Deposit market competition, wholesale funding, and bank risk

Journal of Banking & Finance 37 (2013) 3605–3622

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Journal of Banking & Finance

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Deposit market competition, wholesale funding, and bank risk

0378-4266/$ - see front matter � 2013 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.jbankfin.2013.05.010

⇑ Corresponding author. Tel.: +49 69 95662380.E-mail addresses: [email protected] (B.R. Craig), valeriya.dinger@uni-

osnabrueck.de (V. Dinger).1 Tel: +49 541 9693398.

2 Shy and Stenbacka (2004) argue that this result holds only becauseinsurance makes depositors insensitive to bank risk. If in the absence oinsurance, banks compete in both the risk and the deposit rate dimensionpresence of deposit insurance they compete only in the deposit rate dimen

3 This distinction is especially important in the case of banks that facecompetitive positions in the deposit and loan markets, e.g., because they spedeposit raising not loan production.

Ben R. Craig a,⇑, Valeriya Dinger b,1

a Federal Reserve Bank of Cleveland and Deutsche Bundesbank, Wilhelm-Epstein-Str. 14, 60431 Frankfurt a. M., Germanyb University of Osnabrueck and Leeds University Business School, Rolandstr. 8, 49069 Osnabrueck, Germany

a r t i c l e i n f o a b s t r a c t

Article history:Received 13 July 2011Accepted 5 May 2013Available online 23 May 2013

JEL classification:G21

Keywords:Bank competitionWholesale fundingBank riskDeposit rates

Empirical research on the effect of bank competition on bank risk has so far produced very inconclusiveresults. In this paper we revisit this long-standing debate and propose a new empirical approach that isconcentrated on the relationship between deposit market competition and bank risk. This approach clo-sely follows the traditional theoretical views of the competition and risk relationship and is focused ontesting the classical moral hazard problem of the bank: deposit market competition raises the optimalrisk choice of the bank by raising the costs of bank liabilities. Since banks can substitute between retailand wholesale funding, we relate deposit market competition to wholesale market conditions and exam-ine their joint effect on the risk of bank assets. The analysis is based on a unique, comprehensive dataset,which combines retail deposit rate data with data on bank characteristics and data on local deposit mar-ket features for a sample of 589 US banks. Our results support the notion of a risk-enhancing effect ofdeposit market competition.

� 2013 Elsevier B.V. All rights reserved.

deposit

1. Introduction

Understanding how bank competition affects bank risk is essen-tial for the formulation of appropriate regulatory policies. Giventhe applicability to policy, it is not surprising that a wide body ofresearch has focused on examining, theoretically and empirically,the potential trade-off between competition and stability. How-ever, both the theoretical and particularly the empirical resultsare still controversial. The indefinite state of the debate motivatesus to revisit the question.

In this paper we present a novel empirical approach for estimat-ing the relationship between deposit market competition and risk.This approach aims at testing one of the traditional theoreticalviews of the relationship, which is based on the classical moralhazard problem of the bank. Proponents of this view argue thatthe incentives of the bank to invest in risky projects increase withthe costs of its funding (Allen and Gale, 2000, 2004; Hellmannet al., 2000). The intuition of this argument which is based on aclassical asset substitution problem (Jensen and Meckling, 1976)is that investment in riskier projects brings bank owners high ex-cess returns in beneficial states of the world, while the losses in ad-verse situations are mainly shifted to the creditors of the bank. Inenvironments in which banks are fully funded by retail deposits,

intense bank competition will increase the cost of bank fundingby raising the equilibrium deposit rates. The moral hazard view,therefore, suggests that intense bank competition increases theincentives to invest in risky projects by increasing the costs of bankfunding.2

Despite the substantial importance of the moral hazard view inbanking theory (and in policy), we are not aware of any empiricaltests focused on this mechanism. The empirical studies presentedso far are concerned with an overall estimation of the effect of bankcompetition – without distinguishing between deposit and loanmarkets – on bank risk. The lack of distinction between depositand loan market competition is a crucial limitation since: (i) theintensity of competition banks face in the loan and the depositmarkets can differ substantially3 and moreover regulatory mea-sures can affect deposit and loan market competition differently(e.g. regulation Q is an example of how regulators can limit depositmarket competition without directly affecting the intensity of loanmarket competition); and (ii) the risk effect of loan and deposit mar-ket competition can theoretically work in opposite directions. SoBoyd and de Nicoló (2005) show that the classical moral hazard viewrelating bank risk to bank competition ignores the moral hazard

f deposits, in the

sion.differentcialize in

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3606 B.R. Craig, V. Dinger / Journal of Banking & Finance 37 (2013) 3605–3622

problem that arises with bank borrowers when limited loan marketcompetition drives loan rates and thus the costs of debt for the bor-rowers up.4,5 They argue that when the borrowers’ moral hazard is-sues are accounted for the risk increasing effect of deposit marketcompetition can be offset by the risk decreasing effect of loan marketcompetition.

To address this limitation of existing empirical work we presentin this paper a more structural empirical analysis of the competi-tion and risk nexus which reflecting the theoretical contentionsis explicitly focused on the effect of deposit rather than loan mar-ket competition. The focus on deposit market allows us to concen-trate on the empirical examination of the moral hazard problem ofthe bank as a dominant theoretical concept.

A natural approach to testing the moral hazard problem of thebank is to estimate the effect of the costs of deposits—proxied byretail deposit rates6 on the risk of bank assets. When applied to asample of modern banks this empirical test should not only reflectthe costs of retail deposits but should also incorporate the costs ofwholesale funding as a potential substitute for retail deposits; espe-cially since the wholesale market participation of a bank is not exog-enous with respect to the retail deposit market conditions it faces.

The potential substitutability between retail and wholesalefunds motivates7 us to integrate wholesale market conditions inour analysis, particularly since for many banks, short-term whole-sale liabilities such as fed funds and repo borrowing have becomecrucially important.8,9 By doing so, we extend the scope of the anal-ysis and avoid potential omitted variable bias concerns. These con-cerns are implied in the literature on market discipline, whichargues that the structure of bank liabilities and the risk of bank as-sets are chosen simultaneously. Such concerns have been intensifiedby the recent debate on the risk effects of short-term wholesale lia-bilities (Huang and Ratnovski, 2011; Huang and Ratnovski, 2009;Brunnermeier and Pedersen, 2009). Also, by including wholesalefunding in the analysis, we can compare the risk effects of the costsof insured and uninsured liabilities in a joint empirical framework.

Since these costs, particularly for wholesale liabilities, can be af-fected by the risk of bank assets, we also account for the reversecausality effect introduced by borrowers by estimating a joint sys-tem of equations which models the interrelationships of bank riskand the costs of retail and wholesale debt. The strategy for identi-fication in this paper is to explicitly restrict some of the coefficientsin each equation to be zero, so that the system is over-identified.We also provide a simple dynamic identification scheme as arobustness check.

We estimate the equations using a rich dataset, which consistsof deposit rates, balance sheet data, and characteristics of the mar-

4 Martinez-Miera and Repullo (2010) show that when the decrease of bank marginsfrom loan market operations is accounted for the effect of loan market competition onrisk can take a U-shaped form.

5 Alternative theories suggest that loan market competition is positively related tobank risk. So, Broecker (1990) argues that intense loan market competition alsoincreases bank risk taking.

6 Following Allan and Gale’s (2000) model, we ignore fixed costs of deposits andfocus on their marginal costs.

7 See also Norden and Weber (2010) for an extensive discussion on wholesale retailfunding substitutability.

8 Data from the ‘‘Flow of Funds Accounts’’ by the Federal Reserve Board suggestthat retail deposits represent less than 58% of total bank liabilities in 2002; by 2007the share of retail deposits has fallen below 52%.

9 The shift to wholesale funding is presumably related among others to the spreadof the securitized banking business model (see Gorton and Metrick, 2009 for anextensive discussion of the change of banking industries business model towardssecuritized banking funded by wholesale liabilities). Although funding throughsecuritization of loans also plays a relevant role in the determination of the costs ofbank funding, in this analysis we focus on the examination of on-balance sheetliabilities and their effect on on-balance sheet risk. This focus is motivated by the factthat by being reflected in the Call Reports the dynamics of the on-balance sheetvariables can easily and quickly be employed in supervisory analysis.

ket structure. The deposit rates span 581 US banks in 164 metro-politan statistical areas (MSAs). The time period encompasses1997–2006. The richness of the data allows us to exploit the vari-ation in variables across local deposit markets, across banks, andacross time in the analysis.

In this framework, we consider the substantial degree of heter-ogeneity that exists across banks with regard to the structure oftheir liabilities. While some banks are predominantly funded bywholesale liabilities, others still rely almost exclusively on retaildeposits. We examine the effects of risk on funding costs not onlyfor the full sample of banks but also for subsamples of banks withdifferent liability structures.

The results of our analysis point to a robust, positive, and statis-tically and economically significant relationship between the retaildeposit rates offered by a bank and its asset portfolio and defaultrisk. These results are consistent with the economic insights ofthe moral hazard argument on the relationship between bank com-petition and risk. They show that banks with cheap retail sourcesof funding pursue more conservative risk strategies (Allen andGale, 2000; Hellmann et al., 2000, etc.). They should not, however,be interpreted as a direct support for limiting bank market compe-tition. We present no welfare analysis and thus cannot address thetrade-off between the lack of efficiency resulting from imperfectbank competition and the potential fragility of competitive banks.Also, without an estimate of the threshold above which the risk ofindividual banks should be considered excessive, a direct link tofinancial system stability cannot be made. Our results, however,underline the crucial role of retail funding sources for bank riskbehavior and can be used by regulators to focus regulatory andsupervisory attention on banks with a limited access to retaildeposits.10

This paper contributes to the literature by directly addressingthe main challenges of the existing empirical studies on the rela-tionship between bank competition and risk. Whereas most ofthe existing studies measure competition by broad concentrationratios, which cannot disentangle deposit and loan market competi-tion (Keeley, 1990; Demsetz et al., 1996; Brewer and Saidenberg,1996; Salas and Saurina, 2003; Boyd et al., 2006; De Nicoló andLoukoianova, 2007; Schaeck et al., 2009; Schaeck and Cihak,2008; Bretschger et al., 2012; Tabak et al., 2012), we explicitlymeasure the effect of deposit market competition on bank risk.This approach allows us to address the challenge of disentanglingthe effects of deposit and loan market competition which, as sug-gested by Boyd and de Nicolo (2005), potentially work in oppositedirections. To this end the paper is at closest to Jimenez et al.(2010) who present the only other empirical study that we areaware of that distinguishes between deposit and loan market com-petition. The approach of Jimenez et al. (2010), however, fails to ac-count for both the role of wholesale funding and the endogeneityof a bank’s competitive position. The closing of this gap by present-ing a comprehensive framework jointly analyzing risk and retailand wholesale funding costs represents another major contribu-tion of this study.

The choice of deposit rates as a measure of the intensity of de-posit market competition is driven by the theoretical motivationfor this study: if bank competition affects risk because it increasesthe costs of bank deposits, then a direct empirical test could be de-signed that would exploit the information about the costs of retaildeposits contained in the retail deposit rates. This would be moredirect than going the circuitous route that used rough approximationsof competition intensity such as concentration ratios, Herfindahl

10 As argued by Huang and Ratnovski (2009), this policy implication could also beemployed when comparing banking systems internationally: banks in countries withpredominantly retail banking systems were more resilient to financial distress duringrecent financial crises.

B.R. Craig, V. Dinger / Journal of Banking & Finance 37 (2013) 3605–3622 3607

indices, or Panzar-Rose and Boone competition statistics. An addi-tional advantage of using retail deposit rates offered by a bank as aproxy for the intensity of the deposit market competition it faces isthat doing so allows for the fact that banks operating in the samelocal market can face different intensities of competition, for exam-ple, because of comparative advantages in serving some depositorgroups.11 We can strengthen identification by exploiting deposit ratevariation both across markets and across banks.

