Swedish Savings Banks and Competition
A Panzar-Rosse model approach
Andreas Vigren
Student Spring 2012
Abstract
In this paper the Swedish savings banks sector is analyzed between the years 2002 and 2010 using the Panzar-Rosse model. The model uses the reduced form revenue function to capture a relation with the factor price elasticites. The narrow geographical area for many savings banks along with local presence for many years creating awareness of the bank may suggest that these banks could act as local monopolies. A comparison is also made with commercial banks as well as savings banks of different sizes. Using data for 49 savings banks and eight commercial banks the findings suggests monop-olistic competition behaviour by savings banks and that commercial banks could be characterized by monopoly. The results suggests that neither bank type, nor savings banks of different sizes, can be confirmed acting competitively. The only exception is medium sized savings banks. Thus, the conclusion is that the Swedish banking sector is not competitive.
Acknowledgements
First and foremost I would like to express my sincere thanks and gratitude to my supervisor Thomas Aronsson for his guidance, support, comments and patience before and throughout the writing process. Without his help this thesis would not have been written.
A thanks also to all savings banks who provided data to the study. The Swedish postal service has seen a large increase in revenues during this period.
Furthermore, I owe gratitude to Sherrill Shaffer for his time and help.
A special thanks is sent to the kind people in the front desk of the Swedish Companies Registration Office (Bolagsverket) who not only provided help with computers, but also fetched several cups of well needed coffee.
Audere Est Facere
Contents
1 Introduction 5
1.1 The Swedish banking sector . . . 6
1.2 Previous studies . . . 8
1.3 Purpose . . . 10
1.4 Research question . . . 11
2 Theoretical Framework 11 2.1 The Panzar-Rosse model . . . 12
2.2 Empirical model . . . 19 3 Empirical Framework 20 3.1 Data . . . 20 3.2 Model . . . 22 4 Results 25 5 Conclusion 29 References 32 Appendix A List of banks 34 Appendix B Econometric appendix 35 B.1 Correlation matrices and descriptive statistics . . . 35
B.2 Long-run equilibrium (ROA) test . . . 37
B.3 Estimates including Nordea . . . 38
Appendix C Mathematical appendix 39 C.1 Monopolistic competition (section 2.1.2) . . . 39
1
Introduction
Today, banks are a crucial part of most people’s everyday life handling money, loans, debit and credit cards and so on. One can argue that it is important with a well functioning competition in a market that vital to society. Competition may, in this case, manifest itself in terms of a wide selection of services and activities as well as in terms of prices for these services. A lack of alternatives could, as in all other markets, make the market work more inefficient. The Swedish banking sector is strongly dominated by four banks1 that together
hold about 80% of the total assets in the bank sector, a position that has been relatively unchanged during the last decade (Swedish Bankers Association, 2011). The other 113 banks, both domestic and foreign, share the remaining 20%. This indicates that banks may exhibit market power.
Schaeck et al. (2009) concludes that the greater the competition in a banking market, the less is the risk of suffering a “systemic crisis”. This should speak in favor of having a competitive banking market. In discussing if perfect competition is the market structure that should be preferred, Cetorelli and Gambera (2001) note that a more competitive market tends to increase the quantity of credit, while a a less competitive bank sector instead would increase the quality of the loans (i.e. the borrowers). This is much in line with what happened in Sweden during the late 1980’s after the deregulation of the credit market. When the lending from banks rapidly increased, and the actors on the market were fighting for customers, many bad loans were given leading to massive credit losses.
Sweden has a long tradition of a particular banking form called savings banks, reaching back to 1820, which, in brief, has mainly focused on competing in the local districts’. (K¨orberg, 2007) A more narrowed geographical business area for a bank could increase the knowledge about the bank among the population, and also create sympathy, because of its local presence. This is turn may give additional, and also more loyal, customers for the bank, implying that the customers may, for example, be more reluctant to switching banks or, because of loyalty feelings, not choosing other banks, creating entry barriers on the local market (Nordic competition authorities, 2006). This raises questions about how competitive this market really is. If customers are sticky (i.e. not behaving as in a perfect competitive market) with respect to switching bank, the savings banks could be viewed as local monopolies. Gischer and Stiele (2009) found that the savings banks in the German market, and in particular the smaller ones, are characterized by less competition than the
1
commercial banks. More precisely, Gischer and Stiele found that the savings banks sector is characterized by monopolistic competition. Another study, Sj¨oberg (2007), analyzed the Swedish local banking market and found evidence of more competitive behavior among commercial banks than among the savings banks.
This paper contributes to the empirical literature by investigating the structure of the Swedish savings banks sector between the years 2002 and 2010. A comparison with the commercial banks is also made which clarifies whether there could be differences in competition depending on type of bank (i.e. savings bank or commercial bank).
The paper is organized as follows. The remainder of section 1 describes the Swedish bank sector, and puts special emphasis on the history of the savings banks. There is also a brief discussion of previous studies in this field, followed by the purpose of the paper along with the research question. In section 2 the theoretical framework used for the empirical analysis is presented. Section 3 specifies the data and model to be used in the analysis. The result is presented in section 4 and conclusions in 5.
