The Size Distribution of the Banking Sector and the Effects of Monetary Policy

Transcription

1 The Size Distribution of the Banking Sector and the Effects of Monetary Policy Edgar A. Ghossoub, Robert R. Reed University of Texas at San Antonio; University of Alabama August 26, 2014 Abstract In recent years, the industrial organization of the banking system has received a large amount of attention. In particular, it is generally viewed that the size distribution of the banking sector has changed where it is dominated by a small number of large institutions. In this paper, we develop a model of imperfectly competitive banks that differ in terms of the size of their deposit base. Such differences are important for aggregate credit market activity and the effects of monetary policy. Notably, we explain how the optimal size distribution of the banking system involves trade-offs from distortions in credit markets due to imperfect competition across banking markets. Second, the effects of monetary policy on credit market activity are weaker in an economy dominated by a small number of large banks. Empirical analysis examining the role of concentration among the current members of the European Monetary Union is consistent with the predictions of the model. 1 Introduction In recent years, the competitive structure of the banking system has received a great deal of attention. For example, in the United States, Janicki and Prescott (2006) point out that there have been two major changes that have been taking place during the past thirty years. 1 First, big banks have become increasingly larger over time. Second, the relative number of small banks has been increasing. For example, based upon their analysis in the years just before the crisis, the combination of over 90% of (relatively small) institutions held less than 10% of assets in the banking system. By comparison, over three-quarters of assets in Corresponding Author: rreed@cba.ua.edu. 1 See also Ennis (2001). 1

2 the banking system were held by the biggest banks which make up less than 1% of active institutions in the United States. Furthermore, it is widely acknowledged that the size distribution of banks across the European Monetary Union is highly asymmetric. Notably, the European Banking Federation (2010) reports that the deposit markets in France and Germany are the largest in the EMU at a total of over 3.5 trillion euros in 2009 while many countries such as Cyprus, Greece, and Finland are well below 200 billion euros. As economies emerge from the recent financial crisis, the size distribution of the banking sector is likely to become even more concentrated. 2 In light of these observations, there are a number of important issues that deserve to be studied. First, how does aggregate credit market activity depend on the size distribution of the banking system? What is the optimal distribution of firm size in the financial sector? How does the effectiveness of monetary policy depend on the size distribution? 3 The objective of this paper is to study how credit market activity and the transmission channels of monetary policy depend on the size distribution of the banking system. In order to address these issues, we view that a model must include several key features. First, intermediaries fulfill important economic functions in the financial system. That is, they provide services that are difficult for individual agents. Second, there must be a meaningful transactions demand for money so that the transmission channels of monetary policy are carefully articulated. Third, as intermediaries are aware of their market power in the financial system, the banking system in the model must be composed of imperfectly competitive firms that differ in size so that the distribution of the banking system has a non-trivial effect on economic activity. Our framework satisfies all three requirements. First, as in Diamond and Dybvig (1983), financial intermediaries provide risk pooling services to depositors to insure them against liquidity risk. Second, following Schreft and Smith (1997, 1998), incomplete information and restrictions on asset portability provide a foundation for money. Finally, banks act as Cournot competitors in credit markets which affect the extent of consumption smoothing among borrowers. The size distribution of banks results from a different deposit base across large and small institutions. Due to the presence of imperfectly competitive banks across markets, credit market activity in each market is ineffi ciently low. Moreover, as the size distribution of the banking system moves towards a smaller number of large institutions, total lending in the economy declines. However, owing to the ineffi ciencies across markets, lending in the economy also falls if there is a high degree of concentration of small banking institutions. Therefore, the optimal size distribution of the banking system balances the distortions from market power across large and small institutions. Alternatively, the optimal distribution balances the distortions between big and small markets. 2 Gongloff et al. (2013) and Gandel (2013). 3 In particular, many have argued that the too big to fail problem clogged the standard transmission channels of monetary policy during the crisis. See arguments posed by Fisher and Rosenblum (2009), Contessi (2010), and Rosenblum, Enier, and Alm (2010). 2