Viewed in a broader context the empirical analysis of the effect ofdeposit market competition on bank risk that we present here is alsoan example of an empirical test of the classical asset substitutionproblem (Jensen and Meckling, 1976) and as such its implicationsare not necessarily limited to banking firms. The peculiarities ofthe banking firms, however, are related to the fact that in the caseof banks the effects of loan market competition can modify the costsof funding-risk relationship. Disentangling empirically the effect ofloan from that of deposit market competition is, nevertheless, chal-lenging. This is the case because loan and deposit market competi-tive positions can interact. In particular, bank level loan marketcompetition measures can reflect bank risk preferences which havetheir roots at the bank’s costs of funding. Although a completeseparation of the effects of deposit and loan market competition isempirically not feasible, we include some rough proxies of loan mar-ket competition in order to mitigate the risk of omitted variable biasarising from not accounting for loan market effects.

The rest of the paper is organized as follows. Section 2 intro-duces the data. Section 3 presents the empirical methodology. Sec-tion 4 discusses the main results. Section 5 focuses on the analysisof the relationship between the costs of funding and risk and itsinteraction with the liability structure of the bank. In Section 6we discuss the potential differences in the risk effects of longer-term versus short-term wholesale funding and re-estimate themodel using subordinated debt as an alternative form of wholesalefunding. Section 7 concludes.

2. Data

This study is based on a comprehensive dataset that combinesseveral sources of data. First, we employ BankRate Monitor dataon the retail deposit rates offered by banks in different local mar-kets. The coverage of the BankRate Monitor sample is limited to theinterest rates offered by 589 US banks in each of 164 metropolitanstatistical areas (if the respective bank has a branch in the MSA).For these banks we match the BankRate Monitor data to the finan-cial statements (balance sheets and income statements) reportedin the Quarterly Reports of Conditions and Income (Call Reports).BankRate Monitor deposit rate data have weekly frequency. Tomatch the quarterly frequency of the Call Reports, we use onlythe deposit rates reported on the last week of each quarter. In addi-tion, we merge this with information from stock market prices ofbank equity if the bank is listed and available from the Center forResearch in Security Prices (CRSP). Such information is availablefor a subsample of 136 out of the 589 banks. Also, we match ourbank-market observations with characteristics of the local bankmarket (the MSA) drawn from the Summary of Deposits.12 These

11 We are aware of only three other empirical studies which employ bank-levelcompetition measures. Schaeck and Cihak (2008) use the Boone indicator (Boone,2008) as a competition measure. This indicator does not distinguish between depositand loan market power of the bank. Jimenez et al. (2010) measure deposit and loanmarket competition separately by the deposit and the loan market Lerner index of thebank, respectively. They, however, have only aggregate retail rate data for each of thesample banks and no information about the rates in the different local markets.Berger et al. (2009) employ a bank-level overall Lerner index reflecting output andinput prices in both the deposit and loan market.

12 Summary of Deposits data have annual frequency (as of the end of June). We attachthe same values of the local market variables to all four corresponding quarters.

are enriched by data about unemployment and some demographiccharacteristics at the MSA level from the Bureau of Labor Statistics.The data encompass a period starting on September 19, 1997, andending on July 21, 2006.

After merging our data, we have a multidimensional (unbal-anced) panel dataset consisting of bank-level data (risk variables,bank size, capitalization), market-level data (HHI, market size,average income of the MSA’s population, income growth, etc.),and bank-market-level data (retail deposit rates, share of the MSA’sbranches, branches per deposit volume in the market).

3. Methodology

The traditional theory of bank risk and competition (Allen andGale, 2000; Hellmann et al., 2000) implies that the effect of depositmarket competition on bank risk can be studied with an empiricaltest that is based on the moral hazard problem of the bank. Such atest would focus on the effect that differences in bank fundingcosts (which result from different degrees of competition) haveon the risk of bank assets. Following this argument, the mainhypothesis that we test states that the risk of bank assets increaseswith the interest rates the bank pays on its retail and wholesaleliabilities.

For the empirical test of this hypothesis we start with an equa-tion that describes the impact of deposit13 and wholesale rates onthe risk of bank assets:

ri;t ¼ f ðdi;j;t;wi;t ; controlsÞ; ð1Þ

where r denotes the risk of the bank, d the retail deposit rates, and wthe interest rate on wholesale liabilities. The subscripts i, j, and t re-fer to the bank, the local market (MSA), and the time period, respec-tively. In formulating this equation as a test of the moral hazardproblem, we assume that both retail and wholesale funding havea linear effect on the riskiness of bank assets independent of thestructure of bank liabilities. In Section 5 we explicitly focus on theheterogeneity of bank liability structures and the potential non-linearities, and re-estimate Eq. (1) using subsamples of banks withdifferent liability structures.

Since both retail and wholesale interest rates can be affected bythe riskiness of the bank, we explicitly model this reverse causalityby the following Eqs. (2) and (3). The system is then identifiedusing a zero restriction identification strategy14 that we will discussin detail in Section 3.2.

di;j;t ¼ f ðri;t;wi;t ; controlsÞ: ð2Þwi;t ¼ f ðri;t; di;j;t ; controlsÞ: ð3Þ

Eq. (2) models the dependence of retail deposit rates on bankrisk and the costs of wholesale funding.15 While in formulatingEq. (1) as an empirical test of the bank’s moral hazard problem, de-posit rates are considered as the outcome of deposit market struc-ture, in Eq. (2) we account for the fact that deposit rates are alsoaffected by a bank’s risk and alternative sources of funding. In otherwords, in Eq. (2) we account for the component of deposit rates thatis driven by factors other than deposit market competition.

13 Eq. (1) explicitly accounts only for the variable costs of retail and wholesale funds.We include a number of control and instrument variables to account for the variationin the fixed costs of deposits and wholesale funds.

14 One of the reasons we prefer a static to a dynamic identification scheme (e.g., onebased on lags of the dependent variable) is the rigidity of bank retail deposit rates,which implies that we might observe the same retail rate in two consecutive quarters.

15 Jimenez et al. (2010) is the only other study we are aware of that uses prices as ameasure of the intensity of competition. The authors explore the relation betweencompetition and risk in the Spanish banking sector. They fail to recognize, however,the simultaneity of prices and proceed with a reduced-form model.


The dependence of deposit rates on bank risk is based on theassumption of some risk sensitivity of insured deposits, or in otherwords, the view that bank risk is a determinant of its competitiveposition in the deposit market.

The dependence of deposit rates on wholesale rates has alreadybeen shown in theoretical work (e.g. Kiser, 2004; Park and Pennac-chi, 2008). These papers generally assume that bank assets (e.g.,loans) are the output of a production function that uses retailand wholesale funds as inputs. The assumption is then made that,whereas banks can have market power in the retail deposit market,they are price takers in the wholesale market. In this framework,an exogenous rise in the wholesale rate is related to an increasein the optimum retail deposit rate offered by the bank.16

Eq. (3) describes the risk sensitivity of the wholesale fundingrate.17 Wholesale rates are assumed to be risk-sensitive becausewholesale creditors adjust the interest rate to the probability ofthe borrower’s failure since wholesale liabilities are not covered bydeposit insurance. Furfine (2001), for example, proves that riskierbanks pay higher rates on federal funds. Moreover, Flannery andSorescu (1996) and DeYoung et al. (2001) find that riskier bankspay higher interest on subordinated debt.18 Following Pennacchi(1988), we also allow wholesale rates to depend on retail rates,assuming that banks facing intense deposit market competitionshow a higher demand for wholesale funds. Note that the fact thatobserved wholesale rates might depend on retail deposit rates doesnot imply that the wholesale market is not competitive. By includingdeposit rates as determinants of wholesale rates we control for thepossibility that banks which face high rates on retail deposits willbe more likely to borrow in the wholesale market even when whole-sale market rates are relatively high.19 Also, by including Eq. (3) weexplicitly allow for the interdependence between retail rates andbank risk to be driven by a ‘‘wholesale’’ channel: as shown by Billettet al. (1998), riskier banks might shift from uninsured wholesalefunds to insured retail liabilities. Such a shift requires higher retailrates to attract sufficient retail deposits.

3.1. Measures of bank risk, deposit rates, and wholesale rates

We employ three alternative measures of bank risk in the esti-mations: the volatility of return on assets (ROA volatility), the non-performing loans ratio (NPL)20 and, for the subsample of publiclytraded banks, the stock price volatility.21 The ROA volatility, calcu-lated as the standard deviation of the returns on assets,22 measuresbank risk as signaled by volatile earnings. Alternatively, the choice ofthe NPL as a risk proxy is driven by the fact that we focus on the risk

16 An alternative approach of modeling the relationship between retail andwholesale deposits is taken by Jiminez et al. (2007). These authors concentratesolely on the difference between wholesale and retail rates (deposit market Lernerindex) as a measure of deposit market power and do not explicitly model theinteraction between wholesale and retail rates.

17 Here we deviate from the simple Lerner indices approach presented by Jiminezet al. (2007) which implicitly assumes that all banks, independent of their risk levels,face the same country-wide money market rates.

18 To our knowledge the only study that relates wholesale funding, competition, andrisk is Goyal (2005). In his empirical framework Goyal assumes that high bankcompetition is reflected in low bank charter value and high bank risk, and examinesthe effect of the charter value on the yield and the inclusion of covenants on banksubordinated debt. He finds that low charter values correspond to more covenants inthe subordinated debt contract and higher subordinated debt yields.

19 The results of the empirical estimation are qualitatively the same if we estimatethe wholesale equation without including retail deposit rates as a regressor. Includingit, however, strengthens identification.

20 We have rerun all regressions using the net charge-offs to total loans rather thanthe NPL ratio. Results stay qualitatively unchanged.

21 We have also rerun the regressions using the z-score as risk measure (followingthe approach of Boyd et al. 2006 and Schaeck and Cihak 2008). Results arequalitatively the same.

22 The standard deviations are computed by using a rolling window of 8 quarters.

of bank assets, which have traditionally been measured by the shareof impaired loans (e.g., Jimenez et al., 2010; Demsetz et al., 1996—who use this risk proxy in their analysis of the bank competitionand risk relation—etc.). We compute the NPL ratio as the ratio of im-paired loans to total outstanding loans and use the log of the ratiowith a four-quarter lead.23 The intuition behind introducing the leadis that the risk of the current projects will only be reflected with adelay in the nonperforming loan ratios of the bank.24

Finally, for the subsample of publicly traded banks we includethe stock price volatility as an additional risk measure. The volatil-ity is computed from daily stock prices data through estimation ofa GARCH (1,1) model. For each bank the latest GARCH volatilityestimate of the quarter is used as a risk measure. The intuition be-hind this market- based risk measure is that if the market revealsadverse information about the riskiness of a bank’s business, thisinformation will be reflected in its stock price volatility.25

Turning to bank retail deposit rates as a proxy for the depositmarket competitive position, we choose the rates on money mar-ket deposit accounts (MMDA) as the most suitable for our exercise.This choice is motivated, on the one hand, by the fact that alterna-tive retail deposit products either contain a substantial servicecomponent (e.g., interest bearing checking (NOW) accounts),which we cannot observe because of data limitations, or they areinsensitive to local market conditions (e.g., certificates ofdeposit26). On the other hand, MMDAs are one of the most impor-tant retail deposit product of the banks in our sample: on averagethey represent about a third of bank deposits.27

It is often assumed in the banking literature that multimarketbanks charge uniform rates across local markets (e.g., Radecki,1998; Park and Pennacchi, 2008). A closer look at our sample, how-ever, uncovers a high degree of cross-market variation in multi-market banks’ pricing.

