Deposit Market Competition and Bank Risk

Transcription

1 Deposit Market Competition and Bank Risk Ben R. Craig* and Valeriya Dinger This version: September 2008 Abstract: Although a wide body of theoretical research finds that intense deposit market competition increases the incentives of banks to undertake excess risk, the empirical literature on the topic has not reached a consensus. In this paper we revisit the topic by estimating a system of equations describing the relation between bank risk and the deposit market competitive position. Our model incorporates both the simultaneity of a bank s risk and a bank s deposit market competitive position and the substitutability of wholesale and retail sources of funds. The analysis is based on a large dataset which matches information about the deposit market participation (prices and market shares) of 589 banks in 164 US local deposit markets with balance sheet data of the banks and the characteristics of the local markets. Our results support the notion of a risk-enhancing effect of deposit market competition. Key words: bank competition, bank risk, deposit rates, market discipline JEL: G21 * Federal Reserve Bank of Cleveland and Deutsche Bundesbank Corresponding author. University of Bonn, Lennestr. 37, Bonn, Germany, Tel: , Fax: , valeriya.dinger@uni-bonn.de

2 1. Introduction Banks play a vital function in financial systems by assuring maturity transformation, providing liquidity, and monitoring borrowers, among many other things. However, theoretical research predicts and history has shown that banks are fragile institutions. Their fragility is caused both by the fact that bank runs might be an equilibrium phenomenon (liability-side-driven fragility) and because banks might have incentives to invest in projects characterized by excess risk (asset-side-driven fragility). Deposit insurance schemes are a widely applied cure for bank runs; however, they reduce depositors sensitivity to the risk of their bank and diminish depositors incentives to punish excess risk behaviour by the bank. As formally modelled by Merton (1977), deposit insurance can be seen from a bank s point of view as a put option on the bank s assets. By increasing its risk, a bank is able to maximize the value of this option. However, Keeley (1990) presents empirical evidence that shows that the risk-enhancing role of deposit insurance is realized only in an environment in which banks have little market power, where, as a result, the bank charter has some small value. Keeley posits that deposit insurance alone cannot be the source of excess risk behaviour and argues that as long as banks have high expected returns, they will not endanger the value of their charter by maximizing the value of the put. He concludes that banks increased appetite for risk during the 1980s was caused by the depreciated value of the charter resulting from increased banking competition. Following Keeley s work, research interest in the nexus of competition and risk has intensified in the past few decades. This research has been further propelled by profound changes in the structure of banking markets, which followed banking market liberalization in the United States and Europe and repeated instances of financial system distress. Allen and Gale (2000) present a theoretical model consistent with Keeley s results showing that the optimal risk of failure increases with the number of competitors in the deposit market. Boyd 2

3 and de Nicolo (2005), on the other hand, argue that if loan market competition is also included in the analysis, results may be reversed. In their model, banks face an optimal contracting problem in which the actions of borrowers are unobservable. The number of deposit market competitors is also positively correlated with bank risk, although the number of loan market competitors can negatively affect the risk of failure of bank assets. Despite the theoretical consensus on the risk-enhancing impact of deposit market competition, empirical research on the topic has so far produced limited and mixed results. Demsetz et al. (1996), Brewer and Seidenberg (1996), Saunders and Wilson (1996) and Salas and Saurina (2003) document a positive link between the intensity of bank competition and bank risk, whereas Boyd et al. (2006) and de Nicolo and Loukianova (2007) show the existence of a negative relationship. Given the lack of consensus in the empirical literature, the purpose of this paper is to present a novel, comprehensive empirical analysis of the relation between deposit market competition and bank risk. Convincing empirical evidence on the issue is needed to determine policy recommendations, since wrong policy can lead either to inefficient banking industries and thus endanger the efficiency of financial intermediation and capital allocation, or to a very fragile banking system, which could potentially jeopardize payment systems and liquidity provision 1. In this study we focus on deposit market competition because the theoretical research yields clear results for this market, whereas the effect of loan market competition is ambiguous. Moreover, deposit markets are more local than loan markets, resulting in clearer measures of local deposit market competition. 1 Allen and Gale (2004) show that financial system instability might be efficient and is therefore not necessarily undesirable. Policymakers, however, are often reluctant to face the short-term political cost of dealing with financial instability (as the experience from most recent financial crises clearly illustrates). 3