3 Our model demonstrates that the impact of monetary policy is weaker in economies with a small number of large banks. However, this does not necessarily imply that the monetary transmission mechanism is less effi cient. Interestingly, our results indicate that the elasticity of credit market activity with respect to inflation is stronger in economies dominated by a small number of banks. Once the relative amount of lending in settings plagued by distortions from market power is taken into account, the strength of the transmission mechanism from policy improves. Finally, though welfare is higher in economies with a symmetric size distribution in low and moderate inflation economies, the emphasis on risk-sharing which occurs in a banking system dominated by a small number of institutions can be valuable in high inflation environments. We proceed by testing the predictions of the model empirically. In particular, we study the role of concentration of the banking sector among the current eighteen members of the European Monetary Union. All of the results are consistent with the predictions of our theoretical framework. First, banks in sectors with a higher degree of concentration among the largest firms hold relatively more liquid assets. Second, various measures of credit market activity are lower if the banking sector is more concentrated. Finally, the effi cacy of monetary policy on credit market activity is weaker in countries with a higher degree of concentration. Our work contributes to a recent literature which examines the role of the industrial organization of the banking system. It follows the previous literature which largely treats the competitive structure of the banking system to be exogenous. For example, Boyd and De Nicolo (2005) study how the number of firms affects risk-taking in the banking system. In addition, Martinez-Miera and Repullo (2008) examine the relationship between the exogenously given degree of competition and risk-taking. As a more recent example, Cetorelli and Peretto (2012) study the implications of (exogenous) banking concentration for capital accumulation where intermediaries act as Cournot-competitors. Our key departure from previous work is that we look at the implications of banking concentration in a framework where there is also exogenous variation of the size of the deposit base. Interestingly, Corbae and D Erasmo (2011) endogenize the number of banks and the size distribution through equilibrium entry and exit of firms over time. Another key departure our framework is that we study the implications of the size distribution in a monetary economy. In this manner, our work follows previous research which studies in the effi cacy of monetary policy across the competitive structure of the banking system. Notably, Ghossoub, Laosuthi, and Reed (2012) compare the effects of monetary policy between perfectly competitive and monopolistic banking systems. Under perfect competition, inflation promotes credit market activity through a Tobin-style asset substitution channel. However, inflation has the opposite effect in a monopolistic setting. Based upon the framework in Ghossoub, Laosuthi, and Reed, Matsuoka (2011) studies optimal monetary policy across the two market structures. Similar to this paper, Laosuthi and Reed (2013) develop a model based upon Cournot competition in credit markets. In contrast to our paper, by con- 3

4 struction, monetary policy is super-neutral under fixed entry. Instead, as in Williamson (1986), they focus on the effects of monetary policy through equilibrium entry of intermediaries in the sector. Finally, Ghossoub (2012) demonstrates how prices in capital markets vary across monopolistic and competitive systems. Despite these contributions, none of the papers mentioned look at the implications of the size distribution of the banking system for aggregate credit market activity and the effi cacy of monetary policy. The remainder of the paper is as follows. Section 2 describes the physical environment of the model economy. Section 3 studies activity in steady-state general equilibrium. Section 4 addresses the optimal size distribution of banks and optimal monetary policy. Section 5 extends the model to study credit market activity in the presence of geographic diversification of large institutions. Section 6 provides empirical results in support of our theoretical analysis. Finally, Section 7 offers concluding comments. Details of formal arguments are offered in the Appendix. 2 Environment We study a two-period overlapping generations economy. Time is discrete and indexed by t = 0, 1,.... The economy is divided into two geographically separated, yet symmetric islands. In each island, there are three groups of agents: a continuum of depositors and borrowers, each of measure two, and N > 1 financial intermediaries (or banks). Moreover, each island is divided into two regions, indexed by i = 1, 2. As half of the depositors and borrowers reside in each region, there is a unit population mass of each agent in each region. In contrast, a fraction λ i of bankers are in region i. Each depositor receives an endowment vector of goods (x i, 0) during her young and old age, respectively. Depositors in region 1 have larger endowments than in region 2, implying x 1 > x 2 > 0. However, a depositor born in period t only derives utility from her consumption when old, c d i,t+1. Her utility function when old is u(c d i,t+1 ) = (cd i,t+1) 1 1, where (0, 1) is the coeffi cient of risk aversion. By comparison to depositors, borrowers are identical and receive (0, y) units of goods during their lifetime and value consumption in both periods. The lifetime utility function of a borrower is expressed by: u(c b t, c b t+1) = i,t) 1 (cb 1 +, where β (0, 1] is an exogenous discount factor. As a straightforward means of segregating deposit markets across large and small institutions, borrowers and depositors in each region can only trade with financial intermediaries in the same region. In particular, region 1 has a larger deposit base relative to region 2. In turn, financial institutions in region 1 are bigger than in region 2. 4 In this manner, we can analytically study the optimal β (cb i,t+1) Tarullo (2009) describes the role of small banks which hold much smaller amounts of 4

5 size distribution of the banking system and the effects of monetary policy. Following Townsend (1987), private information and limited communication between islands generate a transactions role for money. That is, if agents relocate to a different island, they can only use cash to transact. Furthermore, as in Schreft and Smith (1997), depositors are subject to random relocation shocks. After portfolios are chosen, a fraction π of depositors is selected at random to move to the other island. These agents are called movers. The probability of relocation, π, is exogenous, publicly known, and the same in each island. Given that agents need cash on the other island, agents must liquidate their assets into cash prior to departing their home island. In this manner, random relocation shocks are analogous to liquidity preference shocks in Diamond and Dybvig (1983). Unlike depositors, borrowers are not subject to relocation shocks. Finally, bankers are risk neutral and do not receive any endowments during their lifetime. Analogous to depositors, they only value second period consumption. A banker in region i of a particular island services his clients in that area. In particular, each banker announces a schedule of rates of return for each unit of deposits received. Moreover, each bank in region i issues a real quantity of one-period loans, li,t s, to its local borrowers and charges a gross real interest rate, R i,t. In addition to issuing loans, each bank chooses to hold fiat money which is used to pay movers (or relocated agents). Denote the real amount of cash held by each bank in region i by m i,t = Mi,t P t, where M i,t is the nominal quantity of money balances held by each bank. Moreover, P t (0, ) is the price of one unit of goods in units of currency in period t which is common across islands and regions. In this manner, one unit of fiat currency held between periods t P and t + 1 yields a real return of t P t+1. Furthermore, define the nominal interest P rate on loans as I i,t, where I i,t = R t+1 i,t P t. The final agent in the economy is a monetary authority that targets the rate of money growth which is constant over time. The total nominal amount of money in each location at time t is given by M t. Denoting the gross growth rate of money by σ > 0, the evolution of money is such that: In real terms: M t+1 = σm t (1) P t m t+1 = σm t (2) P t+1 The monetary authority uses the newly created cash in period t to purchase τ t units of goods, where τ t = σ 1 σ m t (3) deposits in a banking system dominated by a small number of large institutions. Duke (2012) discusses the importance of small banks for the aggregate mortgage market. 5