The data presented in Table 1 illustrate that the variation in thedeposit rates set by a multimarket bank in the different MSAs isequal to about one-third of the variation of all deposit rates offeredby all banks in a MSA.

We explore this cross-market variation in the pricing of multi-market banks as a proxy for local market competitive conditions.Since we observe bank retail rates in different local markets(MSAs), we control for the intensity of local deposit market compe-tition. The deposit rate equation can therefore be identified basedon the variation of local market characteristics across the MSAs.

For each given point of time the offered MMDA rates represent aproxy for the marginal rather than the average retail funding costsof the bank. In terms of testing the moral hazard problem of thebank the average costs of retail funding of the banks (e.g. givenby the average interest rate on retail deposits) could also be ofinterest. However, two shortcomings of the average costs of depos-its motivate us to choose the marginal costs as given by the offeredMMDA rate as a measure of retail funding costs within our empirical

23 Regression specifications using the current (as in Jimenez et al., 2010), the two-quarter, the six-quarter and the eight-quarter lead of the nonperforming loan ratiosresult in qualitatively the same results.

24 As a robustness check we have rerun the model using the ratio of nonperformingloans to equity as a risk measure (again with a four-quarter lead). According toAshcraft (2008), this is a better measure of bank risk since the capitalization of thebank affects the amount of nonperforming loans it can absorb before harming itscreditors. The results of the estimation are very similar to those using nonperformingloans to total loans as a dependent variable.

25 The credit default swap (CDS) spread has been argued to measure bank riskconsistently. Its use, however, would have dramatically reduced our sample size sincemany of the banks we study here have not issued CDS.

26 See Hannan and Prager (1998) and Craig and Dinger (2008).27 As a robustness check we have rerun all regression specifications using the

interest bearing checking account rates as a retail deposit rate measure. The resultsare qualitatively the same as those reported here. Results are available from theauthors upon request.

Table 1Cross-market and cross-bank variation in MMDA rates.

MMDA rates

Year* Variation within the market Variation within the bank

Standarddeviation

Mean absolutedeviation from themean

Standarddeviation

Mean absolutedeviation fromthe mean

1997 0.53 0.38 0.17 0.071998 0.42 0.31 0.25 0.131999 0.58 0.43 0.18 0.102000 0.67 0.50 0.32 0.182001 0.36 0.27 0.10 0.062002 0.23 0.17 0.05 0.032003 0.06 0.05 0.04 0.032004 0.22 0.16 0.05 0.032005 0.36 0.26 0.10 0.072006 0.41 0.29 0.12 0.07

Note: Variation within the market is calculated by first computing the variation(standard deviation or mean absolute deviation from the mean) of the checkingaccount rates offered by all banks in each local market. Then the variation isaveraged across local markets. Variation within the bank is calculated by firstcomputing the variation (standard deviation or mean absolute deviation from themean) of the checking account rates offered in the various local markets by each ofthe multimarket banks in our sample. Then the variation is averaged across allmultimarket banks.* As of first quarter.


framework. First, the identification of the retail rate equation couldnot be based on the above-mentioned variation across local mar-kets if the average costs of deposits are used. Second, since theaverage costs present a rather backward looking estimate of thecosts of funding (they are an average over past offered rates), a for-ward looking bank should be more likely to incorporate the depositrates offered today rather than the deposit rates from the past inthe decision about the riskiness of its projects. Despite the concep-tual difference between the marginal and the average costs, the fo-cus on marginal costs seems to be less crucial from an empiricalpoint of view since the correlation between the marginal costs asmeasured by the offered MMDA rates and the average costs asmeasured by the ratio of interest paid on all deposits to the totalvolume of deposits in our sample is quite high (roughly 60%).

And finally, in our baseline specification, we use the interestrate on ‘‘federal funds purchased and securities sold under agree-ment to repurchase’’ as a proxy for the costs of wholesale funding.We follow King (2008) and impute this interest rate by the ratio ofthe ‘‘expense of federal funds purchased and securities sold underagreements to repurchase’’ (line riad4180 in the Call Report) to‘‘federal funds purchased and securities sold under agreements torepurchase’’ (line rcfd3353 in the Call Report).28 The format ofthe Call Report does not allow us to disentangle federal funds bor-rowing from repos, so that we have a position including both uncol-lateralized (federal funds purchased) and collateralized (securitiessold under agreement to repurchase) borrowing.29 Both types of bor-rowing have in common the fact that they are of a very short maturityand the counterparty is an institutional investor, usually a bank, so wecan assume that the imputed rate represents the cost of overnight

28 This rate on overnight bank liabilities is imputed by dividing average quarterlycosts by average quarterly volumes. For a few observations the ratio is implausiblylarge. We clean the data by excluding observations with a negative rate or a rateabove 20% (29 bank⁄quarter observations are excluded).

29 Starting from the first quarter of 2002 the Call Report provides the volumes offederal funds borrowed and repo transactions in different sub-lines (rcfd b993 andrcfd b995, respectively), however the interest paid on these two types of debt cannotbe disentangled. For the sub-period starting in January 2002 we have re-estimatedthe wholesale equation using the share of federal funds purchase in the sum of federalfunds purchased and repo borrowing as an additional control. The results (which areavailable from the authors upon request) are qualitatively the same as thosepresented in the baseline regression. The coefficient on the share of federal fundspurchased is not statistically significant in any of the regression specifications.

wholesale liabilities. The substantial variation of the costs of over-night wholesale liabilities both across banks and across time givesus additional identification.

If we have traditional banking systems in mind, overnightwholesale liabilities might not seem a close substitute to retaildeposits. Considering the architecture of the modern U.S. bankingsystem, with its shift towards securitized banking (see Gortonand Metrick, 2009; Shleifer and Vishny, 2009 for an extensive dis-cussion), however, suggests that these short-term wholesale liabil-ities indeed turn out to have replaced substantial amounts of retaildeposits. Moreover, the rate a bank pays on federal funds and reposhas been shown to be closely correlated with alternative bankwholesale liabilities (such as subordinated debt, advances fromFederal Home Loan Banks, and others30), which are potentially bet-ter substitutes for retail deposits from a bank’s point of view. Theadvantage of federal funds and repos over these alternative whole-sale liabilities for our framework is that we have observations formost banks in our sample.31 Moreover, comparison across banks isfurther facilitated by the fact that fed funds market borrowing is astandardized ‘‘product’’.32 In Section 6 we alternatively estimatethe model using the subordinated debt rate as a wholesale rateproxy, mainly to control for the potential difference between the riskeffects of short- versus longer-term bank debt, whose importancehas been underscored by recent financial crises (Huang and Ratnov-ski, 2011; Brunnermeier and Pedersen, 2009).

Table 2 illustrates descriptive statistics of the dependent vari-ables in the three equations. It shows substantial variation of theMMDA rate, between 0% and 5.83%. Some of that variation is dueto the time series dimension of our data, which span a period from1997 to 2006 and cover a full interest rate cycle. Our risk measuresalso exhibit substantial variation: the standard deviation of ROAvaries between 0.0004 and 0.38; the nonperforming loan ratiosvary between zero and more than 12% and the stock price volatilityas measured by the GARCH (1,1) model is in the range of 0.0055and 0.0240.

3.2. Identification and Instruments

Our identification follows a ‘‘zero restriction’’ approach. Thisidentification strategy includes additional control variables whichare allowed to enter only some of the equations with a non-zerocoefficient. The coefficients of the rest of the equations are re-stricted to being equal to zero. This identification strategy is equiv-alent to instrumenting each of the endogenous variables by asuitable set of instrumental variables, which are uncorrelated withthe error term but strongly correlated with the instrumentedendogenous variable.

In the case of retail deposit rates, we base the identification onthe assumption that banks control for local deposit market compe-tition when setting their deposit rates.33 Classical measures of de-posit market conditions that have been found to determine retaildeposit rates are the Herfindahl index (see Berger and Hannan,1992; Park and Pennacchi, 2008) and market size (see Prager and

30 Ashcraft (2008).31 In order to account for the noise introduced in the fed funds rate data when the

volume of fed funds liabilities is negligibly small, we introduce a screen based on theshare of fed funds liabilities in total assets in the estimation of Eq. (3) and account forthe potential selection bias by using a Heckman correction (Heckman, 1976).

32 Alternative wholesale funding products bear a substantial non-price componentsuch as covenants (see Goyal, 2005), which should be accounted for, for a precisecomparison. Data about these are, however, unavailable for the broad range of banksincluded in our study.

33 Note that we observe substantial cross-market variation in retail rates within themultimarket banks (which we will discuss in our data section) in our sample, whichcan be employed in the identification.

Table 2Summary statistics of dependent variables. Source: Authors’ calculation.

Variable Number of observations Mean Standard deviation Minimum Maximum

ROA volatility 9213 0.0063 0.0024 0.0004 0.0376NPL (in %) 12098 0.0070 0.0090 0.0000 0.3500Stock price volatility 11164 0.0101 0.0037 0.0055 0.0240MMDA rate (in %) 18715 1.3560 0.8790 0.0000 5.8300Rate on federal funds purchased (in %) 17439 2.4050 2.0610 0.0360 19.6820Rate on subordinated debt (in %) 13279 0.0251 0.1810 0.0000 7.7926

34 Since the stock market volatility measure can only be applied to listed banks thisinstrumental variable is not included in the estimation of the model when risk ismeasured by stock market volatility.

35 Average FICO scores can alternatively be used as a risk instrument. We do nothave the FICO score data for the full sample period at our disposal. Previous research(see Cohen-Cole, 2008), however, suggests a very strong correlation between averageFICO scores and average household income.

36 See, for example, Foos et al. (2010).


Hannan, 2004). The Herfindahl index controls for the concentrationof market power. It is computed as the sum of squares of the depositmarket shares of all banks operating in the MSA (this variable isdrawn from the FDIC Summary of Deposits). The market size variableis the log of the population of the respective market. This variableindicates the volume of potential customers and has been found tobe positively correlated with competitiveness. Since the observed re-tail rate of a bank might also depend on the bank’s branch networkas a proxy for the quality of service and proximity, we add the ratioof branches to deposits computed at the bank-market level as the ra-tio of the number of bank i’s branches in local market j to bank i’stotal deposits (in millions of USD) in this market. Also recent evi-dence (see Acharya and Mora, 2011) suggest that the share of seniorpopulation (aged 65 and above) is a significant determinant of thedeposit supply. Since by affecting deposit supply senior populationalso affects deposit rate we include this variable as an additionalinstrument. We argue that Herfindahl index, market size, branchesto deposits and the senior population are right-hand variables in thedeposit equation only; their coefficients in the other two equationsare restricted to zero. These restrictions are based—consistent withAllen and Gale (2000) and Hellmann et al. (2000)—on the assump-tion that if deposit market structure has an effect on bank risk oron wholesale rates, this effect is realized only through the costs ofretail funding.

Similarly, the instrumentation of the wholesale rate focuses onvariables that affect the rate a bank pays on wholesale liabilitiesbut that do not have a direct impact on deposit rates and bank risk.Our major instrument for the rate on wholesale funds is the aver-age effective level of the federal funds rate (as announced by theFederal Reserve Bank of New York, based on its survey of four ma-jor brokers). The inclusion of this instrument follows the argumentthat the rate banks pay on wholesale liabilities reflects changes inthe average rate on fed funds. Note that by including this instru-ment in the regressions we also control for the general interest ratelevel, so that variation in the MMDA rate is then only related tocross-market and cross-bank variation and not to the general inter-est rate cycle. In other words, average effective fed funds rate ac-counts for the time series variation of wholesale (and as a resultof retail) interest rates.