4 In our research framework we depart from the existing literature in several dimensions. First, when measuring deposit market competition, we concentrate on the intensity of the competition faced by each individual bank, whereas most of the existing empirical studies have employed market-level competition proxies such as concentration ratios, Herfindahl indices, or Panzar-Rose H-statistics. By using a bank-level measure of competitiveness, we account for the possibility that different banks operating in the same local market might face different intensities of competition. Average measures of competition in a given market will give only incomplete information about the competitive position of each individual bank. Our choice for the bank-level measure of the intensity of deposit market competition is the deposit rate offered by a bank in each of the local deposit markets 2,3. It is based on the intuition that controlling for market share alone as a proxy for deposit market power will be insufficient because even small banks with a negligible market share can exert some market power if depositors switching costs are high (as argued by Kiser, 2003, for example). An additional advantage of our competition measure is that it focuses on deposit market competition alone, in contrast to concentration ratios, Herfindahl indices, or Panzar-Rose H-statistics, which can not disentangle deposit from loan market competition. Distinct measures of loan and deposit market competition are, however, crucial for the analysis, because, as Boyd and de Nicolo (2005) suggested, deposit and loan market competition might generate opposing risk effects. More importantly, changes in bank market structure do not necessarily affect deposit and loan market competition in the same direction. As Park and Pennacchi (2008) show, the creation of multimarket banks, for example, may dampen deposit market competition while intensifying the competition in the loan market. 2 To our knowledge, Hutchison and Pennacchi (1996) are the first to use deposit rates offered by a bank relative to a wholesale rate (the T-bill rate) as a proxy for the monopoly rent extracted by the bank in the deposit market. Jimenez et al. (2007) also use the relation between retail (deposit and loan) rates and a wholesale (the money market) rate in a study of the bank risk and competition nexus. They, however, have only aggregate retail rate data for each of the sample banks and no information about the rates in the different local markets. 3 In the robustness checks section we present results based on an alternative bank-level measure of the intensity of deposit market competition. 4

5 From an industrial organization perspective, prices and price mark-ups are straightforward competition measures. However, when deposit rates or deposit mark-downs relative to wholesale funding costs are used to determine whether competition increases risk, the problem of simultaneity arises: riskier banks might be forced to offer higher deposit rates. 4 Note that this is true even when deposits are insured, because depositors may still require a risk premium to compensate them for the potential switching costs should the bank fail. We deal with the simultaneity by explicitly identifying a system of simultaneous equations. To our knowledge, existing studies have ignored this potential simultaneity 5. Another innovation of our study is the explicit inclusion of the market for wholesale funds in the analysis of competition and risk, which we do for two reasons: first, the availability and price of wholesale funding, such as federal funds, subordinated debt, or bank corporate bonds 6, affects the deposit market behaviour of individual banks. Although the link between deposit and wholesale funding has been studied in recent literature on the industrial organization of banking (Kiser, 2003; Park and Pennacchi, 2008), its implication for the competition and risk relationship has so far been ignored. Second, wholesale funds are particularly relevant for the determination of a bank s risk preference, because they are not insured. A number of empirical studies (Furfine, 2001; King, 2007; Ashcraft, 2008; Dinger and von Hagen, 2008) have shown that the availability and costs of wholesale funding are strongly related to bank risk. By including both the retail deposit rate and the cost of wholesale funding in our model, we study the effect of the costs of insured and uninsured bank liabilities on bank risk behaviour within a uniform framework. 4 More generally, most measures of the competitive position on the individual bank level can be argued to be endogenous with respect to bank risk because the risk of the bank offering a deposit product affects the whole range of measures of a bank s deposit market conduct (e.g., prices and market shares). 5 Jimenez et al. (2007) is the only other study we are aware of that use prices as a measure of the intensity of competition. They explore the relation between competition and risk in the Spanish banking sector. The authors of this study, however, fail to recognize the simultaneity of prices and proceed with a reduced-form model. 6 Park and Pennacchi (2008) define wholesale liabilities as large liabilities that have account balances above $100,000 and that are not fully insured by the FDIC. 5

6 The results of our empirical analysis point to a robust, positive, and statistically and economically significant relation between the deposit rates offered by a bank and its asset portfolio and default risk. By showing that more intense deposit market competition increases the bank risk, our results support the implications of Allen and Gale s (2000) and Boyd and de Nicolo (2005) theoretical models. Moreover, we are able to confirm the results of a range of earlier theoretical studies on market discipline by showing a positive relation between the cost of wholesale funding and bank risk. The rest of the paper is organized as follows. Section 2 briefly reviews the literature. Section 3 presents a short overview of the underlying theoretical and empirical discussions of the relation between retail and wholesale deposits and bank risk. Section 4 presents the data. Section 5 illustrates the econometrical model and our identification strategy. Section 6 reveals the results of the empirical estimation, and Section 7 concludes. 2. Literature The relation between bank competition and risk has attracted lively research interest during the past few decades. Earlier theoretical contributions (e.g., Dermine, 1986) show that market power increases banks incentives to invest in safer projects. In a seminal paper, Keeley (1990) shows that deregulation of the U.S. banking market led to more intense competition between banks, which then caused banks to pursue riskier strategies. Keeley argues that if competition is limited, the value of a bank charter is high and banks will restrain from undertaking excess risk in order to protect their charter. When competition is intensified, the value of a bank charter drops (because profits are lower), and banks may choose to finance riskier projects. Based on another line of arguments, Broecker (1990) also shows that the average quality of banks asset portfolios is negatively correlated with the number of loan market competitors, because a rise in the number of banks increases the probability of lemon borrowers to be granted a loan. 6

