2. Proposition 2. Assume that the elasticity of demand in the market for @ei ¼ 0; 8i) and classical and other bank products is locally constant (@q i

that the bank’s cost function is locally linear in every output 2

¼ 0; 8i). Then, (@ @qCð:Þ 2 i

(i) we have that

dHc ðcÞ

q ¼  c ec eo < 0: dc c¼0 pc

ð22Þ

In particular, (ii) if the economies of scope parameter c reduces marginal costs 2  @ Cð:Þ 6 0; 8i , then @q @ c i

dHc ðcÞ 6 0; 8c: dc

ð23Þ

Proposition 2 (i) indicates that if we compare the Panzar– Rosse’s H-Statistic in the market for classical banking products offered by a single-product bank with the corresponding value for a multi-product bank that supplies classical and other banking products, the latter should be lower than the former. Proposition 2 (ii) shows that greater economies of scope enjoyed by multiproduct banks are associated with lower Hc -Statistics. This result should occur because a multi-product bank that supplies classic and other banking products should benefit from economies of scope. Economies of scope reduce a bank’s marginal costs for every product and therefore increase the bank’s price–cost margin (i.e., mark-up) in the banking and non-banking markets. Consequently, a multi-product bank will have a higher mark-up than banks that supply only classic banking products. Having demonstrated in Proposition 2 how economies of scope in multi-product banks affect H-Statistics in the market for classical banking products, the next subsection presents an econometric strategy to test for the empirical implications of that proposition. Our empirical strategy enables the identification of a positive bias in the traditional estimates of competition in which banking multioutput operations are not considered. These empirical implications will be tested in the remainder of the paper. 2.3. The multi-product-adjusted Panzar–Rosse’s statistic and economics of scope: an empirical strategy In the previous subsections, we extended Panzar and Rosse’s (1987) model to the case of a multi-product bank with economies of scope and computed the multi-product Panzar–Rosse H-Statistic. In addition, we showed how economies of scope in 3

qc ; pc ; qo ; po and D are implicit functions of c.

multi-product banks affect H-Statistics in the market for classical banking products, demonstrating that greater economies of scope enjoyed by a multi-product bank are associated with lower Panzar–Rosse Hc -Statistics. This subsection describes the econometric strategy that we use to estimate the change in Hc -Statistic to economies of scope that emerge for multi-product banks. One of the key assumptions in this paper is the existence of economies of scope in banking activities. As part of our empirical strategy, we first present an econometric model to estimate economies of scope in multi-product banks, and we then introduce an econometric specification to estimate the empirical implications of the theoretical model described in Proposition 2. 2.3.1. Estimation of cost functions and economies of scope in the banking industry Economies of scope measure the cost savings obtained by combining the provision of goods and services instead of offering them separately. In the classic study by Baumol et al. (1982), for instance, the degree of economies of scope is measured by the percentage cost saving generated by the total amount of productive activity compared to the separate manufacture of each product. Therefore, to empirically identify economies of scope in multiproduct banks, the first step of the analysis consists of modeling and estimating the bank cost function. Similar to Allen and Rai (1996) and Vander Vennet (2002), we use the translog functional form to estimate the cost function of multi-product banks that supply two outputs: classic and other banking products. The translog is one of the most widely used functional forms in the empirical literature on bank efficiency. It presents the well-known advantages of being a flexible form and including the Cobb-Douglas specification as a particular case. The economies of scope, therefore, will be identified using a translog equation of the cost function, which considers the interaction of the supply of classic and other banking products. The econometric specification of the cost function will thus be as follows:

ln TC bt ðqcbt ; qobt ; w1bt ; w2bt Þ ¼ a0 þ

X

ai lnðqibt Þ þ

i¼c;o

X

di lnðwibt Þ

i¼1;2

þ

1 XX 1 XX aij lnðqibt Þ lnðqjbt Þ þ dij lnðwibt Þ lnðwjbt Þ 2 i¼c;oj¼c;o 2 i¼1;2j¼1;2

þ

1 XX q lnðqibt Þ lnðwjbt Þ þ lb þ 1t þ mbt ; 2 i¼c;oj¼1;2 ij

ð24Þ

where TC bt ð:Þ is the total cost of bank b in the period t; qcbt is the total income from classic banking products; qobt is the income from other banking products; and w1bt and w2bt are input prices. The variables lb , 1t and mbt are the bank-fixed effects, the time-fixed effects and an error term that is assumed to be uncorrelated to the other independent variables in Eq. (24), respectively. Within this specification, the measure of economies of scope in banking operations for classic and other products may be calculated as follows: Scopebt ¼



 TC bt ðqcbt ;0;w1bt ; w2bt Þ þ TC bt ð0; qobt ;w1bt ;w2bt Þ  TC bt ðqcbt ;qobt ;w1bt ; w2bt Þ TC bt ðqcbt ;qobt ; w1bt ; w2bt Þ

ð25Þ where TC bt ð:Þ is estimated by econometric specification (24). We note that by construction, a single-product bank that supplies only classic banking products has Scope equal to zero. Baumol et al. (1982) show that a sufficient condition for overall economies of scope is the existence of weak cost complementarities between products. According to these authors, weak cost complementarities mean that the marginal cost of production of a good is slightly reduced as a result of increases in the quantity of any other good. In particular, weak cost complementarities occur if @ 2 Cð:Þ @qc @qo

6 0, which is the exact assumption about economies of scope

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that we make in the previous subsections.4 In a later section in this paper, we will test the weak cost complementarity condition and estimate the economies of scope in the banking industry using (25). 2.3.2. Multi-product Panzar–Rosse’s statistic and economies of scope Having presented the econometric model to empirically identify economies of scope in multi-product banks, we turn to the description of the econometric strategy that we use to test for the empirical implications of the theoretical model. Proposition 2 in the previous section provides two testable implications of our theory. First, it shows in Proposition 2 (i) in Eq. (22) that in the presence of economies of scope, the Panzar– Rosse’s Hc -Statistic of a multi-product bank that supplies classical and other banking products is lower than the corresponding value for a single-product bank that supplies only classic ones. Second, Proposition 2 (ii) in Eq. (23) indicates that greater the economies of scope enjoyed by multi-product banks are associated with lower Hc -Statistics. To test for those two implications, we follow the banking literature by estimating the change in market power resulting from multi-product banking operations using the empirical approach suggested by Panzar and Rosse (1987). Accordingly, we first estimate the classic banking product revenue equation as a function of bank financial intermediation input prices and compute the Standard Panzar–Rosse Hc -Statistic and the change in the Hc -Statistic to the economies of scope that emerge from multiproduct banking technologies, namely, DHc . To conclude, we obtain the Adjusted Panzar and Rosse H-Statistic for multi-product banks. Aiming to test Proposition 2 (i), we estimate the following revenue equation:

Note that our aim is to investigate whether a bank’s market power increases when its multi-product nature (revenues and costs that stem from other banking products rather than classical banking products) is considered. Hence, this hypothesis is tested in the econometric model described above using the following hypothesis test:

H0 : DHc P 0 and Ha : DHc < 0: If we reject H0 , then the market power of the bank increases when the multi-product nature of the bank is considered. Similarly, testing for Proposition 2 (ii), which predicts that greater economies of scope enjoyed by multi-product banks are associated with lower Hc -Statistics, we estimate the following revenue equation:

lnðRT bt Þ ¼ a þ ln ðwbt Þ0 b þ lnðwbt Þ  Scope0bt h þ Z bt p þ lb þ dt þ ebt ; ð28Þ where Scopebt is the scope of a bank b in the period t, which is estimated using (25). In that context, the change in a traditional Panzar–Rosse Hc -Statistic due to economies of scope in multi-product banks, Pm b 6  DH Consistently, the prediction c , is estimated by DH c ¼ k¼1 h k . of Proposition 2 (ii) will be tested as follows:  H0 : DH c P 0 and Ha : DH c < 0:

For ease of notation, we suppress subscripts in the H-Statistics such that H and DH refer to the H-Statistics in the market for classical banking products in the rest of the paper. 3. Institutional background

0

lnðRT bt Þ ¼ a þ ln ðwbt Þ0 b þ lnðwbt Þ  dumMultiProduct b k þ Z bt p þ lb þ dt þ ebt ;

ð26Þ

where lnðRT bt Þ is the total financial revenue of a bank b at time t. The vector wbt corresponds to the m bank input prices. The variable dumMultiProductb is a dummy variable that is equal to 1 if the bank b supplies other banking products and 0 otherwise. The vector Z bt and the variables lb , dt and ebt are the control variables, the bankfixed effects, the time-fixed effects and an error term that is assumed to be uncorrelated to the other independent variables in Eq. (26), respectively. The usual Panzar–Rosse Hc -Statistic is estimated using the following equation:

Standard-H ¼

m X

b bk;

ð27Þ

k¼1

such that each market competition yields a different Hc -Statistic. The relationship between Hc -Statistic and market competition is described in Table 1.5 The change in a traditional Panzar–Rosse Hc -Statistic due to the multi-product nature of the bank DHc is estimated by P ^ DHc ¼ m k¼1 kk . Therefore, the Adjusted Panzar–Rosse H-Statistic accounting for the multi-product nature of a bank is estimated as P ^ Pm ^  Adjusted-H ¼ m is estimated, k¼1 bk þ k¼1 kk . Notice that once  DHcP ^ its variance can be obtained as follows: Var DHc ¼ m k¼1 Varðkk Þþ PP ^ ^ 2 k k Covð ; Þ. k h 16k
Because the condition for the existence of weak cost complementarities is only locally identified, it is necessary to evaluate different combinations of price levels and @ 2 Cð:Þ production. According to Mester (1987), the test of condition @q 6 0 using the c @qo parameters of a translog function is an approximation of an arbitrary logarithmic cost function along the unity value. 5 A monopoly situation yields a value for Hc -Statistic that may be negative or 0. A monopolist yields values of Hc -Statistic 0 and 1, and perfect competition implies an Hc -Statistic equal to 1 (Degryse et al., 2009).

In this section, we present the Brazilian banking system and discuss the multi-product nature of banks in the country. 3.1. The banking system in Brazil The Brazilian banking system has experienced important changes in the last few decades.7 Since the implementation of the Real Plan, the sector has been characterized by strong financial deepening, and changes in the sector’s structure that have led to the entry of foreign banks and market consolidation. One significant change in the operation of Brazilian banks was caused by the qualitative improvement in the macroeconomic environment. Until the early 1990s, high inflation rates guided the actions of economic agents. With the Real Plan, which was launched in July 1994, the Brazilian inflation rate decreased from the annual average of 715% p.a. between 1980 and 1993 to 22% p.a. in December 1995. Macroeconomic stability has increased economic agents’ predictability, increasing the supply of and demand for banking products, particularly credit. During the hyperinflationary period, Brazilian banking operations concentrated on gains from ’’floating’’ on basic banking services.8 With greater monetary stability and more favorable macroeconomic conditions, particularly in the last decade, banking system actions have targeted the traditional functions of raising funds and providing credit. 6 The variance of DH c may be obtained using the same procedure used to obtain the variance of DHc . 7 For a historical overview of the evolution of Brazilian banks, see Baer and Nazmi (2000) and Ness Jr. (2000). 8 Floating revenues may be defined as financial gains that originate from raising non-indexed and low-cost resources (for example, through bill and tax collection) and investing in interest-indexed financial assets. According to Baer and Nazmi (2000), inflationary revenues from floating operations reached 40% of total banking revenues between 1990 and 1992.