6 As a benchmark, we assume that government purchases are not rebated back into the economy. As a result, we initially focus on cases where σ 1. We relax this assumption in section 4. Finally, in period zero, the initial old generation of depositors is endowed with the aggregate nominal money stock, M 0. We proceed by describing the timing of the events. At the beginning of period t, young depositors receive their endowments and banks announce the schedule of interest rates (rt m if relocated and rt n if not relocated). Given that bankers receive a large volume of deposits, they can exploit the law of large numbers by pooling the idiosyncratic risks among their depositors which is not possible on an individual basis. Therefore, young depositors will intermediate all their savings through their local bank. Next, borrowers make their intertemporal consumption (savings) choices and visit their local bank to take a loan. Banks engage in portfolio allocations by investing their deposits into money balances and loans. In contrast to credit and deposit markets which are segregated on each island, banks in each region are tied together through a common money market. In this market, goods and cash are exchanged. Obviously, banks are the source of demand for cash on each island as they act on behalf of their depositors. On the supply side, there are two sources. First, old relocated agents come to the money market with a total of M t 1 units of currency. In addition, the monetary authority buys τ t units of goods in exchange for σ 1 σ M t units of cash. Subsequently, old borrowers receive their endowments which they use in part to pay back their obligations to their local banks. Banks use these goods to pay old depositors who did not relocate and for their own consumption. Furthermore, a fraction of young depositors is notified that they will relocate to the other location. Movers contact their local banks to withdraw cash. Finally, at the end of period t, relocation occurs and all old agents consume and die. Next, we study the behavior of each group of individuals. 2.1 Borrowers Borrowers do not receive income when young. Given that they value consumption in both periods of their life, they need to borrow in the credit market against their future income. In particular, a borrower in region i chooses to borrow li,t d units of goods which determines her consumption in period t, cb i,t.5 In the following period, a borrower receives her endowment, y, and consumes c b i,t+1 after paying back R i,tli,t d to her local bank. A typical borrower solves the following problem: Max c b i,t,cb i,t+1,ld i,t ( c b i,t ) β ( c b i,t+1 ) 1 1 (4) 5 As a simple benchmark, a borrower in region i views all loans from different banks in the same region are perfect substitutes. In addition, borrowers incur infinite switching costs if they choose to borrow in the other credit market. We relax this restriction in Section 5. 6

7 subject to: and c b i,t = l d i,t (5) c b i,t+1 = y R i,t l d i,t (6) Substituting the constraints into the objective function, the problem reduces to a choice of loans: Max l d i,t ( ) l d 1 ( i,t y Ri,t l d 1 i,t) + β 1 1 Therefore, individual loan demand is given by: li,t d y = R i,t + (βr i,t ) 1 (7) (8) which is strictly decreasing in the cost of credit. Moreover, given that the number of borrowers in each region is equal to one, (8) also reflects the aggregate demand for loans, L d i,t : L d i,t = l d i,t (9) Equivalently, the inverse demand for loans can be expressed as: R i,t R ( L d ) i,t Finally, (8) into (4), the maximized lifetime utility of a borrower yields: 2.2 Depositors u b i,t = L1 i,t 1 ] [1 + β (βr i,t ) 1 (10) (11) Each depositor residing in region i receives x i units of goods when born. Given that they only value old age consumption, all of their endowments go towards deposits in order to save. From the perspective of a depositor, each bank in the same region provides the same level of financial services. 2.3 A Typical Bank s Problem At the beginning of period t, each banker in region i announces deposit rates. Each bank takes the deposit rates offered by other financial institutions as given. Due to price competition in the local deposit market, the deposit market is effectively perfectly competitive. Therefore, each bank receives the same amount x of deposits, i λ. Throughout the analysis, x 1 in λ > x2 1N λ 2N, implying that banks are much larger in region 1 compared to region 2. 7