7 In a more recent work, Allen and Gale (2000) show in a formal model that if banks choose a parameter that determines the default risk of their assets, then the optimal risk of failure is increasing with the number of deposit market competitors. Boyd and de Nicolo (2005), on the other hand, argue that Allen and Gale s (2000) approach assumes that asset portfolios and return distributions are given. If this assumption is dropped, banks face an optimal contracting problem in which the actions of borrowers are unobservable. In this case, the number of competitors may negatively affect the risk of failure of bank assets. The intuition behind this result is that if loan market competition is less intense, banks will set high loan rates, which will drive borrowers to choose riskier projects. Following substantial bank market liberalization in both the United States and Europe, empirical research on the relation between bank market structure and financial stability intensified. Existing empirical studies, however, find only mixed evidence of the riskenhancing effects of deposit market (and generally bank) competition (see Berger et al., 2004, Carletti and Hartmann, 2005, and Jimenez et al., 2007, for comprehensive literature reviews). Whereas Demsetz et al. (1996), Brewer and Seidenberg (1996), Saunders and Wilson (1996), and Salas and Saurina (2003) find empirical support for the charter-value hypothesis (bank competition increases bank risk), Boyd et al. (2006) empirically show that banks in more concentrated banking markets are riskier. A major caveat of the existing research on the competition-risk nexus is that most studies used concentration measures to proxy competition. However, as shown by Leaven and Claessens (2004), the relation between competition and concentration may be weak. In their study they improve on this measure by using the Panzar-Rose H-statistic to gauge competition. This measure, in turn, has other drawbacks, the most relevant being its inability to distinguish between deposit and loan market competition. This distinction is important in the context of Boyd and de Nicolo s (2005) observation on the different effects of loan and deposit market 7

8 competition. Moreover, as Park and Pennacchi (2008) show, some forms of bank market liberalization, such as the legalizing of multimarket bank entry, can result in more intense loan market competition but less intense competition in the deposit market. In this case, the traditional competition measures such as concentration ratios, Herfindahl indices, number of banks, and so on will present incomplete measures of deposit market competition. To our knowledge, Jimenez et al. s 2007 research represents the first empirical study of the competition and risk nexus that explicitly distinguishes deposit from loan market competition. The authors of this study examine the risk effects of deposit and loan competition, measured by the deposit and loan market Lerner indices 7 of individual banks, in separate sets of regressions. The authors show that loan market competition significantly increases risk, whereas the effect of deposit market competition is statistically insignificant. This is a surprising result because the theoretical literature agrees on just the opposite: there is a consensus on the risk-enhancing role of deposit market competition, whereas loan market competition can generate ambiguous effects. By using Lerner indices which relate bank retail interest rates to the rates on wholesale liabilities Jimenez et al. are the first to have introduced (to our knowledge) a price-based measure of competition in the analysis of the nexus of competition and risk. However, since the Lerner indices are derived as the relative mark-down of deposit rates (mark-up of loan rates) over the money market rate, they may be endogenous with respect to risk. This is easily seen in the case of the loan market Lerner index: if a bank finances riskier projects, it will charge higher loan rates. But deposit market Lerner indices might also be endogenous with respect to risk since riskier banks might have to pay higher deposit rates in order to 7 For each bank i in time period t Jimenez et al (2007) compute the deposit market Lerner index as money _ market _ ratet deposit _ rateit LI D = and the loan market Lerner index money _ market _ ratet as loan _ rateit money _ market _ ratet LI L =, where deposit rate it and loan rate it are the rates offered by the bank money _ market _ ratet and money market rate t is the average money market rate in time period t. 8

9 compensate depositors for the bank s increased risk of failure. Note that this effect might be present even if deposits are insured, since failure is undesired by the depositors because they have to bear costs of switching to another bank. The endogeneity of competition and risk can induce inconsistent estimates of reduced-form regressions and therefore requires a more structural estimation approach. Moreover, in the computation of the Lerner indices, Jimenez et al. (2007) make the implicit assumption that all banks, independent of their risk levels, face the same country-wide money market rates. However, a broad strand of empirical papers show that the interest banks pay on wholesale funding depends on bank risk. Furfine (2001), for example, proves that riskier banks pay higher rates on federal funds borrowing. Moreover, Flannery and Sorescu (1996), DeYoung et al. (1998), and Morgan and Stiroh (2001) find that riskier banks pay higher interest on subordinated debt. To our knowledge the only study that relates wholesale funding, competition, and risk is Goyal (2005). In his empirical framework Goyal assumes that high bank competition is reflected in low bank charter value and high bank risk, and examines the effect of the charter value on the yield and the inclusion of covenants on bank subordinated debt. He finds that low charter values correspond to more covenants in the subordinated debt contract and higher subordinated debt yields. All these studies, however, have not explored the interrelation between the risk effects of wholesale funding and the fact that wholesale financing is more attractive for banks that face very intense deposit market competition. In this paper we explicitly address the limitations of the existing literature. First, by estimating a system of equations we explicitly account for the simultaneity of competition and risk. This approach represents a substantial contribution of our model over the reduced-form approaches 9