1.1 The Swedish banking sector
In the beginning of 2011 there were 114 banks doing business in the Swedish banking sector. Of these, 19 were commercial banks, 29 foreign banks and 64 savings banks. Between the years 2000 and 2011 the number of banks operating in Sweden decreased from 124 to 114. The largest drop refers to the number of savings banks, which decreased from 79 in 2000 down to 50 in 2011.2 (Swedish Bankers Association, 2011) The overall decrease in the
number of banks as well as the dominance of the four largest banks could imply that the competition has decreased during these years as the number of competitors has decreased. 1.1.1 The savings banks
Savings banks have a long tradition in the Swedish banking sector. The first savings bank was founded in 1820 in Gothenburg and would become one of the hundreds of savings banks established within the upcoming decades. In 1892, the first savings banks law was established and included all of the 378 savings banks at that time. This law, and the upcoming laws, pointed out some of the characteristics of savings banks’, for example, the idea of promoting savings, local support and the absence of individual profits, which means 2The decrease is partly due to a conversion to commercial banks, done by 14 savings banks, but are also
that the profits that were not reinvested in the savings bank were dispersed as dividends to support the local district. The future laws also opened up, step by step, the possibilities for the savings banks to manage lending and other banking activities apart from only the savings business. These laws were established for the savings banks to be able to compete with the larger commercial banks that did not face restrictions in which services to provide. (K¨orberg, 2007)
During the forty years that passed, the number of savings banks substantially increased. A decentralized business model meant there was little cooperation between the savings banks, and many of them were dependent on commercial banks to, for example, supply the savings banks with cash and, if needed, give credits to the savings banks. By the establishment of Sparbankernas Bank in 1942, which was founded by several savings banks, this dependence on the commercial banks was broken. Sparbankernas Bank acted similarly to a central bank towards the savings banks, by helping them with the same things that the commercial banks previously had done. The founded bank was a commercial bank, but was fully owned by the participating savings banks across the whole country. In 1969, the savings banks law was changed so that the savings banks from then on could compete on precisely the same conditions as the commercial banks because, until then, they had been restricted in especially the lending business. During the next two decades, several larger mergers amongst savings banks were made, leading in many cases to an organization with more or less no coordination between the business units, because of the large and geographically widespread units. This resulted in that the old rule of “the church tower principle”3 was not applied as much as before. More and more, the smaller savings
banks felt the competition from the larger merged savings banks, as well as the commercial banks, and formed the Savings Banks Association which made them a strong counterpart to the larger banks. This association helped them to negotiate more favorable terms of cooperation with other banks, which in turn helped them in their daily business. (K¨orberg, 2007)
The beginning of the 1990s turned out to be a turbulent time in the history of the savings banks. Due to the credit deregulation in 1985, several savings banks had expanded their lending dramatically, which lead to massive credit losses in the financial crisis that struck Sweden in 1991. During the same year, an important change in the savings banks law made it possible to convert savings banks to regular commercial banks, giving the
3
possibility to inject capital from outside sources. This possibility had been impossible for the savings banks, which until then had only been able to rely on the previous profits of the banks. The change made it possible for eleven savings banks to merge into one commercial bank, resulting in the publicly listed Sparbanken Sverige AB. This new bank was formally a public commercial bank, but was to a large extent owned by the savings banks foundations4. A savings banks foundation are, and was, created when a savings
bank converted to become a commercial bank, and owned the shares in the newly created commercial bank. The foundations have similar characteristics to the savings banks, which means that the new commercial banks created by the new law still acted upon the values of the savings banks. A similar merger as the one creating Sparbanken Sverige was made by the F¨oreningsbanks’, creating F¨oreningsbanken AB, which until then had been a corporate bank for the past 80 years. In 1997, Sparbanken Sverige and F¨oreningsbanken merged, creating one of the largest banks in Sweden, F¨oreningssparbanken, which later changed its name to Swedbank. (K¨orberg, 2007)
Today, the majority of the savings banks have a strong connection to Swedbank through an intimate cooperation agreement where they share, for example, technological platforms and possibilities for customers in the savings banks and Swedbank to use each other’s branches for banking services. However, all savings banks that did not participate in the merger to Sparbanken Sverige are, regardless of if it is a “pure” savings bank or a converted commercial bank, still independent firms. A list of these banks are provided in appendix A.
1.2 Previous studies
Today, a vast literature about the competition in the banking sector exists and is based on different statistical methods. In this section, a selection of studies is discussed focusing mainly on the Swedish banking sector, but also studies from Germany as the savings banks have a strong position there.
Vesala (1995) uses the Panzar-Rosse model to investigate competition in the Finnish banking sector. In brief, the Panzar-Rosse model tries to capture the relationship between factor price elasticities and the reduced form revenue function at the firm level. This makes it possible to test whether firms behave as monopolists, monopolistic competitors or in accordance with perfect competition. A more thorough discussion of this model is provided
4
in section 2.1. Vesala conclude that the banks behave in a monopolistic competitive way, which is a common result from the Panzar-Rosse model (see, for example, table 1)
Schaeck et al. (2009) also applied the Panzar-Rosse model, investigating the relationship between competition in the banking sector and financial crises for 45 countries during the years 1980 and 2005. The general findings were monopolistic competition, but the results vary over countries. Schaeck et al. concludes that concentration cannot proxy competition, probably due to that competition is a local issue and that the concentration measures do not capture local competition as they often are conducted at national levels with aggregated data. The authors estimates a H-statistic consistent with monopolistic competition in Sweden, and a concentrate ratio of 0.98 based on the three largest banks.
Carbo et al. (2009) applied a number of different approaches to measure competition in the bank sector in 14 European countries, including Sweden. The approaches used are the net interest margin to total assets, Lerner Index, Ratio of bank net income to the value of total assets, Panzar-Rosse model and also the Hirschman-Herfindahl index. The findings were that the measures are only weakly positively related to each other, meaning that they probably do not measure the same thing. However, any conclusions about the Panzar-Rosse model and its fitness to similar methods are not drawn. The authors do, however, conclude that amongst the four other measures the Lerner index and Returns on assets are more preferred in measuring overall banking activity. In the study, the Swedish banking sector was found to be a monopolistic competitive.
In analyzing the competition of the banking sector in the EU, Bikker and Haaf (2002) found strong evidence for monopolistic competition in most markets, including Sweden, when using the Panzar-Rosse methodology. Estimations were also conducted at small-medium- and large bank sizes where the findings were that the degree of competition declined with the size of the bank. However, this was not true in the Swedish market where the medium-sized banks had the weakest competition measure.
Turning to the savings banks specifically there is a limited number of studies performed in the Nordic countries. Sj¨oberg (2007) found that the Swedish savings banks do not act in a perfectly competitive market, but not in a “Cournot conduct” either. Sj¨oberg also concludes that the competition between savings banks was less than amongst commercial banks.
Table 1: Summary of findings from previous studies
Author Country Time period Banks Method Finding
Schaeck et al. (2009) Sweden1 1980-2005 Whole market P-R MC
Vesala (1995) Finland 1985-1992 Whole market P-R MC
Bikker and Haaf (2002) Sweden1 1988-1998 Whole market P-R MC
Bikker and Groeneveld (2000) Sweden1 1989-1996 Whole market P-R MC
Hempell (2002) Germany 1993-1998 Savings banks P-R MC
Gischer and Stiele (2009) Germany 1993-2002 Savings banks P-R MC
Carbo et al. (2009) Sweden1 1995-2001 Whole market P-R MC
Sj¨oberg (2007) Sweden 1996-2002 Commercial BR Not PC2
Sj¨oberg (2007) Sweden 1996-2002 Savings banks BR Not PC2
MC=Monopolistic competition; PC=Perfect competition; P-R: Panzar-Rosse; BR=Bresnahan and Reiss entry model
1 The paper provides results for more countries than just Sweden
2 The competition amongst commercial banks are significantly higher than amongst
savings banks
banks had a lower degree of competition than the larger ones. They also conclude that the economic problems facing the larger German banks seems not to be due to matters of competition, but rather to “a more difficult market segment” such as financing large corporate groups and trading with complex derivatives. Gischer and Stiele also find that the less competitive savings banks market seems more profitable than the market facing the larger actors.
The results from previous studies discussed in this section are summarized in table 1
1.3 Purpose
The main difference between this and the previous papers studying bank competitions is the focus on savings banks. As far as the author is aware, no similar study has been performed using the Panzar-Rosse model on savings banks specifically. In addition, there are no previous studies analyzing the Swedish banking sector after 2007.
1.4 Research question
Is the Swedish savings banks industry acting competitive, or is it rather characterized by monopolistic competition or behaving as local monopolies? In addition, are there any differences compared to the competition amongst commercial banks or savings banks of different sizes?
