1 2 Competition, concentration and 3 their relationship: An empirical analysis of 4 the banking industry 5 Jacob A. Bikker a, *, Katharina Haaf b 6 a De Nederlandsche Bank, Section Banking and Supervisory Strategies, P.O. Box 98, Nl-1000 AB 7 Amsterdam, Netherlands 8 b McGill University, Montreal, Canada 9 Abstract 10 This article examines competitive conditions and market structure in the banking industry, 11 and investigates their interrelationship. Competition is measured using the Panzar±Rosse 12 model. In order to distinguish competitive behaviour on local, national and international mar- 13 kets, for each country, three subsamples are taken: small or local banks, medium-sized banks 14 and large or international banks. For all 23 countries considered, estimations indicate monop- 15 olistic competition, competition being weaker in local markets and stronger in international 16 markets. Subsequently, a relationship for the impact of the market structure on competition 17 is derived and tested empirically, providing support for the conventional view that concentra- 18 tion impairs competitiveness. Ó 2002 Published by Elsevier Science B.V. 19 JEL classi cation: F36; G2; L1 20 Keywords: Local and international banks; Competition; Concentration; Market structure; 21 Panzar±Rosse model Introduction Journal of Banking & Finance xxx 2002) xxx±xxx 23 European banking markets are undergoing unprecedented changes, caused by the 24 deregulation of nancial services, the establishment of the economic and monetary 25 union EMU) and developments in information technology, which may well turn 26 out to be dramatic. Many of these changes will have vast implications for competi- * Corresponding author. Tel.: ; fax: address: J.A. Bikker) /02/$ - see front matter Ó 2002 Published by Elsevier Science B.V. PII: S )
2 2 J.A. Bikker, K. Haaf / Journal of Banking & Finance xxx 2002) xxx±xxx 27 tion and concentration in the banking and nancial sectors. One of the consequences 28 is already apparent in the recent wave of mergers in the European banking industry. 29 This process of concentration may a ect competition, in particular on local markets 30 for retail banking services. Questions may arise such as: Should concentration be slo- 31 wed down? or Are additional measures needed to ensure su cient competition in lo- 32 cal retail markets? Besides, increased concentration and the size of the new global 33 players may cause concerns about nancial stability. In order to judge the implica- 34 tions of these developments, one has to examine the banking industry's current mar- 35 ket structure, to determine the degree of competition, and to investigate the impact 36 the consolidation is likely to have on the market structure and the behaviour of 37 banks. In recent years, however, relatively few empirical studies have examined com- 38 petition and concentration in European banking markets. This article seeks to mea- 39 sure the degree of competition in the European banking markets, and to investigate 40 the impact of concentration on competition. Moreover, it attempts to compare the 41 situation in Europe with that in the US and other countries. 42 The literature on the measurement of competition may be divided into two main- 43 streams, called the structural and the non-structural approach. 1 The structural ap- 44 proach to model competition includes the structure-conduct-performance SCP) 45 paradigm and the e ciency hypothesis, as well as a number of formal approaches 46 with roots in industrial organisation theory. The SCP paradigm investigates whether 47 a highly concentrated market causes collusive behaviour among larger banks result- 48 ing in superior market performance; whereas the e ciency hypothesis tests whether 49 it is the e ciency of larger banks that makes for enhanced performance. In reaction 50 to the theoretical and empirical de ciencies of the structural models, non-structural 51 models of competitive behaviour have been developed namely the Iwata model, the 52 Bresnahan model, and the Panzar and Rosse P±R) model. These New Empirical In- 53 dustrial Organisation approaches measure competition and emphasise the analysis of 54 the competitive conduct of banks without using explicit information about the struc- 55 ture of the market. In this article we will use one of these non-structural models, the 56 P±R model, to assess the degree of competition in a large number of countries. One 57 of the structural approaches, the SCP paradigm, provides a theoretical relationship 58 between market structure concentration) and conduct competition) which, in the 59 empirical banking literature, is ignored. This article lls in this gap by using the 60 P±R model's measure of competition to test this relationship empirically. 61 Ideally, an evaluation of competitive conditions and the degree of concentration in 62 the banking industry should begin by rigorously de ning the market under consid- 63 eration. The relevant market consists of all suppliers of a particular banking service, 64 including actual or potential competitors, and it has a product dimension and a geo- 65 graphical dimension. The product de nition of a market is based on the equality of 66 the products as regards their ability to ful l speci c consumer wants. The geograph- 67 ical boundaries of a market are determined by actual and potential contacts between 68 actual and potential market participants. These boundaries depend on the products 1 For an overview, see Bikker and Haaf 2001).