10 that have been applied so far in the analysis of the competition risk relationship. Second, we explicitly control for the fact that deposit market competition is related to the costs and availability of wholesale funding. 3. Deposit market competition, markets for wholesale funds, and bank risk In this study we focus on the question of how a bank s competitive position in the deposit market affects its risk behaviour. In formulating this research focus we deviate from a large strand of the literature concentrating on aggregate market-level measures of competition. By focusing on bank-level measures of competitive position and risk in deposit markets, we explicitly allow for banks operating in the same markets to face different intensities of competition. The intuition behind this assumption is that banks can extract some monopoly rents in the deposit market (Hutchison and Pennacchi, 1996), for instance, because of the costs depositors have to bear when switching banks (Kiser, 2003). The risk effects of a bank s competitive position in the deposit market have been theoretically modelled by Allen and Gale (2000) and Boyd and de Nicolo (2005). Their models describe symmetric deposit market equilibria in which the number of banks is positively related to the deposit rate. The deposit rate in turn is positively related to optimal bank risk. Following these theoretical models, we measure the intensity of deposit market competition faced by a bank by the deposit rate offered by the bank and examine the effect of this measure on the risk of the bank. In addition, we control for the substitutability between bank retail and wholesale funds by including the rate a bank pays on wholesale liabilities as a determinant of bank risk. Finding, as we do below, that high retail deposit rates correspond to higher risk preferences can, on the one hand, be interpreted as support for the charter-value hypothesis (if banks expect high returns from their deposit market participation, they will not risk losing their charter by 10

11 undertaking excessively risky projects). On the other hand, consistent with Allen and Gale s and Boyd and de Nicolo s models, the results can imply that when banks have to pay a high rate on their liabilities, their risk preferences are shifted upwards 8. Note that this is true both for retail and wholesale liabilities. Nevertheless, the risk-increasing effect of high wholesale rates will be capped by the fact that wholesale creditors are uninsured and will rather ration wholesale credit than lend to banks at a rate that is bound to result in excess risk 9. Our focus on a micro-level measure of market power makes the deposit rates offered by each bank a suitable competition measure. Although prices and price margins have been widely used as competition measures in the industrial organization literature, their application in banking is limited. This is most probably the case because of the nature of banks as financial intermediaries, in which the distinction of inputs and outputs is challenging (see Freixas and Rochet, 1997, for a discussion). One example of using price margins as a competition measure is Jimenez et al. (2007). As already mentioned, these authors introduce deposit and loan market Lerner indices based on the stark assumption that the banking market is disintegrated in a deposit market (deposits are inputs, and money market funds sold are the output) and a loan market (money market funds purchased are the input, and loans are the output 10 ). Under this assumption, the deposit market Lerner index measures the relative difference between the price of inputs (retail deposits) and outputs (wholesale funds sold). The bank is assumed to be a price-taker in the wholesale market, whereas it can exert some 8 This result is also consistent with the implications of a more general model of the risk effects of the costs of funding for firms with limited liability (see Freixas and Rochet, 1997). 9 As in Stiglitz and Weiss (1981), credit rationing might be the outcome when the implied interest rates correspond to risk levels that imply negative net expected return. 10 The idea of modeling banking markets as vertically integrated deposit and loans markets has previously been exploited by Campbell (1988) and Berlin and Mester (2001). 11

12 market power in the deposit market. This market power is signalled by the price the bank pays on its retail deposits 11. Alternatively, assuming vertically integrated banks which perform both deposit and loan services, Kiser (2003) argues that the rates a bank offers in the deposit market will depend on the rates it pays on wholesale funding. In Kiser s model, loans are seen as the output in a production function that uses retail and 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, Kiser finds that an exogenous rise in the wholesale rate is related to an increase in the optimum retail deposit rate offered by the bank. Following the same line of argument, Park and Pennacchi (2008) assume that only large multimarket banks can borrow wholesale funds at an exogenously given wholesale rate. This access to wholesale funding makes large banks less aggressive when competing for retail funds. This group of models shows that the availability and the cost of wholesale liabilities matter for deposit market competition. Moreover, since wholesale liabilities are risk-sensitive, they should not be ignored in a study of competition and risk. That is why in the formulation of our empirical model we explicitly study the determinants and the effect of the cost of wholesale funding. First, we define the deposit rate as a function of the wholesale rate and bank risk (again, the assumption is made here that even insured depositors might react to the risk of the bank, since they want to avoid the costs associated with switching away from a failed institution). In turn, the rate a bank pays on its wholesale liability is modelled to depend on the risk of the bank. Wholesale rates are risk-sensitive because wholesale liabilities are not covered by deposit insurance. Wholesale creditors would, therefore, adjust the interest rate to the 11 Hutchison and Pennacchi (1996) introduce a similar approach of measuring a bank s deposit market competitive position. They approximate a bank s deposit market rent by the discounted difference between the T-bill rate and a bank s retail deposit rate. 12