A change in the effective fed funds rate is probably also relatedto the amount of risk taken on by the bank (see Jiminez et al.,2007), as well as the deposit rate it can charge, but we assume thatthis impact is realized (consistent with monetary policy transmis-sion theories) only through the costs of overnight wholesale fund-ing faced by the bank. The use of this instrument is based on theassumption that any effect of the fed funds rate on risk and depositrates works through the wholesale rate that the bank pays. More-over, additional identification comes from the fact that the over-night bank wholesale funding rate and the effective fed fundsrate are more strongly correlated than deposit rates and the effec-tive fed funds rate. This is the case because while effective fedfunds rate and bank overnight wholesale rates are at the shortestmaturity end of the yield curve and co-move strongly, deposit ratesimplicitly have a longer maturity, might reflect dynamics of other

yield curve maturity segments, and typically adjust only very infre-quently to market interest rate changes.

We also use a dummy variable, which takes the value of one ifthe bank belongs to a large bank holding company (with total as-sets of 10 billion USD or more) and zero otherwise (large BHC dum-my), as an additional instrument for the wholesale rate. Theintuition behind this instrument is that wholesale funding ischeaper for banks that are members of large bank holding compa-nies (BHCs), but risk choice and the deposit rate do not necessarilydepend on BHC membership. Both the average fed funds rate andthe large BHC dummy are weak instruments. The average fed fundsrate shows no variation across banks, while the large BHC dummyshows almost no variation across time. To strengthen identifica-tion, we also include a dummy variable that takes the value ofone if the bank’s shares are listed for public trade in the stock mar-ket, and zero otherwise (listed), as an additional instrument for thewholesale rate. The inclusion of this instrument is based on theassumption that listed banks could because of their higher trans-parency have an easier access to wholesale funding.34

The identification of bank asset risk is based on the argumentthat the riskiness of bank assets is affected by the general eco-nomic conditions in the geographical regions where the bank oper-ates. Following this argument, we use the annual change in theunemployment level in the markets where a bank operates (unem-ployment) as well as the annual household income growth aver-aged across the markets where a bank operates (incomegrowth)35 as risk instruments. The importance of general economicconditions for bank risk has been empirically confirmed in cross-country comparisons that find that GDP and GDP growth are impor-tant determinants of nonperforming loans (Dinger and von Hagen,forthcoming and Boyd et al., 2006). Recent studies comparing theperformance of loans across US regions also confirm that unemploy-ment change strongly positively correlates with mortgage failures(Campbell and Dietrich 2012) General economic conditions areeffective instruments because, although they significantly affectthe risk of the banks operating in the local market, they do not havea direct impact on wholesale and deposit rates. The use of local eco-nomic conditions as instruments for risk assumes that the wholesalerate paid by a bank does not directly depend on local economic con-ditions. In other words, any effect of the local economic conditionson the wholesale rate paid by the banks goes through the differencein bank risk. In addition to local economic conditions we also includethe growth rates of loans as a risk instrument since it has beenshown to be significantly positively correlated with the riskiness ofbank assets.36

Table 3Summary statistics of control and instrumental variables. Source: Authors’ calculation.

Variable Number of observations Mean Standard deviation Minimum Maximum

Effective fed funds rate (in %) 18715 3.535 1.949 0.938 7.125Loans to total assets 19387 0.539 0.204 0.078 2.313Loan growth rate 15999 0.033 0.138 �0.747 8.094Change in unemployment 19387 0.001 2.243 �17.900 17.909Income growth 18266 0.050 0.027 �0.083 0.175Market size 17879 29.300 49.100 0.799 487.000Herfindahl index 17879 0.159 0.067 0.051 0.773Number of branches per 1000000 USD deposits 17879 0.000 0.000 0.000 0.001Share of senior population 19387 0.172 0.036 0.106 0.334Effective federal funds rate 19387 3.392 1.944 0.938 7.125Large BHC dummy 19387 0.051 0.221 0.000 1.000Listed dummy 19387 0.040 0.195 0.000 1.000Securities to total assets 19387 0.364 0.116 �0.022 0.870


In the case of all instruments, the Stock-and-Watson-rule-of-thumb measure37 confirms the strength of the instrument, and, inthe case of multiple instruments, a Hansen test does not reject theexogeneity of the instruments.

3.3. Control variables

As suggested by earlier research, a few variables such as capital-ization and bank size can affect all three dependent variables (Han-nan and Hanweck, 1988; Furfine, 2001; Boyd et al., 2006). That iswhy we include as control variables in all three equations the ratioof bank equity to total assets as a measure of capitalization, and thelog of the bank’s total assets as a proxy for bank size, as well as thesquared bank size variable (to control for non-linearities in the rela-tionship between bank size and bank risk and retail and wholesalerates). Also we include the ratio of loans to total assets (loans to to-tal assets) as a control variable in all three equations since the shareof loans can affect not only the riskiness of a bank’s portfolio (ifloans are riskier than alternative bank assets) but also a bank’s de-mand and thus costs of funding. This variable is generated as theratio of loans in the balance sheet plus the volume of securitizedloans (defined as the loans securitized and sold with servicing re-tained by the bank38) to the total assets of the bank. We also viewthe loans to total assets ratio as a rough proxy of a bank’s loan marketcompetitive position. The relative volume of loan originationapproximated by this variable is informative about a bank’s loanmarket competitive position since under the assumption that banksgenerate higher income from loan origination than from alternativeassets, banks with a substantial market power in the loan marketwill have a higher share of loans in their portfolio relative to bankswith less favorable loan market positions (Goyal 2005 uses a similarapproach to approximate a bank’s deposit market competitiveposition).39 The use of this loan market competition proxy obviouslyignores the potential interactions between deposit and loan marketcompetition and is therefore not sufficient to strictly disentangleloan from deposit market competition effects. Nevertheless, it allowsus to identify deposit market competition’s effect on risk while con-trolling for an approximate measure of loan market competition.

37 The so-called Stock and Watson rule of thumb (Stock and Watson, 2003) is oftenused as a proxy for the strength of an instrument. According to this rule, the first-stage F-statistic testing the hypothesis that the coefficients on the instruments arejointly zero should be at least 10. In the case of the deposit rate instruments, the F-statistic is 14.5, for the wholesale rate instruments the F-statistic is 13.2, and for therisk instruments the F-statistic is 12.4.

38 Computed as the sum of lines rcfd b706-b711 of the Call Report.39 The use of alternative loan market competition measures is challenging. While

information on loan market share is not available in our data, the use published retailloan rates which are available to us for a subsample of banks endanger identificationsince they strongly depend on bank risk preferences.

The summary statistics of the instrumental and control vari-ables are presented in Table 3.

3.4. Estimation technique

In the estimation of Eqs. (1) and (3), bank-level dependent vari-ables (the risk proxy and the rate on wholesale liabilities) are re-gressed on bank-market-level explanatory variables (e.g., depositrates). In this case, the assumption of uncorrelated error termsacross the observations may be violated (it is likely that observa-tions of the same bank in different markets will show correlatederror terms), resulting in potentially inconsistent estimates. Weadopt three alternative approaches to deal with our multidimen-sional panel.

First, we use the full sample of bank-market observations andcluster the standard errors by bank. This estimation allows us toexplore variation of deposit market competition and risk bothacross banks and across markets.

Second, we alternatively estimate the model at the bank levelby computing the weighted average values of the bank-market-level variables (deposit rate, average income, branches-to-depositsratio, etc.). For each bank and time period, we compute theweighted average value of each of these variables across all the lo-cal markets in which the bank operates.40 Through the aggregation,we achieve consistency of the estimated coefficients but lose infor-mation on the intensity of the local deposit market and dramaticallyreduce the number of observations, which in turn reduces theefficiency of the estimation. Obviously, this estimation approachcan account only for the variation across banks. It has, however,the advantage that it accounts for the possibility that banks reshuffledeposits across local markets. In this case, the average intensity ofdeposit market competition might be the one factor that mattersfor bank risk.

And third, we estimate the model using the subsample of sin-gle-market banks (112 out of our sample of 589 banks operate inonly one MSA). Single-market banks face deposit market competi-tion in one market only, and their bank-level risk is related to thecompetitive conditions in only this deposit market. The drawbackof this approach is that we again dramatically reduce our samplesize.

In the estimation of the wholesale rate equation we control forthe potential selection bias, which arises from the fact that if banksperceive that they have to pay a disadvantageous rate on theirwholesale liabilities, they may refrain from borrowing wholesale

40 We have rerun the estimations using the non-weighted averages. Results arequalitatively the same.

Table 4Estimation of three-equation system: risk, deposit rates, and wholesale rates; sample: all banks; multimarket banks are treated as individual market level observations; wholesalerates are measured by rate on federal funds purchased.

Risk measure ROA volatility NPL Stock price volatility

Coefficient Standard error Coefficient Standard error Coefficient Standard error

Dependant variable: bank riskMMDA rate 0.0026*** 0.0003 0.0020*** 0.0011 0.0019*** 0.0003Rate on federal funds purchased �0.0013 0.0018 0.0008* 0.0005 0.0004** 0.0002Bank size 0.0019*** 0.0005 0.0056*** 0.0015 �0.0007 0.0005Bank size^2 �0.0001*** 0.0000 �0.0002*** 0.0000 0.0002 0.0002Capitalization 0.0088*** 0.0027 �0.0295*** 0.0085 0.0145*** 0.0027ROA 0.1740*** 0.0172 0.2783*** 0.0537 �0.0896*** 0.0150Loans 0.0025*** 0.0004 0.0089*** 0.0012 0.0017*** 0.0003Loan growth 0.0005** 0.0002 0.0010* 0.0006 �0.0002 0.0003Unemployment 0.0001** 0.0001 0.0004** 0.0002 0.0004*** 0.0001Income growth �0.0173*** 0.0018 �0.0087* 0.0052 �0.0302*** 0.0017Constant �0.0165*** 0.0041 �0.0582*** 0.0129 0.0153*** 0.0048Observations 7128 7149 7069R-squared 0.17 0.20 0.24

Dependant variable: MMDA rateBank risk 133.1180*** 22.4539 102.3565*** 18.2004 128.2745*** 8.3988Rate on federal funds purchased 0.2602*** 0.0105 0.5822*** 0.0465 0.2924*** 0.0156Bank size �0.3912*** 0.1278 0.2955*** 0.1654 �0.2140 0.1704Bank size^2 0.0088** 0.0038 �0.0097*** 0.0048 0.0049 0.0048Capitalization 1.4793** 0.6804 7.1846 1.1721 2.9747*** 0.6716Loans �1.8133*** 0.0669 �0.2684 0.2137 �0.7884*** 0.0665Market size 0.0002 0.0004 �0.0002 0.0004 0.0009** 0.0000HHI �1.4739*** 0.2107 �0.3840** 0.2022 �0.4839** 0.1930Branch_deposit 0.9163 0.9763 �3.1111** 1.2393 �0.2353** 0.1067Senior population �1.2706** 0.4983 �1.9903*** 0.5571 �1.0370*** 0.3958Constant 5.0497*** 1.0698 �1.5164 1.4761 1.6173 1.4772Observations 7128 7149 7069R-squared 0.54 0.28 0.48

Dependant variable: rate on federal funds purchasedMMDA rate 0.5382* 0.2852 0.5189*** 0.2010 2.9262*** 0.4561Bank risk 580.4489*** 28.4529 236.2181*** 6.7374 418.4011*** 38.9796Bank size 0.8944*** 0.2515 �0.4835*** 0.1825 2.2123*** 0.3833Bank size^2 �0.0239*** 0.0070 0.0112** 0.0051 �0.0596*** 0.0106Capitalization �22.5385*** 1.4070 �13.5273*** 0.8415 �0.4256 1.7652Loans 0.3567 0.2569 �1.1898*** 0.1888 2.0485*** 0.3921Effective fed funds rate 0.3217*** 0.0829 0.1258** 0.0585 �0.0655 0.1244Large BHC dummy �0.1148 0.1013 �0.1886*** 0.0721 �0.3046** 0.1483Listed �0.3327*** 0.0747 0.1848*** 0.0509Securities 2.0731*** 0.3318 0.5832*** 0.2262 0.9460** 0.4722Constant �10.4411*** 2.3402 5.8644*** 1.7050 �18.2004*** 3.5168Observations 7128 7149 7069Censored observations 596 596 596R-squared – – –