3 J.A. Bikker, K. Haaf / Journal of Banking & Finance xxx 2002) xxx±xxx 3 69 involved: for retail banking, the local dimension of a market is relevant while the re- 70 gional or international dimension is relevant for corporate banking. The desirability 71 to de ne product and smaller-scale) geographical markets makes it harder to apply 72 competition and concentration models to the banking industry, especially given the 73 shortage in European) data with respect to speci c banking products or local re- 74 gions. 75 This article attempts to solve this problem to some extent by applying the P±R 76 model to samples of banks of various sizes, under the assumption that small banks 77 operate mostly at a local scale and that large banks compete more than other banks 78 at the international level, while medium-sized banks occupy an intermediate posi- 79 tion. Furthermore, retail banking is assumed to be concentrated mostly in small 80 banks while corporate banking occurs more at large banks. Banking behaviour in 81 geographical markets of various sizes is observed indirectly, through the data of in- 82 dividual banks used in the P±R model. Of course, this is only a rst step in the right 83 direction, but we do acquire information about the e ect of the size of) geographical 84 markets on competition. 85 The plan of this article is as follows. Section 2 introduces and explains the P±R 86 approach. Section 3 applies this model to banks in 23 industrialised countries. For 87 each country, four samples are taken: small, medium-sized and large banks and, - 88 nally, all banks. This section also displays various concentration indices and applies 89 them to the same) 23 industrialised countries. Finally, the relationship between com- 90 petition and concentration is tested empirically. The ultimate section summarises 91 and draws conclusions The Panzar and Rosse approach 93 Panzar and Rosse 1987) formulated simple models for oligopolistic, competitive 94 and monopolistic markets and developed a test to discriminate between these mod- 95 els. This test is based on properties of a reduced-form revenue equation at the rm or 96 bank level and uses a test statistic H, which, under certain assumptions, can serve as 97 a measure of competitive behaviour of banks. The test is derived from a general 98 banking market model, which determines equilibrium output and the equilibrium 99 number of banks, by maximising pro ts at both the bank level and the industry level. 100 This implies, rst, that bank i maximises its pro ts, where marginal revenue equals 101 marginal cost R 0 i x i; n; z i C 0 i x i; w i ; t i ˆ R i refers to revenues and C i to costs of bank i the prime denoting marginal), x i is the 104 output of bank i, n is the number of banks, w i is a vector of m factor input prices of 105 bank i, z i is a vector of exogenous variables that shift the bank's revenue function, t i 106 is a vector of exogenous variables that shift the bank's cost function. Secondly, at the 107 market level, it means that, in equilibrium, the zero pro t constraint holds R i x ; n ; z C i x ; w; t ˆ0 2
4 4 J.A. Bikker, K. Haaf / Journal of Banking & Finance xxx 2002) xxx±xxx 109 Variables marked with an asterisk ) represent equilibrium values. Market power is 110 measured by the extent to which a change in factor input prices dw ki ) is re ected in 111 the equilibrium revenues dr i ) earned by bank i. Panzar and Rosse de ne a measure 112 of competition H as the sum of the elasticities of the reduced-form revenues with 113 respect to factor prices 2 H ˆ Xm kˆ1 or i w ki ow ki R i 115 The rst market model Panzar and Rosse investigated describes monopoly. The 116 monopoly analysis includes the case of price-taking competitive rms, as long as the 117 prices they face are truly exogenous, that is, as long as their equilibrium values are 118 una ected by changes in the other exogenous variables in the model. An empirical 119 refutation of `monopoly' constitutes a rejection of the assumption that the revenues 120 of the banks in question are independent of the decisions made by their actual or 121 potential rivals. Panzar and Rosse proved that under monopoly, an increase in input 122 prices will increase marginal costs, reduce equilibrium output and subsequently re- 123 duce revenues; hence H will be zero or negative. This is a very generalised result, 124 requiring little beyond the pro t maximisation hypothesis itself. Along similar lines, 125 Vesala 1995) proves that the same result holds for monopolistic competition 126 without the threat of entry, i.e. with a xed number of banks. Thus, this case also 127 falls under what we call `monopoly'. In the case where the monopolist faces a de- 128 mand curve of constant price elasticity e > 1 and where a constant returns to scale 129 Cobb±Douglas technology is