13 probability of the borrower s failure. Empirically, this relation has been documented by Furfine (2001) and King (2008). Moreover, since the observed rate on a bank s wholesale liabilities is the rate at the equilibrium between the demand and supply of wholesale funds (see King, 2008, for a model of the individual bank demand and supply of fed funds) and the demand for wholesale liability depends on a bank s ability to attract retail deposits and its cost of doing so, we include the retail deposit rate as a determinant of the wholesale rate. Given the substitutability of retail and wholesale deposits, banks which have no market power in retail deposit markets will have a higher demand for wholesale funds (King, 2008, and Dinger and von Hagen, 2008) and might therefore pay higher wholesale rates. The relation between the wholesale rate and bank risk is potentially nonlinear. If a bank s risk level corresponds to a very high interest rate on wholesale funding, the wholesale rate might not be observed because high-risk borrowers are either rationed by the wholesale lenders or because riskier banks (aware of the high wholesale rate) do not demand wholesale funds. In other words, a regression of the wholesale rate on bank risk might suffer under endogenous selection bias, since wholesale rates are only observed for a subsample of less risky banks. These selection issues have been explicitly studied by King (2008). Following his approach, we control for the selection issues by estimating the wholesale rate equation via a Heckit estimation technique (see Heckman, 1976). In our case, the wholesale rate is a function of both the retail rate and the risk of a bank. 4. The econometric model The idea of our empirical model is to estimate the relationships between deposit rates, wholesale rates, and bank risk. Reflecting the discussion presented in Section 3, we build a model of three equations. ri, t = f ( di, j, t, wi, t, controls) (1) 13

14 di, j, t = f ( ri, t, wi, t, controls) (2) wi, t = f ( ri, t, di, j, t, controls) (3) where r denotes the risk of the bank, d the retail deposit rates and w the wholesale rate. This model relates three endogenous variables: bank risk, the retail deposit rate, and the costs of wholesale funding. The first equation describes the impact of deposit and wholesale rates on bank risk. The second equation models the dependence of deposit rates on bank risk and the outside option of wholesale funding. The third equation describes the risk sensitivity of the wholesale funding rate and its dependence on the retail deposit rates. The subscripts i, j, and t denote the bank, the local market (MSA), and the time period, respectively Measures of bank risk, deposit rate, and wholesale rates Existing empirical studies have so far employed different risk measures in their analysis. Boyd et al. (2006), for example, concentrate on the risk of the bank measured by the z-score. These authors choose this risk measure because it is closely related to the probability of default. They show that bank competition (measured by the Herfindahl index or the concentration of the banking industry) has a negative impact on this measure. On the other hand, Jimenez et al. (2007) concentrate on the risk of the loan portfolio measured by the ratio of nonperforming loans to total loans. They find that deposit market competition has no significant impact on asset risk, but loan market competition is positively related to the risk of a bank s asset portfolio. In order to deliver results comparable to those of Boyd et al. (2006) and Jimenez et al. (2007), we present alternative regression specifications using the z-score and the nonperforming loans ratio. Following Boyd et al., we compute the z-score as the ratio between the sum of a bank s 14

15 average return on assets (ROA) and capitalization (E/A = equity/total assets) and the standard deviation of the return on assets: ROA + E / A z score =. σ ( ROA) The z-score, therefore, presents information on how many standard deviations of the return on assets are needed to drive the bank into default. Banks with a low z-score are more likely to default. That is, the z-score is decreasing with bank risk. We construct the z-score where σ is computed by using rolling windows of 8 quarters. We followed Ashcraft in constructing our ratio of a nonperforming loans risk measure and use the ratio with a four-quarter lead 12. This differs from Jimenez et al. (2007), who use the current ratio of nonperforming loans. The intuition is that the risk of the current projects will only be reflected with a delay in the nonperforming loan ratios of the bank. In addition to the ratio of nonperforming to total loans, we also adopt the ratio of nonperforming loans to equity as a risk measure (again with a four-quarter lead) 13. According to Ashcraft (2007), this is a better measure of bank risk since the capitalization of the bank affects the amount of nonperforming loans a bank can absorb before harming its creditors. This paper focuses on the choice of a suitable measure of deposit market competition. Following the arguments of Section 3, we adopt the bank s retail deposit rates as a proxy for its deposit market competitive position for our baseline specification. We also look at the share of demand deposits in the total deposits volume as a robustness check. From the variety of deposit rates reported by Bankrate Monitor (checking accounts, money market deposit 12 Regression specifications using the current (as in Jimenez et al., 2007) and the two-quarter-lead of the nonperforming loan ratios result in qualitatively the same results. 13 Both nonperforming loans ratios are used in logarithmic form. 15