2
Theoretical Framework
In measuring competition several methods are used in the literature, and the most fre-quently used methods will be described below. A popular method is the Bresnahan-Lau model. By defining demand- and supply functions for a product or market one can es-timate, assuming that firms are not price takers, a markup (λ) from the price equation (obtained from the supply function), where λ ∈ (0, 1). A value zero implies that the market is characterized by perfect competition, whilst a value of one denotes a monopoly market.(Bresnahan, 1982) (Lau, 1982) As the Bresnahan-Lau model requires data at the market level, it is hard to apply the model on the banking market due to difficulties to find appropriate explanatory variables in the demand and supply functions, especially the price variable.
The Boone indicator has recently been applied (see e.g. van Leuvensteijn et al. (2010) and van Leuvensteijn et al. (2011)). The model is built on the assumption that a more efficient firm (firms with lower marginal cost) will be more competitive than a less effi-cient one. Thus, by analyzing market shares and marginal costs, an indicator is obtained measuring the degree of competition. The indicator has a more negative value (larger in absolute terms) the more competitive a market is.
banks most often make larger profits etc. which can cause problems in the estimation. A solution to this is to divide the sample into different classes of size. In addition, since the Panzar-Rosse model assumes that the sample is in long-run equilibrium the results from a non-long-run equilibrium sample may cause spurious and unreliable results.5 Although the
Panzar-Rosse model has disadvantages, it will be used in this paper as it fits the banking market well and are widely applied in academical literature.
2.1 The Panzar-Rosse model
John C. Panzar and James N. Rosse introduced a test for imperfect market structures, which has been widely used when analyzing the competitiveness of different markets. In brief, the model uses comparative statics from the firms reduced form revenue function, and thereafter the sum of the factor price elasticities to determine the degree of competition. (Panzar and Rosse, 1987) The model is based on the assumptions that the firms in the sample are profit maximizing, that the sample must be in a long-run equilibrium, and that the average cost curve is convex with respect to price and quantity. All of these assumptions are assumed to be fulfilled. The presentation of the model given in section 2.1 mainly follows the articles of Panzar and Rosse (1977) and Panzar and Rosse (1987), if nothing else is referenced. This theoretical framework will be the foundation of the empirical model presented in section 2.2. The model will from now on also be referred to as the PR-model.
2.1.1 The monopoly case
Consider a monopoly firm. If y is a vector of output variables affecting firm revenue, and z a vector of q exogenous variables shifting the revenue function of the curve, the sole firms revenue function can be described as
R= R(y, z) (2.1)
The firm’s cost is either directly, or indirectly, connected to y resulting in a cost function
C = C(y, w, t) (2.2)
5
where w is a vector of factor prices and t a vector of variables shifting the firms cost function. It is also possible for z and t to have common variables. Profits of the firm can be expressed as
π= R − C = π(y, z, w, t) (2.3)
Define y0 = arg maxyπ(y, z, w, t) and y1 = arg maxyπ(y, z, (1 + h)w, t) where the scalar
h > 0. Also define R0 = R(y0, z) ≡ R∗(z, w, t) and R1 = R(y1, z) ≡ R∗[z, (1 + h)w, t],
where R∗is the reduced form revenue function of the firm. By using equation (2.3) and that
the cost function is homogenous of degree one, the following is true by profit maximization R1− (1 + h)C(y1, w, t) > R0− (1 + h)C(y0, w, t) (2.4)
and
R0− C(y0, w, t) > R1− C(y1, w, t) (2.5)
Multiplying (2.5) with (1 + h)
(1 + h)[R0− C(y0, w, t)] > (1 + h)[R1− C(y1, w, t)] (2.6)
and adding (2.6) to (2.4) gives
(1 + h)[R0− C(y0, w, t)] − (1 + h)[R1− C(y1, w, t)]
+R1− (1 + h)C(y1, w, t) − R0+ (1 + h)C(y0, w, t) > 0
− h(R1− R0) > 0 (2.7)
Dividing (2.7) with h2 gives
R1− R0
h =
R∗[z, (1 + h)w, t] − R∗(z, w, t)
h 6 0 (2.8)
Equation (2.8) shows that an equiproportional cost increase results in a decrease in the rev-enues of the firm. Assuming that the firms reduced form revenue functions is differentiable, taking the limit of h and dividing with R∗
which gives the sum of factor price elasticities of the reduced form revenue function. Equa-tion (2.9) shows that the sum of these elasticities must be nonpositive in the case of a monopoly firm.
2.1.2 Monopolistic competition
In the case of differentiated products across various firms, the monopolistic competition case is a possible market imperfection. Panzar and Rosse argue, with a discussion about the work by Chamberlin (1962) and the Chamberlin equilibrium, that
“Each firm, viewed in isolation, would, in both theories6, behave exactly as a monopoly would,
and its actions would satisfy all the conditions of profit maximization. Nevertheless it may be hoped that by examining the effects of changes in exogenous variables the “hidden” forces of Chamberlin’s “group equilibrium” condition may come into focus” - (Panzar and Rosse, 1987, p. 448-449) The analysis is thus based on how the single acts in a long-run equilibrium, when prices and number of firms active on the market have adjusted. A way to distinguish the monopolistic competition case from perfect competition is desirable, and also possible to do by analyzing the elasticity of factor prices derived later in this section. The monopolistic competition concept used here could be called “The long-run monopolistic competition” or ‘Chamber-linian Monopolistic Competition” and is a long-run equilibrium where the number of firms is endogenous.
By using comparative statics and defining R(y, n, z) = yP (y, n, z), where n is the number of firms , the monopolistic competition case is defined by equation (2.10) and (2.11) and describes the long-run equilibrium values y∗and n∗, treating the other variables
as exogenous.
Ry(y∗, n∗, z) − Cy(y∗, w, t) = 0 (2.10)
R(y∗, n∗, z) − C(y∗, w, t) = 0 (2.11)
In order to derive an expression for the factor price elasticities, using that R(y∗, n∗, z) =
R∗(z, w, t) from section 2.1.1 and the chain rule, differentiating (2.11) gives ∂R∗ ∂wi = Cy ∂y∗ ∂wi + ∂C ∂wi = Cy ∂y∗ ∂wi + x∗i (2.12)
where x∗iis the optimal quantity of production factor i, following Shepard’s lemma. Multi-6
plying by (wi/R∗) and summing over equation (2.12) Ψ∗ = i X i=1 wi R∗ ∂R∗ ∂wi = Cy R∗ i X i=1 wi ∂y∗ ∂wi + C R∗ (2.13)
Thus, an expression for the factor price elasticities is defined. ∂y∗/∂w
i is obtained by
totally differentiating (2.10) and (2.11) with respect to y∗, n∗ and wi, and solving using
Cramer’s rule7 ∂y∗ ∂wi = Rn(∂x ∗ i/∂y) − Rynx∗i D∗ (2.14)
where D∗ = (Ryy− Cyy)Rn > 0 from appendix C.1. Substituting (2.11) and (2.14) into
equation(2.13) gives
Ψ∗ = Cy[RnP wi(∂x
∗
i/∂y) − RynP wix∗i]
R∗D∗ + 1
As x∗i represents the cost minimizing input factor i, a change in this when the output level (y) changes should equal marginal cost if multiplied with wi.