employed, Panzar and Rosse proved that H is equal to 130 e 1. Hence apart from the sign, the magnitude of H may also be of importance, as 131 H yields an estimate of the Lerner index of monopoly power L ˆ e 1 =e ˆ H= 132 H Three other commonly employed models for an industrial market investigated by 134 Panzar and Rosse are monopolistic competition and perfect competition and conjec- 135 tural variation oligopoly, all of which happen to be consistent with positive values 136 for H. In these models, the revenue function of individual banks depends upon 137 the decisions made by its actual or potential rivals. For monopolistic and perfect 138 competition, the analysis is based on the comparative statics properties of the 139 Chamberlinian equilibrium model. This model introduces interdependence into 140 banks' structural revenue equations via the hypothesis that, in equilibrium, free entry 141 and exit results in zero pro ts. Under a set of general assumptions, 3 it can be proved 142 that under monopolistic competition, H 6 1. Positive values of H indicate that the 143 data are consistent with monopolistic competition but not with individual pro t 144 maximisation as under monopoly conditions. In other words, banks produce more 145 and the price is less than would be optimal in each individual case. A priori, monop- 146 olistic competition is most plausible for characterising the interaction between 2 See Panzar and Rosse 1987) or Vesala 1995) for details of the formal derivation of H. 3 One of the assumptions is that the market is in a long-run equilibrium. This assumption can be tested empirically. 3
5 J.A. Bikker, K. Haaf / Journal of Banking & Finance xxx 2002) xxx±xxx banks, as it recognises the existence of product di erentiation and is consistent with 148 the observation that banks tend to di er with respect to product quality variables 149 and advertising, although their core business is fairly homogeneous. 150 In the limit case of the monopolistic competition model, where banks' products 151 are regarded as perfect substitutes of one another, the Chamberlinian model pro- 152 duces the perfectly competitive solution, as demand elasticity approaches in nity. 153 In this perfect competition case, H ˆ 1. An increase in input prices raises both mar- 154 ginal and average costs without±±under certain conditions±±altering the optimal 155 output of any individual rm. Exit of some rms increases the demand faced by each 156 of the remaining rms, leading to an increase in prices and revenues equivalent to the 157 rise in costs. 158 Finally, analysing the conjectural variation oligopoly case, Panzar and Rosse show 159 that strategic interactions among a xed number of banks may also be consistent with 160 positive values of H. In general, the value of H is not restricted. In the special case of 161 perfect collusion oligopoly or a perfect cartel, the value of H is non-positive, similar to 162 the monopoly model. Table 1 summarises the discriminatory power of H. 163 The Chamberlinian equilibrium model described above provides a simple link be- 164 tween H and the number of banks, so between market behaviour and market struc- 165 ture. The model is based on free entry of banks and determines not only the output 166 level but also the equilibrium number of banks. Vesala 1995) proves that H is an 167 increasing function of the demand elasticity e, that is, the less market power is exer- 168 cised on the part of banks, the higher H becomes. This implies that H is not used 169 solely to reject certain types of market behaviour, but that its magnitude serves as 170 a measure of competition. One of the general assumptions underlying the Chamber- 171 linian equilibrium model mentioned above is that the elasticity of perceived demand 172 facing the individual rm, e x; n; w, is a non-decreasing function of the number of 173 rival banks. Panzar and Rosse call this a standard assumption, eminently plausible 174 and almost a truism. Vesala's result and this assumption together provide a positive 175 theoretical) relationship between H and the number of banks, or±±in a more loose 176 interpretation±±an inverse relationship between H and banking concentration The empirical P±R model 178 The empirical application of the P±R approach assumes a log-linear marginal cost 179 function dropping subscripts referring to bank i) Table 1 Discriminatory power of H Values of H Competitive environment H 6 0 Monopoly equilibrium: each bank operates independently as under monopoly pro t maximisation conditions H is a decreasing function of the perceived demand elasticity) or perfect cartel. 0 < H < 1 Monopolistic competition free entry equilibrium H is an increasing function of the perceived demand elasticity). H ˆ 1 Perfect competition. Free entry equilibrium with full e cient capacity utilisation.