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The improvement in the macroeconomic environment was not the only determinant of the recent growth in the provision of banking services. The Brazilian government has also promoted important reforms of the financial system’s institutional environment, which have contributed to the expansion of the credit markets in Brazil. Costa and De Mello (2006) argue that these governmental measures were implemented to reduce information asymmetries in the credit market, increase the quality of collateral instruments, increase the enforcement of contracts, improve the regulatory system for addressing insolvency and create alternative mechanisms for credit.9 As a result of these improvements in Brazil’s macroeconomic conditions and in the institutional environment, the country’s economy underwent a robust process of financial deepening. The proportion of total credit to GDP increased from an average of 27% between 1998 and 2003 to 53% in 2012. In addition to the process of financial deepening, the Brazilian banking system has also been characterized by important structural changes. The end of easy gains from floating operations induced painful adjustments in the sector. Along with the international crises of the 1990s, this change created great difficulties for domestic banks, resulting in a credit crunch and increasing losses. The problems in Brazil’s banking system in the 1990s led the Brazilian government to promote a series of packages intended to restructure the industry. The Program of Incentives for the Restructuring and Strengthening of the National Financial System (PROER), Program of Incentives for the Reduction of the State-Level Public Sector in Bank Activity (PROES) andProgram for the Strengthening of the Federal Financial Institutes (PROEF) represented the beginning of important changes in the market structure of Brazilian banking.10 One of these programs generated an increase in market concentration with a reduction in the number of commercial banks. During this period, foreign banks represented the only segment of the economy that experienced market gains. Foreign institutions such as HSBC, ABN Amro and Santander took advantage of the consolidation of commercial banks to enter the Brazilian market. Finally, it is important to stress the remarkable position of state-owned banks in Brazil. Despite the reduction in the public banking sector promoted by PROES, state-owned banks are still widespread in Brazil. Three state-owned banks, Banco do Brasil (BB), Caixa Econômica Federal (CEF) and BNDES, were the largest banks in the country in terms of total assets as of December 2012. Furthermore, state-owned banks accounted for 44% of assets, 49% of credit and 49% of total deposits in the banking sector in December 2012. The leading position of state-owned banks gives the Brazilian government an important role in credit market dynamics. For example, the Brazilian government used its stateowned institutions to provide liquidity to the markets after the global financial crisis broke in 2008.

3.2. Multi-product operations and conglomerates in the Brazilian banking system This paper aims to investigate the effects of multi-product operations in banking sector on competition levels. To empirically evaluate the theoretical propositions derived in the last section, we have to consider the information on conglomeration in the banking industry. Using the operations of affiliated institutions, a 9 Examples of such measures include the approval of the New Bankruptcy Law (Law 11,105/2005) and the Law on Positive Registers (Law 12,414/2011) and the stricter rules for risk credit operation classification and provision (Resolution 2,682/ 1999). For further discussion of these institutional changes, see Costa and De Mello (2006). 10 For a more detailed discussion, see Baer and Nazmi (2000), Ness Jr. (2000) and Nakane and Weintraub (2005).

7

conglomerate may offer products in classical banking and other non-banking markets. In fact, conglomerates play a major role in the Brazilian banking market. According to BCB, in 2012 only 20% of total loans were provided by independent banking institutions. Other market indicators show an identical pattern. In addition, banks associated with conglomerates hold the greatest amount of total deposits (78%), banking branches (85%) and total assets (84%) in Brazil. The financial system in Brazil comprises a large variety of individual institutions that may be roughly classified into three groups: credit, financial and insurance companies.11 The first group includes all institutions that focus on the provision of loans as their core activity, including commercial banks, investments banks, housing finance companies and consumer finance companies. Brokers and dealers that specialize in the administration and negotiation of foreign exchange, government bonds, corporate securities, stocks and futures contracts are the institutions in the second category. The credit and financial segments are under the supervision of the Brazilian Central Bank (BCB) and the Securities and Exchange Commission (CVM). Finally, the insurance sector includes a variety of insurance and reinsurance companies, capitalization funds and entities operating private pension funds. The Private Insurance Superintendence (Susep) is responsible for supervising this insurance market. Fig. 1 illustrates the types of conglomerates with which Brazilian banks are typically associated. At the first level, banks may form financial conglomerates in partnership with other credit institutions or financial companies. The formation of a financial conglomerate in association with other financial companies allows a bank to expand its production set beyond traditional credit lines. A higher level of conglomeration is produced by the junction of individual banks or financial conglomerates with insurance institutions or insurance conglomerates under Susep’s supervision. This type of arrangement gives rise to economic-financial conglomerates. Economic-financial conglomerates make it possible for individual banks and financial conglomerates to operate in the insurance market. The various possibilities stemming from the formation and service provision of conglomerates are the basis of the multiproduct classification that will be proposed in the next section.

4. Estimation and results 4.1. Data As stated in the last section, Brazilian banking institutions, whether individually or as part of a conglomerate, may offer credit, financial and insurance services. To build a dataset that is consistent with the production set in our theoretical model, we listed 212 individual institutions, including individual banks, and financial entities and insurance companies associated with a banking group for which we have complete accounting information. Then, for each single institution, we classified the various segments according to the services that each company had been authorized to offer. The Brazilian Central Bank’s website has a complete list of services that banks and financial entities are authorized to charge for and offer.12 Insurance companies supervised by Susep were automatically assigned to the insurance segment. Table 2 describes the three different classes of products that banks may offer in Brazil. The second step in the procedure is the agglomeration of individual institutions into financial and insurance conglomerates. This process was based on the supervision entities’ records regarding 11 More details on the organization and the structure of the Brazilian financial system can be found in Fortuna (2010). 12 This information is available at http://www.bcb.gov.br/?TARBANINST.

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the governance structure of conglomerates. The BCB and Susep maintain lists that make it possible to link each individual entity to its corresponding conglomerate. Finally, using the website’s information on insurance institutions and insurance conglomerates, we matched these companies with individual banks and financial conglomerates. At the end of this procedure, we group the initial 212 individual institutions into 73 banking conglomerates. Within this framework, the units of analysis in this article, which we refer to simply as banks, are the banking conglomerates operating in Brazil. It is noteworthy that an individual bank that is not affiliated with any banking conglomerate is considered as a single-company banking conglomerate. Fig. 1 shows the distribution of Brazilian conglomerates into different categories. First, we have conglomerates categorized into individual banks, non-banking financial companies and insurance entities (Conglomerate-type I). Our sample includes 9 conglomerates in this category, which are formed by the association of a total of 113 individual institutions. The second possibility is the conglomeration combining individual banks and non-banking financial companies (Conglomerate-type II). A total of 31 institutions are grouped to constitute the 10 conglomerates classified in this category. Third, we have the possibility of a conglomerate composed by individual banks and insurance entities (Conglomerate-type III). In our sample, only one conglomerate has this configuration. Finally, there are conglomerates formed only by individual banks (Conglomerate-type IV). This is the most recurrent structure in our sample, with 53 conglomerates constituted by grouping 66 banking institutions. Appendix C provides a description of the procedures used to arrange individual institutions into conglomerates and to identify the different banking products (classic, financial and non-financial) offered by each banking conglomerate in our dataset. Table 18 from the Online Appendix lists all 73 banking conglomerates that are in our final sample. It also reports information on banking products, ownership, capital origin, the number of observations and the number of institutions that belong to each conglomerate. It is important to reinforce that our study aims to evaluate the competitive effects of multi-product operations and that the analyses of conglomerates is only the strategy to empirically address the question.13 Table 18 from the Online Appendix also reports the financial statement numbers (income statements and balance sheets) from which we obtained the financial accounts for each banking conglomerate. Brazilian banks present their statements to local regulators at three levels of consolidated accounts: economicfinancial (EFC)14, financial (FC)15 and single units (II).16 The economic-financial accounts refer to the set of companies of any nature that integrate the economic group, including financial and nonfinancial companies. The financial records are the accounting statements for the set of banks and financial companies that compose the economic group. Finally, the single-unit accounts refer to the individual banks composing the economic group. To analyze the multi-product operation of banks as proposed in this article, we use EFC for conglomerates classified in categories (I) and (III) in Fig. 1 because these accounts cover a range of company types, including financial and insurance institutions. In cases in which the banks do not belong to any banking economic-financial conglomerate, we use information from financial records (FC) for

13 One may see in the second line of Table 18 from the Online Appendix, for example, that Banco ING is a conglomerate with two individual institutions but with single-product operation (offering only classic banking products). 14 Economic-financial conglomerate (CONEF) records: documents 7006, 7007 and 7013 from the BCB. 15 Financial conglomerate records: documents 7010 and 7011 from the BCB. 16 Single unit records: documents 7002 and 7003 from the BCB.

conglomerates formed by banks and financial companies (category II) or groups of individual banks (category IV). Finally, we employ the single-unit records (II) to obtain the financial information on the individual banks operating in category IV. Brazil is one of few countries for which this consolidated information on the global operations of conglomerates is available. This fact is important in the present context because the attempt to build accounting statements by simply aggregating individual records could yield misleading results. For example, intra-group credit operations, which could be miscalculated in an aggregation procedure, are accounted for in the consolidated statements. In the end, we have built a unique dataset describing the multi-product banking operations in Brazil according to the three classes of products proposed in this article. The data used in this paper were obtained from the BCB database. The data were obtained from the BCB’s online reports, more specifically its Informações Financeiras Trimestrais (IFT). These reports provide information from the financial statements of all financial institutions authorized to operate in Brazil at all three levels described above on a quarterly basis. The reports may be downloaded directly from the BCB website free of charge.17 Our final sample is an unbalanced panel composed of 73 banking conglomerates with a total of 2,189 observations. Column 7 in Table 18 from the Online Appendix reports the distribution of the observations within the banking conglomerates in the sample, whereas Table 4 shows this distribution over time. Particularly for economic-financial conglomerates, the accounting statements are uploaded with a large temporal lag. Consequently, the banking conglomerates in categories I and III (Fig. 1) as well as the last years in the sample have fewer available observations. Tables 3, 5, 6, 7 and 8 in the appendix show a complete description of our dataset. All figures are expressed in real values from 2001Q1 according to the official Brazilian consumer price index (IPCA). Table 3 presents the number of banks and their distribution by ownership and capital origin. Most of the banking conglomerates in the sample are private and national. Only 25% (18) of the conglomerates are foreign, and ten (13.7%) are state-owned. Table 3 shows the distribution of banks in the proposed three-product division. The majority of the banking conglomerates operate only in the classical banking segment, which indicates the prevalence of single-output operations in the banking industry. However, 27.4% of the conglomerates operate jointly and offer other types of products, particularly financial banking products. Finally, only 9 conglomerates are active in all three segments. Market structure varies across the segments, with signals of higher levels of market concentration in the multi-output definitions of supply. As is shown in the second column in Table 6, banks that supply only classic products typically have a lower average market share in terms of total assets. The average market share of classic banks is 2.8%, whereas the corresponding figure is 15.7% for conglomerates supplying classic and other financial products and 15.5% for conglomerates supplying classic and nonfinancial products. The same pattern arises regardless of whether market share is calculated in terms of total revenue or whether the Herfindahl–Hirschman Index (HHI) is used to capture the level of concentration within the segments. Finally, the banks offering each set of products are different. Tables 7 and 8 show that in general, more diversified banking conglomerates are larger and enjoy a higher market share and higher input prices. Table 7 presents figures for conglomerates that supply only classic banking products (in the third column) and conglomerates that operate simultaneously in classic and financial or

17

Data available from: https://www3.bcb.gov.br/iftimagem.

