Interbank Competition and Bank Credit Risk

Transcription

1 Interbank Competton and Bank Credt Rsk An Investgaton on the Euro Area Author: Ll Chang (ANR ) Supervsor: Prof. H.P. Huznga Abstract: The recent fnancal turmol renews the debate that bank competton mproves or threatens bank soundness. In ths thess, we emprcally explore ths ssue lmtng our study to the countres wthn the Euro zone. As a frst step, we employ advanced and precse measures to capture the competton and credt rsk degree n the bankng sector. Then we buld the model specfcaton based on exstng theores and estmate t by varous econometrc methods. As shown by the results, there s strong evdence supportng the theory that hgher bank competton would result n more bank credt rsk especally for loan markets wthn the Euro zone.

2 Table of Contents 1 Introducton Lterature Revew Theoretcal Lterature Emprcal Lterature Bank Competton Indces Methodology Data Emprcal Results Bank Credt Rsk Indcators Methodology Data Emprcal Results The Emprcal Evdence The Model Specfcaton and Data Emprcal Results Concluson Table 3.1 Varables used n the estmaton of translog cost functon Table 3.2 Number of banks nvolved n the estmaton Table 3.3 Margnal cost of loans for each country over Table 3.4 Lerner ndex for each country over Table 3.5 Boone ndcator for each country over Table 3.6 Rankngs of each country by Lerner ndex and Boone ndcator Table 4.1 Non-performng loan rato for each country from 1999 to Table 4.2 Credt Rsk Indcator for each country over Table 4.3 Rankngs of each country by the CRI and the NPL Table 5.1 Emprcal results for countres wthn the Euro zone Table 5.2 Emprcal results for orgnal EU member states Appendx

3 1 Introducton The global fnancal crss and ts aftermath restart a debate revolvng the bankng system. One dmenson of ths debate s the effects of nterbank competton on bank rsk takng behavor and hence on bank credt rsk. In fact, ths has been an area of theoretcal and emprcal academc dedcaton snce the 1990s where, however, no consensus has been reached yet. It therefore would be worthwhle to launch a further nvestgaton for a better understandng of the relatonshp between nterbank competton and bank credt rsk. Two competng vews bascally domnate the prevous lterature regardng the competton-stablty relatonshp n the bankng sector. The tradtonal vew supports that greater bank competton reduces market power and profts margn, whch essentally lowers the franchse value of banks. Ths as a result wll ncrease banks ncentves to take on more rsk for profts so as to make up the loss of declned franchse value. On the contrary, the revsonst vew argues that more bank competton drags nterest rates down, reducng moral hazard and adverse selecton problems among borrowers and thus reducng loan default rates, whch benefts bank soundness. On top of these two camps, Martnez, Mera and Repullo (2008) document a way to reconcle these two competng vews and conclude a U-shaped relatonshp between bank competton and stablty. The objectve of ths thess s to emprcally examne the nature of the relatonshp between bank competton and bank credt rsk---postve, negatve or U-shaped---as suggested n theory. We conduct the nvestgaton n the context of the bankng system wthn the Euro zone. Among the prevous studes, some papers opt for worldwde cross-country sample set to nvestgate the lnk between bankng competton and stablty whle others concentrate on a sngle bankng market n a partcular country. The problem of the former analyss s a lack of comparablty across varables due to 3

4 sgnfcant segmentaton of bankng sectors from one county to another. The later analyss, despte avodng the concern of comparablty, cannot be a convncng proof n general. The bankng system wthn the Euro area provdes a fertle ground to address these two weaknesses snce ncreased ntegraton, especally the ntroducton of the euro, levels the playng feld whch elmnates the separaton of bankng system to a large extent. Another mportant ssue n testng theores s the approprate measures of bank competton and bank credt rsk. As noted by many scholars, the structure approach (concentraton rato and Herfndahl-Hrschman ndex) would not suffce to capture the competton degree due to strong nformaton asymmetry n the bankng sector. As for bank credt rsk measures, the effectve measures are even more rare. Ths thess dfferentates tself from pror studes n two regards. Frst, we calculate multple more precse ndces to better capture and to compare the extent to whch banks compete wthn the Euro zone. Second, we launch the emprcal examnaton from the specalzed perspectve of bank credt rsk and focus on countres wthn the Euro area where there are lack of detaled research. By way of prevew, we fnd reasonable evdence supportng the tradtonal vew that greater bank competton leads to more bank credt rsk. As both competton and credt rsk measures put more emphass on the lendng market, the concluson would hold especally for loan markets wthn the Euro zone. Ths mples a tradeoff for polcymakers between competton and credt soundness n the bankng ndustry. The rest of the thess s organzed as follows. Chapter 2 contans a bref dscusson of the theoretcal and emprcal lterature relatng to the nexus between bank competton, stablty and rsk based on whch we develop our testable hypotheses. In Chapter 3 and Chapter 4, we calculate varous ndces measurng bank competton and bank credt rsk. Chapter 5 concentrates on the emprcal examnaton on the relatonshp 4

5 between bank competton and bank credt rsk. Chapter 6 summarzes concludng remarks. 2 Lterature Revew As noted n the Introducton, the nexus between bank competton and bank credt rsk remans controversal despte the dedcated efforts that a large number of scholars have put on ths ssue. In ths secton, we wll summarze the representatve vewponts both n the theoretcal and emprcal lterature. 2.1 Theoretcal Lterature The tradtonal competton-nstablty vew, also called franchse value paradgm 1, was frstly developed by Keeley (1990). The man dea s that hgher bank competton ncreases banks rsk-takng ncentves. Suppose that the bankng market s perfectly compettve, banks current and future profts would be zero. Wthout potental to make future profts,.e. zero franchse value, bankers wll relax ther nvestment selecton requrements. They wll have more ncentves to take hgh-rsk and hgh-yeld projects as they have nothng to lose. Conversely, f banks have some market power and hence a postve franchse value, they wll be more prudent to take the rsk as they have somethng to lose. 2 Therefore, the franchse value paradgm suggests a tradeoff between bank competton and bank credt rsk. In support of the franchse value paradgm, an agent model developed n Keeley s semnal paper and used more recently n Allen and Gale (2004) shows that competton motvates banks to take more rsk through reducng ther franchse value. Matutes and Vves (1996, 2000) document that hgher market power reduces a bank s 1 See Jmenez (2007) for a revew of franchse value paradgm. 2 See Colvn (2009) for a comparatve revew of two dfferent vews on the nature of the relatonshp between bank competton and stablty. 5