i X i=1 wi(∂x∗i/∂y) = ∂C ∂y = Cy From this, and using thatPi
i=1wix∗i = C, it follows that
Ψ∗= 1 + Cy[RnCy− RynC] R∗D∗
Again using (2.10) and (2.11)
Ψ∗ = 1 +Ry[RnRy− RRyn]
R∗D∗ (2.15)
By using the inverse demand function and the fact that R = P y, the bracketed term 7
(RnRy− RRyn) can be rewritten as
(P yn+ yPn)(P + yPy) − P y(Pn+ ynPy+ yPyn)
= y2PnPy− y2P Pyn+ P2yn
The term P2y
n will disappear. The intuition is that a the change in n will not affect the
markets output, as the monopolistic equilibrium quantity is reached only with a specific number of firms acting simultaneously in the long-run equilibrium. Entry of one more firm must result in an exit of another, otherwise the long-run equilibrium will not hold. Hence, output will not change, yn= 0 and the final equation reduces to
y2(PnPy− P Pyn) = (RnRy− RRyn) (2.16)
Inserting (2.16) into (2.15) yields
Ψ∗= 1 + Ry[y
2(P
nPy − P Pyn)]
R∗D∗ (2.17)
An assumption made by Panzar and Rosse in deriving the monopolistic competition outcome is that
“The elasticity of perceived demand facing the individual firm [...] is a nondecreasing function of the number of (symmetric) rivals ”- (Panzar and Rosse, 1987, p. 450)
Writing the elasticity as e(y, n, z) ≡ −P/(y∂P/∂y), where P = P (y, n, z) and ∂P/∂y ≡ Py < 0. We also say that ∂P/∂n ≡ Pn < 0. This leads to the fact that en > 0, which
implies that if there are entries into the market, and thereby more substitutes, the demand facing the sole firm becomes more elastic and reduces the market power exhibited by that firm (Vesala, 1995). en can be expressed as
en = P yPyn (yPy)2 − Pn yPy = −PnPy − P Pyn yP2 y (2.18) As en > 0, the numerator must be less than zero. Knowing this, its possible to sign Ψ.
zero the second term in equation (2.17) must be negative. This implies that
Ψ < 1 (2.19)
which states that if the factor prices are increased with one percent, there will not be an equally large increase (or decrease) in the reduced form revenue.
2.1.3 Perfect competition
The conditions for perfect competition, price equal to marginal cost and zero profit, must be fulfilled. These are written as
pc− Cy(yc, w, t) = 0 =⇒ pc= Cy(yc, w, t) (2.20)
pcyc− C(yc, w, t) = 0 =⇒ pcyc= Rc(w, t) = C(yc, w, t) (2.21) where pcand ycis the equilibrium price and output, respectively, in the perfect competition
case, and Cythe firms marginal cost with respect to output. Equation (2.20) represents the
single firms first order profit maximizing condition, whilst equation (2.21) is the long-run equilibrium condition. Using these two equations and totally differentiating with respect to yc, pcand w
i, and then solving by Cramer’s rule yields8
∂yc ∂wi = x ∗ i − yc(∂x ∗ i/∂yc) ycC yy (2.22) Using (2.21) and Shepard’s lemma, the derivative of Rc with respect to w
i yields ∂Rc ∂wi = Cy ∂yc ∂wi + x∗i Multiplication by wi and summarize
i X i=1 wi ∂Rc ∂wi = Cy i X i=1 wi ∂yc ∂wi + i X i=1 wix∗i (2.23) 8
Inserting (2.22), dividing with Rc and using (2.20) and (2.21) to simplify and rewrite the expression in (2.23) Ψc = i X i=1 ∂Rc ∂wi wi Rc = Cy Rc i X i=1 wi x∗i − yc(∂x∗ i/∂y) ycC yy + i X i=1 wix∗i R = Cy RcycC yy (C − ycCy) + C Rc = P RcycP y (pcyc− pcyc) +R c Rc = 1 (2.24)
Thus, equation (2.24) shows that the sum of elasticities of the reduced form revenue func-tion with respect to factor prices is equal to the one in the long-run partial equilibrium, meaning that a proportional increase in factor prices leads to an equiproportional increase in revenues in the long-run equilibrium.
2.1.4 The Ψ-statistic
From the previous sections Ψ is defined as Pi
i=1[(∂R/∂wi)(wi/R)] which represents the
sum of elasticities of the reduced from revenue function. From now on this elasticity is called the Ψstatistic. Summing up the findings regarding Ψ obtained in sections 2.1.1 -2.1.3 produces table 2 where the Ψ-statistic and its implications are presented. Earlier studies often denote the measure as a H-statistic. However, this paper will follow the original notation (Ψ) by Panzar and Rosse.
There are, however, four additional possible outcomes that were not derived above. Perfectly collusive oligopoly outcome (oligopoly in a contestable market) which occurs at Ψ 6 0 (Shaffer, 1983), conjectural variation oligopoly at Ψ > 0 (Panzar and Rosse, 1987) re-spective natural monopoly and a “sales maximizing firm subject to a break-even constraint” which both corresponds to Ψ = 1 (Shaffer, 1982). These outcomes are not analyzed further as the Swedish banking sector, most likely, are not an oligopoly market, following from the extensive control systems laid out by the government which should notice this type of un-desirable behavior. A natural monopoly is neither likely as firms are able to stay in the market and still make profits, which are not in line with this structural form.
Table 2: Outcomes of the Ψ-statistic Type of market Ψ = 1 Perfect competition Ψ < 1 Monopolistic competition
Ψ 60 Monopoly
equilibrium (Panzar and Rosse, 1987) (Shaffer, 1982). If the firms are not in equilibrium, adjustments in, for example, prices and quantities or entry and exit will most likely occur, leading to effects not incorporated in the analysis and, thus, inaccurate estimates (Shaffer, 1982) (Vesala, 1995). A simple test for ensuring equilibrium is described in section 2.2.1.
2.2 Empirical model
The theoretical PR-model must be transformed into an empirical model in order to be estimated. Following Bikker and Haaf (2002) the reduced form revenue function could be written as a regression model as
ln R∗ = α + m X i=1 βiln wi+ n X l=1 δlln cl (2.25)
where cl is a vector of n bank specific variables containing the variables z and t from the
revenue respective cost equations (2.1) and (2.2). This empirical version of the PR-model can be used in estimating the elasticities of the factor prices, and therefore test whether the firms behave as monopolists, monopolistic competitors or in accordance with perfect competition. By taking the natural logarithm of each variable the parameter estimates can be directly interpreted as elasticities. This imply that the Ψ-statistic is
Ψ =
m
X
i=1
βi
Scaling the dependent variable makes the revenue function become a price function, which will not work in the estimations of the Ψ-statistic. (Bikker et al., 2011). In this study, the dependent variable will not be scaled, nor will any separate scaling factor, such as total assets, be included which is in line with the discussion of Bikker et al.