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non-financial products (second column). The fourth and fifth columns present the test for mean equality, with strong evidence of heterogeneity for these two types of banks. The null hypothesis of equality cannot be rejected for the variable of fixed capital cost. However, in Table 8, we compare the characteristics of banks that supply all three products and the average characteristics of all other conglomerates. The nature of the results remains the same. On average, multi-product operations are associated with larger banks operating in an environment with greater concentration and higher input prices. 4.2. Variables To test for the existence of global economies of scope in the Brazilian banking industry and empirically evaluate the implications of Proposition 2, we estimate a translog cost function, as noted in SubSection 2.3. This procedure requires the definition of three sets of variables: (i) a vector of products in the banking industry; (ii) a vector of input prices and (iii) a measure of the total cost production. In line with the definition presented in the previous sections, the cost function specification identifies three outputs in the banking industry: classic, financial and non-financial banking products. The proxies for each banking output are defined as follows:  Classic banking revenue (Revenue): revenue from traditional banking products, measured by the total revenue from Financial Intermediation, which is used as a dependent variable in Panzar and Rosse’s (1987) equation.  Other banking revenue (financial or non-financial): revenue originating from other financial banking products, such as brokerage, trust fees, commissions from financial markets and payment card services and revenue from insurance activities, capitalization and bond markets. To assess the robustness of the results, the econometric models in this article use narrower measures of intermediation revenue. In particular, we employ two variables formed by the portion of financial intermediation revenue more related to lending products: the total interest income on loans, credit and leasing activities (Interest Revenue) and the total interest income on loans and credit activities (Credit Revenue). The vector wit containing the input prices of banking activity is given by.  Funding expenses (ln (cost of capital)): the natural logarithm of the ratio of total expenses associated with raising funds (capital) to shareholder equity.  Personnel expenses (ln (wage)): the natural logarithm of the ratio of total payroll to shareholder equity.  Fixed capital expenses (ln (cost of fixed capital)): the natural logarithm of the ratio of total fixed capital (own and leased) to shareholder equity. The input prices supporting this multi-product operation are the same as defined in Panzar and Rosse’s (1987) test, corresponding to the use of funds (cost of capital), labor (wage) and fixed capital (cost of fixed capital). As Berger and Mester (1997) argue, this specification with financial assets as the output and financial and physical resources as inputs is compatible with the traditional approach of the financial intermediation of banking activity (Sealey and Lindley (1977)). Finally, these inputs are associated with total operational costs, including funding expenses, payroll expenses and other administrative expenses. To estimate the values of Standard-H and Delta-H, as in Section 2.3, we run the regression (26) using the natural logarithm

9

of the total revenues of financial intermediation (ln (Revenue)) as the dependent variable. The variable dumMultiProduct i is a dummy variable that is equal to 1 if the banking conglomerate i supplies financial products (e.g., interbank credit, market trades, brokerage and currency exchange services) or non-financial banking products (e.g., insurance, capitalization bonds and reinsurance) in addition to classic banking products, and zero otherwise. We also estimate Eq. (26), examining the profiles of various products: (i) classic and other financial banking products; (ii) classic and other non-financial banking products and (iii) classic and financial and non-financial products. We compare banks that offer such products with banks that offer only classic products. The estimated models include a set of control variables Z it to capture the effects of other relevant factors on revenue18:  Provision rate: the ratio of the total of provision for doubtful accounts to shareholder equity.  Profitability: the return on equity by the ratio of total profits to shareholder equity.  Market share: the banking conglomerate’s market share in terms of total assets.  HHI: the Herfindahl–Hirschman Index in the relevant market in terms of total assets. The construction of all variables used in the work is detailed in Table 19 from the Online Appendix. The estimation and econometric results are presented in the following subsection. 4.3. Econometric results This subsection illustrates the main results of our econometric estimations. We begin by presenting pieces of evidence in favor of the existence of global scope economies in Brazilian banking, which corroborates the theoretical channel suggested in this article for the competitive effects of multi-product activity. We then evaluate the competitive effects when banks offer any other banking product. The results indicate that multi-product banks have higher market power than banks that offer only classic products. Next, we present econometric results supporting the hypothesis that economies of scope increase the market power in multi-product banks, as stated in the theoretical model. Finally, the econometric models test for the robustness of these results in different subsamples and evaluate which of the other banking products (financial or nonfinancial) produce increases in multi-product banking market power. 4.3.1. Economies of scope The economies of scope will be identified using a translog-type equation of the cost function, which considers the interaction of the supply of classic and other banking products (financial, nonfinancial or both). Within this specification, the measure of economies of scope in banking operations reflects the percentage cost saving generated by the joint production of classic and other banking products compared to the separate provision of each product. The estimated parameters for the translog cost function are shown in Table 9. In column (1), the figures correspond to the estimation of the cost function for banks that supply classic and other banking products, using the total revenue from financial intermediation (Revenue) as a proxy for revenue from classic banking 18 One common alternative specification includes the natural logarithm of total assets as an additional firm-specific control variable [for example, Bikker and Haaf (2002), Claessens and Laeven (2004) and Coccorese (2009)]. However, Bikker et al. (2012) show that the H-statistic calculated from a scaled revenue equation fails as a test of market power because positive values of that statistic are consistent with monopoly or oligopoly.

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products. Column (2) also reports the estimation of the cost function but uses the total interest income on loans, credit and leasing activities (Interest Revenue) as a proxy for revenue from classic banking products. Finally, column (3) reports the estimated parameter for the cost function using the total interest income on loans and credit activities (Credit Revenue) as a proxy for revenue from classic banking products. Fig. 2 shows the distribution of the economies of scope in our sample, computed as described in Eq. (25) and based on the estimated parameters in Table 9. Figs. 2 (a), (b) and (c) represent the economies of scope using the revenue from financial intermediation, the interest income on loans, credit and leasing activities and the interest income on loans and credit activities, respectively, as a proxy for revenue from classic banking products. In all of these cases, there is a concentration of positive values indicating the economies generated by the joint provision of these banking products. Table 10 provides the descriptive statistics for the measure of economies of scope for both the whole sample and its domestic, foreign, private and public banking segments. Again, we employ the three different proxies for revenue from classic banking products. The estimated values for the economies of scope are positive and statistically significant with no large variations in the values obtained for the segments that were tested. The measures of cost complementarities for the supply of classic and other banking products are shown at the bottom of Table 9. Baumol et al. (1982) show that a sufficient condition for overall economies of scope is the existence of weak cost complementari2

@ Cð:Þ ties between products; that is, @q 6 0. Using the 10% significance c @qo

level, we may reject the hypothesis that the estimated value is non-negative in the model using the total revenue from financial intermediation as proxy for revenue from classic banking products. In the other models, the null hypothesis may be rejected even at the 5% significance level. Taken in conjunction with the figures in Table 10, this result appears to suggest that the occurrence of economies of scope in the Brazilian banking sector during the period under study corroborates the empirical analysis and the channel proposed in this article for the competitive effects of multiproduct activity. 4.3.2. Multi-product banks and Panzar and Rosse’s (1987) test Table 11 presents several estimates of Eq. (26), relating the multi-product banking operations to Panzar and Rosse’s (1987) test. The independent variables of interest are the input prices (ln (cost of capital), ln (wage), and ln (cost of fixed)) and the interaction of input prices with the dummy variable dummy banks with classic and other banking products. The dummy variable assumes a value of 1 if the bank offers classic and some other banking products (financial or non-financial products) and a value of 0 otherwise. The coefficients associated with these independent variables are used to estimate the Standard-H, DH and the Adjusted-H to account for the multi-product nature of the banks. These estimates are included at the bottom of the table. Each column in Table 11 corresponds to a different estimated specification of Eq. (26). In column (1), we estimate Eq. (26) using generalized least squares (GLS), in which we include the natural logarithm of the total financial intermediation revenue as the dependent variable. To assess the robustness of the results, we included in columns (2) and (3) narrower measures of intermediation revenue as the dependent variable. In particular, the econometric model employs the natural logarithm of the total interest income on loans, credit and leasing activities (Interest Revenue) in column (2) and the natural logarithm of the total interest income on loans and credit activities (Credit Revenue) in column (3). In all specifications, we consider the panel structure of the dataset by including fixed effects for each bank, quarter and year. Our

aim is to control for unobservable bank characteristics and some trend dependence in the banks’ revenues. Moreover, we estimate the coefficients of interest, including observable characteristics of banks and market structures. In particular, we include the provision rate, profitability, bank market share and industry HHI as independent variables in all specifications. First, we observe that in all specifications, the estimated Standard H is between 0 and 1, which supports the hypothesis that there is monopolistic competition among Brazilian banks. This observation is consistent with previous works by Belaish (2003), Araujo et al. (2005) and Lucinda (2010). However, we find that in all of the regressions, the estimated DH is negative, which indicates that banks offering classic banking products and other banking products have greater market power than banks that offer classic products only. As a result, the estimated Adjusted-H is negative. The negative Adjusted-H suggests that banks supplying classic and other banking products operate in an environment with little competition. To examine whether DH is statically negative, we test the following hypothesis: H0 : DH P 0 and Ha : DH < 0. The results of these one-sided tests reject H0 at 3.8 percent at the specification in column (1) and at 3.3 and 3.2 percent at the specifications in columns (2) and (3), respectively. These results indicate that the estimated market power of banks that offer classic banking products and other banking products is greater than the market power estimated for banks that offer only classic products. Finally, note that the results are robust for different specifications, albeit the punctual estimated DH is larger when the econometric models include the narrower measures of intermediation revenue as a dependent variable. 4.3.3. Economies of scope and Panzar and Rosse’s (1987) test Table 12 reports the estimations of Eq. (28), in which we test the second part of Proposition 2 regarding the effects of economies of scope on the market power of multi-product banks that jointly supply classic and other banking products (financial, non-financial or both). The variables of interest are the input prices and the interactions of input prices with the continuous variable of economies of scope Scope of Banks with classic and other banking products. The values of economies of scope in multi-product banks are computed as described in Eq. (25), based on the estimated parameters in column (3) of Table 9. The calculation of economies of scope employs the most restricted proxy for revenue from classic banking products in the translog cost function insofar as it represents an accurate description of this product set. Nonetheless, the results are qualitatively the same when the economies of scope are calculated using the other proxies for revenue from classic products in the translog function (available by request). As in Table 11, the coefficients associated with the independent variables are used to estimate the Standard-H, DH and Adjusted-H. These estimates are included at the bottom of the table. Moreover, each column in Table 11 corresponds to a different estimated specification of Eq. (20). In column (1), we estimate Eq. (28) using generalized least squares (GLS), in which we include the total financial intermediation revenue as the dependent variable. The econometric model employs the natural logarithm of the total interest income on loans, credit and leasing activities (Interest Revenue) in column (2) and the natural logarithm of the total interest income on loans and credit activities (Credit Revenue) in column (3). In all of the specifications, we include fixed effects for each bank, quarter and year and the banking observable characteristics of the provision rate, profitability, market share and industry HHI as independent variables. In all of the regressions, the estimated DH is negative, which indicates that economies of scope increase the market power in multi-product banks. The hypothesis test with H0 : DH P 0 and

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K. Barbosa et al. / Journal of Banking & Finance xxx (2014) xxx–xxx

Ha : DH < 0 rejects H0 at the 10% significance level in all specifications tested. Therefore, higher levels of economies of scope are associated with greater market power among multi-product banks. 4.3.4. Robustness checks To evaluate the robustness of the results regarding the competitive effects of multi-product banking operations, we implement two additional econometric exercises. First, we seek to identify which of the other banking products (financial or non-financial products) produce increases in multi-product banking market power. In Tables 13–15, we estimate the DH for the banks that offer each different subset of products. The independent variables of interest are the input prices and the interaction of input prices with the dummy variable that indicates the multi-product banking structure being examined. Table 13 estimates the market power of the banks offering classic and other financial banking products (such as brokerage and currency exchange services) relative to that of banks that only offer classic products. The models include the dummy variable dummy banks with classic and financial banking products, which takes a value of 1 if the bank offers classic and financial products and 0 otherwise. In Table 14, we estimate the DH for banks that offer classic and other non-financial banking products (such as insurance, life insurance, capitalization bonds and reinsurance). The dummy variable dummy banks with classic and non-financial bank products assumes a value of 1 if the bank offers classic and non-financial products and 0 otherwise. Finally, Table 15 estimates the DH for those banks that offer classic, financial and non-financial products relative to those that offer only classic products. In this case, the dummy variable dummy banks with classic, financial and non-financial bank products takes a value of 1 if the bank offers the three classes of products simultaneously and 0 otherwise. As in Table 11, each column in Tables 13–15 corresponds to a different specification of Eq. (26), only varying the proxy for the intermediation revenue used as the dependent variable. All of the specifications also include fixed effects for each bank, quarter and year and the banking observable characteristics of the provision rate, profitability, market share and industry HHI as independent variables. The estimates of the Standard-H, DH and AdjustedH are included at the bottom of the tables. We find that in all of the regressions, the estimated DH is negative, which indicates that banks that offer classic and other products - financial, non-financial or both - have more market power than banks that offer only classic products. The hypothesis test with H0 : DH P 0 and Ha : DH < 0 rejects H0 at usual levels of statistical significance in all specifications tested. The second robustness check consists of splitting our dataset into two subsamples. As stated in Section 3, the leading participation of state-owned banks and the entry of foreign institutions have been two major characteristics of the Brazilian banking system. To evaluate the sensibility of our results to the presence of public and foreign banks, the econometric exercise is implemented in two subsamples containing only private and domestic banks. The results from these subsamples are presented in Table 16, using a similar structure as the previous tables. The estimations in columns (1) to (3) include only private banks, whereas those in columns (4) to (6) include only domestic banks. Moreover, the dependent variable in columns (1) and (4) is the natural logarithm of the total revenue from financial intermediation (Revenue). The dependent variable in columns (2) and (5) is the natural logarithm of the total interest income loans, credit and leasing activities (Interest Revenue). Finally, the dependent variable in columns (3) and (6) is the natural logarithm of the total interest income on loans and credit activities (Credit Revenue). In all of the regressions, the estimated DH is negative, and the null hypothesis of