6 default probablty n a dynamc model of mperfect competton. Lkewse, Hellmann, Murdock, and Stgltz (2000) assert that competton can exert a negatve mpact on the prudent behavor of banks. The newly-emerged competton-stablty vew was bult by Boyd and De Ncolo (2005) n challenge to the franchse value paradgm. They argue that less competton leads to hgher nterest rate for loans, whch could ncrease the default possblty due to borrowers moral hazard. As a result, banks have to deal wth ncreased problem loans. Therefore, they support that there s a postve relatonshp between bank competton and stablty. Boyd and De Ncolo (2005) develop the frst model as a mlestone n ths strand of vewponts, followed by Boyd, De Ncolo and Jalal (2006 and 2009) who further enrch the theory and moreover put forward emprcal evdence. Dfferent from the two manstream vews above, Martnez-Mera and Repullo (MMR 2008) modfy the model n Body and De Ncolo (2005) and demonstrate a U-shaped relatonshp between competton and bank falure rsk. Specfcally, the probablty of bank falure frst goes down but then goes up after a certan pont as bank competton ncreases. 2.2 Emprcal Lterature Degryse et al (2009) provdes an excellent summary of emprcal studes on the relatonshp between bank competton and bank stablty. Smlar to the theoretcal debate, the conclusons of the extant emprcal lterature vary greatly and depend heavly on the measures chosen and data used. Keeley (1990) uses Tobn s q whch s defned as the rato of a bank s equty market valuaton to ts book value to measure the degree of bank competton. He fnds a postve relatonshp between Tobn s q and bank s solvency ratos, whch on aggregate supports the franchse value paradgm. Beck, Demrgüç-Kunt and Levne 6

7 (2006) document that natonal bankng systems are subject to a lower rsk of systemc bankng crss, and hence are more stable, as the bankng market becomes more concentrated. However, they cast doubts on the approprateness of the C3 rato and related measures as proxes for competton n a natonal bankng system. Usng the H-statstc to approxmate competton, Levy-Yeyat and Mcco (2007) fnd that an ncrease n bank competton leads to an ncrease n bank rsk for eght Latn Amercan countres. In contrast, Boyd, De Ncolo and Al Jalal (2006) provde emprcal evdence supportng a postve relatonshp between banks market power and banks falure rsk. They employ Herfndahl-Hrschmann ndex to measure bank competton and capture bank rsk usng a z-score measure based on returns on assets. Schaeck, Chak and Wolfe (2009) pont out that more compettve natonal bankng systems are less lkely to undergo systemc crses accordng to ther cross-country analyss ncludng 38 countres. Moreover, Schaech and Chak (2010) further support ths result by showng that competton benefts bank soundness va the effcency channel n ther paper where Boone ndcator s used to measure bank competton. It s obvous that the bggest obstacle for emprcal research s how to measure nterbank competton and the degree of bank rsk, whch s part of reasons for the mxed conclusons on the exact relatonshp between bank competton and rsk as well. Tradtonal ndces such as concentraton ratos and Herfndahl-Hrschmann ndex mght not be accurate enough to reflect the competton degree n the bankng sector due to the sgnfcant exstence of nformaton asymmetry. In terms of bank rsk measures, the avalable measures are even more lmted. And the worse thng s that most of them do not dstngush whch aspect of rsks they effectvely approxmate. Ths thess wll contrbute to the lterature n two folds. One s that advanced measures of competton wll be used to crcumvent the problems assocated wth 7

8 Herfndahl-type ndces. And the focus of bank rsk wll be placed on bank credt rsk whch s measured by the nnovatvely-bult Credt Rsk Indcator (CRI) by Wagner and Knaup (2009). The other contrbuton s to make up the empty land n the extant lterature by nvestgatng banks wthn the Euro zone where ncreased ntegraton puts double competton pressure on banks. In the end, we establsh the followng testable hypotheses based on the exstng theores regardng the relatonshp between bank competton and bank credt rsk. Hypothess 1 bank competton ncreases bank credt rsk. Hypothess 2 bank competton decreases bank credt rsk. Hypothess 3 a U-shaped relatonshp exsts n terms of bank competton and bank credt rsk. 3 Bank Competton Indces In ths secton we wll calculate two measures of bank competton----lerner ndex and Boone ndcator----both of them emphasze on dfferent aspects of competton. In order to fulfll more accurate approxmaton, we frst estmate the margnal cost of loans through estmatng the translog cost functon. Then we calculate two competton ndces usng estmated margnal costs. 3.1 Methodology Lerner Index Lerner ndex s a more accurate measure of market power than standard concentraton measures. To compute Lerner ndex for commercal loans, we need n the frst step to estmate the margnal cost of loans. In lne wth van Leuvenstejn et al (2007), we buld the transcendental logarthmc (translog) cost functon (TFC) for each country usng ndvdual bank observatons. We specfy a mult-product, three-output, three- 8

9 nput translog cost functon as follows: lntc j1 3 1 h1 lny j h j ln X 3 1 ln X ln X h 3 3 j j 3 3 j1 1 lny j jk ln X lny j lny k (3.1) where the dependent varable TC denotes the total cost of an ndvdual bank n a certan year. Y j are output varables ncludng loans, other earnng assets and other servces (approxmated by other operatng ncome). X are nput prces varables ncorporatng wage rates, depost rates and the ratos of other operatng expenses to fxed assets. The parameters,,, and are to be estmated. On top of that, there are several restrctons on the parameters of the translog cost functon. The symmetrc restrcton requres, h h. Furthermore, the lnear jk kj homogenety restrcton requres the sum of all nput prce elastctes equal to 1 whereas the coeffcents of the square of nput prces and of cross terms have to be added up to zero respectvely,.e. 1, 0, Accordng to the smplfcaton made by van Leuvenstejn et al (2007), we derve the margnal cost MC of loans for a certan country n a partcular year as follows: 3 1 h 3 1 j MC l TC TC lntc * (3.2) Y Y lny l l l lntc The term s the frst-order dervatve of Equaton (3.1) of the total cost to loans. ln Y l Substtutng the frst-order dervatve nto Equaton (3.2), the margnal cost of output category loans l n the bankng sector wthn a certan country can be obtaned n the followng equaton: MC l TC Y l 3 3 *( lny ln X ) (3.3) l k1 lk k 1 l In a nutshell, we ntally estmate a separate translog cost functon for the bankng sector n each country based on Equaton (3.1). As a next step, we calculate the 9