6 6 J.A. Bikker, K. Haaf / Journal of Banking & Finance xxx 2002) xxx±xxx ln MC ˆ a 0 a 1 ln OUT Xm iˆ1 b i ln FIP i Xp jˆ1 c j ln EX COSTj 181 where OUT is output of the bank, FIP are the factor input prices regarding e.g. 182 funding, personnel expenses and other non-interest expenses) and EX COST are other 183 variables, exogenous to the cost function C i t in Eq. 1)). Equally, the underlying 184 marginal revenue function has been assumed to be log-linear of the form ln MR ˆ d 0 d 1 ln OUT Xq kˆ1 f k ln EX REVk 186 where EX REV are variables related to the bank-speci c demand function z in Eq )). For a pro t-maximising bank, marginal costs equal marginal revenues in 188 equilibrium, yielding the equilibrium value for output denoted by an asterisk)! ln OUT ˆ a 0 d 0 Xm b i ln FIP i Xp c j ln EX COSTj Xq f k ln EX REVk, d 1 a 1 iˆ1 190 The reduced-form equation for revenues of bank i is the product of the equilibrium 191 values of output of bank i and the common price level, determined by the inverse- 192 demand equation, which reads, in logarithms, as ln p ˆ n g ln P i OUT i. 193 In the empirical analysis, the following operationalisation of the reduced-form 194 revenue equation is used: ln INTR ˆ a b ln AFR c ln PPE d ln PCE X f j ln BSF j jˆ1 g ln OI e where INTR is the ratio of total interest revenue to the total balance sheet, 4 AFR is 197 the ratio of annual interest expenses to total funds, or the average funding rate, PPE 198 is the ratio of personnel expenses to the total balance sheet, or the approximated) 199 price of personnel expenses, PCE is the ratio of physical capital expenditure and 200 other expenses to xed assets, or the approximated) price of capital expenditure, 201 BSF are bank speci c exogenous factors without explicit reference to their origin 202 from the cost or revenue function), OI is the ratio of other income to the total 203 balance sheet, and e is a stochastic error term. AFR, PPE and PCE are the unit 204 prices of the inputs of the banks: funds, labour and capital, or proxies of these prices. 205 In the notation of Eq. 7), the H statistic is given by b c d. In order to verify 206 whether the competitive structure has changed over time as a result of liberalisation 207 and deregulation, model 7) is applied to a pooled cross-section across banks) and 4 Here we follow the speci cation of the dependent variable of Molyneux et al. 1994). Other authors use unscaled revenues. Re-estimation of the equation with unscaled revenues yields similar results, particularly if one of the bank-speci c factors is `total assets'. kˆ
7 J.A. Bikker, K. Haaf / Journal of Banking & Finance xxx 2002) xxx±xxx time-series analysis over the time span 1988±98. We are assuming that the long-term 209 equilibrium market structure underlying the P±R analysis shifts gradually over time 210 due to institutional changes as mentioned in the introduction) not incorporated into 211 the model equation. Ignoring market dynamics may lead to imprecise parameter 212 estimates and biased H statistics, which could in turn result in wrong inferences 213 about the competitive nature of the banking industry. Therefore, we multiply the 214 elasticities of H by a continuous time-curve model exp e TIME ln INTR ˆ a b ln AFR c ln PPE d ln PCE e etime X f j ln BSF j g ln OI e Note that e ˆ 0 indicates that H is constant over time. Without this assumption of 217 gradual change, the results may be implausibly erratic, as found by Molyneux et al ), who applied the P±R model to a series of subsequent years. 219 The dependent variable is the `ratio of total interest revenue to the total balance 220 sheet', as in Molyneux et al. 1994). The decision to consider only the interest part 221 of the total revenue of banks is consistent with the underlying notion inherent in 222 the P±R model, that nancial intermediation is the core business of most banks. 223 However, Sha er 1982) and Nathan and Neavel 1989) took total revenue as their 224 dependent variable. In our sample, the share of non-interest revenues to total reve- 225 nues is, on average, only 14%. However, it has increased in recent years, doubling 226 between 1990 and In order to account for the in uence exerted by the gener- 227 ation of other income on the model's underlying marginal revenue and cost func- 228 tions, we also include the ratio of other income to the total balance sheet OI) as 229 an explanatory variable. Actually, the P±R model we will apply, Eq. 8), encom- 230 passes the model of Molyneux et al. g ˆ 0). 231 The `ratio of personnel expenses to the number of employees' PENE) could be a 232 plausible alternative to the `ratio of personnel expenses to the total balance sheet' 233 PPE) included in our estimations. However, the former ratio is available for only 234 a small subset of our sample. Furthermore, empirical exercises reveal that results 235 based on PENE closely approximate those based on PPE. This is probably due to 236 the size of the sample used, which makes the results less sensitive to measurement 237 errors. The `ratio of physical capital and other expenses to xed assets' is a proxy 238 of the price of capital. 5 In particular, the balance sheet item ` xed assets' appears 239 to be unrealistically low for some banks. However, the exclusion of outliers or a cor- 240 rection for xed assets, such as applied by Resti 1997), did not lead to remarkable 241 changes in the estimation results. 242 Bank-speci c factors BSF) are additional explanatory variables which re ect dif- 243 ferences in risks, costs, size and structures of banks and should, at least theoretically, 244 stem from the marginal revenue and cost functions underlying the empirical P±R Eq ). The risk component can be proxied by the ratio of risk capital or equity to total 246 assets EQ), the ratio of loans to total assets LO) and the ratio of non-performing 5 `Capital expenses' includes the cost of premises, equipment and information technology.