11

DH P 0 is rejected at usual levels of statistical significance in all specifications tested. Therefore, our result of more market power in banks that offer classic and other products (financial or nonfinancial) compared to banks that offer only classic products is not due to the presence of public or foreign banks in the sample. These robustness checks are also implemented to evaluate the results related to the effects of economies of scope on market power. First, the econometric exercise is implemented using an alternative measure of economies of scope calculated from the joint production of classical and other financial banking products. It is important to note that there are no degrees of freedom to consistently estimate the economies of scope in the joint production of classic and other non-financial banking products because only 1 bank has this specific production configuration (see Table 3). To estimate the economies of scope in the combined production of classic and other financial banking products, the restriction is reduced. However, this reduction is not substantial because we have information for only 10 banks. Nonetheless, the procedures using this metric corroborate the results reported above. In Table 20 from the Online Appendix, we have the estimated parameters for the translog cost function. The corresponding measures of economies of scope are described in Fig. 3 and Table 21 from the Online Appendix and generally reproduce the same pattern discussed previously. The figures in Table 21 show strong evidence of economies of scope in the provision of classic and financial banking products. In the same direction, the measures of weak complementarities in the provision of these products, reported at the bottom of Table 20, are negative but not statistically significant. Table 22 from the Online Appendix employs the values of economies of scope in multi-product banks that jointly supply classic and other financial banking products, computed as described in Eq. (25) based on the estimated parameters in column (3) of Table 20. The estimates of the Standard-H, DH and the Adjusted-H are included at the bottom of the table. Again, in all of the regressions, the estimated DH is negative, indicating that the economies of scope in this alternative set of banking products also increase the market power in multi-product banks. Finally, using the initial measure of economies of scope for the joint production of classic and other banking products (financial, non-financial or both), we estimate the econometric models in the subsamples containing only private and domestic banks. The results are reported in Table 23 from the Online Appendix. In all of the regressions, the estimated DHs are also negative, which suggests that our previous conclusions are not attributable to the presence of public or foreign banks in the sample. Albeit negative, the estimated DH values are not statistically significant, which is most likely a result of the low number of observations in those subsamples. 5. Conclusion In this paper, we investigated the competitive aspects of multiproduct banking operations. Extending Panzar and Rosse’s (1987) test to the case of multi-product banking firms, we used a new dataset for Brazilian banking conglomerates to determine the impact of multi-product operations on market power. We found that banks that offer classic and other banking products have substantially greater market power than banks that offer classic products only. Various tests developed by Panzar and Rosse (1987) reveal that market power is underestimated when multi-product information is not considered. In addition, our estimates show that banks with any of the product profiles studied have greater market power than banks that offer only classic products. These results indicate that both financial and non-financial banking products can increase a bank’s market power.

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Future research could extend this project by investigating the causal effects of the positive relationship between market power and a bank’s decision to supply classic and other banking products.

Lemma 2. Let Cðqc ; qo ; w1 ; w2 Þ be the cost function defined in Eq. (18). Then, Cð:Þ is homogenous of degree 1 in input prices ðw1 ; w2 Þ, such that:

Cðqc ; qo ; kw1 ; kw2 Þ ¼ kCðqc ; qo ; w1 ; w2 Þ; k > 0:

ð31Þ

Appendix A. Proofs Proof of Lemma 2. Part-I: In this part we will show that Proof of Proposition 1. The first-order conditions described by Eqs. (2) and (3) define the qc ¼ qc ðw1 ; w2 ; cÞ and qo ¼ qo ðw1 ; w2 ; cÞ as implicitly functions of w1 , w2 , and c. For convenience, we will c o prove Proposition 1 by showing a general expression for @q and @q @k @k for any exogenous variable k ¼ w1 ; w2 ; c. We then conclude the proof by showing that the expressions (9)–(11) hold. Differentiating the first-order conditions, Eqs. (2) and (3), with respect to k, we obtain the following expressions:



2

2

@ 2 Cð:Þ @qc qo

  pc 1  ec @qc @q @ 2 Cð:Þ þc o ¼0 2 qc ec @k @k @qc @k   po 1  eo @qo @q @ 2 Cð:Þ þc c  ¼0 2 qo eo @k @k @qo @k

ð29Þ ð30Þ

Eqs. (29) and (30) define the following system of equation: 1ec e2c

c po qo

c

h

1eo e2o

C iA

@qc @k @qo @k

0

!

¼@

@ 2 Cð:Þ @qc @k @ 2 Cð:Þ @qo @k

1

D¼

pc po qc qo

D

!

0

po B qo

¼@

h

1eo e2o

c

i pc qc

10 1 @ 2 Cð:Þ c C@ @qc @k A h iA 2 1ec e2c

ðqc ; qo ; x1 ; x2 Þ 2 Y;

ð32Þ

s:t:

ðqc ; qo ; x1 ; x2 Þ 2 Y;

ð33Þ

Hence, from the program (32), we have that w1 x01 þ w2 x02 >   w1 x001 þ w2 x002 , which implies that k w1 x01 þ w2 x02 > k w1 x001 þ w2 x002 . However, from the program (33), we have that  kw1 x001 þ kw2 x002 > kw1 x01 þ kw2 x02 , which implies that k w1 x001 þ  w2 x002 Þ > k w1 x01 þ w2 x02 . This inequality contradicts the previous one. So, we have a contradiction. Part-II: In this part we explicitly show that Cðqc ; qo ; kw1 ; kw2 Þ ¼ kCðqc ; qo ; w1 ; w2 Þ, for k > 0. So, by definition, Cðqc ; qo ; w1 ; w2 Þ ¼ w1 x01 þ w2 x02 , and Cðqc ; qo ; kw1 ; kw2 Þ ¼ kw1 x01 þ kw2 x02 , which is  equal to k w1 x001 þ w2 x002 , that is equal to kCðqc ; qo ; w1 ; w2 Þ. So, Cðqc ; qo ; kw1 ; kw2 Þ ¼ kCðqc ; qo ; w1 ; w2 Þ. Secondly, we will show that:

"

# @ 2 Cð:Þ @ 2 Cð:Þ @Cð:Þ w1 þ w2 ; 8i: ¼ @qi @w1 @qi @w2 @qi

ð34Þ

By definition, we have:

@Cðqc ; qo ; kw1 ; kw2 Þ Cðqc þ h; qo ; kw1 ; kw2 Þ  Cðqc ; qo ; kw1 ; kw2 Þ ¼ lim : h!0 @qc h

  ec  1 eo  1  c2 P 0 2 2 ec eo

be the determinant of the coefficient matrix on the left. Note that it is the same expression in Eq. (7). Then, @qc @k @qo @k

s:t:

A:

Let



Proof of Part-I: By contraction. Suppose not:

 0 0 x1 ; x2 ¼ arg minw1 x1 þ w2 x2

x1 ;x2

i

pc

ðqc ; qo ; x1 ; x2 Þ 2 Y:

  such that x01 ; x02 – x001 ; x002 .

can be written as follows:

1

s:t:

x1 ;x2

but

¼ c, the elasticity of demand in both   @ei ¼ 0; 8i , and bank’s cost function markets are locally constant @q i   2 is locally linear in every output @@qCð:Þ 2 ¼ 0; 8i , the equations above

i

ðqc ; qo ; x1 ; x2 Þ 2 Y;

if, and only if,

 0 0 x1 ; x2 ¼ arg minkw1 x1 þ kw2 x2

 00 00 x1 ; x2 ¼ arg minkw1 x1 þ kw2 x2

As we have assumed that the banking technology has constant economies of scope,

s:t:

2

pc 1  ec @qc @ Cð:Þ @qc @ Cð:Þ @qo @ Cð:Þ    ¼0 @q2c @k @qc @qo @k @qc @k qc e2c @k   po 1  eo @qo @ 2 Cð:Þ @qc @ 2 Cð:Þ @qo @ 2 Cð:Þ    ¼0 2 @q2o @k @qo @k qo eo @k @qc @qo @k

B qc @

x1 ;x2

x1 ;x2



0 h

 0 0 x1 ; x2 ¼ arg minw1 x1 þ w2 x2

@ Cð:Þ @qo @k

So, we have that

"  #  @qc 1 po 1  eo @ 2 Cð:Þ @ 2 Cð:Þ ¼ c ; D qo @qc @k @qo @k @k e2o "  #  @qo 1 pc 1  ec @ 2 Cð:Þ @ 2 Cð:Þ ¼  c : D qc @qo @k @qc @k @k e2c

By Lemma 2, we know that Cðqc ; qo ; w1 ; w2 Þ, defined in Eq. (18), is homogenous of degree 1 in input prices ðw1 ; w2 Þ. Therefore, the equation above can be written as follows:

@Cðqc ; qo ; kw1 ; kw2 Þ Cðqc þ h; qo ; w1 ; w2 Þ  Cðqc ; qo ; w1 ; w2 Þ ¼ klim : h!0 @qc h So,

@Cðqc ; qo ; kw1 ; kw2 Þ @Cðqc ; qo ; w1 ; w2 Þ ¼k : @qc @qc Differentiate it with respect to k, we have that

@ 2 Cðqc ; qo ; kw1 ; kw2 Þ @ 2 Cðqc ; qo ; kw1 ; kw2 Þ þ w2 @qc @w1 @qc @w2 @Cðqc ; qo ; w1 ; w2 Þ ¼ : @qc

w1

Replacing k by w1 ; w2 or c, we obtain the Eqs. (9)–(11) in Proposition 1. 

Evaluating the equation above at k ¼ 1, we have that Proof of Lemma 1. We prove Lemma 1 in 3 steps. First, we to show that Cðqc ; qo ; w1 ; w2 Þ, defined in Eq. (18), is homogenous of degree 1 in input prices ðw1 ; w2 Þ. That is in Lemma 2. 

"

# @ 2 Cð:Þ @ 2 Cð:Þ @Cð:Þ ¼ w1 þ w2 ; @qc @w1 @qc @w2 @qc

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which is exactly what we want to show for the case of i ¼ c. Since the same analysis also applies for i ¼ o, so we have proved that Eq. (34) holds. The third step concludes the proof showing that Eq. (19) holds. From, the first-order conditions described by Eqs. (2) and (3), we know that a profit-maximizing bank equates marginal revenue and marginal cost in each product-market. That implies that

@Ri ð:Þ @Cð:Þ ¼ ; 8i: @qi @qi

ð35Þ

Replacing Eq. (35) in (34), we obtain (19).