2.2.1 Test for long-run equilibrium
As was described in section 2.1.4, the sample used in estimating the Ψ-statistic needs to be in a long-run equilibrium. A widely used method (see (Nathan and Neave, 1989), (Claessens and Laeven, 2004) or (Gischer and Stiele, 2009)) is the one proposed by (Shaffer, 1982) where an empirical test for equilibrium is conducted by replacing the dependent variable with a variable representing rate of return. Shaffer writes
“If the risk level of a bank is unaffected by its input prices within the observed range of prices, and if all banks in the sample compete in the same capital market, then equilibrium rates of return should not be statistically correlated with input prices. If, however, the banks are in transition toward a new equilibrium, then an increase (decrease) in factor prices would show up as a temporary decline (increase) in the rate of return producing a negative correlation between factor prices and the rate of return.” - (Shaffer, 1982, p. 230)
Thus, by using returns on assets (ROA) as the dependent variable, an approach adopted by many other studies, if the ΨROA-statistic sums to zero, and a hypothesis test confirms
equality to zero, the sample is indeed in long-run equilibrium. The statistic is defined as
ΨROA =X∂ROA ∂wi wi ROA
3
Empirical Framework
3.1 DataThe data is a strongly balanced panel data set collected from the annual reports of each bank. The banks included in the sample are shown in appendix A. The time range is 2002 to 2010. The choice of time period is mainly due to that the Swedish Companies Registration Office (SCRO)9 only keeps digital copies of the annual reports up to ten years, and the
reports for the year 2011 have not been published yet by the majority of banks. The data is partly also available through Statistics Sweden (SCB), but because of the analysis of
9
savings banks, which often tend to be small and do not report to SCB, this source does not contain much of the data needed.10 The banks included in the data set are retail banks,
meaning that they offer regular bank services (e.g. mortgage lending and debit- and credit cards) to the broad public. This is to make sure the market is fairly the same for all banks in the sample and are therefore excluding niche banks.
The collected data mainly follows the international accounting standard IFRS. Nordea and ICA Banken reports their results in euro for the whole time period respective since 2009. The yearly average exchange rate EUR/SEK for respective year is used to convert the numbers into Swedish kronor, which is the currency used in the data set. All monetary variables are expressed with their real values in 2012 by the consumer price index provided by SCB.
3.1.1 Exclusion of banks
Unfortunately it is not possible to use data for all savings banks. The main reason is that 15 out of 64 savings banks are missing data due to missing records of annual reports in the archives of the SCRO. Attempts to contact these banks and receive reports directly from them have also been made without any success. A full list of which savings banks not included is provided in appendix A. Although 15 savings banks are missing, it is a fair assumption that the results of this paper will not be affected significantly and the estimation process still be valid as there are 49 banks remaining.
In the estimation of competition within commercial banks there is also firms missing. A list of banks is provided in appendix A. The majority of banks excluded are done so because their main business area in Sweden are not retail banking but instead have a niche towards, for example, investment banking or savings11.
The banks included are also acting mainly in the Swedish market, meaning that the majority of their income originates from Swedish customers, which excludes for example Danske Bank and DnB Nor which have their largest share of customers in Denmark and Norway. A consequence of this is that one of the four largest banks acting at the Swedish market, Nordea, is also excluded. The reason being that the income from the Swedish market represents about 25% of their total income. Including Nordea could alter the assumption of banks acting in the same market because of their large involvement in
10
The same reasoning holds for other databases, such as Bankscope or OSIRIS
11It is important to distinguish between savings banks (the bank type) and banks involved only or mainly
other countries, and therefore also competition with other actors that the other banks in the sample do not face. For completeness, estimations including Nordea is provided in appendix B.3. The same reasoning could be applied on especially Swedbank and SEB due to their activity in the Baltic countries, but also Handelsbanken and its involvement in the British bank market. These three banks are, however, not excluded because their share of income from the Swedish market is at least about 70% of their respective total income and are therefore considered to compete mainly on the Swedish market. As the purpose of this thesis mainly is to write about the competition of savings banks, the exclusion of Nordea do not affect the savings banks result, nor the commercial bank results which is obvious by comparing table 4 and 10.
3.2 Model
There are almost as many different variations of the Panzar-Rosse model as there are articles. One common factor is, however, the dependent variable, corresponding to the revenue, which most often is proxied by the total income (TI) of the bank or total interest income (TII), both collected from the income statement in the annual reports. The reason for using total income is that banks today have other business areas than just the ones generating interest income, such as debit card and insurances, and that all of them should be taken into account. A drawback of using total income is that, for example, losses in a banks trading activity is included (as well as profits) lending to dramatically lower income for several savings banks in 2008 and 2009, partly due to the massive drop in the Swedbank share price. As the main business of banks is leading, using total interest income should also make a good proxy for the revenue variable. For completeness, both dependent variables (TI and TII) are regressed in different specifications.
The proxies for factor prices are the funding rate, cost of personnel and capital expen-diture. These three factor price variables are widely applied when using the Panzar-Rosse model (see, for example, Gischer and Stiele (2009) and Molyneux et al. (1996)), although different calculation methods are used. Definitions of the variables are provided in table 3. Funding rate is included as this is probably the single most important input factor for the bank, being able to fund lending. The funding is made partly by deposits and also other sources such as the central bank and a higher value implies that the bank’s cost of borrowing are higher.
branches. The bank employees could also be viewed as salesmen trying to improve the income of the bank. The variable is scaled by the number of employees.
Other operating costs refer to all non-personnel costs a bank faces and proxy the phys-ical cost of capital, and is scaled with total assets. This post includes, among other things, marketing and IT expenses as well as rent.
Turning to the bank specific variables (cl in equation (2.25)), there is usually variables
included reflecting risk, funding mix, banking behavior and other control variables. In order to measure risk, equity to total assets (EQ) is included. A higher equity ratio usually means the bank is not taking as high risks as with a lower equity, and therefore may not earn as much income. A higher equity, however, also implies that the bank needs not seek as much external financing, leading to less interest costs. The sign of this coefficient is therefore expected to be ambiguous.
Lending towards the public to total assets ratio reflects the banks portfolio composition and business mix. A higher share of outstanding loans to the public (mainly consumers and companies) should lead to increased interest revenues, as well as total revenues. The sign is expected to be positive.
The number of branches operated by the bank is affecting the possibility to be close to the customer and thereby offering local services and potential additional sales. Many branches may, in short, lead to a closeness with the community and customers, which could lead to a larger share of the customers in the area, and thereby also increasing profits. Branches are, however, associated with higher costs not only for the personnel and facilities, but also for security and handling cash. The sign of this coefficient is therefore expected to be ambiguous.
The dependent variable used for determining whether the sample is in long-run equi-librium is defined as the operating result divided by total assets, plus one to account for negative operating results.
In addition, regressions will be conducted to analyze if there is any difference in com-petitive behavior between small, medium sized and large savings banks. Findings from, for instance, Gischer and Stiele (2009) suggest that smaller savings banks tend to behave less competitive than larger ones. Thus, this is an interesting aspect to investigate also in Sweden. The division between different sizes is based on the number of employees where the 33 and 66 percentile has been used as limits for respective size. The 33 percentile occurs at 25 employees, and the 66 percentile at 70.