16 accounts, and certificates of deposits with a maturity of three months to up to five years), we choose the checking account rates as the most suitable for our exercise. Previous research has documented that checking account rates are more sensitive to changes in the local bank market structure than money market deposit rates (Hannan and Prager, 1998, Craig and Dinger, 2008), whereas rates on certificates of deposits do not significantly react to such changes. We have also run all the following regressions using the money market deposit account rates instead of the checking account rates; results do not change qualitatively. And finally, in our baseline specification, we use the interest rate on federal funds purchased as a proxy for the costs of the wholesale funding. Purchased federal funds are liabilities with very short maturity and thus not perfect substitutes for retail deposits. The rate a bank pays on purchased federal funds is, however, shown to be closely correlated with alternative bank wholesale liabilities (such as subordinated debt, advances from Federal Home Loan Banks, and others), which are potentially better substitutes for retail deposits from a bank s point of view. The advantage of purchased federal funds over these alternative wholesale liabilities for our framework is that we have fed funds observations for most banks in our sample 14. Moreover, comparison across banks is further alleviated by the fact that the fed funds market has a standardized product 15. We follow King (2008) and approximate the interest rate on fed funds purchased by the ratio of expense of federal funds purchased and securities sold under agreements to repurchase (line riad4180 in the Call Report) to federal funds 14 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 the share of fed funds liabilities in total assets in the estimation of equation (3) and account for the potential selection bias by using a Heckman correction (Heckman, 1976). 15 Alternative wholesale funding products bear a substantial nonprice component such as covenants (see Goyal, 2005) which should be accounted for, for a precise comparison. Data about these are, however, unavailable for the broad range of banks included in our study. 16

17 purchased and securities sold under agreements to repurchase (line rcfd3353 in the Call Report) Identification and Instruments For the identification of the system of equations (1) to (3) we have to find suitable instruments for each of the equations. Econometric theory suggests that a valid instrument should be uncorrelated with the error term but strongly correlated with the instrumented endogenous variable. Our identification strategy consists of instrumenting the endogenous variables in our model (retail deposit rate, rate on wholesale funding, and bank risk) by variables which have been shown by earlier research to be strongly correlated with the respective endogenous variable, but for which we can argue exogeneity with respect to the error terms, especially for those necessary equations in the system where they are not included as a right-hand variable. In the case of retail deposit rates, the literature has found that ratio of branches to deposits, the share of the branches of the bank, and the market size are significant determinants of a bank s retail deposit rates (see Prager and Hannen, 2004). We argue that these variables are only right-hand variables for the deposit rate equation, not the wholesale rate or risk equations, and thus employ these variables as instruments for the retail deposit rate. The branches-todeposits ratio is computed at the bank-market level as the ratio of the number of bank i s branches in local market j to bank i s total deposits in this market. The share of the branches is computed as the proportion of the branches of the bank to the total number of bank branches in the local market. The market size is the log of the population of the respective market. The underlying assumptions when using these variables as deposit rate instruments is that banks with more branches (better geographical proximity to retail customers) can attract 16 As King (2008) notes, this approximation includes the cost of securities sold under agreements to repurchase, which is a collateralized liability of the bank and might be less sensitive to bank risk. The fact that a substantial risk sensitivity is shown even when repos are included further strengthens our argument. 17

18 deposits at lower rates. On the other hand, neither the wholesale rate nor the risk preference of the bank directly depends on the number of branches 17. The instrumentation of the wholesale rate in the deposit and risk equations focuses on variables which affect the rate a bank pays on wholesale liabilities but do not have an impact on deposit rates and bank risk. Our major instrument for the wholesale fund is the average effective level of the federal funds rate (as announced by the Federal Reserve Bank of New York, based on its survey of four major brokers. The inclusion of this instrument follows the argument that the rate banks pay on wholesale liabilities reflects changes in the fed funds target rate set by the Fed. We also use a dummy variable, which takes the value of one if the bank belongs to a bank holding company and zero otherwise, as an additional instrument for the wholesale rate. The intuition behind this instrument is that wholesale funding is cheaper for banks that are members of large BHCs, but risk choice and deposit rate do not necessarily depend on BHC membership. Finally, following the work of King (2008), who shows that the growth rate of the volume of loans in the bank balance sheet is a significant determinant of the rate banks pay for federal funds, we include loan growth as an instrument of the wholesale rate. The underlying assumption is that when a bank faces an increase in loan demand which it cannot match with retail deposits, its demand for wholesale funding will shift upwards, corresponding to a higher equilibrium rate on the wholesale borrowing. While a change in portfolio is probably also related to the amount of risk taken on by the bank, as well as the deposit rate it can charge, we believe that in the case of these two equations, these concerns are of a second-order effect, once we have controlled for other factors that might affect these two variables more specifically. However, our system is overidentified, so that we also have tried including this variable in the risk equation, for example, with little change in the results. The risk of a bank can be instrumented by the average economic conditions in the local 17 An overidentification restriction test confirms the exogeneity of the instruments. 18