" #

dHc ðcÞ

1 ðec  1Þ2 ðeo  1Þ2 pc p2o ¼  : dc c¼0 e3c e3o qc q2o Dðc ¼ 0Þ2

" # 1 pc po ðec  1Þ2 ðeo  1Þ po ðec  1Þ ðeo  1Þ Hc ¼  þc ; D qc qo e2o ec eo e2c qc

Replacing Dðc ¼ 0Þ from Eq. (7) into the expression above, we obtain that

dHc ðcÞ

q2c q2o e4c e4o ðec  1Þ2 ðeo  1Þ2 pc p2o ¼  : dc c¼0 p2c p2o ðec  1Þ2 ðeo  1Þ2 e3c e3o qc q2o

where D is defined in Eq. (7) as equal to:

DðcÞ ¼

pc po ec  1 e2c qc qo



("

 

dHc ðcÞ

1 ðec  1Þ2 ðeo  1Þ d pc po

¼  dc c¼0 e2o dc qc qo c¼0 e2c Dðc ¼ 0Þ2     p ðec  1Þ ðeo  1Þ pc po ec  1 eo  1 þ o 2 2 ec eo ec eo q qc qo "c #)  

ec  1 ðeo  1Þ d pc po pc po ðec  1Þ2 ðeo  1Þ :  e2c e2o dc qc qo c¼0 qc qo e2o e2c After some algebraic manipulations, we have that

Proof of Proposition 2. Part-(i): From Eq. (21), we have that



Replacing Eqs. (7), (36), (40) and (42) into Eq. (38), we obtain that

 eo  1  c2 : e2o

After some algebraic manipulations, we have that

Define X as follows:

p p ðe  1Þ2 ðeo  1Þ p ðec  1Þ ðeo  1Þ XðcÞ ¼ c o c 2 þc o : e2o ec eo qc qo ec qc

ð36Þ

which is negative, since ec and eo are positive. Part-(ii): Define UðcÞ as follows:

So,

  dHc ðcÞ 1 dXðcÞ dDðcÞ : ¼ Dð c Þ  X ð c Þ dc dc DðcÞ2 dc

dHc ðcÞ

q ¼  c ec eo < 0; dc c¼0 pc

ð37Þ

UðcÞ ¼

In particular,

"



# dHc ðcÞ

1 dXðcÞ

dDðcÞ

: ¼ Dðc ¼ 0Þ  Xðc ¼ 0Þ dc c¼0 dc c¼0 dc c¼0 Dðc ¼ 0Þ2 ð38Þ

dXðcÞ dDðcÞ DðcÞ  XðcÞ : dc dc

So, if we want to show that

ð43Þ

dHc ðcÞ , dc

defined in Eq. (37), is negative,

then we have to show that UðcÞ > 0 for all c > 0. Replacing Eqs. (7), (36), (39) and (41) into Eq. (43), we obtain that

("

   #     ) ðec  1Þ2 ðeo  1Þ d pc po po ðec  1Þ ðeo  1Þ ðec  1Þ ðeo  1Þ d po pc po ec  1 eo  1 2 þ  c UðcÞ ¼ þc e2o dc qc qo ec eo ec eo dc qc e2c e2o e2c qc qc qo # ("   ) pc po ðec  1Þ2 ðeo  1Þ po ðec  1Þ ðeo  1Þ ec  1 ðeo  1Þ d pc po  2  þ c c : e2o ec eo e2c e2o d c qc qo qc qo e2c qc

The derivative of XðcÞ with respect to c is equal to 2



After some algebraic manipulations of the equation above, we have that



dXðcÞ ðec  1Þ ðeo  1Þ d pc po p ðec  1Þ ðeo  1Þ þ o ¼ dc e2o dc qc qo ec eo e2c qc   ðec  1Þ ðeo  1Þ d po : þc ec eo dc qc

UðcÞ ¼ ð39Þ

ðaÞ

 

dXðcÞ

ðec  1Þ2 ðeo  1Þ d pc po

p ðec  1Þ ðeo  1Þ ¼ þ o :

2 2 dc c¼0 eo dc qc qo c¼0 qc ec eo ec ð40Þ The derivative of DðcÞ in Eq. (7) with respect to c is equal to

ð41Þ

Hence,

  dDðcÞ ec  1 ðeo  1Þ d pc po j : jc¼0 ¼ dc e2c e2o dc qc qo c¼0

ðbÞ

    p ðec  1Þ ðeo  1Þ pc d po d pc po  þc o dc qc qo qc e3c e3o qo dc qc |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl ffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl ffl} |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} 2

Hence,

  dDðcÞ ec  1 ðeo  1Þ d pc po  2c: ¼ dc e2c e2o d c qc qo

p2c po ðec  1Þ2 ðeo  1Þ2 p p ðec  1Þ2 ðeo  1Þ þ2c c o 2 3 3 e2o qc qo ec eo qc qo e2c |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl ffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl ffl} 

ðdÞ

ðcÞ

"

c2

2

 # po ðec  1Þ ðeo  1Þ ðec  1Þ ðeo  1Þ d pc po  ec eo e2o dc qc qo qc e2c |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} 2

ðeÞ



  ðec  1Þ ðeo  1Þ d po þ c3  : ec eo dc qc |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl ffl} ðf Þ

ð42Þ

Note that (a), (b) and (c) are positive because ec P 1 and eo P 1 (from the profit maximization problem).

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h

i Computing ddc pqc pqo , we obtain that c o       d pc po 1 @p @q @p @q @q @q pc o o þ po c c qc qo  pc po qo c þ qc o : ¼ 2 dc qc qo @qo @ c @qc @ c @c @c ðqc qo Þ

2

i From Proposition 1, we have that @q P 0; 8i if @@qCð:Þ 6 0; 8i. Therefore, @c i @c h i p d o is negative. Hence, expression (f) is positive. dc qc

We still have to show that (d) is positive. Note that (d) is defined as



    pc d po d pc po  : dc qc qo qo dc qc

After some algebraic manipulations of the equation above, we have that

ðdÞ ¼

        d pc po 1 1 @qo 1 @qc ¼ : p q p 1 þ þ p p q 1 þ c c o c o o dc qc qo eo @ c ec @ c ðqc qo Þ2

Replacing (44) and (45) into (47), we obtain that

ð44Þ From Proposition 1, we know that if we assume that the economies of scope parameter c reduces marginal costs such that

2

@ Cð:Þ @qi @ c

ðdÞ ¼

ð46Þ

  pc po eo  1 1 @qo 1 @qc ; þ qc qo ec eo qo @ c qc @ c

6 0; 8i, which is positive if we assume

@ 2 Cð:Þ @qi @ c

ð47Þ

6 0; 8i.

then the optimal supply of classical and other banking products   i P 0; 8i . Thereincreases as the economies of scope increase @q @c h i fore, ddc pqcc pqoo is negative. Hence, expression (e) is positive. h i Computing ddc pqo , we obtain that

Given that the expressions from (a) to (f) are positive for all c, then UðcÞ > 0; 8c. Therefore, dHdccðcÞ < 0; 8c. 

    d po 1 @p @q @q ¼ 2 qc o o  po c : dc qc qc @qo @ c @c

Appendix B. Figures

c

After some algebraic manipulations of the equation above, we have that

    d po p 1 1 @qo 1 @qc ¼ 0 : þ dc qc qc e o qo @ c qc @ c

ð45Þ

Figs. 1 and 2. Appendix C. Tables Tables 1–17.

Conglomerate Type Structure (I)

Conglomerate Type Structure (II)

Banking Conglomerates

Banking Conglomerates

9 Instuons

10 Instuons

Individual Banks

Non banking Financial Companies

Non Banking Non Financial Companies

(54 Instuons)

(24 Instuons)

(35 Instuons)

Individual Banks

Non banking Financial Companies

(19 Instuons)

(12 Instuons)

Conglomerate Type Structure (III)

Conglomerate Type Structure (IV)

Banking Conglomerates

Banking Conglomerates

1 Instuon

53 Instuons

Individual Banks

Non banking Non Financial Companies

(1 Instuon)

(1 Instuon)

Individual Banks (66 Instuons)

Fig. 1. Banking conglomerate-type structures in Brazil. This figure presents all structures of the banking conglomerates in Brazil. In our sample, there are 73 banking conglomerates, which are made up of 212 different individual institutions. Conglomerate-type structure (I) is composed by individual banks, non-banking financial companies and non-banking non-financial companies. conglomerate-type structure (ii) is composed by individual banks and non-banking financial companies. Conglomerate-type structure (iii) is composed by individual banks and non-banking non-financial companies. Conglomerate-type structure (IV) is composed only by individual banks. Notes: (a) The different banking conglomerate-type structures presented in this figure were constructed from the list of the individual institutions and financial conglomerates in Brazil reported by the Brazilian Central Bank (BCB) in the Informações Financeiras Trimestrais (IFT). (b) Individuals banks are commercial banks (institutions that accept deposits, make business loans, and offer basic investment products), or investment banks (institutions that underwrite debt and equity, assist company deals - advisory services, underwriting, mergers and acquisitions and advisory fees – and restructure debt into structured finance products). Non-banking financial companies are financial institutions that provide banking services without meeting the legal definition of a bank (e.g., foreign exchange services companies, brokers, asset management and hedge funds, custody services). Non-banking non-financial companies are institutions that offer insurance, life insurance, capitalization services, and underwrite insurance, and consortium. (c) An individual bank that is not affiliated with any banking conglomerate was considered as a single-company banking conglomerate, and appears at the conglomerate-type structure (IV).

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K. Barbosa et al. / Journal of Banking & Finance xxx (2014) xxx–xxx

(a) Classic Bank Revenue (Financial Revenue) Frequency of Observations 1 1.5 2 2.5 3 3.5

4

Table 1 H-Statistic and market competition. Standard-Hc

Market power

Standard-Hc 60 Standard-Hc 2 ð0; 1Þ Standard-Hc = 1

Monopoly or monopoly competition Monopoly competition Perfect competition

.5

This table relates the value of the usual Panzar and Rosse Hc-Statistic (i.e., StandardHc) to the market power of banks in the credit markets.

0

Table 2 Banking products. -1

-.8

-.6

-.4

-.2

0

.2

.4

Density

.6

.8

1

1.2

1.4

Kernel Density

Other financial banking products

Other non-financial banking products

Working capital

Interbank credit, asset management Market trades (currency, money, etc.) Payment card services

Life insurance

4

(b) Classic Bank Revenue (Interest Revenue)

Other bank products Classic bank products

Frequency of Observations 1 1.5 2 2.5 3 3.5

Credit cards Personal loans

Capitalization bonds Other insurance

0

.5

This table presents the 3 different classes of products that a bank may offer in Brazil: (i) classic banking products, (ii) financial banking products, and (iii) nonfinancial banking products. Classic banking products are defined as all banking services related to credit supply activities as business and personal loans, credit cards, working capital loans, and others. Financial banking products are defined as all non-lending financial products supplied by a bank, which comprise intercredit bank, payment card services, foreign exchange services, brokerage, asset management, custody services, and others. Non-financial banking products are life insurance, car insurance, reinsurance, capitalization services, underwrite insurance, consortium, and other insurance. -.4

-.2

0

.2

.4

.6

Density

.8

1

1.2

1.4

Kernel Density

Table 3 Banks: Ownership, capital origin and products.

0

.5

Frequency of Observations 1 1.5 2 2.5 3 3.5 4

4.5

(c) Classic Bank Revenue (Interest Revenue)

-.1

0

.1

.2

.3

.4

.5

Density

.6

.7

.8

.9

1

1.1 1.2 1.3

Kernel Density

Fig. 2. Overall distribution of the economies of scope in multi-product banks. The figure below represents the distribution of the estimated economies of scope in multi-product banks that supply classic and other banking products. For estimation it was only considered the sample of banks that supply classic and other banking products (financial and non-financial). The values of economies of scope were computed as described in Eq. (25), based on the estimated equations in Table 9. The bars represent the density of the economies of scope in the multi-product banks using bin size 60. The line denotes the kernel density estimation using Epanechnikov kernel function and the ’’optimal’’ bandwidth. Figure (a) represents the economies of scope using the total revenue from financial intermediation (revenue) as proxy for revenue of classic banking products. Figure (b) represents the economies of scope using the total interest income loans, credit and leasing activities (Interest Revenue) as proxy for revenue of classic banking products. Figure (c) represents the economies of scope using the total interest income on loans and credit activities (Credit Revenue) as proxy for revenue of classic banking products.

Description

Number of banks

All banks Ownership Private banks Public banks

73 63 10

Capital origin Domestic banks Foreign banks

55 18

Bank products (classic and other bank products) Only classic bank products Classic and other bank products

73 53 20

Bank products (classic, other financial and non-financial bank products) Only classic bank products Classic products and Only financial bank products Only non-financial bank products All types of bank products

73 53 20 10 1 9

This table presents the number of banks in our sample, and their distribution by ownership, capital origin and sort banking products supplied. According to ownership, banks are classified as state-owned (public) and private. Banks are also classified as Domestic and Foreign Banks. We refer to Domestic a bank which is controlled by domestic shareholders, and to Foreign a bank which is controlled by foreign shareholders. Banks may supply 3 different classes of products in Brazil: (i) classic banking products, (ii) financial banking products, and (iii) non-financial banking products. According to the product basket that a bank supplies, it can be classified as a bank that supplies only classic banking products, or a one that offers classic and other banking products. The latter can be divided in the 3 sub-groups: one that supplies only financial products, only non-financial products, or all types of products.

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K. Barbosa et al. / Journal of Banking & Finance xxx (2014) xxx–xxx

Table 4 Number of observations and banks by year.