Table 3: Proxies for revenue- and cost variables
Variable Calculation
FP1 Funding rate Total liabilities - (Equity + Reserves)Interest expenses
FP2 Personnel cost Number of employeesPersonnel expenses
FP3 Other costs Non-personnel expensesTotal assets
EQ Attitude towards risk Total equityTotal assets
CL Business mix by public loans Lending towards the public Total assets
BR Branches Number of branches
ROA Return on assets 1 +Operating resultTotal assets
Specification 1:
ln T Ii,t =α0,i+ β1ln F P1i,t+ β2ln F P2i,t+ β3ln F P3i,t + δ1ln EQi,tδ2ln CLi,t+ δ3ln BRi,t+ i,t
(3.1)
Specification 2:
ln T IIi,t=α0,i+ β1ln F P1i,t+ β2ln F P2i,t+ β3ln F P3i,t + δ1ln EQi,tδ2ln CLi,t+ δ3ln BRi,t+ i,t
(3.2)
Descriptive statistics and correlation matrices for all savings banks, commercial banks and overall sample is provided in appendix B.1. All specifications are estimated using a fixed effects estimator along with robust standard errors. The robust standard errors, and the fact that the variables are scaled down and in logarithmic form, is a way of coping with potential heteroskedasticity, which is common in panel data. Fixed effects are used to account for bank specific characteristics that could influence the predictions, which are not desirable. Instead the time specific effects are captured.
with that of other banks, thus a Hausman test is conducted to every group to determines if the fixed effects estimator is the appropriate one to use, or if the random effects estimator should be used instead. All χ2-statistics produced from the Hausman test are significant
at 5%-level or less which confirms the use of the fixed effects estimator. In order to test whether the obtained Ψ-statistics are statistically distinct from unity (perfect competition) and/or zero (monopoly), Wald test’s is conducted. Thus, the hypothesis of these tests are Ψ = 0 and Ψ = 1.
The test for long-run equilibrium is performed by regressing the model
ln ROAi,t =α0,i+ φ1ln F P1i,t+ φ2ln F P2i,t+ φ3ln F P3i,t + δ1ln EQi,tδ2ln CLi,t+ δ3ln BRi,t+ i,t
(3.3)
As specification 1 and 2 contain the same independent variables, only one equilibrium specification is needed. A fixed effects estimation is done with robust standard errors also for this model. As explained in section 2.2.1, the sum of factor price elasticities in equation (3.3) should be zero for the models to be in long-run equilibrium, thus
ΨROA = φ1+ φ2+ φ3 = 0 (3.4)
4
Results
The estimation results from specification I and II are provided in table 4 on pages 26 and 27. Applying Wooldridge’s test for serial correlation12 in fixed effects panel data
sets no significant p-values was generated, meaning no serial correlation was found. The correlation matrices in appendix B.1 show no sign of correlation between variables that must be corrected for.
The long-run equilibrium test is provided in appendix B.2. All specification’s and groups yield ΨROA estimates around zero, implying a long-run equilibrium bank sector.
By using a Wald test, the null hypothesis that ΨROA = 0 could not be rejected.
Turning to the main results from the estimations, the banks funding rate (β1) has a
significant effect in all cases, but one, and yields a slightly negative estimate using total income as dependent variable, but positive if using total interest income. The p-values using
Table 4: Estimation results (a)
All banks Savings banks Commercial banks
I II I II I II FP1 (β1) -0.057∗∗ 0.321∗ -0.037∗∗∗ 0.325∗ -0.248∗∗ 0.256 (0.023) (0.023) (0.022) (0.019) (0.094) (0.167) FP2 (β2) 0.420∗ 0.469∗ 0.332∗ 0.482∗ 0.754∗∗∗ 0.110 (0.966) (0.067) (0.054) (0.070) (0.355) (0.269) FP3 (β3) -0.124∗∗ -0.285∗ -0.092∗∗ -0.209∗ -0.313∗∗∗ -0.677∗ (0.049) (0.060) (0.037) (0.046) (0.150) (0.104) EQ (δ1) -0.035 -0.527∗ 0.131 -0.446∗ -1.296∗ -0.730∗ (0.293) (0.073) (0.144) (0.071) (0.205) (0.182) CL (δ2) 0.060∗∗∗ 0.016 0.254 0.054 0.191∗ 0.078∗∗ (0.031) (0.018) (0.193) (0.165) (0.206) (0.028) BR (δ3) 0.106 0.132∗ 0.144∗ 0.095∗∗ -0.411∗∗∗ 0.208 (0.069) (0.049) (0.041) (0.042) (0.213) (0.168) Constant 7.427∗ 7.564∗ 8.720∗ 7.611∗ 5.237∗∗ 9.717∗ (0.940) (0.584) (0.567) (0.526) (1.718) (1.701) Obs. 513 513 441 441 72 72 R2-adj 0.988 0.995 0.980 0.990 0.980 0.989 F-value 10.92 46.25 19.69 57.56 135.86 246.23 Ψ 0.239 0.505 0.203 0.598 0.193 -0.311 Ψ = 01 3.32 24.21 8.37 35.71 0.14 0.48 [0.074] [0.000] [0.006] [0.000] [0.724] [0.512] Ψ = 11 33.50 23.37 129.69 16.11 2.35 8.46 [0.000] [0.000] [0.000] [0.000] [0.169] [0.023]
Notes: Robust standard errors in parentheses. p-values in brackets.
∗p <0.01,∗∗p <0.05,∗∗∗p <0.10
All Ψ-statistics are in long-run equilibrium
1 F-value for Wald-test that β
1+ β2+ β3equals zero or unity.
Variables: FP1, funding rate; FP2, personnel cost; FP3, other costs; EQ, equity to total assets; CL, public lending to total assets; BR, number of branches
Dependent variables: I, Total income; II, Total interest income
Table 4: Estimation results (b)
Small savings banks Medium savings banks Large savings banks
total income are above the 10%-level for all regressions run on different sizes. Increasing the funding of the bank yields higher interest income, but lower total income.
The personnel costs (β2) have a positive effect in both specifications which is significant
mostly at the 1%-level. The personnel as factor price has a positive impact on the sales of the bank, not only in yielding good interest income but also when it comes to other business areas, proxied by the total income variable. This variable has the greatest impact on Ψ and could therefore be regarded as the most important feature of the bank.
The estimated effects of other costs (β3) imply that increasing this post will yield lower
total- and interest income. Being significant mostly at the aggregated regressions (e.g. including all banks of each type) it implies that increasing costs referring to, for example, rents or marketing would decrease income.