8 Furthermore, banks seek to maximize the expected utility of their depositors. In contrast to the deposit market, banks engage in Cournot competition in the credit market. That is, each bank chooses the quantity of loans, li,t s, taking the reaction function of other financial intermediaries as given. In addition to issuing loans, each bank chooses to hold a real amount of cash, m i,t to pay relocated agents. Therefore, the following balance sheet condition must be satisfied: x i λ i N m i,t + l s i,t (12) Returns to relocated agents are dependent on the amount of money balances that are held: P t π λ i N rm i,tx i = m i,t (13) P t+1 where r m i,t x i reflects payments made to a mover (her consumption). We study equilibria where money is dominated in rate of return. Therefore, the bank will not hold excess reserves and payments made to non-movers are financed from the revenue from loans: 1 π λ i N rn i,tx i = R i,t ( L d i,t ) l s i,t (14) Finally, given that depositors types (ex-post) are private information, the following incentive compatibility constraint must be satisfied: r n i,t r m i,t 1 (15) Otherwise, the bank will run out of cash reserves (triggering a liquidity crisis) as non-movers claim to be movers. In summary, a typical bank solves the following problem: Max r m i,t,rn i,t,mi,t,ls i,t π ( ri,t m x ) 1 i + (1 π) (r n t x) 1 1 (16) subject to (10) and (12) (15). Substituting the constraints into the objective function, the decision of the bank can be reduced to the choice of l s i,t : Max l s i,t ( π x i λ in ls i,t ) 1 ( λ in π ) 1 [ P t P t+1 + (1 π) λ in 1 (1 π) R ( ) ] 1 L d i,t l s i,t (17) subject to: L d i,t = L s y i,t R i,t + (βr i,t ) 1 λ in = ln,i,t s (18) n=1 8

9 Focusing on interior solutions, a bank s optimal choice of li,t s is such that the marginal benefit from issuing loans, denoted as MB ( li,t) s is equal to its marginal cost, MC ( li,t) s : MB ( ( ) [ ] li,t s ) 1 λi N = (1 π) (R i,t (L i,t) l i,t) R i,t L i,t 1 π L i,t li,t s li,t s + R i,t (19) and MC ( ( ) li,t s ) ( xi = π λ i N l λi N i,t π P t P t+1 ) 1 (20) The marginal cost of allocating one additional unit of deposits towards loans reflects lower payments to movers due to holding one unit less in cash. Obviously, the marginal benefit is the additional utility to non-movers. The term in solid brackets on the right-hand-side of (19), reflects a bank s degree of market power, with Ri,t < 0. Under perfect competition, R i,t L i,t L i,t l s i,t can be expressed as: [ L i,t L i,t li,t s = 0. Furthermore, it is easy to verify that the degree of distortion ] R i,t L i,t li,t s + R i,t = 1 L i,t l s i,t 1 R i,t + (βr i,t ) Nλ i β 1 1 R i,t + R i,t (21) which clearly suggests that if there are less banks in a particular region (lower λ i ), the degree of distortions will be higher in the market. In equilibrium, the demand for money balances by a financial institution operating in region i is: m i,t = π ( ) 1 Pt 1 π P t+1 λ i, N [ y 1+β 1 1 R i,1 1 R i,t+(βr i,t) 1 Nλ i 1+ 1 β 1 1 R i,t + R i,t ] 1 (22) which strictly decreases when the interest on loans is higher. In addition, banks hold more cash (for a given interest rate) when the degree of market power is bigger (the term in solid brackets is smaller). Furthermore, the relative return to depositors is such that: Equivalently: r n i,t r m i,t = 1 1 R i,t + (βr i,t ) Nλ i β 1 1 R + R i,t i,t 1 (Pt+1 P t ) 1 (23) 9

10 r n i,t r m i,t = 1 Nλ i β 1 R i,t β 1 1 R i,t 1 ( ) P t+1 R i,t P t For a given return on money, depositors receive less insurance when the return on loans is higher as banks hold less cash reserves. In addition, the expression for the relative return to depositors suggests that banks provide better insurance against idiosyncratic risk when they increase in size (lower λ). Notably, the Friedman Rule where both money and loans yield the same P rate of return, R t+1 i,t P t = 1, is not a feasible allocation when banks have market power in the credit market. This imposes a lower bound on the real return on loans for a given return on money. In particular, define R i,t : rn i,t ri,t m R i,t >> = 1, where Pt P t+1. The incentive compatibility constraint holds if the interest rate is at least as high as the lower bound, R i,t. Using (12), (17), (22), and (23), the maximized discounted expected utility of a depositor can be expressed as: u d i,t = π [ π 1 π y 1 1+β 1 Ri,t (1 ) ] 1 [ r n i,t r m i,t 1 ] π (24) π Clearly, depositors welfare is adversely affected when the amount of insurance received from banks is reduced ( rn i,t r is higher). i,t m 3 General Equilibrium We proceed to characterize equilibrium in the steady-state. A banking equilibrium( is characterized ) by a set of non-negative quantities, (m 1, m 2, l1, l2) and P prices, t P t+1, R1, R2, that clear the money and loans markets. Due to the presence of a single aggregate money market, the money market clears when : Equivalently: 2 m = λ i Nm i i=1 m = λ 1 Nm 1 + (1 λ) Nm 2 (25) Furthermore, imposing steady-state on the evolution of money, (2), the rate of money growth, σ is equal to the inflation rate, Pt+1 P t. In addition, using (12) and (22), the supply of loans by a bank in region i is: 10