Note: Two-stage least squares IV estimations. Endogenous variables are: bank risk (measured by z-score, NPL), MMDA rate and the rate on fed funds purchased and securitiessold under agreement to repurchase. The fed funds rate equation is estimated using a Heckman procedure to control for potential selection bias.* Indicate significance at the 10% level.** Indicate significance at the 5% level.*** Indicate significance at the 1% level.


funds.41 Consequently, for such banks we will observe no (or onlynegligible volumes) of wholesale funding. For these reasons we usethe censored regression specification suggested by Heckman(1976) when estimating the wholesale rate equation. Unless theshare of wholesale liabilities is large enough, the purchased fundsare likely to represent unusual purchases made under extreme timepressure and are thus unlikely to represent the price of wholesalefunds as deposit substitutes. Because of this, we did not include anobservation in the estimated wholesale funds equation unless thevolume of federal funds purchased represented at least 1% of thebank’s assets.42 The Heckman specification creates an auxiliary var-iable in the first stage, the ‘‘inverse Mills ratio,’’ which represents the

41 These selection issues have been explicitly studied by King (2008).42 As robustness check we have re-estimated the model using both a fixed volume

for the federal funds purchased as a trigger point (1 million USD, as in King, 2008) andalternative trigger values for the fed funds purchased as a share of total assets (0.05%and 2%). Results do not change qualitatively.

bias caused by the censoring process. As noted by Heckman, instru-mental variable estimators are still consistent, once the predicted in-verse Mills ratio is included in the system.43

Despite the fact that standard formal tests confirm the strengthand the exogeneity of the instruments in our zero restrictionframework some doubt on the validity of the instruments can stillpersist because of the fundamental non-testability of exclusionrestrictions. To address this we also re-estimate the model usinga simple dynamic identification scheme based on Arellano andBond’s (1991) GMM approach as a robustness check.

In addition, we illustrate the empirical relevance of endogeneityby presenting as a benchmark the results of an exercise ignoringthe endogeneity issues and estimating each of the three equations

43 Note that the Mills ratio is significant in the estimation of all specifications of thewholesale equation.

Table 5Estimation of three-equation system: risk, deposit rates, and wholesale rates; sample: all banks; multimarket banks are averaged across individual market level observations;wholesale rates are measured by rate on federal funds purchased.



Dependant variable: bank riskMMDA rate 0.0007* 0.0004 0.0016 0.0028 0.0009* 0.0006Rate on federal funds purchased �0.0003 0.0002 0.0003 0.0015 0.0008** 0.0004Bank size 0.0007 0.0008 0.0062 0.0058 0.0005 0.0012Bank size^2 0.0000 0.0000 �0.0002 0.0002 0.0000 0.0000Capitalization 0.0170*** 0.0028 0.0347** 0.0171 0.0157*** 0.0050ROA 0.1063*** 0.0243 0.1591 0.1353 �0.0955*** 0.0271Loans 0.0019*** 0.0004 0.0084*** 0.0031 0.0022*** 0.0007Loan growth 0.0004** 0.0002 0.0003 0.0010 �0.0005 0.0006Unemployment 0.0001** 0.0000 �0.0004 0.0003 0.0002 0.0001Income growth 0.0078*** 0.0016 0.0085 0.0129 �0.0272*** 0.0048Constant �0.0045 0.0063 �0.0587 0.0478 0.0051 0.0101Observations 3375 2286 1515R-squared 0.46 0.16 0.17Dependant variable: MMDA rateBank risk 126.4808** 50.5552 �89.9742** 40.2528 80.5642*** 27.5503Rate on federal funds purchased 0.4362*** 0.0285 0.6484*** 0.0870 0.3836*** 0.0354Bank size �0.9746*** 0.2751 �0.1749 0.3631 �0.6304 0.4415Bank size^2 0.0269*** 0.0088 0.0053 0.0113 0.0168 0.0133Capitalization 1.6731 1.4176 9.3105** 3.9237 0.2648 1.3610Loans �1.4346*** 0.1558 0.0226 0.4736 �0.8428*** 0.1508Market size 0.0015* 0.0009 �0.0005 0.0011 0.0014 0.0014HHI �3.0378*** 0.5747 0.1149 0.8780 �1.8202*** 0.4481Branch_deposit 0.7280 1.8342 �7.1756** 3.4982 �0.8666 3.1528Senior population �0.3939 0.8168 �2.0203 1.4592 �1.0226 0.9746Constant 9.1475*** 2.1758 1.5968 3.0981 5.9707* 3.6898Observations 3375 2286 1515R-squared 0.30 0.16 0.49Dependant variable: rate on federal funds purchasedMMDA rate 0.7990*** 0.1581 1.5515*** 0.1689 1.0877*** 0.1673Bank risk 322.6662*** 14.4356 182.6639*** 8.7880 �319.6689*** 34.0153Bank size 0.6666*** 0.2289 0.9712*** 0.2322 1.1240*** 0.2399Bank size^2 �0.0170** 0.0071 �0.0299*** 0.0072 �0.0325*** 0.0075Capitalization �12.7031*** 1.1286 �15.5620*** 1.2061 �2.0145*** 1.1217Loans �0.7764*** 0.2683 �1.8195*** 0.2895 1.5800*** 0.2878Effective fed funds rate 0.1388*** 0.0504 �0.1969*** 0.0564 0.3491*** 0.0536Large BHC dummy �0.0592 0.0801 0.0967 0.0810 �0.1065 0.0843Listed �0.2439*** 0.0581 0.1600*** 0.0569Securities 0.3582 0.2817 �0.5571* 0.2855 0.7635** 0.3066Constant �6.2105*** 1.9505 �6.0341*** 1.9908 �7.2727*** 2.0489Observations 4215 4215 1515Censored observations 348 348 268R-squared – – –

Note: Two-stage least squares IV estimations. Endogenous variables are: bank risk (measured by z-score, NPL), MMDA rate and the rate on fed funds purchased and securitiessold under agreement to repurchase. Bank-market-level variables are averaged at the bank level. The fed funds rate equation is estimated using a Heckman procedure tocontrol for potential selection bias.

* Indicate significance at the 10% level.** Indicate significance at the 5% level.

*** Indicate significance at the 1% level.


independently from the others using a simple panel ordinary leastsquares approach.

4. Estimation results

In this section we present the results of a baseline model, usingthe rate on federal funds purchased and securities sold underagreement to repurchase as a proxy for the wholesale funding rateand the money market deposit account rate as a proxy for theintensity of deposit market competition.

To start with Table 4, which contains a column for each of therisk measures (ROA volatility, the nonperforming loans ratio(NPL) and stock price volatility), reflects the estimation resultsbased on the full sample of bank–market-level observations witha quarterly frequency. These results show a statistically significantpositive link between deposit rates and bank risk, which is robustto the choice of the risk measure. The estimated coefficients

suggest a relatively large economic significance of the results. So,a one-standard-deviation increase of the MMDA rate (0.879) corre-sponds to a rise in ROA volatility of 0.002 (equal to about one of thestandard deviation of ROA volatility); an increase in the nonper-forming loans ratio of 0.002 (again equal to roughly one standarddeviation of the nonperforming loans ratio) and a rise in stock pricevolatility of 0.016 (corresponding to about 0.5 of the standard devi-ation of this risk measure). These results are both statistically andeconomically substantially stronger than the ones generated whenendogeneity is ignored.

The rate on federal funds purchased enters the regression usingthe ROA volatility as a risk measure with a statistically insignificantcoefficient. Its effect on the nonperforming loans ratio and on thestock price volatility is, however, positive and statistically signifi-cant: banks paying higher rates on federal funds have on averageriskier loan portfolios and more volatile stock prices. The magni-tude of the estimated coefficient, however, suggests that the

Table 6Estimation of three-equation system: risk, deposit rates, and wholesale rates; sample: single market banks only; wholesale rates are measured by rate on federal funds purchased.

Risk measure ROA volatility NPL stock price volatility


Dependant variable: bank riskMMDA rate 0.0019*** 0.0007 0.0007 0.0016 0.0018 0.0018Rate on federal funds purchased �0.0010** 0.0004 �0.0012 0.0010 0.0004 0.0012Bank size �0.0004 0.0060 �0.0023 0.0113 0.0030 0.0082Bank size^2 0.0000 0.0002 0.0002 0.0004 �0.0001 0.0003Capitalization 0.0267** 0.0112 0.1138 0.0323 �0.0020 0.0159ROA 0.1058*** 0.0295 0.4437 0.0616 �0.0258 0.0455Loans 0.0032** 0.0013 �0.0001** 0.0033 0.0029* 0.0020Loan growth 0.0017 0.0015 0.0213 0.0046 �0.0024 0.0029Unemployment �0.0004 0.0003 �0.0008 0.0010 0.0012 0.0012Income growth 0.0236*** 0.0076 0.0996 0.0261 �0.0401** 0.0173Constant �0.0001 0.0446 �0.0117 0.0847 �0.0113 0.0623Observations 359 362 121R-squared 0.52 0.54 0.28

Dependant variable: MMDA rateBank risk 83.1137** 36.5601 �17.7497** 8.8684 137.6725*** 45.8328Rate on federal funds purchased 0.2559*** 0.0441 0.2634*** 0.0408 0.1500 0.0770Bank size �3.8459*** 1.2659 �6.0497*** 1.3870 �2.6996 2.8589Bank size^2 0.1225*** 0.0440 0.2046*** 0.0475 0.0901 0.0932Capitalization �0.9248 3.4410 4.6357* 2.8369 2.4984 4.3606Loans �1.6562*** 0.2731 �1.5399*** 0.2640 �0.7824*** 0.2814Market size �0.0028 0.0037 �0.0105*** 0.0037 �0.0038*** 0.0005HHI �1.3857*** 1.0053 1.1116*** 1.2183 �0.9749 1.6225Branch_deposit �13.2160* 7.7754 �21.3009** 9.0232 �2.0682 25.7686Senior population �2.4129 3.8865 �1.3659 4.8875 �2.3353 6.7258Constant 31.8009*** 9.0760 46.4152*** 10.0268 20.6038 21.5841Observations 359 362 121R-squared 0.47 0.42 0.64

Dependant variable: rate on federal funds purchasedMMDA rate �0.6237 1.1396 �0.0207 0.6568 �0.0478 0.8657Bank risk 145.3430 125.9697 68.4614** 35.4982 �157.6496 182.3815Bank size �0.9444 5.7722 �1.5660 3.3615 �1.2670 4.2262Bank size^2 0.0232 0.1983 0.0504 0.1153 0.0395 0.1449Capitalization �18.0631 16.1612 �14.0037*** 8.2817 �5.6389 9.0012Loans �1.2707 2.2307 �0.8630 1.2373 0.1830 1.5517Effective fed funds rate 0.5932 0.4008 0.4142* 0.2483 0.5701* 0.2948Large BHC dummy �0.0937 1.7218 �0.8123 1.0097 �0.5129 1.2461Listed �0.7161 1.0215 �0.3741 0.5245Securities �0.8333 2.7020 0.0204 1.5775 �0.1941 1.9975Constant 13.2353 43.1114 15.2108 25.1560 13.9304 31.6044Observations 768 768 121Censored observations 108 108 6R-squared – – –

Note: Two-stage least squares IV estimations. Endogenous variables are: bank risk (measured by z-score, NPL), MMDA rate and the rate on fed funds purchased and securitiessold under agreement to repurchase. The fed funds rate equation is estimated using a Heckman procedure to control for potential selection bias.