10 margnal cost n the loan market of each country usng Equaton (3.3). And eventually we obtan Lerner ndex by the formula L p mc, where p s the prce of loans. To p approxmate the prce of loans, we collect the rato of nterest ncome on loans to average gross loans for each bank of each country from the database. The rato of nterest ncome on loans to average gross loans reflects the average rate of nterest that a bank charges on ts loans. We aggregate these bank-specfc ratos nto countrylevel rates by takng the average, whch approxmates the nterest rate of loans for each country Boone Indcator The ntuton underlyng Boone ndcator s that more effcent banks,.e. banks wth lower margnal costs, obtan hgher profts at the expense of neffcent compettors. Ths proft-shft effect ncreases as market competton ncreases. As noted n Boone et al (2005) and Schaeck and Chak (2010), the demand curve n the bankng sector where bank produces one product (or product portfolo) q can be wrtten as follows: P ( q, q ) a bq d q (3.4) j j where each bank s assumed to have constant margnal cost c. The parameters a, b and d are presumed to satsfy the condton that s a and 0 d b. It s c noteworthy that b denotes the market elastcty of demand and that d measures the extent of substtutablty of dfferent products n the bankng sector from the vewpont of consumers. The bank chooses the optmal output level q n order to maxmze ts profts ( p c ) q. (3.5) Then n the equlbrum, we get the frst order condton: a 2bq d q c 0 (3.6) j j 10

11 Lkewse, for the bankng ndustry wth N ndvdual banks whch all produce postve output levels, we can wrte down the N frst-order condtons: q ( c ) [(2b / d 1) a (2b / d N 1) c c j ]/[(2b d( N 1))(2b / d 1)] (3.7) It s assumed that proft s varable proft excludng entry costs, whch means a bank enters the market f and only f n equlbrum. The ntuton s that competton can ncrease n two ways. One s that competton ncrease as servces and products provded by dfferent banks become closer substtutes,.e. the bgger d ( 0 d b ). The other way to ncrease competton s to declne entry cost. Combnng Equaton (3.5) wth Equaton (3.7), the proft can be expressed n a quadratc way of margnal cost c. j 2 ( ct ) b[ q( ct )] (3.8) In an attempt to calculate Boone ndcator, we establsh the followng specfcaton n accordance wth Boone (2004 and 2008), Leuvenstejn et al (2007), and Schaeck and Chak (2010). t ct ) t Where ln( (3.9) t and c t denote the proft and the margnal cost of bank at tme t respectvely. The slope coeffcent s Boone ndcator whch s expected to be negatve. It represents the percentage decrease (ncrease) n profts of bank caused by one percentage ncrease (decrease) n margnal costs. The larger the beta s n ts absolute value, the stronger the competton exsts n the market. Accordng to Schaeck and Chak (2010), we control a bank-specfc effect to allow for heterogenety and adjust Equaton (3.9) to estmate Boone ndcator across countres over tme. The modfed Boone ndcator s based on the followng equaton: d ln( c ) d u (3.10) t t t t t t 1... T t1...( T 1) t t In ths setup, we use ROA (Return on Asset) as a proxy for the proft. We get the t 11

12 margnal cost of each bank from the prevous estmaton of translog cost functon. d t s a tme dummy varable from 1999 to Data The translog cost functon to be estmated are ncorporated three varable groups: total costs, outputs and nput prces. Total costs consst of nterest expenses and nonnterest expenses. We employ loans, other earnng assets and non-nterest ncome to approxmate outputs of a typcal bank whle usng wages, deposts and other operatng expenses to measure correspondng nputs. Ths approach s wdely consdered to be an approprate way to capture the nature of modern banks. (Green et al 2004 and Leuvenstejn 2007). The varables and ther emprcal proxes are summarzed n Table 3.1. [Insert Table 3.1] In the estmaton, we use annually bank-specfc data from the Bankscope database coverng Due to a large amount of mssng data, our focus s abstracted on 10 countres wthn the Euro area excludng Cyprus, Estona, Fnland, Greece, Malta, Slovaka and Slovena. Also we nclude Swtzerland, Unted Kngdom, Sweden and Denmark whch enables us to extend the nvestgaton to the EU. Consderng data suffcency, we nclude all types of bank n the data set except central bank and clear & custody bank n each nvestgated country. Table 3.2 gves a descrpton of the number of banks nvolved n the estmaton for each year. [Insert Table 3.2] As for Lerner ndex, the bank-specfc rato of nterest ncome on loans to average gross loans s avalable n the Bankscope database. We take average of these ratos to approxmate the country-level nterest rate of loans. In terms of calculatng Boone ndcator, the margnal cost data s obtanable from the translog cost functon. We 12

13 further calculate ROA as a proxy for profts whch s defned as the rato of net ncome to total assets. We estmate Equaton (3.10) usng ordnary least squares (OLS) adjusted for heteroskedastcty. 3.3 Emprcal Results Lerner Index The margnal cost of loans for each country durng 1999 to 2011 s descrbed n Table 3.3. In Appendx 1 we present the estmated results for Germany n It s obvous that for each country the margnal cost of provdng loans decreases wth the process of tme although the speed and magntude of ths declne vary across countres. Ths mght be due to dfferent development n bankng technology, legslaton and supervson n each country. As for countres wthn the Euro zone, the margnal costs are very smlar except Belgum whch has the hghest margnal cost of loans about 6.3%. The margnal cost n Netherlands, Portugal and France are relatvely hgh compared to the low margnal cost around 3.3% n Germany, Ireland and Span. Among the EU group, euro countres are apparently hgher than the rest of state members n terms of margnal costs of provdng loans. [Insert Table 3.3] The ntuton behnd Lerner ndex s that greater competton n the market pushes the prce of loans close to ts margnal cost resultng n a smaller Lerner ndex. Table 3.4 presents Lerner ndex for each country over tme. Generally speakng, Lerner ndces fluctuate sgnfcantly across countres, whch ndcates the competton level n the loan market for each country dffers consderably. Lerner ndces are relatvely hgh for Luxembourg, Germany and Ireland, meanng that the bankng sectors n these countres are less compettve. By contrast, Portugal, Netherlands and France wth lower Lerner ndces are consdered to have more competton n ther lendng markets. It s noteworthy that for Belgum the margnal cost of loans s very hgh durng