19 markets where a bank operates. Cross-country evidence suggests that bank default risk (Boyd and de Nicolo, 2006) and nonperforming loans (Dinger and von Hagen, 2008) are negatively related to average income and economic growth. For the United States, Mian and Sufi (2008) demonstrate for the case of mortgage lending a negative relation between default rates and MSA average income. Moreover, theoretical and empirical research shows that lending standards depend on local economic growth (see Ruckle, 2004, for a discussion). General economic conditions are effective instruments because, although they significantly affect the risk of the banks operating in the local market, they do not have a direct impact on the wholesale and deposit rates. Following this line of argument, we instrument the risk of a bank by the ratio of the current level of personal income for the local market to average income for the local market over time. In the case of all instruments, the Stock-and-Watson-rule-of-thumb measure 18 confirms the strength of the instrument, and, in the case of multiple instruments, a Hansen test does not reject exogeneity of the instruments Control variables As suggested by earlier research, a few variables such as capitalization, bank size, and the prevailing level of the interest rate in the economy can affect all three dependant variables (Hannan and Hanwick, 1998, Furfine, 2001, Boyd et al, 2006). To this end, we include as control variables in all three equations the ratio of bank equity to total assets as a measure of capitalization and the log of the bank s total assets as a proxy for bank size. 18 The so-called Stock and Watson rule of thumb (Stock and Watson, 2003) is often used 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 are jointly 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 the risk instruments the F- statistic is

20 4.4. Data and samples The analysis is based on a large dataset combining three main data sources. Deposit rates are drawn from BankRate Monitor, Inc. The data encompass deposit rates offered by 589 U.S. banks in 164 local markets (metropolitan statistical areas) for the period starting on September 19, 1997, and ending on July 21, Bankrate Monitor reports cover a comprehensive set of deposit products (checking accounts, money market deposit accounts, and certificates of deposits with a maturity of three months to up to five years). In the regressions presented in the paper we concentrate on checking account rates only 19. We exclude the rates on certificates of deposit because they are investment products with a relatively high minimum denomination, and we expect them to react less to local market conditions. 20 Radecki (1998) presents evidence that multimarket banks tend to offer uniform rates across local markets. In our sample, however, we observe a sufficient variation of the rates offered by banks in different local markets. Subsequently, we use this variation to account for the different intensity of competition a bank may face in different local markets. We match the deposit rate data with a broad range of bank characteristics reported in the Quarterly Reports of Conditions and Income (Call Reports). BankRate Monitor deposit rate data have weekly frequency. To match the quarterly frequency of the Call Reports, we only use the deposit rates reported on the last week of each quarter. We also include control variables for the local markets. The source of the local-market controls is the Summary of Deposits, and these data are available only at an annual frequency. 19 We have rerun all regression specifications using the money market deposit account rates as a retail deposit rate measure. The results are qualitatively the same as in the case when the checking account rate is employed as retail deposit rate measure, although statistical significance is sometimes lower. Results are available from the authors upon request. 20 Hannan and Prager (1998), for example, find no significant impact of changes in deposit market structure on certificate of deposit rates. 20

21 After merging our data we have a multidimensional 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 rates, share of the MSA s branches, branches per deposit volume in the market, etc.). In the estimation of equations (1) and (3), bank-level dependent variables (the risk proxy and the rate on wholesale liabilities) are regressed on bank-market-level explanatory variables (e.g., deposit rates). In this case, the assumption of uncorrelated error terms across the observations may be violated (it is likely that observations of the same bank in different markets will show correlated error terms) resulting in potentially inconsistent estimates. We adopt three alternative approaches to deal with our multidimensional panel. First, we use the full sample of bank-market observations and cluster the standard errors by bank. Second, we alternatively estimate the model on the bank level by computing the average values of the bank-market-level variables (deposit rate, average income, branches-to-deposits ratio, etc.). For each bank and time period, we compute the average value of each of these variables across all the local markets in which the bank operates. Through the aggregation, we achieve consistency of the estimated coefficients but lose information on the local deposit market intensity and dramatically reduce the number of observations, which in turn reduces the efficiency of the estimation. This estimation approach can only account for the variation across banks. It has, however, the advantage that it accounts for the possibility that banks reshuffle deposits across local markets. In this case, the average intensity of deposit market competition might be the one that matters for bank risk. And third, we estimate the model using the subsample of single-market banks (143 out of our sample of 589 banks operate in only one MSA). Single-market banks (SMBs) face deposit market competition in one market only, and their bank-level risk is related to the competitive conditions in only this deposit market. The drawback of this approach is that we again dramatically reduce our sample size. 21