45 One potential concern is that relationship between bank competition and riskmight have changed during the sample period, which spans almost a decade. As arobustness check, we have re-estimated the model using time dummies as additional


economic significance of the wholesale rate’s impact is substan-tially lower than that of retail deposit rates.44

Turning to the control variables, the coefficients of the bank sizevariables suggest a humped shape for the relationship betweenbank size and bank risk. Moreover, well-capitalized banks are sup-posed to have more volatile returns and stock prices but less riskyloans. Banks holding more loans on their portfolios are signifi-cantly riskier. This result suggests that, on the one hand, loansare riskier than alternative bank assets. On the other hand, it isconsistent with Boyd and de Nicolo’s (2005) argument that whenbanks have high loan market power—signaled by a large share ofloans in total assets—their risk might be increased because of theborrowers’ moral hazard. This result could as well be affected by

44 The lower economic and statistical significance of the wholesale rate relative tothe retail rate coefficients might be due to the fact that our measure of retail rates isless noisy than our wholesale rate measure (imputed from Call Reports) and that ourretail rate instruments are stronger than the wholesale rate instruments.

accounting conventions since the unrealized gains and losses inthe securities portfolio are not reflected in the income statement.And last but not least, larger (positive) changes in unemploymentand lower income growth correspond to higher bank risk levels.Their coefficients in the bank risk regression supports their useas efficient instrumental variables for bank risk in the deposit rateand wholesale rate equations.45

control variables. Results are qualitatively the same. However, since the effectiveaverage federal funds rate has no cross-sectional variation, the efficiency of theestimation is dramatically reduced because of colinearity. Alternatively, we have re-estimated the model for two sub-periods (1997–2000 and 2001–2006). Results,which are available from the authors upon request, are robust. However, for the lattersubsample we observe both economically and statistically stronger effects.

Table 7Panel OLS estimation of the bank risk, the MMDA rate and the wholesale rate equations independently from each other; Sample: All banks; Multimarket Banks are treated asindividual market level observations; Wholesale rates are measured by rate on federal funds purchased.



Dependant variable: bank riskMMDA rate 0.0001*** 0.0000 0.0001 0.0002 0.0010*** 0.0001Rate on federal funds purchased �0.0001*** 0.0000 0.0014*** 0.0001 0.0004*** 0.0000Bank size 0.0010*** 0.0003 0.0048*** 0.0014 0.0003 0.0005Bank size^2 �0.0003*** 0.0001 �0.0001*** 0.0000 �0.0001 0.0001Capitalization 0.0170*** 0.0012 0.0340*** 0.0062 0.0124*** 0.0020ROA 0.0518*** 0.0026 0.2400*** 0.0135 �0.0839*** 0.0055Loans 0.0008*** 0.0002 0.0069*** 0.0008 0.0002 0.0002Loan growth 0.0002** 0.0001 0.0010* 0.0006 �0.0003 0.0003Unemployment 0.0001*** 0.0000 �0.0002 0.0001 0.0004*** 0.0001Income growth 0.0097*** 0.0008 �0.0110*** 0.0042 �0.0266*** 0.0016Constant �0.0047* 0.0029 �0.0467*** 0.0119 0.0087** 0.0042Observations 7184 7205 7623R-squared 0.32 0.20 0.24

Dependant variable: MMDA rateBank risk 1.1486 3.2733 �0.4003 0.6436 21.7595*** 1.2376Rate on federal funds purchased 0.0599*** 0.0028 0.0600*** 0.0031 0.0622*** 0.0029Bank size �0.2315** 0.1060 �0.2393** 0.1056 0.3006*** 0.1124Bank size^2 0.0021 0.0031 0.0023 0.0031 �0.0114*** 0.0032Capitalization 0.6209** 0.3129 0.5962* 0.3110 0.2119 0.2946Loans �2.4073*** 0.0398 �2.4127*** 0.0402 �1.5768*** 0.0312Market size �0.0018*** 0.0003 �0.0019*** 0.0003 �0.0009*** 0.0002HHI �0.8978*** 0.1366 �0.8985*** 0.1358 �0.3647*** 0.1208Branch_deposit 3.4629*** 0.6659 3.4693*** 0.6656 0.7622*** 0.2580Senior population �1.6264*** 0.4544 �1.6286*** 0.4557 �1.6527*** 0.3010Constant 5.9680*** 0.8922 6.0511*** 0.8896 0.1380 0.9906Observations 9000 9024 10068R-squared 0.49 0.49 0.50

Dependant variable: rate on federal funds purchasedMMDA rate 0.3400*** 0.0333 0.3105*** 0.0319 0.3895*** 0.0281Bank risk �12.7955 8.5576 73.0711*** 1.7793 28.0959*** 3.9250Bank size 0.3663* 0.1962 0.0377 0.1949 1.1802*** 0.2664Bank size^2 �0.0112** 0.0056 �0.0034 0.0056 �0.0342*** 0.0073Capitalization �10.4759*** 0.8667 �11.4613*** 0.8197 �10.1328*** 0.5190Loans 0.9080*** 0.1980 0.5595*** 0.1910 0.0248*** 0.1220Effective fed funds rate 0.4631*** 0.0188 0.4244*** 0.0179 0.3276*** 0.0116Large BHC dummy 0.0259 0.0893 0.1435* 0.0879 �0.1219*** 0.0905Listed �0.1528*** 0.0539 �0.1139** 0.0548Securities 0.6933** 0.2742 1.3419*** 0.2644 0.2436 0.2000Constant �2.4690 1.7214 0.2992 1.7045 �8.8404*** 2.3923Observations 9181 9205 11141Censored observations 501 518 213R-squared – – –

Note: Random-effects panel OLS estimation. The fed funds rate equation is estimated using a Heckman procedure to control for potential selection bias.* Indicate significance at the 10% level.

** Indicate significance at the 5% level.*** Indicate significance at the 1% level.


The results of the estimation of the deposit rate equation in thisbaseline specification also confirm the positive link between bankrisk and deposit rates.

So, for example, banks with a high ROA volatility are expectedto pay lower deposit rates. Similarly, banks with high relative vol-umes of nonperforming loans with accompanying highly volatilestock prices offer higher deposit rates.

We also find support for a positive relation between the MMDArate and the rate on federal funds purchased. This result is consis-tent with the substitutability of retail and wholesale funding, and itconfirms the arguments of Kiser (2004) and Park and Pennacchi(2008).

And finally, the results of the estimation of the wholesale rateequation support the hypothesis that banks which pay high retaildeposit rates also pay on average higher wholesale rates relativeto their peers. That is, within a comprehensive empirical frame-work, we are able to confirm a positive relationship between thecost of retail and wholesale funding. Also, bank risk enters the

wholesale rate regression with a positive statistically significantcoefficient for all three alternative risk measures.

Next, we re-estimate the model using a sample of observationsaveraged at the bank level. That means that we have only oneobservation for each bank and quarter and we cannot account forthe market-level variation. But it allows us to control for the pos-sibility that banks reshuffle deposits across local markets. The re-sults of these estimations are presented in Table 5. Qualitatively,these results are very similar to the bank-market-level results pre-sented in Table 4. The key result concerning the positive relation-ship between retail deposit rates and bank risk is also confirmed inthis specification. However, the reduced number of observations isreflected in the lower power of the estimations.

And finally, we estimate the model on the sample of banksoperating in only one local market (see Table 6). In this case, weare again able to qualitatively replicate the main results from thebank-market-level estimation: we find a significant positiverelation between MMDA rates and risk when measured by ROA

Table 8Dynamic GMM panel estimation of the risk equation.

All banks, bank-market level observations: GMM estimates of the risk equation



Dependant variable: bank riskLagged risk variable 0.6202*** 0.0167 0.1591*** 0.0124 �0.2111*** 0.0126MMDA rate �0.0001*** 0.0000 0.0015*** 0.0003 0.0026*** 0.0002Rate on federal funds purchased 0.0000 0.0000 0.0005*** 0.0000 0.0006*** 0.0000Bank size �0.0007 0.0011 0.0378*** 0.0095 0.0543*** 0.0051Bank size^2 0.0000 0.0000 �0.0012*** 0.0003 �0.0016*** 0.0001Capitalization �0.0006 0.0012 �0.0925*** 0.0102 �0.0194*** 0.0046ROA �0.0108*** 0.0015 0.3031*** 0.0130 �0.1857*** 0.0081Loans �0.0002 0.0001 0.0125*** 0.0013 �0.0031*** 0.0005Loan growth 0.0003*** 0.0001 �0.0011* 0.0006 �0.0003 0.0003Unemployment 0.0000** 0.0000 �0.0009*** 0.0001 0.0002*** 0.0001Income growth �0.0011* 0.0006 �0.0013 0.0055 �0.0421*** 0.0030Constant 0.0110 0.0088 �0.2944*** 0.0794 �0.4413*** 0.0451Observations 5846 5866 5718

All banks, bank-level observations: GMM estimates of the risk equationLagged risk variable 0.4597*** 0.0178 0.2804*** 0.0227 �0.1632*** 0.0288MMDA rate �0.0001 0.0001 �0.0014** 0.0007 0.0015*** 0.0003Rate on federal funds purchased 0.0000 0.0000 0.0002*** 0.0001 0.0003*** 0.0001Bank size �0.0013 0.0018 �0.0605** 0.0270 0.0267** 0.0109Bank size^2 0.0000 0.0001 0.0018** 0.0009 �0.0008*** 0.0003Capitalization �0.0005 0.0016 �0.2115*** 0.0216 �0.0191*** 0.0099ROA �0.0130*** 0.0022 0.0897*** 0.0282 �0.0936*** 0.0148Loans 0.0002 0.0002 0.0055* 0.0031 �0.0033 0.0012Loan growth 0.0000 0.0001 �0.0008 0.0012 �0.0007 0.0007Unemployment 0.0000 0.0000 �0.0006*** 0.0002 0.0000 0.0001Income growth 0.0017* 0.0010 �0.0141 0.0138 �0.0167*** 0.0068Constant 0.0154 0.0139 0.5188 0.2124 �0.1925 0.0900Observations 2757 1719 1217

Single-market banks only: GMM estimates of the risk equationLagged risk variable 0.3070*** 0.3070 0.6322*** 0.0577 �0.0138 0.1117MMDA rate �0.0002*** 0.0001 �0.0015* 0.0008 0.0031** 0.0017Rate on federal funds purchased 0.0000 0.0000 0.0000 0.0000 0.0007*** 0.0004Bank size �0.0014 0.0028 �0.1209*** 0.0293 �0.0071 0.0797Bank size^2 0.0001 0.0001 0.0044*** 0.0010 0.0002 0.0024Capitalization 0.0080*** 0.0025 0.0650** 0.0278 �0.0134 0.0413ROA �0.0061* 0.0034 0.3280*** 0.0367 �0.0708* 0.0411Loans �0.0005* 0.0003 �0.0107*** 0.0034 0.0042 0.0045Loan growth 0.0003 0.0002 0.0023 0.0018 �0.0013 0.0014Unemployment 0.0000 0.0000 �0.0009** 0.0004 0.0015** 0.0008Income growth �0.0028 0.0015 0.0162 0.0159 �0.0308 0.0300Constant 0.0134 0.0197 0.8242*** 0.2072 0.0733 0.6584Observations 281 284 86

Note: GMM estimation of linear dynamic panel model following Arellano and Bond (1991). Endogeneity is avoided by using the first differenced regressors as instruments.* Indicate significance at the 10% level.


46 For the case of parsimony of exposition we only report the results concerning therisk equation which is of key interest in this analysis. The results of the dynamic GMMestimation of the retail deposit and the wholesale rate equation, which are availablefrom the authors upon request, are also qualitatively similar to those of zerorestriction approach.


volatility. However, the small sample size again results in relativelylow statistical power for the estimations. The economic signifi-cance of the retail rate’s effect on bank risk in this case is againcomparable to the one found in the full sample of bank-market-le-vel observations found in Table 4.