14 to 2009 whch leads to the abnormal negatve Lerner ndces n these years. Compared to state members outsde the Euro zone, the nsde markets tend to be more compettve than the outsde ones on average Boone Indcator [Insert Table 3.4] Table 5 ndcates Boone ndcators across countres from 1999 to In general, Boone ndcators for each country are negatve and sgnfcant albet only a few postve but nsgnfcant ndcators n certan years. A possble explanaton for these postve coeffcents s that we do not correct for other explanatory varables such as the qualty of loans. As a consequence, the estmates of Boone ndcator mght be lack of robustness. However, the approach that we use s proved to be effectve by many studes whch should be far enough to be used n our paper. Our results suggest on average Dutch, Austran and Italan bankng sector reman comparatvely hgh level of competton n contrast to less compettve market n Sweden and Belgum. Furthermore, the competton n the lendng market wthn the Euro zone s, on average, hgher than that of other EU members such as Sweden, Unted Kngdom and Denmark. In terms of the evoluton trend, our estmates of Boone ndcator show a declnng trend for Span, Portugal, France, Ireland and Italy, whch suggests the ncreasngly ntensve bank competton n these countres. However, Swtzerland, Unted Kngdom and Luxembourg have been experencng an upward trend whle Netherlands and Sweden reman rather stable when t comes to Boone ndcators Correlaton [Insert Table 3.5] It s nterestng to have a look at the correlaton between these two competton measures as they reflect competton degree n common but are based on dfferent 14

15 ratonales. The correlaton between Lerner ndex and Boone ndcator s about whch s rather weak. As we dscussed earler, Lerner ndex and Boone ndcator are derved from dfferent ratonales and emphasze on dfferent aspects of competton; therefore, the correlaton could not be strong. In addton, we rank each country n terms of competton degree by both ndcators (See Table 3.6). In order to make comparsons, we roughly dvde these countres nto two groups by average (.e. above average and below average). We can see that most countres fall nto the same group by both ndces except Belgum, Austra, Sweden and Portugal. It should be notced that the raw data for such small countres are qute lmted and the estmated results fluctuate consderably, whch would heavly nfluence ther averages over years and hence ther rankngs. Takng ths explanaton nto consderaton, we are confdent that both ndces yeld consstent results. [Insert Table 3.6] 4 Bank Credt Rsk Indcators In ths secton we wll estmate two emprcal measures of bank credt rsk. One s the tradtonal measure of loan qualty, Non-performng loan rato (NPL). And the other s Credt Rsk Indcator (CRI) nnovatvely desgned by Wagner and Knaup (2009) Methodology Non-performng loan rato The non-performng loan rato (NPL) s a wdely-used measure of loan qualty n the pror lterature. Dfferent from Credt Rsk Indcator whch s a rather drect proxy for bank credt rsk, the NPL ndrectly reflects bank credt rsk through the rato of mpared loans relatve to gross loans. In our emprcal work, we use ths ndctor for two reasons. One s that the NPL can be obtaned n the entre sample perod of tme, whch makes up the dsadvantage of short avalablty of Credt Rsk Indcator. The 15

16 other s that we use multple ndces to capture the degree of bank competton and bank credt rsk so that we could better check the robustness of our results n Secton 5. Accordng to the standard formula, the non-performng loan rato equals to the mpared loans dvded by gross loans. mparedloans NPL (4.1) grossloans It s worth notng that we further aggregate the bank-level non-performng loan rato nto the country-level data by takng the weghted average of each rato, where the weght s gven by the rato of every bank s gross loans n a certan country to the whole bankng sector s gross loans n ths country Credt Rsk Indcator Accordng to Wagner and Knaup (2009), the ratonale of Credt Rsk Indcator (CRI) stems from the balance sheet of a bank. On the asset sde of a balance sheet are loans (L) and securtes (S) whle on the lablty sde are equty (E) and debt (D). These two sdes are supposed to be equal n terms of market value (V (.)) whch can be ndcated n unt of shares as follows: V( E) V( D) V( S) V( L) (4.2) V(E) equals to a bank s share prce p. V(D) can be approxmated by ts dscounted book value at an approprate nterest rate. As for the market value of loans, we need to consder the rsk of default. Suppose that PD s the probablty of default and LGD s the loss gven default. Therefore, the expected loss on a loan EL can be expressed as EL PD * LGD. It s further assumed that there are two types of loans, hgh rsk and low rsk loans. We use h and l to denote the amount of each type of loans respectvely. The value of the loan portfolo s gven by: h l V ( L) h(1 EL ) l(1 EL ) (4.3) 16

17 The Credt Rsk Indcator (CRI) s defned as the share of hgh rsk loans n the loan portfolo. h CRI (4.4) h l In a successful attempt to measure the expected losses on hgh and low rsk loans, Wagner and Knaup (2009) use the prces of Credt Default Swaps (CDS) ndces as proxes, denotng h h EL CDS and l EL CDS l. We follow ths strategy n our estmaton of the CRI. Next we wrte Equaton (4.2) n the form of changes from whch the CRI can be derved. V( E) V ( S) V ( L) (4.5) Where represents the absolute change from t-1 to t and where the debt of a bank s assumed to be constant. Furthermore, we opt for the change of a market ndex M as a proxy for the change of the securty portfolo n accordance wth Wagner and Knaup S (2009) and hence we get V ( S) M. Then substtutng the proxes of loans M portfolo and of securty portfolo nto Equaton (4.4), we get the followng equaton: S M h l p M hcds lcds (4.6) In order to mplement the estmaton, we add control varables to Equaton (4.6) and establsh the followng specfcaton at the bank level: p M CDS CDS X (4.7) t t h t l t Where subscrpt and t represent the bank and tme. The vector X contans three control varables ncludng long-term nterests, short-term nterests and nflaton rates. Note that we only focus on the country-level aggregate CRI n our estmaton and thus we employ a pooled verson of Equaton (4.7) for ths purpose. Then the CRI can be expressed as follows. CRI (4.8) t t 17