Appendix D. Procedure for identifying banking products

Period (Year)

Number of observations

Number of banks

2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2001–2012

173 177 176 177 193 214 232 264 211 122 122 128 2189

45 46 46 46 51 55 62 69 54 31 31 33 73

This table indicates the number of observations for each year of the sample time span (2001–20012). It also shows the number of banks for which financial information is available in year of the sample. The bottom line of the table describes the total number of observations and banks in the entire sample. Notes: (a) Brazilian Central Bank’s online reports on financial statements of financial and economic-financial conglomerates (7007, 7011 and 7013 income statements, 7006 and 7010 balance sheets) are available only from 1T2001 to 4T2009. Those reports for individual institutions (7003 income statements, and 7002 balance sheets) are available for the entire time span (1T2001 to 4T2012). (b) BCB did not report the financial statements of a few banks for some trimesters of the sample time span. Hence, there is no financial account information for some banks in every trimester.

The Brazilian Central Bank (BCB) and the Private Insurance Superintendence (Susep) maintain lists with all individual institutions supplying banking products, and all banking conglomerates operating in Brazil. Those lists also link each individual institution to its corresponding banking conglomerate. Hence, by looking at the products that each individual institution supplies, we can determine the banking products supplied by each banking conglomerate. In order to identify which banking products each single individual bank and non-banking financial company supplies, we based on the BCB’s information on which services that each financial company is authorized to offer in Brazil. The BCB’s website has a complete list of services that banks and financial entities are authorized to offer and to charge for. That list includes the following products: business and personal loans, credit cards, working capital loans, interbank credit, payment card services, foreign

Table 5 Descriptive characteristics: bank characteristics and market concentration. Variable

Number of observations

Mean

Standard deviation

Min

Max

Panel A – bank characteristics Dummy private bank Dummy Brazilian bank Dummy banks with other bank products Dummy banks with other financial products Dummy banks with other non-financial products Total assets Revenue Income Revenue Credit Revenue Other Banking Revenue Financial Services Revenue Non-Financial Revenue Total expenses Wage Cost of capital Cost of fixed capital Provision rate Profitability Market share (assets) Market share (revenue)

2189 2189 2189 2189 2189 2189 2189 2189 2189 2189 2189 2189 2189 2189 2189 2189 2189 2189 2189 2189

0.803 0.740 0.211 0.206 0.106 10,600,000 384,593 223,743 209,693 241,458 78,921 161,778 468,243 0.043 0.197 0.203 0.009 0.032 0.022 0.022

0.398 0.439 0.408 0.405 0.308 42,500,000 1,504,865 882,721 822,176 1,248,823 336,749 986,889 1,891,582 0.054 0.671 0.781 0.018 0.117 0.070 0.068

0.000 0.000 0.000 0.000 0.000 277 0 8,529 8,530 0 0 0 25,757 0.000 0.723 0.000 0.060 2.485 0.000 0.000

1.000 1.000 1.000 1.000 1.000 403,000,000 17,100,000 11,600,000 10,500,000 14,200,000 3,346,189 12,400,000 24,800,000 0.584 29.552 11.873 0.240 1.818 0.501 0.507

Panel B – market concentration HHI (assets) HHI (revenue)

2189 2189

0.25 0.24

0.04 0.04

0.19 0.15

0.39 0.36

This table reports summary statistics of bank characteristics and market concentration. Panel A presents descriptive statistics for bank characteristics, and Panel B for market concentration. The variable dummy private bank is equal to 1 if the bank is private-owned bank, and zero otherwise. The variable dummy Brazilian bank is equal to 1 if the bank is a domestic bank and zero otherwise. The variables Total assets, revenue, Income Revenue, Credit Revenue, Other Revenue, Financial Services Revenue, Non-Financial Revenue and total expenses in Brazilian Reals and deflated by the quarterly official price index (IPCA = 1 in 2001Q1). All variables were constructed as described in Table 19 from the Online Appendix.

Table 6 Market concentration and banking products. Product sets and banking products

Banks supplying Classic products Classic and other bank products Classic and other financial products Classic and other non-financial products

Market concentration: average market share and HHI Market share (Assets) Average

Market share (Revenue) Average

HHI (Assets)

HHI (Revenue)

0.028 0.078 0.157 0.155

0.028 0.078 0.157 0.155

0.182 0.288 0.363 0.311

0.154 0.279 0.324 0.314

This table reports some measures of market concentration for each different set of banking products. All market share indicators were constructed as described in Table 19 from the Online Appendix. All figures are represented by their sample average and are deflated by the quarterly official price index (IPCA = 1 in 2001Q1).

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K. Barbosa et al. / Journal of Banking & Finance xxx (2014) xxx–xxx

Table 7 Mean difference test – banks – only classic versus other banks. Variable

Banks supplying

t-test

Classic and other bank products (1)

Only classic bank products (2)

t-Statistics (3)

p-value (4)

Panel A – market share and bank size Market share (assets) Market share (revenue) Total assets Revenue

0.07 0.07 46,200,000 1,683,258

0.01 0.01 1,039,240 37,179

18.98 19.76 22.52 23.33

0.000 0.000 0.000 0.000

Panel B – other characteristics Dummy private bank Dummy Brazilian bank Wage Cost of capital Cost of fixed capital Provision rate Profitability Number of observations

0.69 0.94 0.08 0.35 0.22 0.005 0.05 462

0.83 0.69 0.03 0.16 0.20 0.010 0.03 1727

7.03 11.05 17.69 5.68 0.51 4.96 3.50

0.000 0.000 0.000 0.000 0.612 0.000 0.001

The table below presents the difference between unconditional means of the bank characteristics and market concentration measures for banks that supply classic and other banking products vis-à- vis banks that offer only classic ones. Columns (1) corresponds to the mean of the variables for the sample composed only by banks that supply classic and other banking products. Columns (2) corresponds to the mean of the variables for the sample comprised by banks that supply only classic products. The t-statistics and p-values are, respectively, reported in column (3) and (4). All figures are deflated by the quarterly official price index (IPCA = 1 in 2001Q1).

Table 8 Mean difference test – banks supplying classic, financial and non-financial bank products versus other banks. Variable

Banks supplying classic and all other banks products

Other banks

t-test

(1)

(2)

t-statistics (3)

p-value (4)

Panel A – Market Share and Bank Size Market share (assets) Market share (revenue) Total assets Total bank products revenue

0.14 0.14 91,800,000 3,282,865

0.01 0.01 1,370,592 55,847

34.27 34.72 39.28 39.87

0.000 0.000 0.000 0.000

Panel B – other characteristics Dummy private bank Dummy Brazilian bank Wage Cost of capital Cost of fixed capital Provision rate Profitability

0.68 0.96 0.09 0.36 0.33 0.005 0.05

0.82 0.71 0.04 0.18 0.19 0.091 0.03

4.50 8.17 14.99 3.76 2.53 3.55 2.50

0.000 0.000 0.000 0.000 0.012 0.000 0.012

Number of observations

223

1966

The table below presents the difference between unconditional means of the bank characteristics and market concentration measures for banks that supply all the 3 classes of banking products (classic, financial and non-financial) vis-à- vis other banks. Columns (1) corresponds to the mean of the variables for the sample composed only by banks that supply all the 3 classes of products. Columns (2) corresponds to the mean of the variables for the sample comprised by the other banks. The t-statistics and p-values are, respectively, reported in column (3) and (4). All figures are deflated by the quarterly official price index (IPCA = 1 in 2001Q1).

Table 9 Estimation of translog cost function of multi-product banks. Independent variables

(1)

ln (revenue)

0.560 (0.336) 0.628⁄⁄⁄ (0.146) 0.115 (0.290) 1.625⁄⁄⁄ (0.438) 0.414 (0.243) 0.045⁄⁄ (0.019) 0.060⁄⁄⁄ (0.019) 0.006

ln (other banking revenue) ln (wage) ln (cost of capital) ln (cost of fixed capital) ln (revenue)⁄ln (Other Banking Revenue) ln (revenue) square ln (other banking revenue) square

(2)

(3)

0.659⁄⁄⁄ (0.113) 0.366 (0.394) 1.137⁄⁄⁄ (0.254) 0.001 (0.201)

0.616⁄⁄⁄ (0.148) 0.569 (0.415) 1.236⁄⁄⁄ (0.267) 0.211 (0.189)

0.008⁄

0.007 (continued on next page)

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K. Barbosa et al. / Journal of Banking & Finance xxx (2014) xxx–xxx

Table 9 (continued) Independent variables ln (wage)⁄ln (cost of capital) ln (wage)⁄ln (cost fixed of capital) ln (wage) square ln (cost of capital) square ln (cost of capital)⁄ln (cost fixed of capital) ln (cost fixed of capital) square ln (wage)⁄ln (Revenue) ln (cost of capital)⁄ln (Revenue) ln (cost fixed of capital)⁄ln (Revenue) ln (wage)⁄ln (Other Banking Revenue) ln (cost of capital)⁄ln (Other Banking Revenue) ln (cost fixed of capital)⁄ln (Other Banking Revenue)

(1)

(2)

(3)

(0.004) 0.011 (0.028) 0.028 (0.027) 0.064⁄⁄ (0.025) 0.081⁄⁄⁄ (0.016) 0.064⁄⁄ (0.024) 0.012 (0.011) 0.048⁄ (0.023) 0.162⁄⁄⁄ (0.044) 0.055 (0.033) 0.023 (0.016) 0.072⁄⁄⁄ (0.019) 0.021 (0.018)

(0.004) 0.008 (0.038) 0.037 (0.038) 0.031 (0.033) 0.066⁄⁄⁄ (0.012) 0.043 (0.033) 0.006 (0.016)

(0.004) 0.009 (0.041) 0.060 (0.036) 0.025 (0.035) 0.063⁄⁄⁄ (0.013) 0.027 (0.035) 0.006 (0.018)

0.004 (0.022) 0.034 (0.025) 0.032 (0.020) 0.270⁄ (0.157) 0.050⁄⁄⁄ (0.015) 0.047⁄⁄⁄ (0.006) 0.007 (0.041) 0.085⁄⁄ (0.039) 0.043 (0.036)

0.007 (0.022) 0.028 (0.025) 0.036⁄ (0.018)

ln (Interest Revenue) ln (Interest Revenue)⁄ln (Other Banking Revenue) ln (Interest Revenue) square ln (wage)⁄ln (Interest Revenue) ln (cost of capital)⁄ln (Interest Revenue) ln (cost fixed of capital)⁄ln (Interest Revenue)

0.326⁄ (0.188) 0.045⁄⁄ (0.019) 0.046⁄⁄⁄ (0.009) 0.010 (0.043) 0.086⁄⁄ (0.039) 0.063⁄ (0.034)

ln (Credit Revenue) ln (Credit Revenue)⁄ln (Other Banking Revenue) ln (Credit Revenue) square ln (wage)⁄ln (Credit Revenue) ln (cost of capital)⁄ln (Credit Revenue) ln (cost fixed of capital)⁄ln (Credit Revenue) Cost complementary @2 C @qc @qo

0.397

0.227

0.246

0.289 0.094

0.096 0.015

0.129 0.036

Fixed effects Bank fixed-effect Quarter fixed-effect Year fixed-effect

Yes Yes Yes

Yes Yes Yes

Yes Yes Yes

Observations R-square

432 0.926

432 0.906

431 0.900

Estimated

Standard deviation p-value test Ho:

@2 C @qc @qo

P 0, Ha:

@2 C @qc @qo

<0

The table below reports estimated coefficients of translog cost function of Multi-product Banks based on the estimation of Eq. (24). The dependent variable is the natural logarithm of the total operational expenses (Total Expenses). The column (1) reports the estimation of cost function for banks that supply classic and other banking products (financial and non-financial) using the total revenue from financial intermediation (Revenue) as proxy for revenue of classic banking products. The column (2) also reports the estimation of cost function for multi-product banks supplying classic and other banking products, but it uses the total interest income loans, credit and leasing activities (Interest Revenue) as proxy for revenue of classic banking products. The column (3) reports the estimation of cost function for multi-product banks using the total interest income on loans and credit activities (Credit Revenue) as proxy for revenue of classic banking products. In bottom of the table it is reported the results of the crosscomplementarity test. All figures are deflated by the quarterly official price index (IPCA = 1 in 2001Q1). Notes: (a) All regressions are estimated with intercept. (b) Robust standard errors in parenthesis. ⁄ p < 0.10 ⁄⁄ p < 0.05 ⁄⁄⁄ p < 0.01

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K. Barbosa et al. / Journal of Banking & Finance xxx (2014) xxx–xxx Table 10 Estimated economies of scope in multi-product banks Economies of scope

Mean

Standard deviation

Min

Max

Panel A – classic bank revenue (Financial Revenue) Overall

1.029

0.180

0.909

1.359

Bank type Domestic banks Foreign banks Private banks Public banks

1.028 1.040 0.989 1.109

0.185 0.104 0.206 0.055

0.909 0.889 0.909 0.964

1.315 1.359 1.359 1.282

Panel B – classic bank revenue (Interest Revenue) Overall

0.962

0.206

0.274

1.271

Bank type Domestic banks Foreign banks Private banks Public banks

0.965 0.925 0.919 1.050

0.210 0.131 0.234 0.076

0.274 0.742 0.274 0.935

1.271 1.153 1.271 1.234

Panel C – classic bank revenue (Credit Revenue) Overall

0.971

0.194

0.123

1.259

Bank type Domestic banks Foreign banks Private banks Public banks

0.973 0.931 0.930 1.051

0.198 0.131 0.222 0.074

0.123 0.731 0.123 0.924

1.259 1.134 1.259 1.234

The table below represents the estimated economies of scope in multi-product banks. The values of economies of scope were computed as described in Eq. (25), based on the estimated equations in Table 9. Panel A reports the economies of scope using the total revenue from financial intermediation (revenue) as proxy for revenue of classic banking products. Panel B reports the economies of scope using the total interest income loans, credit and leasing activities (Interest Revenue) as proxy for revenue of classic banking products. Panel C reports the economies of scope using the total interest income on loans and credit activities (Credit Revenue) as proxy for revenue of classic banking products.