8 8 J.A. Bikker, K. Haaf / Journal of Banking & Finance xxx 2002) xxx±xxx 247 loans to total loans NPL). More than one variable for risk is considered, as there are 248 cases where one of these variables may be unavailable for a particular bank. The ra- 249 tio of interbank deposits to total customers and short-term funding BDEP) and the 250 ratio of demand deposits from customers to total customer and short-term funding 251 DDC) are used to capture di erences in the deposit mix. Correspondent bank activ- 252 ities are taken into consideration when the ratio of cash and due from depository 253 institutions or banks) to total deposits CDFB) is included. total assets TA) are 254 used as a scaling factor. 255 A positive parameter for LO is expected, because more loans re ect more potential 256 interest rate income. The coe cient for OI is probably negative as the generation of 257 other income may be at the expense of interest income. Regarding the signs of the 258 coe cients of the other explanatory variables, several writers hold con icting theo- 259 ries 6 while others do not have a priori expectations Empirical results Competition in the banking industry 262 The P±R model has been applied to banks from 23 European and non-european 263 countries, as listed in Table 2. The data have been obtained from the database of the 264 International Bank Credit Analysis Ltd Fitch-IBCA), a London-based bank credit 265 rating agency. In principle, data from individual banks are used for the years 1988± , but the actual starting dates of the samples vary across countries. 7 For each 267 country, Table 2 reports the number of banks and available number of observa- 268 tions. 8 The total number of banks is 5444 and the total number of observations is 269 almost 29,000. Hence, on average, the sample includes more than 5 observations 270 in fact years) for each bank, since some of the observations are lacking due to 271 non-reporting of all relevant) data by banks in their annual report, mergers or 272 new entries in the sample period. 273 For each country, the model has been adopted to a sample of all banks, as well as 274 to subsamples of small banks, medium-sized banks and large banks, respectively. 275 This partition into small, medium-sized and large is based on total assets of the 276 banks: for each year, the smallest 50% of all banks of the world-wide sample consti- 277 tute the small-banks sample, the largest 10% of all banks constitute the large-bank 278 sample, whereas the remainder make up the medium-sized sample. The large-bank 6 For example, Molyneux et al. 1994) expect a negative coe cient for EQ, because less equity implies more leverage and hence more interest income. However, on the other hand, capital requirements increase proportionally with the risk on loans and investment portfolios, suggesting a positive coe cient. 7 Data of earlier years would be less useful due to serious free entry restrictions in European countries. 8 Note that ignoring observations of non- nancial institutions, which also provide nancial intermediation in some subdivision of the banking market, does not distort the current analysis, as the actual overall) competitive conditions are observed directly, irrespective of the providers of intermediation services.