18 4.2 Data As for the non-performng loan rato, our nput data comes from the Bankscope database. In order to keep consstency wth bank competton ndcators, we only exclude central bank and clear & custody bank out of our sample when calculatng the NPL. The bank-specfc NPL s straghtforwardly avalable from the Bankscope database. We further collect the absolute amount of gross loans for each bank to calculate the weght whch s used for aggregaton. When t comes to Credt Rsk Indcator, we collect monthly data on share prces of all lsted bank n each country, two CDS ndces and the market return ndex S&P for each country from the Datastream database. And we get long-term nterest rates, short-term nterest rates as well as nflaton rates from the OECD database. Due to the fact that two CDS ndces are only avalable for the last 7 years, our estmates of CRI are only from 2005 to In terms of the hgh and low rsk CDS ndex, Wagner and Knaup (2009) use Dow Jones CDX North Amerca Crossover and Dow Jones CDX North Amerca Investment Grade. Lkewse, we opt for the European verson of these ndces Markt Itraxx Europe and Markt Itraxx Crossover. Markt Itraxx Europe conssts of 125 CDS referencng European nvestment grade credts. These reference enttes are the most lqud enttes traded n the CDS market and equally-weghted n the calculaton. Markt Itraxx Crossover comprses 40 equally-weghted referencng subnvestment grade credts. The Itraxx ndces vary consderably wth dfferent maturtes rangng from one to ten years. Snce the reference maturty for CDS contracts s 5 year, we use the 5-year maturty ndex. Furthermore, both CDS ndces are expressed n bass ponts of spreads. A hgher spread suggests a hgher default rsk. Fnally n order to separate the effect of dfferent nfluental elements on the share 18

19 prce change, we apply the orthogonalzaton method n accordance wth Wagner and Knaup (2009) to the S&P ndex for each country and Markt Itraxx Europe ndex n the estmaton of Equaton (4.7). 4.3 Emprcal Results Non-performng loan rato Table 4.1 summarzes non-performng loan ratos for each country over There s an apparent ncrease n the non-performng loan rato durng our sample perod of tme for all of the countres. Especally durng the senstve tme of economy from 2007 on, the NPL rses sgnfcantly. Wthn the Euro zone, Italy s subject to the hghest non-performng loan rato (4.1% on average). Ireland, Austra and Belgum have hgh-level mpared loans relatve to gross loans as well whch on average account for 3.1%, 2.8% and 2.3% respectvely. By contrast, other European countres outsde the Euro zone reman defntely lower non-performng loan ratos, whch s a postve sgn for a healthy and stable bankng market. Overall, the entre loan market wthn the Euro area turns out to bear more credt rsk than other European countres outsde due to the nferor loan qualty Credt Rsk Indcator [Insert Table 4.1] The estmated Credt Rsk Indcators for each country over are presented n Table 4.2. We would ntally lke to pont out that the coeffcents of CDS ndces n Equaton (4.7) have correct sgns but not very sgnfcant. Ths mght be because we use monthly data nstead of daly data whch would conceal the change of share prce. However, nterest rates and nflaton rates are not avalable n more detaled frequency than monthly data. Furthermore, even f there s a bas due to the nferor data, we ntroduce t to all the countres so that the entre trend of credt rsk for each country wll not change. 19

20 As stated by Wagner and Knaup (2009), the CRI measures the relatve senstvtes to the hgh and low rsk. Therefore a hgher CRI suggests a hgher proporton of hgh rsk loans relatve to the low rsk loans, whch would ncrease the possblty of credt rsk. From Table 4.2, we could see that the CRI fluctuates strongly so that there s no apparent tme trend. Nevertheless, n the course of the global fnancal crss from 2007 to 2008, the CRI s defntely hgher than any other year for most of the countres. Compared countres nsde and outsde of the Euro area, the CRI s qute smlar for the two country groups Correlaton [Insert Table 4.2] We calculate the correlaton between the CRI and the NPL to see how they are related to each other. As the result shows, the correlaton s around 0.14 that s not very strong. Accordng to Wagner and Knaup (2009), the correlaton s not an effcent way to observe the assocaton of these two ndces as the nformaton n the estmaton of the CRI s not fully used n the computaton of correlaton. 3 As a next step, we rank each country by the CRI and the NPL to see whether both ndcators suggestng the same credt rsk level. From Table 4.3 we could see that there s no contradctng rankng for any country albet that the rankngs change slghtly by dfferent ndcators. [Insert Table 4.3] 5 The Emprcal Evdence In the two prevous sectons, we calculate multple ndcators to measure bank competton and bank credt rsk respectvely usng varous emprcal methods. Each and every type of ndces s based on dfferent ratonales and hence emphaszes on 3 Wagner and Knaup (2009) develop a method to estmate the relatonshp between the CRI and the NPL nstead of computng the correlaton and demonstrate that banks wth a hgher NPL also have a hgher CRI. 20

21 dfferent aspects of ether bank competton or bank credt rsk. In ths secton, we wll emprcally nvestgate the relatonshp between bank competton and bank credt rsk usng these measures. 5.1 The Model Specfcaton and Data As dscussed earler, we establsh three hypotheses correspondng to the extant theoretcal development. Accordng to the franchse value paradgm supported by many scholars n the 1990s, we put forward the frst hypothess that s bank competton ncreases bank credt rsk. Based on the semnal studes by Boyd et al (2005, 2006 and 2009), we buld the second hypothess, opposte to the frst one, that s bank competton decreases bank credt rsk. On top of these, we set up the thrd hypothess n lne wth Martnez-Mera and Repullo (2008) that s the relatonshp between bank competton and bank credt rsk s U-shaped. In order to test the abovementoned hypotheses, we set up the regresson specfcaton as follows: R t 2 1 ct 2ct 1gdpg t r2loansze t t (5.1) where the subscrpts and t refer to the country and year respectvely. The dependent varable s bank credt rsk measures such as the NPL and the CRI. Among ndependent varables, ct denotes competton measures for whch we wll use Lerner ndex and Boone ndcator as proxes. We nclude the square of competton measures n our model specfcaton to test the U-shaped lnk behnd the thrd hypothess. The rest of explanatory varables are control varables consstng of the real GDP growth and the country-level loan sze. The coeffcents 1 and 2 are parameters of our nterest. If both parameters are sgnfcantly postve, bank competton would decrease bank credt rsk, whch supports Hypothess 2. On the contrary, negatve and sgnfcant 1 and 2 are the 21