11 l s i = x i λ i N π 1 π 1 σ 1 y 1+β 1 1 R i Nλ i [ β Nλ i Ri β 1 Ri 1 ] 1 R 1 i (26) In each region, there are λ i N banks. Therefore, the total supply of loans in a particular region is: L S i = x i π 1 π 1 σ 1 [ y 1+β 1 1 R i 1 1 Nλ i 1+β 1 Ri β 1 Ri while from (9), the total regional demand for loans is: L d y i = R i + (βr i ) 1 1 ] 1 R 1 i (27) Finally, denote the steady-state welfare in a particular region by W i with W i = u b i + ud i. In this manner, aggregate welfare, W is: W = 2 ( u b i + u d ) i i=1 (28) where u b i and ud i are respectively, (11) and (24) in the steady-state. We begin by characterizing the supply and demand for credit in the following Lemma: Lemma 1. i. dls i dr i > 0, lim R i LS i x i, and L S i (R i) = x i π 1 π ii. dld i dr i < 0, lim R i Ld i 0, and lim R i 0 Ld i. y 1+β 1 (Ri ) 1 σ > 0. The lemma states that the supply of credit is strictly increasing in R while the demand curve is downward sloping as illustrated in Figure 1 below. 11

12 Figure 1. Equilibrium In The Credit Market Proposition 1. Suppose y y, where y : R 1 = R 1. Under this condition, R 1 R 1, and a banking equilibrium exists and is unique. From our discussion of the bank s problem, a banking equilibrium requires the real interest on loans to be suffi ciently high in each region, R i R i. Given that the supply of credit is higher in region 1, the interest rate is lower compared to that in region 2. Therefore, banks are operating in both regions in equilibrium if banks in region 1 are active, which takes place when R 1 R 1. Therefore, in order for banks to be active in both regions, the demand for credit in region 1 must be suffi ciently high, y y. We proceed to discuss how variations in the distribution of banks size affect credit market conditions in the following proposition. Proposition 2. dli dλ i > 0, dri dλ i ( < 0, d r n ) i r i m dλ i > 0. The result in Proposition 2 indicates that as the relative number of banks in region 1 declines, financial intermediaries become larger and their ability to distort financial markets grows. Therefore, banks issue less loans and charge higher interest rates. Given that banks hold a more liquid portfolio if they are bigger, they also provide better insurance against idiosyncratic risk to their depositors. As depositors receive better insurance, their welfare is higher. By comparison, borrowers welfare will be adversely affected by the higher interest 12

13 rates. As a benchmark, in the absence of market power ( Ri,t L i,t L i,t l = 0), credit i,t s activity in each market is invariant to the size distribution of the banking sector. 4 The Optimal Size Distribution of the Banking System and Monetary Policy In this section, we study the optimal size distribution of the banking system. As the size distribution of banks across markets changes, the level of distortions in each market also change. Consequently, lower levels of distortions in large markets are commensurate with greater distortions in small markets. At the aggregate level, the net impact on the credit market depends on which distortion dominates. For example, if the biggest banks become even larger, total credit volumes are likely to decline because the relief in distortions generated by a large number of small banks won t offset the distortions imposed by the largest institutions. The optimal size distribution of the banking system balances the degree of distortions across markets. In order to draw further insight, we construct a numerical example with results in Table 1 below. The following parameters are used: x 1 = 800, x 2 = 200, y = 170, β = 0.95, π =.9, =.5, σ = 1.05, and N = 100. Notably, 80% of total deposits are concentrated in region 1 - the market with the largest intermediaries. When 80% of deposits are controlled by the largest 5 banks in the economy (which is actually less concentrated than recent observations by Janicki and Prescott, among others, mentioned in the introduction), the market is highly distorted and the credit volume is very low. As the size distribution changes due to an increase in the relative number of large banks, distortions in the largest market are relieved and credit market activity improves. The increase in consumption smoothing by borrowers in region 1 increases enough so that aggregate welfare across all markets also improves. However, when the number of large banks exceeds some threshold level, 60, adding more large banks into the economy adversely affects total lending and welfare. This takes place because the relief in distortions imposed by the large institutions does not offset the losses from increased concentration among the small banks. 13

14 Banks Region 1 Banks Region 2 L 1 L 2 L W λ Table 1. Banking Size Distribution, Lending, and Welfare In this manner, our results indicate that the optimal size distribution favors a large number of large banks. As large banks have access to a large deposit base, their ability to promote consumption smoothing and credit market activity is quite strong. By comparison, banks in small markets don t have access to the same level of resources in order to fund borrowers. Therefore, the optimal distribution favors relief in credit markets dominated by large institutions at the expense of distortions imposed by small institutions. Consequently, the welfare gains from the recent domination of large institutions in the United States and other countries are questionable. We proceed to study the effects of monetary policy in the following Proposition. Proposition 3. dli dσ dri > 0, dσ < 0, dii dσ r n d( r > 0,and ) m dσ > 0. The intuition behind Proposition 3 is straightforward. A higher rate of money growth reduces the value of money which stimulates bank lending. The higher supply of loans lowers their real yield. However, the nominal interest rate is higher. Furthermore, as banks hold a less liquid portfolio, they provide less insurance against liquidity risk. We proceed to answer the following question. Does the size distribution of the banking sector matter for monetary policy? For example, are the effects of monetary policy stronger if the economy is dominated by a small number of large banks? As we discussed above, the primary transmission channel of monetary 14