In order to illustrate the empirical relevance of the endogeneityissues discussed in the previous section we also present in Table 7the output of a model which estimates Eqs. (1)–(3) independently,without controlling for the potential endogeneity. Since the endo-geneity of deposit rates in the risk equation and risk in the depositequation threatens the consistency of the estimates, these resultsare presented as a benchmark rather than as something with aneconomic interpretation. They illustrate how when endogeneityis ignored the estimated effects of retail deposit rates on risk aresubstantially smaller relative to those produced with the zero-restriction identification strategy. The difference in the estimationresults between the benchmark case and the case when the endo-geneity is accounted for strengthens our belief that the additionalinformation gained by explicitly formulating the reverse causalities

is worth carrying the burden of challenging identification. Never-theless, we also understand that although we have done our bestto choose suitable instruments and standard econometric testsfor strength and exogeneity of the instruments are passed, the nat-ure of instrument – and in particular the validity of the exclusionrestrictions – is always debatable.

To strengthen the robustness of the results provided here weadd an alternative estimation of the risk equation which is basedon a simple dynamic identification scheme.46 To this end we re-write the risk Eq. (1) in a dynamic form by adding the lagged riskof bank assets as an additional regressor and then estimate the mod-el using the dynamic panel GMM approach proposed by Arellano andBond (1991).

Table 9Two-stage estimation of the effect of deposit rates and bank risk on the volume of wholesale funding; sample: all banks; multimarket banks are treated as individual market levelobservations; wholesale rates are measured by rate on federal funds purchased.

Dependant variable: share of purchased funds



MMDA rate 0.0109*** 0.0023 0.0085*** 0.0019 0.0277*** 0.0039Bank risk 3.3078* 1.9003 �0.5526*** 0.3393 �0.3565 0.6220Bank size 0.0534*** 0.0103 0.0596*** 0.0102 �0.0352** 0.0168Bank size^2 �0.0017*** 0.0003 �0.0018*** 0.0003 0.0009* 0.0005Capitalization �0.3154*** 0.0394 �0.2517*** 0.0271 �0.2480*** 0.0325Loans 0.0170** 0.0076 0.0147** 0.0070 0.0417*** 0.0065Effective fed funds rate �0.0020*** 0.0002 �0.0009 0.0007 �0.0035*** 0.0003Large BHC dummy �0.0011 0.0029 �0.0017 0.0029 0.0065* 0.0037Listed 0.0221*** 0.0035 0.0241*** 0.0032Securities 0.0791*** 0.0157 0.0564*** 0.0090 0.0773*** 0.0104Constant �0.3964*** 0.0924 �0.4201*** 0.0883 0.3875*** 0.1481Observations 7128 7128 7069R-squared 0.09 0.06 0.05

Note: Two-stage least squares IV estimations.* Indicate significance at the 10% level.


47 The sample includes both small regional banks funded almost exclusively byretail deposits and the largest money-center banks with a substantial wholesaleexposure. The 25%, 50% and 75% quantiles of the ratio of overnight wholesaleliabilities to total assets are 0.028726, 0.060116 and 0.103086, respectively. For thesake of comparability the same thresholds (those generated by the distribution of the


To control for the general market interest rates level which inthe system of equation case was used as instruments for retailand wholesale costs of funding we also include the average effec-tive fed funds rate here as an additional regressor in the dynamicmodel. The results of the dynamic GMM estimation of the riskequation for the bank-market level, bank level and the single-mar-ket bank specifications are reported in Table 8.

The advantage of the dynamic GMM approach is that it avoidsthe search of exogenous instrumental variables outside the systemof regressors and solely explores the information in the time-seriesof the variables.

A major shortcoming of this approach– and the main reason wedecided for a classical zero restriction strategy in the baseline spec-ification – is the fact that the structure of the modeled relation isnot explicitly analyzed.

The dynamic GMM estimation generates results qualitativelyvery similar to those presented in the estimation of the systemof equations. In particular, a positive change in the MMDA rate isassociated with a significantly higher risk as measured by the Z-score in all three subsamples. The results concerning the effect ofthe rate on wholesale funding are characterized by weaker statis-tical significance but still point to a positive relation between thecosts of funding and bank risk.

In sum, we find a statistically and economically significant po-sitive relationship between deposit rates and bank risk. Our empir-ical results, therefore, support the implications of a series oftheoretical papers (e.g., Allen and Gale, 2000; Hellmann et al.,2000) that deposit market competition drives bank risk up byincreasing the costs of bank retail deposits. Moreover, we find thatwholesale funding rates also positively affect bank risk. This resultextends the scope of the competition and risk argument to a moregeneral interdependence between the banks’ costs of funding andrisk.

liability structure of all sample banks) are used for each three risk measures eventhough the stock price volatility measure is only used for a subsample of listed bankswhich has a different liabilitiy structure distribution.

48 A straight-forward way to control for the volume of wholesale funding will be toinclude the share of wholesale to total liabilities as a control variable in the system ofequations. However, given the endogeneity of wholesale funding volume with respectto both bank risk and deposit market competition the inclusion of wholesale volumewould have imposed additional identification challenges. Moreover, the issue of non-linearities would have remained unresolved.

49 Moreover, if banks shift to wholesale funding when deposit market competitionaccelerates the costs of retail funding above a certain threshold, the heterogeneityacross banks may reflect a nonlinearity of the effect of retail deposit rates on bankrisk.

5. Deposit market competition and bank risk: the role ofliability structure

The results reported above point to a strong statistically signif-icant positive effect of the costs of retail and wholesale funds onthe riskiness of bank assets. These results are generated by a sam-ple of almost 600 banks, which exhibit a large degree of heteroge-neity, especially with regard to the structure of their liabilities. Forexample, in more than 10% of the bank-quarter observations, the

share of overnight wholesale liabilities to total assets is below1%, while for 10% of the bank-quarter observations this share is lar-ger than 17%.47 Obviously, the relationship between the costs of re-tail and wholesale liabilities and bank risk can depend on thestructure of liabilities. So, for example, the risk of banks predomi-nantly funded by wholesale liabilities might not react to observeddeposit market rates but rather to wholesale market conditions.48

However, if the costs of retail funding affect the structure of bank lia-bilities, deposit market competition will have an indirect effect onbank risk even though the effect of observed retail deposit rates onbank risk is insignificant.49

In this section we examine this dimension of bank heterogene-ity in two steps. First, we show that liability structure depends onthe conditions a bank faces in the deposit market. Second, we re-estimate the risk Eq. (1) for subsamples of banks with differentshares of overnight wholesale liabilities.

We examine the effect of deposit market competition on the lia-bility structure by estimating the following model:

liability structurei;t ¼ f ðri;t; di;j;t ; controlsÞ; ð4Þ

where liability_structurei,t, is measured by the ratio of wholesale lia-bilities (federal funds purchased and securities sold under theagreement to repurchase) to total assets and the risk, ri,t, and the de-posit market structure, di,j,t, which are defined as above.

Since bank risk and retail deposit rates are also potentiallyendogenous with respect to the liability structure, we estimatethe equation using the same instruments for bank deposit rates

Table 10Two Stage Estimation of the effect of Deposit Rates and Bank Risk on the Volume of Wholesale Funding: subsamples of banks with different liability structures.

Quartiles of liability structure distribution 0–25 25–50 50–75 75–100

Panel A: Dependent variable ROA volatilityMMDA rate 0.0006* 0.0004 0.0011*** 0.0002 0.0024*** 0.0005 0.0001 0.0003Rate on federal funds purchased �0.0002 0.0002 �0.0006*** 0.0001 �0.0012*** 0.0003 �0.0002 0.0001Bank size 0.0014** 0.0006 0.0026*** 0.0007 0.0018** 0.0008 0.0034*** 0.0011Bank size^2 0.0000** 0.0000 �0.0001*** 0.0000 0.0000* 0.0000 �0.0001*** 0.0000Capitalization 0.0296*** 0.0032 0.0092*** 0.0029 0.0020 0.0046 0.0230*** 0.0051ROA 0.1159*** 0.0260 0.0778*** 0.0127 0.1348*** 0.0229 0.0469*** 0.0138Loans 0.0026*** 0.0004 0.0003 0.0005 0.0014* 0.0008 �0.0003 0.0004Loan growth 0.0010*** 0.0002 0.0008*** 0.0003 0.0006 0.0008 �0.0011*** 0.0003Unemployment 0.0003*** 0.0001 0.0000 0.0000 �0.0003*** 0.0001 0.0001 0.0001Income growth 0.0089*** 0.0023 0.0095*** 0.0017 0.0240*** 0.0039 0.0124*** 0.0016Constant �0.0109** 0.0053 �0.0184*** 0.0062 �0.0150* 0.0077 �0.0260*** 0.0093Observations 1798 1903 1754 1673R-squared 0.44 0.18 0.11 0.2

Panel B: Dependent variable NPLMMDA rate �0.0017 0.0023 0.0011 0.0009 0.0007 0.0012 �0.0040*** 0.0015Rate on federal funds purchased 0.0019 0.0012 0.0031*** 0.0005 0.0037*** 0.0006 0.0032*** 0.0008Bank size 0.0041 0.0031 0.0018 0.0021 0.0016 0.0021 0.0007 0.0032Bank size^2 �0.0001 0.0001 0.0000 0.0001 0.0000 0.0001 0.0000 0.0001Capitalization 0.0934*** 0.0154 0.0188* 0.0102 0.0324*** 0.0110 0.0741*** 0.0214ROA 0.1272 0.1156 0.1545*** 0.0431 �0.0402 0.0584 0.1573** 0.0692Loans 0.0058 0.0022 0.0178*** 0.0020 0.0187*** 0.0019 0.0007 0.0018Loan growth 0.0013 0.0014 �0.0035*** 0.0013 0.0003 0.0016 0.0049*** 0.0012Unemployment 0.0000 0.0005 0.0007*** 0.0002 0.0005** 0.0002 �0.0002 0.0003Income growth 0.0262** 0.0131 �0.0579*** 0.0069 �0.0398*** 0.0097 �0.0307*** 0.0074Constant �0.0441 0.0255 �0.0300* 0.0177 �0.0283 0.0194 �0.0038 0.0275Observations 1819 1903 1754 1673R-squared 0.16 0.29 0.18 0.11

Panel C: Dependent variable stock price volatilityMMDA rate 0.0011 0.0010 0.0040*** 0.0003 0.0009*** 0.0004 0.0003 0.0006Rate on federal funds purchased 0.0006 0.0005 �0.0005*** 0.0002 0.0010*** 0.0002 0.0013*** 0.0003Bank size 0.0018 0.0016 �0.0033*** 0.0010 �0.0032*** 0.0011 0.0056*** 0.0011Bank size^2 �0.0001 0.0000 0.0001*** 0.0000 0.0001*** 0.0000 �0.0002*** 0.0000Capitalization 0.0232*** 0.0073 0.0045 0.0060 0.0182*** 0.0054 0.0118** 0.0054ROA �0.0496 0.0473 �0.0917*** 0.0167 �0.1180*** 0.0177 �0.1571*** 0.0272Loans 0.0006 0.0007 0.0003 0.0008 0.0035*** 0.0008 0.0025*** 0.0005Loan growth �0.0013** 0.0007 0.0038*** 0.0006 0.0010 0.0016 �0.0010* 0.0006Unemployment 0.0004*** 0.0001 0.0004*** 0.0001 �0.0001 0.0001 0.0006*** 0.0002Income growth �0.0326*** 0.0049 �0.0198*** 0.0033 �0.0274*** 0.0035 �0.0222*** 0.0030Constant �0.0042 0.0137 0.0363*** 0.0093 0.0356�� 0.0096 �0.0386*** 0.0092Observations 1301 1956 1722 2090R-squared 0.35 0.30 0.08 0.41

Note: Two-stage least squares IV estimations. Endogenous explanatory variables are: MMDA rate and the rate on fed funds purchased and securities sold under agreement torepurchase.




and bank risk that we defined in Section 3. The results of the esti-mations are presented in Table 9, which, as Tables 4–6, above, con-tains a column for each of the three alternative risk measures.