22 supportve evdence for Hypothess 1 that s bank competton would ncrease bank credt rsk. And f 1 s sgnfcantly negatve but 2 s sgnfcantly postve, Hypothess 3 would hold, suggestng a U-shaped relatonshp between competton and credt rsk n the bankng sector. Addtonally, we expect both of control varables to have negatve sgns snce mpared loans are more lkely to ncrease n bad tmes or due to excessve amounts of loans. Regardng the data, we have already estmated bank competton and bank credt rsk ndces. As a supplement, we addtonally collect the real GDP growth rate from the OECD database and calculate the aggregate loan sze for each country. 5.2 Emprcal Results Table 5.1 presents the estmated results for countres wthn the Euro zone. Panel A gves the results usng the non-performng loan rato as the dependent varable whle n Panel B Credt Rsk Indcator s used as the dependent varable. We use varous econometrc methods to run the regresson ncludng OLS, fxed affects, random effects and level GMM n order. We summarze the coeffcents of Lerner ndex as competton ndcator n the frst column and the coeffcents of Boone ndcator as competton measure n the second column for each method that we employ. [Insert Table 5.1] Regardng Panel A, we can see that the coeffcents of bank competton measures and ther squares are sgnfcantly negatve n almost all the cases except the frst OLS estmaton n column 1. Lerner ndex reflects market power---a larger Lerner ndex mples a larger market power---but competton s lower. As for Boone ndcator, t emphaszes on the effect of an ncrease n margnal cost on the decrease n profts. Snce Boone ndcator s negatve, a larger Boone ndcator suggests the change of margnal cost has less nfluence on profts, whch means the market s subject to less 22

23 competton. Therefore, both negatve sgns for competton measures and ther squares ndcate that bank credt rsk declnes as bank competton reduces. It s strong supportve evdence for Hypothess 1. As for Panel B, the results become complcated. It can be seen that the relatonshp between Credt Rsk Indcator and Lerner ndex are qute ambguous. The coeffcents are postve but nsgnfcant for most of the cases. By contrast, the lnks between Credt Rsk Indcator and Boone ndcator stll reman the same as Panel A. However, note that the sgnfcance of some coeffcents turns out to be weakened (OLS (2) and GMM (2)). In addton, the control varables have unexpected sgns and are nsgnfcant as well, whch suggests the nvaldty of estmaton. A possble reason mght be the naccurate calculaton of the CRI. As we mentoned before, the CRI mght be based due to the low-frequency data that we appled. Although such based CRI enables us to make comparsons over tme or across countres, t could lead to problems n the model regresson. Furthermore, the CRI s only avalable snce 2005, whch makes the dataset contract to a small one. Ths mght be another explanaton for the vague results n Panel B. As a complementary proof, we estmate Equaton (5.1) usng all the orgnal EU member states. Table 5.2 shows the results n the same structure as Table 5.1. On the one hand, t s very clear that the results reman the same as those for countres wthn the Euro zone n general. And the better part for ths enlarged sample set s that the sgnfcance of coeffcents s obvously mproved especally for Panel B where all the coeffcents of Boone ndcator and ts squares become sgnfcant. On the other hand, t could be treated as a robustness check of the results whch further strengthens our concluson. [Insert Table 5.2] Overall, we conclude wth supportve evdence that an ncrease n bank competton 23

24 would lead to an ncrease n bank credt rsk. Furthermore, as our measures both for competton and credt rsk manly focus on the lendng market, t should be kept n mnd that ths concluson s qute subject to loan markets. 6 Concluson The relatonshp between competton and stablty n the bankng sector has sparked much debate snce the 1990s. Scholars have put consderable amounts of effort n nvestgatng ths ssue, but unfortunately no consensus has been reached so far. However, the recent global crss and the dsastrous turmol t brngs to the fnancal system around the world put ths ssue on the agenda agan. A convncng answer to the ambguous nexus between bank competton and bank credt health would not only resolve the academc debate but also yeld rather valuable polcy mplcatons sheddng lght on the chaos of the current bankng ndustry. Two competng vews domnate the theoretcal lterature concernng the relatonshp between bank competton and bank stablty. One of them supports that less competton n the bankng market leaves more franchse value for banks and that n order to preserve ths relatvely hgh franchse value, bankers attempt to lmt ther nvestment projects, especally reducng the rsky ones so that the bank stablty could be more guaranteed. The challengng vew aganst the franchse value paradgm emphaszes that market concentraton could result n ncreased lendng rates whch rase both the default probabltes of repayment and the borrower s ncentves for rsker projects. For ths reason bank stablty wll be harmed nstead of beng mproved. In addton, Martnez-Mera and Repullo (2007) develop a compromsng theory and argue that the real relatonshp between competton and bank soundness presents U-shaped. Accordngly, a large body of emprcal lterature emerged on the bass of theoretcal 24

25 development. The conclusons however vary sgnfcantly wth dfferent research methods and dfferent measures on bank competton, rsk or stablty that were employed n the studes. Ths on the one hand can be attrbuted to the root reason for non-consensus concluson whle on the other hand leavng much room for the future scholars to make mprovements especally on the valdty of measures. In an attempt to further emprcally explore ths ssue, we apply more precse ndcators to approxmate the competton and credt rsk degree n the bankng sector. We manly focus on the lendng market wthn the Euro zone as the advent of euro levels the playng ground to the largest extent whch provdes an deal sample for our research. In order to check the robustness and make comparsons, we nclude four European countres out of the Euro area n the dataset that have developed bankng ndustres. Summng up, our study dstngushes from the pror lterature n two senses usng multple more precse measures to capture bank competton and bank credt rsk and concentratng on the Euro land both of them consttute a meanngful complement to the lterature. In terms of our emprcal results, we fnd strong evdence n support of the franchse value paradgm that s ncreased bank competton rases bank credt rsk. To be specfc, both Lerner ndex and Boone ndcator as bank competton proxes are sgnfcantly negatvely lnked wth the non-performng loan rato whch s a measure for bank credt rsk. However, ths negatve nexus become weak when we approxmate bank credt rsk wth Credt Rsk Indcator bult by Wagner and Knaup (2009). Ths mght largely be due to the bas that s ntroduced nto the CRI when we substtute daly data wth monthly data n the calculaton of CRI. But the better part s that the major coeffcents of nterest are negatve despte the lower sgnfcance. We therefore conclude from the emprcal results that a hgher bank competton would result n a hgher bank credt rsk at least for countres wthn the Euro area. 25