Table 11 Single-product versus multi-product banks: Panzar and Rosse’s (1987) H and DH Statistics regressions. Independent variables ln (wage) ln (cost of capital) ln (cost of fixed capital) ln (wage)⁄ Dummy banks with classic and other banking products ln (cost of capital)⁄ Dummy banks with classic and other banking products ln (cost of fixed capital)⁄ Dummy banks with classic and other banking products Control variables Provision rate Profitability Market share (Assets) HHI (assets) H-Statistics (Panzar and Rosse) Standard H DH Adjusted H = Standard H + DH

DH-Statistics Estimated DH Standard deviation DH Degrees of freedom p-value Ho: DH P 0, Ha: DH < 0 Confidence interval (95%) Fixed effects Bank fixed-effect Quarter fixed-effect

(1)

(2)

(3) ⁄

0.196 (0.122) 0.356⁄⁄⁄ (0.060) 0.011 (0.045) 0.132 (0.141) 0.052 (0.082) 0.104 (0.089)

0.256 (0.147) 0.508⁄⁄⁄ (0.081) 0.044 (0.049) 0.045 (0.181) 0.231⁄⁄ (0.116) 0.126 (0.115)

0.222 (0.141) 0.501⁄⁄⁄ (0.080) 0.100⁄⁄ (0.048) 0.075 (0.168) 0.226⁄ (0.117) 0.143 (0.115)

1.626 (1.979) 1.494⁄⁄⁄ (0.302) 0.163 (0.509) 0.881 (0.977)

2.577 (2.384) 1.339⁄⁄⁄ (0.259) 0.492 (0.633) 0.116 (0.870)

2.316 (2.466) 1.317⁄⁄⁄ (0.253) 0.527 (0.660) 0.130 (0.865)

0.149 0.288 0.139

0.208 0.402 0.194

0.179 0.444 0.265

0.288 0.159 71 0.038 0.553/0.023

0.402 0.215 70 0.033 0.758/0.046

0.444 0.216 70 0.022 0.803/0.085

Yes Yes

Yes Yes

Yes Yes (continued on next page)

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K. Barbosa et al. / Journal of Banking & Finance xxx (2014) xxx–xxx

Table 11 (continued) Independent variables

(1)

(2)

(3)

Year fixed-effect

Yes

Yes

Yes

Observations R-square

1998 0.416

1987 0.394

1986 0.370

The table below reports H and DH statistics based on the estimation of Eq. (26). The dependent variable in column (1) is the natural logarithm of the total revenue from financial intermediation (Revenue). The dependent variable in column (2) is the natural logarithm of the total interest income loans, credit and leasing activities (Interest Revenue). The dependent variable in column (3) is the natural logarithm of the total interest income on loans and credit activities (Credit Revenue). All figures are deflated by the quarterly official price index (IPCA = 1 in 2001Q1). Notes: (a) All regressions are estimated with intercept. (b) Robust standard errors in parenthesis. ⁄ p < 0.10 ⁄⁄ p < 0.05 ⁄⁄⁄ p < 0.01

Table 12 Economies of scope and Panzar–Rosse’s (1987) statistics regressions. Independent variables

(1)

(2)

(3)

ln (wage)

0.253⁄⁄ (0.118) 0.347⁄⁄⁄ (0.060) 0.002 (0.043) 0.036 (0.178) 0.037 (0.082) 0.174⁄⁄ (0.079)

0.316⁄⁄ (0.140) 0.496⁄⁄⁄ (0.080) 0.035 (0.049) 0.100 (0.223) 0.169 (0.111) 0.154 (0.122)

0.292⁄⁄ (0.139) 0.488⁄⁄⁄ (0.080) 0.089⁄ (0.049) 0.131 (0.204) 0.144 (0.112) 0.202⁄⁄ (0.097)

0.163 (1.106) 1.389 (1.985) 1.486⁄⁄⁄ (0.292) 0.135 (0.521) 0.903 (0.980)

0.834 (1.426) 2.241 (2.367) 1.331⁄⁄⁄ (0.245) 0.534 (0.657) 0.029 (0.865)

0.784 (1.444) 1.947 (2.442) 1.311⁄⁄⁄ (0.240) 0.562 (0.687) 0.185 (0.866)

0.092 0.175 0.083

0.145 0.223 0.078

0.107 0.215 0.108

0.175 0.120 71 0.074 0.374/0.024

0.223 0.152 71 0.072 0.475/0.029

0.215 0.156 70 0.087 0.475/0.045

Yes Yes Yes

Yes Yes Yes

Yes Yes Yes

1988 0.412

1977 0.388

1977 0.364

ln (cost of capital) ln (cost of fixed capital) ln (wage)⁄ Scope of banks with classic and other banking products ln (cost of capital)⁄ Scope of banks with classic and other banking products ln (cost of fixed capital)⁄ Scope of banks with classic and other banking products Control variables Scope of banks with classic and other banking products Provision rate Profitability Market share (assets) HHI (assets) H-Statistics (Panzar and Rosse) Standard H DH Adjusted H = Standard H + DH

DH-Statistics Estimated DH Standard deviation DH Degrees of freedom p-value Ho: DH P 0, Ha: DH < 0 Confidence interval (95%) Fixed effects Bank fixed-effect Quarter fixed-effect Year fixed-effect Observations R-square

The table below reports H and DH statistics based on the estimation of Eq. (28). The values of economies of scope in multi-product banks were computed as described in Eq. (25), based on the estimated equations at column (3) in Table 9. The dependent variable in column (1) is the natural logarithm of the total revenue from financial intermediation (Revenue). The dependent variable in column (2) is the natural logarithm of the total interest income loans, credit and leasing activities (Interest Revenue). The dependent variable in column (3) is the natural logarithm of the total interest income on loans and credit activities (Credit Revenue). All figures are deflated by the quarterly official price index (IPCA = 1 in 2001Q1). Notes: (a) All regressions are estimated with intercept. (b) Robust standard errors in parenthesis. ⁄ p < 0.10 ⁄⁄ p < 0.05 ⁄⁄⁄ p < 0.01

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21

K. Barbosa et al. / Journal of Banking & Finance xxx (2014) xxx–xxx Table 13 Single-product versus multi-product banks: Panzar and Rosse’s (1987) H and DH statistics regressions – classic and financial banking products. Independent variables

(1)

(2)

(3)

Independent variables

(1)

(2)

(3)

ln (wage)

0.196 (0.122) 0.356⁄⁄⁄ (0.060) 0.012 (0.045) 0.130 (0.142)

0.256⁄ (0.147) 0.508⁄⁄⁄ (0.081) 0.044 (0.049) 0.044 (0.181)

0.222 (0.141) 0.501⁄⁄⁄ (0.080) 0.100⁄⁄ (0.048) 0.074 (0.169)

ln (wage)

0.198 (0.122) 0.355⁄⁄⁄ (0.061) 0.012 (0.045) 0.171 (0.176)

0.261⁄ (0.146) 0.508⁄⁄⁄ (0.081) 0.045 (0.050) 0.175 (0.238)

0.226 (0.141) 0.501⁄⁄⁄ (0.081) 0.101⁄⁄ (0.049) 0.070 (0.218)

0.055 (0.082)

0.232⁄ (0.117)

0.228⁄ (0.118)

0.033 (0.075)

0.129 (0.114)

0.104 (0.119)

0.105 (0.089)

0.127 (0.115)

0.143 (0.115)

0.098⁄ (0.057)

0.040 (0.090)

0.145⁄⁄ (0.068)

1.590 (1.980) 1.495⁄⁄⁄ (0.302) 0.166 (0.509) 0.864 (0.978)

2.563 (2.386) 1.340⁄⁄⁄ (0.259) 0.491 (0.633) 0.111 (0.871)

2.304 (2.469) 1.317⁄⁄⁄ (0.253) 0.526 (0.660) 0.125 (0.866)

0.148 0.29 0.142

0.208 0.403 0.195

0.179 0.445 0.266

0.290 0.159 70 0.036 0.556/ 0.024

0.403 0.215 69 0.032 0.761/ 0.045

0.445 0.216 69 0.022 0.805/ 0.085

ln (cost of capital) ln (cost of fixed capital) ln (wage)⁄ Dummy banks with classic and financial banking products ln (cost of capital)⁄ Dummy banks with classic and financial banking products ln (cost of fixed capital)⁄ Dummy banks with classic and financial banking products Control variables Provision rate Profitability Market share (assets) HHI (assets) H-Statistics (Panzar and Rosse) Standard H DH Adjusted H = Standard H + DH

DH-Statistics Estimated DH Standard deviation DH Degrees of freedom p-value Ho: DH P 0, Ha: DH < 0 Confidence interval (95%) Fixed effects Bank fixed-effect Quarter fixed-effect Year fixed-effect

Yes Yes Yes

Yes Yes Yes

Yes Yes Yes

Observations R-square

1988 0.417

1977 0.394

1976 0.370

The table below reports H and DH statistics based on the estimation of Eq. (26). The estimations in this table include banks supplying classic and financial banking products. The dependent variable in column (1) is the natural logarithm of the total revenue from financial intermediation (Revenue). The dependent variable in column (2) is the natural logarithm of the total interest income loans, credit and leasing activities (Interest Revenue). The dependent variable in column (3) is the natural logarithm of the total interest income on loans and credit activities (Credit Revenue). All figures are deflated by the quarterly official price index (IPCA = 1 in 2001Q1). Notes: (a) All regressions are estimated with intercept. (b) Robust standard errors in parenthesis. ⁄ p < 0.10 ⁄⁄ p < 0.05 ⁄⁄⁄ p < 0.01

exchange services, brokage, asset management, custody services, and others.19 To assign banking products to each non-banking non-financial company, we based on the website’s information of each individual institution and/or its corresponding non-financial conglomerate. Every institution provides a list of non-financial banking products (e.g., life insurance, car insurance, reinsurance, capitalization services, underwrite insurance, consortium, and other insurances) that they supply in the Brazilian Market. 19

Table 14 Single-product versus multi-product banks: Panzar and Rosse’s (1987) H and DH statistics regressions – classic and non-financial banking products.