These results indicate that banks facing higher retail depositrates are more likely to use larger volumes of wholesale funding.They are, therefore, consistent with our argument that depositmarket competition and the structure of bank liabilities are related.Further, the relationship between retail deposit market competi-tion and wholesale volume connects our discussion on the risk ef-fects of deposit market competition to the risk effects of thestructure of bank liabilities, in the way Huang and Ratnovski(2009) suggested it should be done.

Having established the relevance of the costs of retail funding tothe structure of bank liabilities in step one, we next focus on exam-ining how the heterogeneity of the liability structure affects therelationship between the costs of funding and bank risk. In the fol-lowing step two we explore the robustness of the results for groupsof banks with different liability structures. We start by drawing thedistribution of banks’ shares of wholesale liabilities and dividingthe full sample into four subsamples using the quartiles of the

distribution as cut-off points. We then rerun the risk Eq. (1) foreach of the subsamples. To control for potential sample selectionbias in the subsamples, we estimate the model using the censoredregression specification by Heckman (1976) that we explain inSection 3.4.

The results of the estimation of the risk equation for the subs-amples are presented in Table 10 which contains a panel for eachof the three alternative bank risk measures (ROA volatility, NPLand stock price volatility), and graphically illustrated in Chart. 1.The results of the estimations of the bank level regressions andthe single-market regressions which for the sake of parsimoniousexposition are not reported here are qualitatively the same asthose presented in Table 10.

These results indicate that, depending on the structure of bankliabilities, the relationship between bank risk and the cost of retailand wholesale funding is indeed different. The positive effect of re-tail deposit rates on bank risk is strongest in the subsamples with alow share of wholesale liabilities. This effect is statistically insignif-icant in the quartile of observations with the highest share ofwholesale liabilities. These results are still consistent with the

Risk measure: ROA volatility

Risk measure: NPL

Risk measure: Stock price volatility

Risk measure: NPL

Full sample with Subsamples with

confidence interval confidence interval

Risk measure: Stock price volatility

Risk measure: ROA volatility

(A) MMDA rate’s coefficient in quartile risk regression (B) Federal funds rate’s coefficient in quartile risk regression

Chart 1. Estimated coefficients in subsamples with different liability structure.


moral hazard argument: the observed costs of retail funding mat-ters most for the risk of those banks that rely heavily on this formof funding.

However, the results also underscore a nonlinearity in the rela-tionship between bank risk and deposit rates: once banks havechosen to focus on wholesale funding (a decision codeterminedby the deposit market conditions they face), their risk is no longerdriven by retail deposit market conditions.

To further explore the effect of liability structure heterogeneityon the relationship between bank funding costs and risk, we havealternatively estimated the model using a quantile regressionframework.50 The results of this estimation are not reported herefor reasons of space. This exercise requires introducing the liabilitystructure as an additional endogenous regressor in the estimationof Eq. (1). As already mentioned, identification is challenging in thiscase. One avenue we explore is to reuse the set of instruments thatwe used for the MMDA rate and wholesale rate identification. Theweakness of the identification in this case is then reflected in the

50 These results are available from the authors upon request.

very weak statistical significance of the estimation results in thelower (up to the 50th) quantiles. Similar to the results reported inTable 10 for the higher liability structure quantiles, the risk-increasingeffect of MMDA rates is statistically insignificant but that of the costsof wholesale liabilities is high and strongly statistically significant.

These results do not imply that deposit market competition isirrelevant for the risk of predominantly wholesale-funded banksbut rather that the effect of retail deposit competition on bank riskis realized through the changed structure of bank liabilities.

6. Longer-term bank wholesale liabilities

A potential limitation of our approach is that we proxy the costsof wholesale funding by the rate on overnight wholesale liabilities.To check the robustness of this approach and also to compare therisk effects of the costs of short- to longer-term wholesale liabili-ties, we re-estimate the model using the rate banks pay on subor-dinated debt as an alternative measure of the cost of wholesaleliabilities. Because of its longer maturity, subordinated debt canbe considered a better substitute for retail deposits than federal

Table 11Estimation of 3 equation system: risk, deposit rates, and wholesale rates; sample: all banks; multimarket banks are treated as individual market level observations; Wholesalerate is measured by the subordinated debt rate.

All banks; the rate on subordinated debt is used as a wholesale rate measure



Dependant variable: bank riskMMDA rate 0.0012*** 0.0001 0.0037*** 0.0004 0.0026*** 0.0001Rate on subordinated debt �0.0012*** 0.0001 0.0015*** 0.0003 0.0000 0.0001Bank size 0.0011 0.0007 �0.0032 0.0021 �0.0025*** 0.0006Bank size^2 0.0000* 0.0000 0.0001* 0.0001 0.0001*** 0.0000Capitalization 0.0130*** 0.0022 0.0195*** 0.0059 0.0123*** 0.0029ROA 0.2067*** 0.0157 0.2227*** 0.0446 �0.0640*** 0.0096Loans 0.0006* 0.0004 0.0122⁄⁄⁄⁄ 0.0010 0.0015*** 0.0003Loan growth 0.0023*** 0.0003 0.0002 0.0009 �0.0002 0.0004Unemployment �0.0003*** 0.0001 0.0001 0.0002 0.0003*** 0.0001Income growth 0.0100*** 0.0015 �0.0101* 0.0040 �0.0292*** 0.0018Constant �0.0025 0.0063 0.0140 0.0185 0.0313*** 0.0057Observations 5395 5402 6117R-squared 0.31 0.14 0.23Dependant variable: MMDA rateBank risk 118.0131*** 15.7181 168.1042*** 15.2021 144.4629*** 8.0562Rate on subordinated debt 0.0159*** 0.0043 �0.4531*** 0.0460 0.0897*** 0.0084Bank size 1.1920*** 0.2270 1.3317*** 0.3515 0.9031*** 0.2601Bank size^2 �0.0378*** 0.0064 �0.0418*** 0.0099 �0.0265*** 0.0073Capitalization �1.1926** 0.4851 �6.1682*** 1.1758 �1.6675*** 0.6372Loans �2.4128*** 0.0496 �3.4570*** 0.1433 �1.3178*** 0.0616Market size 0.0000*** 0.0000 0.0000*** 0.0000 0.0000*** 0.0000HHI �0.8428*** 0.1814 �1.4226*** 0.3723 �0.2485 0.2136Branch_deposit 5.1664*** 1.0954 6.8938*** 2.0378 1.8021 1.2712Senior population �1.6599*** 0.5435 0.9955 0.8176 �1.4906*** 0.5031Constant �7.1996*** 2.0109 �7.0089** 3.0943 �7.3961*** 2.2971Observations 5395 5402 6117R-squared 0.45 0.12 0.43Dependant variable: rate on subordinated debtMMDA rate 0.8585*** 0.2079 �0.0696 0.1895 3.6846*** 0.2458Bank risk 721.8055*** 23.8922 332.0297*** 7.3721 513.4183*** 23.6888Bank size 1.7767*** 0.4036 �0.0061 0.3899 3.8527*** 0.4229Bank size^2 �0.0472*** 0.0110 �0.0051 0.0106 �0.1067*** 0.0115Capitalization �33.8447*** 1.2238 �24.6285*** 0.9936 �5.5607*** 1.0980Loans �0.9478*** 0.1651 �1.1758*** 0.2079 3.2158*** 0.2315Effective fed funds rate �0.0999* 0.0618 0.0606 0.0557 �0.3641*** 0.0661Large BHC dummy �0.7506*** 0.1326 �0.1346 0.1264 �0.8926*** 0.1361Listed �0.6416*** 0.0618 �0.1299** 0.0550Securities 0.2852** 0.1035 2.5133*** 0.2833 2.7513*** 0.3093Constant �13.5036*** 3.6155 4.4255 3.5314 �29.1162*** 3.8113Observations 5395 5402 6117Censored observations 516 516 516R-squared – – –

Note: Two-stage least squares IV estimations. Endogenous variables are: bank risk (measured by z-score, NPL), MMDA rate and the subordinated debt rate. The sub debt rateequation is estimated using a Heckman procedure to control for potential selection bias.




funds. Nevertheless, subordinated debt has other drawbacks forour research framework, especially if we consider that subordi-nated debt issues might not be related to a shortage of retail fundsbut rather to the eligibility of subordinated debt as tier-2 capital.

We impute the subordinated debt rate in an analogous calcula-tion to our fed funds rate. We used the ratio of ‘‘interest on subor-dinated notes and debentures’’ (line riad4200) and the amount ofoutstanding ‘‘subordinated notes and debentures’’ (line rcfd3200)of the Call Report. Again, when estimating the wholesale rate equa-tion, we account for the potential selection issue by estimating aHeckman model with instrumental variables.51 The results of theestimation of this model specification are presented in Table 11.

51 The results presented in Table 11 are based on the following censoring rule: thesubordinated debt is accounted for if the share of subordinated debt in total assets isat least 1%. Alternative trigger points (0.5% and 2%) yield qualitatively the sameresults.

These results show that the positive link between retail rates,wholesale rates, and bank risk is robust to the choice of the whole-sale rate measure. The statistical and economic significance of thewholesale rate and risk relationship is even stronger in the case ofsubordinated debt rate than in the federal funds purchased rate,52

showing that the maturity of wholesale exposures is an importantdeterminant of the relationship between bank risk and the costs ofwholesale funding.

7. Conclusion

Despite the intense political and academic interest into the is-sue of the potential risk effects of bank competition, the literaturehas not yet reached a consensus on whether bank competition

52 This positive link has already been shown by DeYoung et al. (2001) and Morganand Stiroh (2001).


indeed has a positive effect on bank risk. In this paper we revisitthe debate by estimating a system of equations which describethe relationship between deposit market competition, the costsof wholesale funding, and bank risk. Although wholesale fundingaffects both the risk of a bank and its behavior in the deposit mar-ket, the wholesale market for funds has so far been ignored in thecompetition and risk literature. The main contribution of this studyis, therefore, the integration of the market for wholesale bankfunding into the analysis of the competition and risk nexus.

The results of our empirical estimation show a robust positivelink between the intensity of deposit market competition facedby a bank and the risk of the bank. We interpret these results asevidence for the risk-increasing effects of deposit market competi-tion and suggest that banks with less deposit market power aremore likely to choose riskier strategies. However, our results reflectonly potential costs of bank competition. The examination of thetrade-off between the efficiency gains of a competitive versus oli-gopolistic banking sector and the higher risk of banks operating ina competitive environment go beyond the scope of this study. Thistrade-off, which is essential for the formulation of regulatory poli-cies, is still underexplored in the empirical banking literature andshould be subject to further research.

Acknowledgements

We thank Viral Acharya, Allen Berger, Jörg Breitung, Hans Deg-ryse, Hendrik Hakenes, Lars Norden, Tara Rice, Klaus Schaeck,James Thompson, Jürgen von Hagen and participants of the 2010North American Winter Meeting of the Econometric Society, 2ndFinancial Stability Conference, 2009 European Banking Sympo-sium, the 2009 Financial Intermediation Research Society Meeting,the 2008 Dutch Central Bank Annual Research Conference and theUniversity of Bonn Macro-Workshop for useful comments on ear-lier versions of the paper. Dinger gratefully acknowledges financialsupport by the Deutsche Forschungsgemeinschaft (Research GrantDI 1426/2-1). This research reflects the views of the authors andnot necessarily the views of the Deutsche Bundesbank, the FederalReserve Bank of Cleveland, or the Board of Governors of the FederalReserve System.

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Deposit market competition, wholesale funding, and bank risk