26 References Allen, F. and Gale, D Competton and fnancal stablty, Journal of Money, Credt and Bankng, vol.36, no.3, pp Beck, T., Demrguc-Kunt, A. and Levne, R. 2006, Bank concentraton, competton and crses: frst results, Journal of Bankng and Fnance, vol.30, no.5, pp Berger, A.N., Klapper, L.F. and Turk-Arss, R Bank competton and fnancal stablty, World Bank Workng Paper No Boone, J A new way to measure competton, The Economc Journal, vol.118, no.531, pp Boyd, J.H. and De Ncoló, G The theory of bank rsk takng and competton revsted, Journal of Fnance, vol.60, no.3, pp Boyd, J.H., De Ncolo, G. and Jalal, A.M. 2006, Bank rsk takng and competton revsted: New theory and new evdence, IFM Workng Paper, WP Boyd, J.H., De Ncolo, G. and Jalal, A.M Bank competton, rsk and asset allocatons, IMF Workng Paper WP/09/143. Colvn, C.L What determnes nterbank competton and why should we care? Oxford Unversty Economc Studes. vol.4, no.1, pp Degryse, H., Km, M. and Ongena, S Mcroeconometrcs of bankng, Oxford Unversty Press. Green, C.J., Murnde, V. and Nkolov, I Are foregn banks n central and eastern Europe more effcent than domestc banks? Journal of Emergng Market Fnance. Vol.3, no.2, pp Hellmann, T. F., Murdock, K.C. and Stgltz, J.E Lberalzaton, moral hazard n bankng, and prudental regulaton: Are captal requrements enough?, Amercan Economc Revew, vol.90, no.1, pp Jmenez, G., Lopez, J.A. and Saurna, J How does competton mpact bank rsk-takng? FRB Workng Paper No Keeley, M.C., Depost nsurance, rsk and market power n bankng, Amercan Economc Revew, vol.80, no.5, pp

27 Knaup, M. and Wagner, W A market-based measure of credt portfolo qualty and banks performance durng the subprme crss, EBC Dscusson Paper No S Knaup, M Market-based measures of bank rsk and bank aggressveness, PHD Thess Seres of Tlburg Unversty. Levy Yeyat, E. and Mcco, A Concentraton and foregn penetraton n Latn Amercan bankng sectors: Impact on competton and rsk, Journal of Bankng and Fnance, vol.31, no.6, pp Martínez-Mera, D. and Repullo,R Does competton reduce the rsk of bank falure? CEMFI Workng Paper No Martínez-Mera, D. and Repullo,R Does competton reduce the rsk of bank falure? The Revew of Fnancal Studes, vol.25, no.5, pp Matutes, C. and Vves, X Competton for deposts, fraglty, and nsurance, Journal of Fnancal Intermedaton, vol.5, no.2, pp Matutes, C. and X. Vves, Imperfect competton, rsk takng, and regulaton n bankng, European Economc Revew, vol.44, no.1, pp Schaeck, K., Chak, M. and Wolfe, S Are compettve bankng systems more stable? Journal of Money, Credt and Bankng, vol.41, no.4, pp Schaeck, K. and Chak, M Competton, effcency, and soundness n bankng: an ndustral organzaton perspectve, EBC Dscusson Paper No S. Stgltz, J. and Wess, A Credt ratonng wth mperfect nformaton, Amercan Economc Revew, vol.71, no.3, pp Van Leuvenstejn, M., Bkker, J.A., van Rxtel, A.A.J.R.M. and Sorensen, C.K A new approach to measurng competton n the loan markets of the Euro area, ECB Workng Paper No

28 Table 3.1 Varables used n the estmaton of translog cost functon Varable Observable varables Total costs TC nterest expenses + non-nterest expenses Loans Y 1 gross loans Outputs Other earnng assets Y 2 total earnng assets - gross loans Non-nterest ncome Y 3 non-nterest ncome Wages IN 1 personnel expenses Inputs Deposts IN 2 nterest expenses Other expenses IN 3 other operatng expenses Wage rate X 1 approxmated by personnel expenses/total assets Depost rate X 2 nterest expenses/total fundng Prces of Inputs Source: author s summary Prce of other expenses X 3 Table 3.2 Number of banks nvolved n the estmaton approxmated by other operatng expenses/fxed assets Country Austra Belgum Germany Span France Ireland Italy Luxembour g Netherlands Portugal UK Denmark Swtzerland Sweden Source: author s calculaton

29 Table 3.3 Margnal cost of loans for each country over Country Average Austra 0,043 0,041 0,052 0,045 0,032 0,038 0,032 0,039 0,046 0,043 0,042 0,036 0,033 0,040 Belgum 0,068 0,079 0,058 0,036 0,044 0,070 0,022 0,032 0,116 0,085 0,101 0,044 n.a 0,063 Germany 0,041 0,041 0,039 0,039 0,033 0,037 0,034 0,043 0,036 0,022 0,030 0,028 0,037 0,035 Span 0,058 0,042 0,034 0,030 0,025 0,024 0,027 0,030 0,032 0,037 0,027 0,029 0,036 0,033 France 0,061 0,051 0,076 0,074 0,062 0,045 0,044 0,047 0,041 0,040 0,033 0,035 0,032 0,049 Ireland n.a n.a n.a n.a n.a n.a 0,039 0,025 0,041 n.a. n.a. n.a. n.a. 0,035 Italy 0,053 0,046 0,036 0,059 0,080 0,058 0,023 0,028 0,034 0,043 0,027 0,017 0,021 0,040 Luxembourg 0,081 0,075 0,060 0,051 0,047 0,032 0,036 0,050 0,032 0,034 0,031 0,030 n.a 0,047 Netherland n.a n.a n.a n.a n.a 0,037 0,051 0,054 0,053 0,042 0,040 0,067 n.a 0,049 Portugal n.a. n.a. n.a. n.a. n.a. n.a. 0,040 0,052 0,040 0,069 0,052 0,044 n.a. 0,049 Sweden n.a. n.a. 0,064 0,044 0,069 0,050 0,011 0,021 0,027 0,037 0,008 0,006 0,009 0,031 Swtzerland 0,042 0,051 0,052 0,047 0,023 0,016 0,033 0,039 0,037 0,019 0,013 0,017 0,013 0,031 Denmark 0,045 0,035 0,040 0,027 0,009 0,017 0,025 0,041 0,034 0,033 0,025 0,021 0,018 0,028 Unted Kngdom 0,031 0,027 0,018 0,027 0,023 0,033 0,047 0,040 0,036 0,032 0,028 0,028 0,022 0,030 Average 0,052 0,049 0,048 0,043 0,041 0,038 0,033 0,039 0,043 0,041 0,035 0,031 0,024 0,040 Source: author's calculaton 29