Turning to the coefficients not associated with the Ψ-statistic there is fairly poor sig-nificance for each of them depending on specification and group analyzed. The coefficient taking risk into account (δ1) is in most cases negative or just slightly positive, while the
opposite is true for δ2. For to branches (δ3), an increased number of branches seems to
favor income of the bank as the coefficient is positive for all specifications and groups. The estimated effects of factor price elasticities give Ψ-statistics that mostly are con-sistent with monopolistic competition. The one exception is for commercial banks where using total interest income as dependent variable yields a negative Ψ. Applying Wald test’s on each statistic, in order to determine if the statistics are different from zero and/or unity, confirms the conclusion of monopolistic competition for all banks, all savings banks and small savings banks. This is also true using specification I for medium- and specification II for large savings banks. Applying the Wald test on specification I for large savings banks and commercial banks, neither hypothesis of Ψ = 0 or Ψ = 1 can be rejected im-plying that the structure can not be statistically confirmed by the Ψ-statistic. Looking at medium savings bank, the hypothesis of perfect competition can not be rejected. Turning to specification II for commercial banks the unity Wald test can be rejected, but not the monopoly hypothesis, which is consistent with the negative value of Ψ. Thus, commercial banks could, using interest income as dependent variable, be characterized by monopoly behavior.
level of significance for each coefficient.
One explanation of the low significance levels when estimating the model based on data for the commercial banks, and savings banks of different sizes, are the small number of observations. In the case of commercial banks a relaxation of the restriction only to include retail banks could be made, which would increase the number of participating banks a bit.
5
Conclusion
The purpose of this paper is to study the Swedish savings banks sector and determine if it is characterized by perfect competition. Earlier studies suggest that the Swedish banking sector as a whole is acting in a monopolistic competitive manner, and that this also holds for the savings banks specifically. The analysis is made with the Panzar-Rosse model, which has been widely applied amongst the academic literature when analyzing bank competition. The panel data set, obtained from the annual reports of each bank, contains 49 savings banks and 8 commercial banks. The time period stretches from year 2002 to 2010. Using a fixed effects model with robust standard errors the estimation results, provided in table 4, are obtained. The dependent variables used are total income of the bank, and total interest income.
players hold the majority of the assets, all of which are commercial banks. This might justify the low Ψ-statistic estimated for these banks. An interesting aspect of this would be to analyze the four major banks specifically, as one might suspect that the monopolic behavior can be tracked to them alone.
The findings of monopolistic competition in the whole banking sector are much in line with previous studies performed on the Swedish banking sector. See, for example, Bikker and Groeneveld (2000), Bikker and Haaf (2002) and Carbo et al. (2009) which all find this with the Panzar-Rosse model, or Sj¨oberg (2007) who concludes that the local banking market is not characterized by perfect competition. A comparison of the results for savings banks with previous studies is not possible to do for the Swedish market as the Panzar-Rosse model has not yet been applied on the Swedish savings banks sector by other studies. However, studies performed in the German market are also concluding monopolistic competition in the savings banks sector (see Gischer and Stiele (2009) and Hempell (2002)). Hempell (2002) found that the savings banks are less competitive than commercial banks, which is not the finding in this paper. Also, Gischer and Stiele (2009) find that the Ψ-statistic is larger for larger savings banks when using total interest income as dependent variable, which is not entirely the findings in this paper.
Year-to-year estimates for the Ψ-statistics would have been interesting in order to see the development in competition for every year in the Swedish banking sector. Unfortunately the number of observations corresponding to each year makes it hard to obtain significant parameter estimates and valid models for these regressions, especially for the commercial banks but also for the savings banks. At the same time it is hard to obtain data for more banks, as the Swedish bank market is relatively small why another approach than the Panzar-Rosse, or a restated econometric model, might be appropriate.
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A
List of banks
Table 5: Savings banks
Attmars Sparbank* Orusts Sparbank Sparbanken ¨Oresund (C)
Bergslagens Sparbank (C) Roslagens Sparbank Swedbank Sjuh¨arad (C)
Bjurs˚as Sparbank Sala Sparbank S¨odra Dalarnas Sparbank*
Dalslands Sparbank Sparbanken i Karlshamn S¨odra Hestra Sparbank
Ekeby Sparbank* Sidensj¨o Sparbank S¨olvesborg-Mj¨allby Sparbank
Falkenbergs Sparbank Skurups Sparbank S¨ormlands Sparbank
Frenninge Sparbank* Snapphanebygdens Sparbank Tidaholms Sparbank
Fryksdalens Sparbank Sparbanken 1826 Tjustbygdens Sparbank (C)
F¨ars & Frosta Sparbank (C) Sparbanken Alings˚as (C) Tj¨orns Sparbank
H¨alsinglands Sparbank Sparbanken Boken Ulricehamns Sparbank
H¨aradssparbanken M¨onster˚as Sparbanken Eken* (C) Vadstena Sparbank*
H¨ogsby Sparbank Sparbanken Gotland Valdemarsviks Sparbank
Ivetofta Sparbank i Brom¨olla* Sparbanken G¨oinge* Varbergs Sparbank (C) Kinda-Ydre Sparbank Sparbanken i Enk¨oping* (C) Vimmerby Sparbank (C)
Laholms Sparbank* Sparbanken Lidk¨oping (C) Virserums Sparbank
Lekebergs Sparbank Sparbanken Nord Westra Wermlands Sparbank
Leksands Sparbank Sparbanken Rekarne (C) ˚Alems Sparbank*
L¨onneberga-Tuna-Vena Sparbank* Sparbanken Skaraborg (C) ˚Ase och Viste h¨arads Sparbank
Markaryds Sparbank Sparbanken Syd ˚Atvidabergs Sparbank
Mj¨ob¨acks Sparbank** Sparbanken Tanum Olands Bank (C)¨
Norrb¨arke Sparbank* Sparbanken Tranemo*
N¨ars Sparbank Sparbanken V¨astra M¨alardalen
∗ Data not available (14 banks) Total: 64 banks (49 used in analysis)
∗∗ Chose not to participate (1 bank) (C)=Commercial savings bank
Table 6: Commercial banks
Handelsbanken SBAB
ICA Banken SEB
IKANO Bank Skandiabanken
L¨ansf¨ors¨akringar Bank Swedbank Nordea∗13
∗ Excluded (1 bank) Total: 9 banks
B
Econometric appendix
B.1 Correlation matrices and descriptive statistics
Correlation matrices are provided at page 35. Descriptive statistics are found at page 36. Table 7: Correlation matrices
All banks Savings banks
Variables FP1 FP2 FP3 EQ CL BR Variables FP1 FP2 FP3 EQ CL BR FP1 1.000 FP1 1.000 FP2 0.023 1.000 FP2 -0.152 1.000 FP3 -0.029 -0.146 1.000 FP3 0.039 -0.053 1.000 EQ -0.233 -0.008 0.005 1.000 EQ -0.028 0.205 -0.072 1.000 CL -0.264 -0.181 0.280 0.258 1.000 CL -0.072 0.127 0.020 0.159 1.000 BR 0.190 -0.017 -0.263 -0.427 -0.534 1.000 BR 0.060 -0.123 0.145 -0.276 0.069 1.000
Commercial banks Small savings banks
Variables FP1 FP2 FP3 EQ CL BR Variables FP1 FP2 FP3 EQ CL BR FP1 1.000 FP1 1.000 FP2 0.180 1.000 FP2 -0.142 1.000 FP3 -0.228 -0.185 1.000 FP3 0.039 0.089 1.000 EQ -0.160 -0.299 0.628 1.000 EQ -0.026 0.339 0.169 1.000 CL -0.027 -0.185 0.660 0.358 1.000 CL -0.106 -0.164 -0.084 -0.404 1.000 BR -0.051 -0.282 -0.582 -0.353 -0.656 1.000 BR 0.127 -0.281 -0.124 -0.313 0.096 1.000
Medium sized savings banks Large savings banks
B.2 Long-run equilibrium (ROA) test
Only estimations from the factor price variables are presented in table 9, as these are the interesting coefficients in the ROA-test. The estimated model corresponds to equation (3.3) and is run for each group. A complete result table is available upon request.