15 policy occurs through banks balance sheets (bank lending). We initially focus on a particular region by partially differentiating the supply of loans with respect to σ to obtain: Moreover: L S i σ = 1 1 σ π 1 π σ 1 [ y 1+β 1 1 R i 1 1 Nλ i 1+β 1 Ri β 1 Ri 1 ] 1 R 1 i > 0 L S i σ λ i < 0 From an individual firm s perspective, as the number of big banks increases, the marginal effects of monetary policy decline in region 1 and increase in region 2. However, as our results below demonstrate, this result is due to the fact that a bank has a smaller base of deposits to fund credit activity as the number of institutions changes. Consequently, monetary policy will not stimulate lending as much with a lower deposit base. In aggregate, however, the effects of policy work in the opposite direction. In particular, if the biggest deposit market is dominated by a small number of large banks, the credit market is also highly distorted as banks are holding too much cash reserves. Therefore, the demand for money is highly sensitive to price changes. The net impact on the aggregate credit market is ambiguous and should depend on the initial size distribution of the banking sector. Notably, the effects of monetary policy are weaker in a banking system that moves towards a small number of large institutions. However, this does not imply that policy is permanently more effective in stimulating aggregate credit market activity. If there is a large number of large banks, then credit activity funded by the smallest institutions becomes highly distorted which also clogs the standard monetary transmission channel. As an example, consider the parameters studied in Table 1. The impact of monetary policy is illustrated by an increase in the growth rate of money from 0 to 10%. Table 2 confirms our finding that bank size distribution has a non-monotonic impact on the effectiveness of monetary policy. λ dl 1 / dσ dl 2 /dσ dl/dσ Table 2. Bank Size Distribution and Monetary Policy 15

16 At low levels of λ, the effects of monetary policy are magnified when the number of large banks is relatively higher. Once the fraction of large banks exceeds 65% of total banks, raising the number of large banks weakens the effects of monetary policy. The analysis so far focuses only on the change in the volume of credit in response to a particular change in the rate of money growth. Notably, the results demonstrate that the impact of monetary policy is weaker in economies dominated by a small number of large banks. However, this does not necessarily imply that the monetary transmission mechanism is less effi cient. That is, the effi cacy of the monetary transmission mechanism should also take the initial amount of credit activity into account. To do so, we examine the elasticity of credit market activity with respect to inflation in relationship to the size distribution. Once the relative amount of lending in settings plagued by distortions from market power is taken into account, the strength of the transmission mechanism from policy improves. We proceed by constructing two numerical examples to address this issue. In contrast to the previous experiments which only focus on the relative proportion of institutions, the following numbers also highlight the size of the deposit base. For example, in Table 4, x 1 = 300 and x 2 = 200. In this manner, large banks in region 1 control 60% of total deposits in the economy compared to 80% in the previous example (Tables 1-3). Clearly when large banks initially dominate the credit market, the effects of monetary become stronger when the number of large banks increases as observed in Table 3. In contrast, the marginal effects of monetary policy are weakened when λ is higher if large banks are less dominant. λ σ %ΔL / %Δσ %ΔL / %Δσ %ΔL / %Δσ %ΔL / %Δσ Table 3: Effects Of Monetary Policy and Size Distribution: A System Dominated by a Small Number of Large Banks 16

17 λ σ %ΔL / %Δσ %ΔL / %Δσ %ΔL / %Δσ %ΔL / %Δσ Table 4: Effects Of Monetary Policy and Size Distribution: Large Banks Less Dominant 4.1 Optimal Monetary Policy In all of the previous analysis, the monetary authority s objective is to target long-run inflation. Therefore, in the steady-state, inflation is at its target and is treated exogenously. Instead, we choose to study optimal monetary policy in relationship to the size distribution of the banking system. That is, the inflation target is chosen to maximize the steady-state total welfare function, (28). Due to the complexity of this exercise, we are unable to proceed analytically. Therefore, we resort to numerical simulation. As a start, we follow our previous structure by assuming that seigniorage income is not rebated back into the economy. In this environment, inflation affects different agents asymmetrically. In particular, a higher rate of money creation directly reduces the welfare of depositors in both regions as they receive a lower amount of insurance against stochastic liquidity shocks. However, depositors welfare could increase as they are able to borrow more as credit gets cheaper under an expansionary monetary policy. Under a large set of parameters, marginal increases in the rate of money growth adversely affect total welfare. As a result, complete risk sharing is optimal. As we demonstrate in the appendix, the condition for existence can be written as a one on σ. In particular, define σ 1 1 such that complete risk sharing is achieved in region 1 which constitutes the lower bound on inflation for an equilibrium to exist. Moreover, σ 1 is strictly decreasing in λ and there exists a threshold level of λ, below which σ 1 > 1. Consequently, optimal inflation is zero when the number of large banks exceeds λ. In contrast, positive inflation is optimal when loans are highly concentrated in a small number of large banks. Subsequently, we assume that the central authority rebates seigniorage revenue in equal lump sum transfers to depositors in both regions. That is, in addition to their endowments, each depositor in every region receives τ 2 units of 17