30 Table 3.4 Lerner ndex for each country over Country Average Austra 0,383 0,654 0,528 0,489 0,547 0,474 0,584 0,586 0,466 0,565 0,483 0,424 0,396 0,506 Belgum 0,059 0,010 0,036 0,395 0,323-0,436 0,527 0,401-0,993-0,744-0,927 0,605 n.a. -0,062 Germany 0,559 0,582 0,623 0,625 0,639 0,606 0,637 0,510 0,640 0,788 0,656 0,639 0,754 0,635 Span 0,058 0,494 0,390 0,210 0,058 0,384 0,445 0,497 0,568 0,694 0,439 0,389 0,063 0,361 France 0,083 0,294-0,028-0,355 0,347 0,467 0,476 0,497 0,536 0,567 0,593 0,480 0,390 0,334 Ireland n.a. n.a n.a n.a n.a. n.a. 0,224 0,874 0,721 n.a. n.a. n.a. n.a. 0,606 Italy 0,233 0,338 0,686 0,410-0,261 0,064 0,589 0,599 0,507 0,477 0,438 0,576 0,454 0,393 Luxembourg 0,829 0,850 0,893 0,875 0,863 0,859 0,874 0,867 0,946 0,953 0,868 0,796 n.a. 0,873 Netherlands n.a. n.a. n.a. n.a. n.a. 0,439 0,239 0,393 0,846 0,397 0,478-0,537 n.a. 0,323 Portugal n.a. n.a. n.a. n.a. n.a. n.a. 0,563 0,699 0,635-0,041-0,530 0,073 n.a. 0,233 Sweden n.a. n.a. 0,057 0,341-0,271-0,047 0,755 0,549 0,530 0,399 0,806 0,859 0,834 0,437 Swtzerland 0,523 0,547 0,410 0,360 0,453 0,574 0,423 0,397 0,496 0,688 0,630 0,457 0,535 0,499 Denmark 0,229 0,474 0,253 0,536 0,849 0,701 0,552 0,283 0,503 0,572 0,624 0,643 0,703 0,532 Unted Kngdom 0,536 0,602 0,727 0,479 0,559 0,406 0,465 0,667 0,704 0,705 0,537 0,493 0,632 0,578 Average 0,349 0,485 0,416 0,397 0,373 0,374 0,525 0,558 0,507 0,463 0,392 0,454 0,529 0,448 Source: author's calculaton 30

31 Table 3.5 Boone ndcator for each country over year Austra t-statcs Belgum t-statcs Germany t-statcs Span t-statcs France t-statcs Ireland t-statcs Italy t-statcs ,011-3,350-0,022-0,540 0,003 1,960-0,008-0,110 0,029 6,180 n.a. -0,071-4, ,017-3,000-0,047-4,230-0,028-10,980-0,059-3,990-0,077-8,210 n.a. -0,046-4, ,033-5,770-0,036-5,220-0,076-22,900-0,061-7,570-0,040-5,420 n.a. -0,050-11, ,122-26,680-0,023-3,930-0,076-25,190-0,224-5,830-0,043-10,830 n.a. -0,063-9, ,040-9,730-0,029-6,470-0,051-17,290-0,048-1,900-0,031-1,960 n.a. -0,053-2, ,242-19,550-0,032-4,360-0,002-0,880-0,045-7,930-0,040-9,690 n.a. -0,102-6, ,016-2,550-0,054-5,340-0,024-4,900-0,019-6,360-0,027-6,000-0,023-3,540-0,042-16, ,127-7,770-0,014-1,290-0,021-8,100-0,025-5,840 0,118 6,360-0,042-5,240-0,058-22, ,050-13,140 0,142 7,790-0,018-5,990-0,029-7,650-0,022-4,210-0,092-1,130-0,075-17, ,038-4,550-0,133-2,770-0,041-8,110-0,035-8,160-0,025-3,760 n.a. -0,065-4, ,057-13,790-0,033-6,770-0,024-10,280-0,014-5,560-0,032-2,840 n.a. -0,045-0, ,038-13,000-0,031-7,690-0,020-9,540-0,029-6,060-0,014-2,630 n.a. -0,024-0, ,023-2,460 n.a. -0,031-5,460-0,038-2,250-0,302-9,630 n.a. -0,085-0,920 Average -0,063-0,026-0,031-0,049-0,039-0,052-0,060 year Luxembourg t-statcs Netherlands t-statcs Portugal t-statcs Sweden Swtzerland Denmark t-statcs Unted Kngdom t-statcs ,051-4,890 n.a. n.a. -0,038-2,640-0,053-12,510-0,015-0,950-0,033-9, ,031-6,570 n.a. n.a. 0,082 10,630-0,077-16,120-0,015-1,410-0,042-1, ,035-9,350 n.a. n.a. -0,010-5,670-0,064-12,450-0,083-7,070-0,035-5, ,037-3,370 n.a. n.a. -0,021-11,830-0,144-14,110-0,036-3,800-0,027-4, ,025-5,550 n.a. n.a. -0,054-7,950-0,032-5,050-0,020-3,500-0,013-3, ,018-4,200-0,018-3,340 n.a. -0,020-4,640-0,021-4,980-0,027-1,520-0,039-4, ,017-5,510 0,001 0,060-0,028-5,640-0,028-9,090-0,046-6,370 0,000 0,090-0,034-5, ,050-12,440-0,058-2,910-0,035-6,270-0,021-7,040-0,042-5,130-0,011-2,660 0,000 0, ,042-15,310-0,035-1,850-0,020-3,470-0,040-11,380-0,061-8,290-0,007-1,580-0,067-4, ,034-4,150-0,563-10,690-0,062-7,060-0,023-3,310-0,045-6,490-0,032-2,010-0,075-5, ,028-6,290-0,027-2,360-0,029-4,330-0,012-4,830-0,015-1,270-0,090-6,770-0,023-2, ,023-8,270-0,025-2,360-0,047-7,220-0,018-3,880-0,032-13,350-0,022-1,680-0,040-5, n.a. n.a. n.a. -0,026-11,750-0,027-8,100-0,043-4,680-0,018-2,710 Average -0,033-0,104-0,037-0,018-0,051-0,031-0,034 Source: author's calculaton 31