22 Table 1 illustrates descriptive statistics of the variables included in our estimations. It shows that the checking account rate varies between 0 and 3.8%. It is important to note that some of the variation is due to the time series dimension of our data. Our sample covers 1997 to 2006, which encompasses a period longer than a full interest rate cycle. The Z-score varies between 2 and 492. The nonperforming loan ratios vary between zero and almost 12% Estimation technique We estimate each of the three equations with a two-stage instrumental-variable estimating technique with clustered standard errors. The estimation of the wholesale rate equation is more challenging because of the potential selection bias, which arises from the fact that if banks perceive that they have to pay a disadvantageous rate on their wholesale liabilities they may restrain from borrowing wholesale funds. Consequently, for such banks we will observe no (or only negligible volumes) of wholesale funding. Since the wholesale rate for banks that have very small volumes of wholesale liabilities contains a lot of noise, we use the censored regression specification suggested by Heckman (1976) when estimating the wholesale rate equation. Unless the share of wholesale liabilities is large enough, the purchased funds are likely to represent unusual purchases made under extreme time pressure and are thus unlikely to represent the price of wholesale funds substituted these for deposits. Because of this, we did not include an observation in the estimated wholesale funds equation unless the volume of federal funds purchased represented at least 0.5% of the bank s assets. 21 This induces a problem of censoring, because the included observations might not represent the population of banks as a whole. The Heckman specification creates an auxiliary variable in the first stage, the inverse Mills ratio, which represents the bias caused by the censoring process. As noted 21 As robustness check we have reestimated the model using both a fix volume of the federal funds purchased as a trigger point (1 Mio. USD, as in King, 2008) and alternative trigger values of the fed funds purchased share in total assets (0.01% and 1%). Results do not change qualitatively. 22

23 by Heckman, instrumental variable estimators are still consistent, once the predicted inverse Mills ratio is included in the system. 5. Estimation results We first present the results of the baseline model, with the rate on federal funds purchased as a wholesale funding rate proxy and the checking account rate as a proxy of the intensity of deposit market competition. The results of this specification are illustrated in Table 2, which contains a column for each of the three risk measures: z-score, the ratio of nonperforming loans to total loans (F4NPL), and the ratio of nonperforming loans to equity (F4NPL_EQ). The results of this estimation show a statistically significant positive link between deposit rates and bank risk. In particular, a rise in deposit rates is associated with a drop in the z-score (which implies a lower distance to default) and higher relative volumes of nonperforming loans. These results are consistent with the theoretical prediction of the risk-enhancing impact of deposit market competition and are robust to the choice of the risk measure. The results of the estimation of the deposit rate equation in this baseline specification also confirm the positive link between bank risk and deposit rates. So, for example, banks with a high z-score are expected to pay lower deposit rates. Similarly, banks with high relative volumes of nonperforming loans offer higher deposit rates. It is interesting to note that in these regression specifications we find a positive relation between the checking account rate and the rate on federal funds purchased. This result is consistent with the substitutability between retail and wholesale funding and confirms the implications of Kiser s (2003) model. And finally, the results of the estimation of the wholesale rate equation suggest again that the rate on federal funds purchased is positively related to the retail deposit rate. This relation is, however, statistically significant only when the z-score is used as a risk proxy. The results also confirm a positive relation between bank risk and the cost of wholesale funding. This 23

24 result is robust to the choice of the risk measure and is consistent with Furfine (2001), who also uncovers a positive relation between a bank risk and the rate paid on wholesale liabilities. Next, we re-estimate the model using a sample of observations averaged at the bank level. That is, for each bank and quarter we now use only one observation and cannot account for the market-level variation. The results of these estimations are presented in Table 3. Qualitatively, they are very similar to the bank-market-level results. However, the reduced number of observations is reflected in the lower efficiency of the estimations. And finally, we estimate the model on the sample of banks operating in only one local market. In this case, we are again able to replicate the results for the full sample of banks. Again, the small sample size results in relatively low efficiency of the estimations. In sum, we find a very robust, statistically significant, and positive relation between the intensity of deposit market competition faced by a bank (measured by the retail deposit rate) and its risk level. Our empirical results, therefore, support the conclusion of a series of theoretical papers (e.g., Allen and Gale, 2000, and Boyd and de Nicolo, 2005) that intense deposit market competition results in high bank risk. Moreover, within a more comprehensive framework, our empirical model is able to replicate the results of earlier studies showing that the costs of wholesale funding depend on bank risk (DeYoung et al., 1998, Morgan and Stiroh, 2001, and Furfine, 2001) and a positive relation between the cost of retail and wholesale funding (Kiser, 2003). 6. Robustness checks In this section we describe a series of alternative estimations performed to confirm the robustness of the results. To start with, we introduce the rate banks pay on subordinated debt as an alternative measure of the cost of wholesale liabilities. Because of its longer maturity, subordinated debt can be considered as a better substitute for retail deposits than federal funds 24