18 goods from the government, where τ is defined in (3). Due to a larger deposit base in region 1, total money holdings are much larger compared to region 2. Therefore, a higher tax on money constitutes a transfer of resources from depositors in region 1 (large money holders) to those in region 2. In this manner, marginal rates of money growth can be welfare improving over a certain range. Interestingly, we show that the optimal rate of money growth is higher in an economy dominated by a small number of large banks compared to an economy with a higher number of large banks. In order to highlight this point, we construct the following example. Suppose N = 8000, x 1 = 500, x 2 = 400, y = 550, β = 0.99, π =.5, and =.25. We illustrate in Figure 2 the relationship between total welfare and the rate of money creation for two economies. In the first economy, the bank size distribution is symmetric (λ = 0.5). In the other economy, four banks operating in region 1 dominate the deposit market. Two important results emerge here. First, in low and moderate inflation environments, it is easy to see that the symmetric distribution of banks produces higher welfare since the credit market distortions imposed by the biggest banks are lower. By comparison, it takes a lot of inflation for a banking system dominated by a small number of institutions to generate higher welfare than a relatively symmetric number of banks. Second, the welfare-maximizing rate of money growth depends on the size distribution of banks. In particular, it is optimal to impose a higher inflation tax when the number of large banks is relatively small. In the example shown, the optimal rate of money growth is 13.12% when only four banks dominate the deposit market compared to 7.03% under a symmetric distribution. This occurs because banks in region 1 are holding an ineffi ciently high amount of cash reserves as they exploit their market power when they are very large. These results serve to indicate that optimal monetary policy should adjust to structural changes in the banking sector. 18

19 Total Welfare σ Welfare λ= Welfare λ=0.5 Figure 2. Welfare and the Effects of Inflation Across the Size Distribution 5 Large Banks Operate in Both Regions We proceed to extend our work by allowing credit to flow between both regions. To be specific, we permit large banks from region 1 to also issue loans to borrowers in region 2. 6 However, small banks in region 2 can only issue loans in their own region. This reflects the varying roles of large and small intermediaries in the banking system. For example, Tarullo (2009) describes how large institutions have geographically diversified in recent years and compete with small banks in local banking markets. As in our baseline model, banks in each region can only take deposits in their own region. However, given the large deposit base of intermediaries in region 1, there may be incentive to allocate some of the deposits from region 1 to the credit market in region 2. We begin by examining the problem of a typical bank that accepts deposits in region 1. Define l j i,t to be the amount of loans issued by a bank in region i to borrowers in region j. In this manner, a bank operating from region 1 has the following resource constraint in period t: x 1 λ 1 N = m 1,t + l 1 1,t + l 1 2,t (29) The constraint on payments to movers, (13), still holds. However, payments to nonmovers are now financed from revenue from credit issued in both regions: 6 We thank an anonymous referee for highlighting this point which resulted in this extension of our previous work. 19

20 x 1 (1 π) ri,t n λ 1 N = R 1,t (L 1,t ) l1,t 1 + R 2,t (L 2,t ) l2,t 1 (30) Finally, the incentive compatibility constraint, (15) must hold. A bank operating from region 1 sets its deposit rates, ( r1,t, m r1,t) n and makes its portfolio choice ( m 1,t, l1,t, 1 l2,t) 1 to maximize the expected utility of its depositors, (16) subject to (10), (13), (29), and (30). Upon substituting the binding constraints, the bank s problem reduces to the problem of choosing the amount of loans to offer in each market: π Max l1,t 1,l1 2,t ( x 1 λ 1N l1 1,t l 1 2,t ) 1 ( λ 1N π ) 1 [ P t P t+1 + (1 π) λ 1N (1 π) 1 As in the previous section, the bank s optimal choice of lending in each region is such that the marginal benefit from issuing loans is equal to its marginal cost. In particular the choice of lending in region 1, l 1 1,t is such that: ( R1,t (L 1,t ) l 1 1,t + R 2,t (L 2,t ) l 1 2,t) ] 1 ( ) ( ) 1 π x1 λ 1 N l1 1,t l2,t 1 Pt = (1 π) [( ] R 1,t (L 1,t) l1,t 1 + R 2,t (L 2,t ) l 1 )] [ R 1,t L 1,t 2,t P t+1 L 1,t l1,t 1 l1,t 1 + R 1,t (31) whereas the choice of loans issued in region 2, l2,t 1 is such that: ( ) ( ) 1 π x1 λ 1 N l1 1,t l2,t 1 Pt = (1 π) [( R 1,t (L 1,t) l1,t 1 + R 2,t (L 2,t ) l 1 )] [ R 2,t 2,t P t+1 (32) The intuition behind (31) and (32) is analogous to a bank s choice of credit derived in the previous section. Therefore, we omit any remaining interpretation behind the optimizing conditions. Together, (31) and (32) show that a bank from region 1 issues loans to depositors in both regions up to the point where the return on loans is equalized at the margin. That is, the following no-arbitrage condition applies: R 2,t L 2,t l2,t 1 + R 2,t = R 1,t L 1,t l1,t 1 + R 1,t (33) L 2,t L 1,t l 1 2,t l 1 1,t In this manner, large geographically diverse institutions from region 1 reduce interest rate spreads on loans across credit markets. In addition, upon using (10), (29), (32), and (33) the demand for money by a bank in region 1 is such that: ( R1,t l1,t 1 + R 2,t l2,t) 1 m 1,t = 1 π π [ ( R 2,t+(βR 2,t) 1 ) 2 ( 1+ 1 (βr2,t) 1 R 1 2,t )y l1 2,t + R 2,t ] 1 ( ) 1 Pt+1 P t (34) L 2,t L 2,t l 1 2,t l 1 2,t + R 2,t ] 20