This information is available at http://www.bcb.gov.br/?TARBANINST.

ln (cost of capital) ln (cost of fixed capital) ln (wage)⁄ Dummy banks with classic and nonfinancial bank products ln (cost of capital)⁄ Dummy banks with classic and nonfinancial bank products ln (cost of fixed capital)⁄ Dummy banks with classic and nonfinancial bank products

Control Variables 1.599 2.684 (2.038) (2.444) 1.497⁄⁄⁄ 1.334⁄⁄⁄ (0.308) (0.260) 0.398 0.291 (0.437) (0.588) 0.902 0.320 (1.077) (0.943)

2.431 (2.521) 1.319⁄⁄⁄ (0.257) 0.284 (0.609) 0.258 (0.957)

0.145 0.236 0.091

0.202 0.344 0.142

0.174 0.319 0.145

0.236 0.157 61 0.069 0.498/ 0.026

0.344 0.236 60 0.075 0.739/ 0.051

0.319 0.227 60 0.083 0.699/ 0.061

Fixed effects Bank fixed-effect Quarter fixed-effect Year fixed-effect

Yes Yes Yes

Yes Yes Yes

Yes Yes Yes

Observations R-square

1786 0.455

1775 0.418

1774 0.392

Provision rate Profitability Market share (assets) HHI (assets) H-Statistics (Panzar and Rosse) Standard H DH Adjusted H = Standard H + DH

DH-Statistics Estimated DH Standard deviation DH Degrees of freedom p-value Ho: DH P 0, Ha: DH < 0 Confidence interval (95%)

The table below reports H and DH statistics based on the estimation of Eq. (26). The estimations in this table include banks supplying classic and non-financial banking products. The dependent variable in column (1) is the natural logarithm of the total revenue from financial intermediation (Revenue). The dependent variable in column (2) is the natural logarithm of the total interest income loans, credit and leasing activities (Interest Revenue). The dependent variable in column (3) is the natural logarithm of the total interest income on loans and credit activities (Credit Revenue). All figures are deflated by the quarterly official price index (IPCA = 1 in 2001Q1). Notes: (a) All regressions are estimated with intercept. (b) Robust standard errors in parenthesis. ⁄ p < 0.10 ⁄⁄ p < 0.05 ⁄⁄⁄ p < 0.01

Below we provide an example describing the entire procedure to identify the banking products of a important bank in Brazil.

D.1. An Example: Banco do Brasil Table 17 provides an example of the procedure used in the dataset base on the information from Banco do Brasil, a state-owned bank with a leading position in the Brazilian banking market. In the first row, we can see the classification of this bank as a provider of credit and other financial services. In association with other banks and financial companies, Banco do Brasil makes up the financial

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22

K. Barbosa et al. / Journal of Banking & Finance xxx (2014) xxx–xxx

Table 15 Single-product versus multi-product banks: Panzar and Rosse’s (1987) H and DH statistics regressions – classic and all other banking products. Independent variables

(1)

(2)

(3)

ln (wage)

0.198 (0.122) 0.355⁄⁄⁄ (0.061) 0.012 (0.045) 0.174 (0.176)

0.261⁄ (0.146) 0.508⁄⁄⁄ (0.081) 0.045 (0.050) 0.177 (0.240)

0.226 (0.141) 0.501⁄⁄⁄ (0.081) 0.101⁄⁄ (0.049) 0.071 (0.218)

ln (cost of capital) ln (cost of fixed capital) ln (wage)⁄ Dummy banks with classic, fin. and nonfinancial bank products ln (cost of capital)⁄ Dummy banks with classic, fin. and nonfinancial bank products ln (cost of fixed capital)⁄ Dummy banks with classic, fin. and nonfinancial bank products Control variables Provision rate Profitability Market share (assets) HHI (assets) H-Statistics (Panzar and Rosse) Standard H DH Adjusted H = Standard H + DH

DH-Statistics Estimated DH Standard deviation DH Degrees of freedom p-value Ho: DH P 0, Ha: DH < 0 Confidence interval (95%)

0.026 (0.075)

0.130 (0.116)

0.103 (0.122)

0.098⁄ (0.058)

0.041 (0.090)

0.147⁄⁄ (0.068)

1.565 (2.039) 1.497⁄⁄⁄ (0.308) 0.399 (0.437) 0.881 (1.078)

2.668 (2.447) 1.334⁄⁄⁄ (0.260) 0.290 (0.588) 0.330 (0.944)

2.418 (2.524) 1.319⁄⁄⁄ (0.257) 0.283 (0.609) 0.267 (0.958)

0.145 0.246 0.101

0.202 0.348 0.146

0.174 0.321 0.147

0.246 0.156 60 0.060 0.507/ 0.015

0.348 0.238 59 0.075 0.746/ 0.050

0.321 0.229 59 0.083 0.703/ 0.061

Fixed effects Bank fixed-effect Quarter fixed-effect Year fixed-effect

Yes Yes Yes

Yes Yes Yes

Yes Yes Yes

Observations R-square

1776 0.456

1765 0.418

1764 0.391

The table below reports H and DH statistics based on the estimation of Eq. (26). The estimations in this table include include banks supplying classic, financial and nonfinancial banking products. The dependent variable in column (1) is the natural logarithm of the total revenue from financial intermediation (Revenue). The dependent variable in column (2) is the natural logarithm of the total interest income loans, credit and leasing activities (Interest Revenue). The dependent variable in column (3) is the natural logarithm of the total interest income on loans and credit activities (Credit Revenue). All figures are deflated by the quarterly official price index (IPCA = 1 in 2001Q1). Notes: (a) All regressions are estimated with intercept. (b) Robust standard errors in parenthesis. ⁄ p < 0.10 ⁄⁄ p < 0.05 ⁄⁄⁄ p < 0.01

conglomerate BB, which offers credit and other financial products (institutions 1–7). Additionally, the affiliated insurance conglomerate BB Seguros is composed of 6 entities (institutions 8–13) that provide insurance and capitalization services. BB and BB Seguros are branches of the economic-financial conglomerate Banco do Brasil that, through BB’s affiliated conglomerates, offer traditional products (credit), other financial products and insurance products. The figures included in the data set are derived from the BB economicfinancial conglomerate’s accounting statements, which provide consolidated information on individual entities 1–13.

Table 16 Single-product versus multi-product banks: Panzar and Rosse’s (1987) H and DH Statistics regressions – private and domestic banks. Independent variables

(1)

(2)

(3)

(4)

(5)

(6)

ln (wage)

0.169 (0.133) 0.358⁄⁄⁄ (0.062) 0.037

0.215 (0.165) 0.518⁄⁄⁄ (0.083) 0.061

0.180 (0.160) 0.512⁄⁄⁄ (0.083) 0.118⁄⁄

0.119 (0.148) 0.350⁄⁄⁄ (0.063) 0.094⁄⁄

0.169 (0.189) 0.543⁄⁄⁄ (0.109) 0.137⁄⁄⁄

0.175 (0.189) 0.542⁄⁄⁄ (0.109) 0.141⁄⁄⁄

(0.043) 0.197 (0.172)

(0.047) 0.062 (0.225)

(0.048) 0.038 (0.220)

ln (cost of capital) ln (cost of fixed capital) ln (wage)⁄ Dummy banks with classic and other banking products ln (cost of capital)⁄ Dummy banks with classic and other banking products ln (cost of fixed capital)⁄ Dummy banks with classic and other banking products

(0.052) (0.060) (0.059) 0.162 0.136 0.173 (0.170) (0.216) (0.202)

0.052 0.212⁄ 0.207⁄ 0.063 (0.083) (0.123) (0.123) (0.096)

0.336⁄⁄ 0.340⁄⁄ (0.138) (0.141)

0.148 0.187 0.204

0.002

0.025

0.049

(0.125) (0.166) (0.164)

(0.088)

(0.111)

(0.115)

0.748 (1.303) 1.215⁄⁄⁄ (0.221) 0.769 (0.525) 0.026 (0.480)

3.109 (2.374) 1.182⁄⁄⁄ (0.237) 0.269 (0.594) 0.238 (0.665)

3.077 (2.394) 1.183⁄⁄⁄ (0.233) 0.258 (0.590) 0.054 (0.610)

0.137 0.262 0.125

0.237 0.373 0.136

0.226 0.427 0.201

0.362 0.535 0.584 0.220 0.299 0.298

0.262 0.183

0.373 0.253

0.427 0.254

61 0.052

53 0.080

52 0.073

52 0.049

Control variables Provision rate

1.732 (1.972) Profitability 1.790⁄⁄ (0.581) Market share (assets) 4.027 (3.066) HHI (Assets) 1.706 (1.319)

3.210 (2.466) 1.718⁄⁄⁄ (0.439) 4.373 (4.021) 0.484 (1.171)

2.982 (2.557) 1.675⁄⁄⁄ (0.444) 4.914 (4.094) 0.533 (1.181)

H-Statistics (Panzar and Rosse) Standard H 0.152 0.242 0.214 DH 0.362 0.535 0.584 Adjusted H 0.210 0.293 0.370 = Standard H + DH

DH-Statistics Estimated DH Standard deviation DH Degrees of freedom p-value Ho: DH P 0, Ha: DH < 0 Confidence interval (95%)

60 0.039

60 0.055

0.729/ 1.034/ 1.082/ 0.568/ 0.797/ 0.005 0.036 0.086 0.044 0.051

0.852/ 0.002

Fixed effects Bank fixed-effect Quarter Fixed-Effect Year fixed-effect

Yes Yes Yes

Yes Yes Yes

Yes Yes Yes

Yes Yes Yes

Yes Yes Yes

Yes Yes Yes

Observations R-square

1566 0.424

1555 0.397

1554 0.372

1474 0.423

1473 0.452

1472 0.444

The table below reports H and DH statistics based on the estimation of Eq. (26). The estimations in columns (1) to (3) include only Private banks. The estimations in columns (4) to (6) include only Domestic Banks. The dependent variable in columns (1) and (4) is the natural logarithm of the total revenue from financial intermediation (Revenue). The dependent variable in columns (2) and (5) is the natural logarithm of the total interest income loans, credit and leasing activities (Interest Revenue). The dependent variable in columns (3) and (6) is the natural logarithm of the total interest income on loans and credit activities (Credit Revenue). All figures are deflated by the quarterly official price index (IPCA = 1 in 2001Q1). Notes: (a) All regressions are estimated with intercept. (b) Robust standard errors in parenthesis. ⁄ p < 0.10 ⁄⁄ p < 0.05 ⁄⁄⁄ p < 0.01

Appendix E. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.jbankfin.2014. 05.003.

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23

K. Barbosa et al. / Journal of Banking & Finance xxx (2014) xxx–xxx Table 17 Example of bank product assignment in an economic-financial conglomerate. Economic-financial conglomerate

Financial/insurance conglomerate

Individual institution

Core activity

BANCO DO BRASIL

BB

1. BANCO DO BRASIL S.A.

BANCO DO BRASIL

BB

2. BANCO NOSSA CAIXA S.A.

BANCO DO BRASIL BANCO DO BRASIL

BB BB

BANCO DO BRASIL BANCO DO BRASIL

BB BB

3. BB ADMINISTRADORA DE CONSORCIOS S.A. } DISTRIBUIDORA DE TÍTULOS E 4. BB GESTÃO DE RECURSOS U VALORES M 5. BB-BANCO DE INVESTIMENTO S/A 6. BB-LEASING S/A ARRENDAMENTO MERCANTIL

Credit and other financial services Credit and other financial services Other financial services Other financial services

BANCO DO BRASIL

BB

BANCO BANCO BANCO BANCO BANCO BANCO

BB BB BB BB BB BB

DO DO DO DO DO DO

BRASIL BRASIL BRASIL BRASIL BRASIL BRASIL

SEGUROS SEGUROS SEGUROS SEGUROS SEGUROS SEGUROS

7. BESC-DISTRIBUIDORA DE TITULOS E VALORES MOBILIARIOS SABESCV 8. ALIANÇA DO BRASIL SEGUROS S.A. 9. BB CAPITALIZAÇÃO S.A. 10. BRASILCAP CAPITALIZAÇÃO S.A. 11. BRASILPREV SEGUROS E PREVIDÊNCIA S.A. 12. BRASILVEÍCULOS COMPANHIA DE SEGUROS 13. COMPANHIA DE SEGUROS ALIANÇA DO BRASIL

Other financial services Credit and other financial services Other financial services Insurance Capitalization Capitalization Insurance Insurance Insurance

This table provides an example of the procedure used in the database to identify different banking products (classic, financial, non-financial) offered by a bank in our database. For the example, it is used information from Banco do Brasil. The column Economic-financial conglomerate reports the name of the bank, and the columns Financial/insurance conglomerate and Individual institution, respectively, links each individual institution to its corresponding bank. The column Core activity describes the banking services that each individual institution is authorized to offer in Brazil.

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Please cite this article in press as: Barbosa, K., et al. Assessing competition in the banking industry: A multi-product approach. J. Bank Finance (2014), http://dx.doi.org/10.1016/j.jbankfin.2014.05.003