9 J.A. Bikker, K. Haaf / Journal of Banking & Finance xxx 2002) xxx±xxx 9 Table 2 Sample period and number of observations per country Country Sample No. of years No. of banks No of observation per bank type period All Small Medium Large Australia 1991± Austria 1989± Belgium 1989± Canada 1988± Denmark 1990± Finland 1990± France 1988± Germany 1988± , Greece 1990± Ireland 1992± Italy 1988± Japan 1989± Korea South) 1992± Luxembourg 1990± Netherlands 1991± New Zealand 1990± Norway 1989± Portugal 1991± Spain 1990± Sweden 1989± Switzerland 1988± UK 1989± US 1991± Total In % sample was kept relatively small to ensure that only the really large banks are in- 280 cluded. The nal numbers of observations are a ected by the availability of data, 281 which actually appears to be correlated with the size of the bank. Of course, the size 282 distribution di ers across the countries, see Table 2. An alternative would be to make 283 the size subdivision per country. However, the border between small and medium- 284 sized banks in, say, 1997 would then range from US$ 166 million in Denmark to 285 US$ 12,660 million in South Korea and between medium-sized and large banks 286 would range from US$ 2797 million in Germany to US$ 111,280 million in Canada. 287 This alternative is less desirable because it makes it very hard to compare subsamples 288 across countries 9 and, therefore, has not been considered. 289 Due to the small number of assumptions mainly the cost minimisation and duality 290 hypotheses) underlying the P±R approach, the validity of the test is fairly general. 291 Nevertheless, a few caveats are in order. As we employ consolidated banking data, 292 the banking market of country X is de ned as the hypothetical market where banks 9 Then, for instance, so-called) large banks in Denmark, Germany or Switzerland could be smaller than so-called) small banks in Finland, Japan or Korea.
10 10 J.A. Bikker, K. Haaf / Journal of Banking & Finance xxx 2002) xxx±xxx 293 from country X are active and not, say, the banking market within the national bor- 294 ders of that country. Moreover, banks operate in various segments of the market, both 295 geographically and in terms of banking products and, for that matter, also in various 296 input markets as well. This remark is particularly true of large universal banks with 297 sizeable foreign activities. These internationally active banks are obviously confronted 298 by other competitive forces than small regional banks. The P±R result H re ects only 299 some kind of average over all these market segments. Finally, in certain segments of 300 the markets, banks face competition from non-bank nancial institutions. 301 However, the P±R approach does not require observations of non-banks, as the H 302 statistic is a direct measure of the degree of competition taking competitive e ects 303 from other institutions in its stride. 304 A critical feature of the H statistic is that the P±R approach must be based on ob- 305 servations that are in long-run equilibrium. An equilibrium test exploits the fact that 306 in competitive capital markets, risk-adjusted rates of return will be equalised across 307 banks. In such a case, the return rates will not be correlated with input prices. 10 We 308 nd that the hypothesis of equilibrium H ˆ 0) cannot be rejected on the 95% signif- 309 icance level, which justi es the applied methodology. 310 As an illustration, Appendix A presents tables with the estimation results of the 311 various bank-size categories for three countries. Tables for the other countries consid- 312 ered can be found in Bikker and Haaf 2000). 11 For New Zealand and South Korea, 313 the number of small banks is too small to make adequate estimations. Our basic ap- 314 proach was to create a model each country and bank size combination, which in- 315 cluded all selected bank-speci c factors. Actually, for some countries, data are 316 unavailable for part of these variables, or available only for a limited number of 317 banks. In the latter case, we accepted only a slight reduction in the sample and oth- 318 erwise disregarded that particular variable. 12 Finally, BSF were deleted, if their coef- 319 cients were not signi cant. This was done mainly to prevent the number of 320 observations from being reduced by the extra explanatory variables, and also for 321 economy's sake. For the latter reason, insigni cant coe cients of the time-trend vari- 322 able were also deleted. Sensitivity analyses con rm that the H estimates are only 323 slightly, if at all, a ected by the deletion of the non-signi cant variables. 324 The crucial variable H is equal to b c d exp e TIME) and, hence, depends 325 on TIME, provided e 6ˆ 0. In the latter cases, H has been calculated for 1991 as well 326 as The coe cient of the average funding rate, b, appears to be most signi cant 327 and almost invariably positive and, hence, the main contributor to H. The coe cient 328 representing labour cost, c, is also signi cant and positive in most cases, but usually 329 smaller than b. The coe cient of the price of capital expenses, d, varies in size, sign 10 An equilibrium test is provided by Eq. 7), after replacement of the dependent variable by the rate of return on total assets ROA) or equity ROE). H ˆ 0 would then indicate equilibrium, whereas H < 0 would point to disequilibrium. 11 These tables are available upon request from the authors. 12 For this reason, the number of observations of small, medium-sized and large banks of a country do not necessarily add up to the number of all banks. This would only be the case if the model speci cation were the same for all bank-size types.