21 Given that banks from region 2 only issue credit in their own region, the problem a typical bank solves in that region is identical to that in the previous section. Therefore we proceed to clear the credit market in each region. In particular, the credit market clears in region 1 when: L d 1,t = L s y 1,t R 1,t + (βr 1,t ) 1 by comparison, in region 2, we have: λ 1N = ln,1,t 1 (35) n=1 L d 2,t = L s y 2,t R 2,t + (βr 2,t ) 1 where l2,t 2 is such that: λ 1N = n=1 λ 2N ln,2,t 1 + n=1 l 2 n,2,t (36) ( ) 1 ( ) π Pt [ R2,tl2,t 2 ] [ x2 = (1 π) P t+1 λ 2 N R2,t l2 2,t ] L 2,t L 2,t lt 2 l2,t 2 + R 2,t (37) As large intermediaries actively participate in both credit markets, interest rates across the banking system are no longer geographically independent from the other region. In particular, the no-arbitrage condition from (33) shows that lending takes into account demand conditions across both banking markets. This additional aspect of market power in the banking system introduces additional complexity into our analysis where we are unable to proceed analytically. Therefore, we proceed to validate our previous findings numerically. However, as we illustrate in our numerical work below, the basic insights regarding the effi cacy of monetary policy from the segmented markets approach continue to emerge. Adopting the same parameters we used to construct Table 1 above, we repeat the same exercise from Table 5 below: 21

22 λ Banks Region 1 Banks Region 2 L 1 L 2 L W Table 5: Banking Size Distribution, Lending, and Welfare in the Presence of Geographic Diversification of Large Banks. In contrast to the results from the segmented markets approach shown in Table 1, the largest amount of lending takes place in the smallest market if large banks geographically diversify. As the second market provides another opportunity to generate revenues from the credit market, large institutions actively lend in both banking markets. As a result, diversification leads to higher levels of lending and higher welfare. Table 6 below continues to show that the effi cacy of monetary policy suffers if the size distribution favors a small number of large banks: λ dl 1 / dσ dl 2 /dσ dl/dσ Table 6. The Effi cacy of Monetary Policy in the Presence of Geographic Diversification of Large Banks. As the size distribution moves towards a smaller number of large institutions, the results indicate that monetary policy is less effective if the banking sector is more concentrated. Therefore, our analysis continues to demonstrate that the effects of monetary policy depend on the size distribution of the banking sector regardless of geographic diversification or segmented credit markets. 22

23 6 Empirical Results We now seek to look to empirical results to test the main assumptions and predictions of the model. First, a key aspect of our framework is that changes in the size distribution of the banking sector affect the amount of cash reserves held in the banking system. In particular, due to their desire to impose their market power in the credit market, intermediaries will hold relatively more cash reserves in concentrated banking sectors. Second, credit market activity will be lower in concentrated banking systems. As a result, the effects of monetary policy will be weaker in countries with a high degree of concentration. This is the third prediction that we seek to test empirically. Monetary policy is associated with a Tobin-type effect in our model where an increase in the rate of money growth leads to an increase in lending in the credit market. An increase in the rate of money growth leads to an asset substitution channel in which intermediaries switch from liquid assets to interestbearing bank loans. However, as intermediaries take into account that they face downward-sloping demand curves for loanable funds, the effects of money growth are weaker if banks have greater market power. Consequently, it is imperative that we study a relatively homogeneous group of countries in which it would be expected that money growth leads to an increase in credit market activity. For this reason, we study the connections between the effi cacy of monetary policy and banking concentration among the eighteen current members of the European Monetary Union. 7 Due to the relatively small group of countries that we study, we examine the role of banking concentration through panel regressions. Looking at the data using a panel approach takes time-series variation into account as well as country-specific unobservables. As a starting point, we begin by examining the prediction that concentrated sectors hold more cash reserves. To do so, we look at the behavior of bank liquid reserves to bank assets (LRBA) from the World Development Indicators of the World Bank. It measures the relative amount of domestic currency holdings and deposits with monetary authorities to assets of banks in a country in a given year. 8 As observed in Table 7, the number of observations varies across countries in the sample. More than half of the countries have ratios below 3%. The lowest ratio is observed in Italy at 1.38%. Only two countries have ratios 7 There are numerous other examples in the literature that stress the value of studying the impact of monetary policy across a relatively homogeneous group of countries. For example, Bullard and Keating (1995) point out that the effects of money growth may be qualitatively different in low inflation countries than high inflation countries. Furthermore, Ahmed and Rogers (2000) concentrate on the United States to investigate the impact of policy on economic activity and find evidence of a Tobin effect. Thus, it is reasonable to conclude the connections between monetary policy, banking concentration, and credit market activity are best examined across a similar group of countries. Furthermore, Ghossoub and Reed (2010) and Schreft and Smith (1997, 1998) develop rigorous theoretical frameworks to demonstrate that the effects of monetary policy depend on the stage of economic development. 8 World Development Indicators: FD.RES.LIQU.AS.ZS; Accessed May