Table 9: Estimation results ROA test
All banks SB CM Small Medium Large
FP1 (φ1) -0.003∗ -0.003∗ -0.005 -0.003∗∗ –0.003∗∗∗ -0.002 (0.001) (0.001) (0.004) (0.001) (0.002) (0.002) FP2 (φ2) -0.001 -0.002 0.000 -0.001 0.002 0.001 (0.002) (0.002) (0.010) (0.003) (0.006) (0.013) FP3 (φ3) 0.002 0.004 -0.004 -0.002 0.005 -0.004 (0.002) (0.002) (0.005) (0.003) (0.006) (0.006) Obs. 513 441 72 151 143 147 R2-adj 0.366 0.348 0.496 0.349 0.410 0.2875 F-value 4.77 9.25 3.07 8.71 5.74 7.03 ΨROA -0.002 -0.001 -0.009 0.006 0.004 0.003 Ψ = 01 0.14 0.10 0.27 0.19 0.19 0.02 [0.711] [0.752] [0.620] [0.665] [0.667] [0.876]
Notes: Robust standard errors in parentheses. p-values in brackets.
∗p <0.01,∗∗p <0.05,∗∗∗p <0.10 1F-value for Wald-test that φ
1+ φ2+ φ3= 0.
Abbrevations: SB. Savings banks; CM, Commercial banks
B.3 Estimates including Nordea
For completeness a result table including the commercial bank Nordea is provided. The models used are the same as in equations (3.1) through (3.3). Comparing table 10 and 4 show that the estimates does not differ much. The Ψ-statistics are almost identical as well as the estimates. Therefore the assumption that the exclusion of Nordea does not change the estimates appreciably is justified.
Table 10: Estimation results including Nordea
All banks Commercial banks
I II ROA I II ROA FP1 (β1/φ1) -0.058∗∗ 0.322∗ -0.003∗ -0.231∗∗ 0.275 -0.005 (0.023) (0.023) (0.001) (0.09) (0.157) (0.004) FP2 (β2/φ2) 0.430∗ 0.470∗ -0.001 0.697∗∗∗ 0.071 -0.002 (0.097) (0.067) (0.002) (0.341) (0.258) (0.010) FP3 (β3/φ2) -0.128∗∗ -0.288∗ 0.002 -0.293∗∗∗ -0.668∗ -0.004 (0.049) (0.059) (0.002) (0.143) (0.096) (0.005) EQ (δ1) -0.344 -0.526∗ 0.002∗ -1.284∗ -0.725∗ -0.000 (0.292) (0.072) (0.005) (0.222) (0.194) (0.010) CL (δ2) 0.060∗∗∗ 0.016 -0.002∗∗ 0.185∗ 0.074∗∗ 0.001 (0.031) (0.018) (0.001) (0.025) (0.025) (0.001) BR (δ3) 0.112 0.136∗ 0.003 0.095 0.232 -0.025 (0.069) (0.049) (0.002) (0.210) (0.167) (0.008) Constant 7.457∗ 7.629∗ 0.058∗ 6.170∗ 10.198∗ -0.026 (0.932) (0.572) (0.021) (1.480) (1.324) (0.035) Obs. 522 522 522 81 81 81 R2-adj 0.990 0.996 0.365 0.984 0.990 0.492 F-value 11.58 46.87 4.76 263.52 303.81 2.96 Ψ 0.244 0.504 -0.002 0.173 -0.322 -0.011 Ψ = 01 3.27 24.18 0.13 0.11 0.51 0.33 [0.076] [0.000] [0.7191] [0.748] [0.4941] [0.5808] Ψ = 11 32.87 23.49 — 2.50 8.65 — [0.000] [0.000] — [0.1522] [0.0187] —
Notes: Robust standard errors in parentheses. p-values in brackets.
∗p <0.01,∗∗p <0.05,∗∗∗p <0.10 1F-value for Wald-test that β
1+ β2+ β3 equals zero or unity.
Variables: FP1, funding rate; FP2, personnel cost; FP3, other costs; EQ, equity to total assets; CL, public lending to total assets; BR, number of branches
C
Mathematical appendix
C.1 Monopolistic competition (section 2.1.2)
Totally differentiating equations (2.10) and (2.11) with respect to y∗, n∗ and wi yields
equation (C.1) and (C.2)
(Ryy− Cyy)∂y∗+ Ryn∂n∗ = Cywi∂wi (C.1)
(Ry− Cy)∂y∗+ Rn∂n∗= Cw i∂wi (C.2)
writing in matrix form gives " (Ryy− Cyy) Ryn 0 Rn # " ∂y∗/∂wi ∂n∗/∂wi # = " Cywi Cw i # (C.3)
The term (Ry − Cy) = 0 because of the definition of equation (2.10). Applying Cramer’s
rule on the matrix in equation (C.3) it is possible to solve for ∂y∗/∂wi, which is interesting
in the forthcoming analysis in section 2.1.2.
∂y∗ ∂wi = Cywi Ryn Cwi Rn (Ryy− Cyy) Ryn 0 Rn
Solving the equation yields
∂y∗ ∂wi = CywiRn− CwRyn (Ryy− Cyy)Rn = CywiRn− CwRyn D (C.4)
where D is the determinant and are strictly bigger than zero due to the second order conditions from (2.10). By using Shepards lemma (Cy = x∗i), (C.4) can be rewritten as
∂y∗ ∂wi = Rn(∂x ∗ i/∂y∗) − Rynx∗i D (C.5)
C.2 Perfect competition (section 2.1.3)
Totally differentiating equations (2.20) and (2.21) with respect to yc, pc and w
i yields
equation (C.6) and (C.7)
− Cyy∂yc+ ∂pc= Cyw∂wi (C.6)
(pc− C
y)∂yc+ yc∂pc= Cw∂wi (C.7)
Rewriting in matrix form yields
" −Cyy 1 0 y # " ∂yc/∂wi ∂pc/∂wi # = " Cywi Cwi # (C.8) (pc− C
y) = 0 by equation (2.20). Solving for ∂yc∂wi by Cramer’s rule yields
∂yc ∂wi = Cywi 1 Cwi y c −Cyy 1 0 yc = y cC ywi− Cw −ycC yy
