Bank Capital Regulation in the Presence of Unregulated Competitors

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1 Bank Capital Regulation in the Presence of Unregulated Competitors David Martinez-Miera Universidad Carlos III de Madrid CEPR Eva Schliephake Harvard University University of Bonn May 2017 Abstract We analyze optimal bank regulation in a setup where regulated banks are confronted with competition from unregulated institutions. The appearance of unregulated competitors alleviates the (possible) contraction in loan access resulting from stricter regulation as borrowers gain access to alternative funding sources. This effect increases optimal regulation and the welfare of the economy. In contrast, with moderate market power of banks, increased efficiency in the unregulated sector can harm welfare and result in lower optimal regulation because market power may cause inefficient lending allocation under strict regulation. Keywords: Bank Regulation, Competition, FinTech, Unregulated Institutions We would like to thank Franklin Allen, Mike Burkart, Elena Carletti, Hendrik Hakenes, Robert Marquez, Fausto Panunzi, George Pennacchi, Sebastian Pfeil, Rafael Repullo, Paolo Siciliano, Javier Suarez and conference participants at the European Summer Symposium on Financial Markets in Gerzensee (2016) and the CEPR Conference on Competition and Regulation in Financial Markets (2017) for valuable comments and suggestions. C/Madrid 126, Getafe (Spain), Phone: (+34) ; dmmiera@emp.uc3m.es Center for European Studies at Harvard; 27 Kirkland Street, Cambridge, MA 02138; Phone: (+1) ; schliephake@fas.harvard.edu 1

2 1 Introduction The recent informational and technological revolution has altered the landscape of financial intermediation by affecting how loan granting decisions can be made. The availability of new information processing methodologies and new sources of information have allowed (new) institutions to enter the financing business even in the presence of informational asymmetries that previously prevented such institution from lending. As a result, commercial banks are challenged in one of their key functions for society, that of firm financing. New non-bank institutions, such as FinTech companies, have taken advantage and entered the business of granting loans to borrowers. These new companies have business models that are based on obtaining information from sources that traditional banks do not use and that have only recently become available. Examples of these sources are profiles from social networks, Internet activities and connections among different networks and users etc. The increasing efficiency of unregulated lending creates a threat to the business model of commercial banks which is based on collecting (insured) household deposits and reallocate the funds to borrowers. In doing so banks take advantage of the information they created during previous interactions with the borrower, which also allows banks to take advantage of the market power they have created. The appearance of these new FinTechs limit the scope in which commercial banks can continue to exert their market 2

3 power. Thereby, the new dimension of competition affects the amount of loans granted, the quality and quantity of information obtained as well as the overall loan allocation efficiency. This paper studies the new regulatory challenges imposed by this disintermediation of traditional financial activities, more specifically firm financing. The aim of the paper is to examine how the appearance and increased efficiency of new unregulated competitors in the financial sector, like Fin- Tech companies alters the optimal allocation of firm financing as well as how it changes the pre-existing competitive structure in the traditional banking sector. We study how the effects of an increased competitive intensity of unregulated entities depend on the competitive structure of the traditional (and regulated) banking sector. We extract conclusions regarding the welfare effects of an increase in efficiency of the unregulated sector and how this affects the optimal regulation of the traditional banking sector, focusing on capital requirements. Although the new competitors in firm financing are different from commercial banks in many different aspects, in this paper we are going to focus on three main differences: First, FinTech companies are not considered as banks by regulators, and therefore do not have to comply with certain regulations that banks have, for example, capital regulation. Second, FinTechs are not funded by insured deposits but rely on funds from uninsured investors. Third, FinTechs rely on information publicly available rather than information created by a relationship with the customer. 3

4 We first examine the similarities and differences between FinTech lending business models and commercial banks. We then characterize the asymmetric competition that arises because of these differences and explore how the aggregate loan provision is determined and what are the real effects for the economy. Taking the existence of a bank safety net and the according necessity to regulate commercial banks as given, we derive the optimal response of a welfare maximizer that regulates the commercial banks to an increase in the efficiency of the unregulated FinTech sector. In doing so we focus on how this response is affected by the competitive intensity in the regulated banking sector. Our results suggest that optimal capital regulation with unregulated Fin- Tech entities is complex and depends on the degree of regulated bank competition as well as on the relative efficiency of the unregulated entities compared to the regulated banks. As a result, the increase of efficiency of unregulated institutions can increase or decrease welfare. In response, the welfare optimizer should increase or decrease capital requirements depending on the actual situation of the economy. When unregulated entities become more efficient their capacity to attract borrowers from banks increases. This has two effects: on the one hand it increases the financing options for entrepreneurs, which can lead to more loans being granted, but it also can distort entrepreneurs financing decisions. As FinTech become more efficient entrepreneurs have the option of switching from their (more expensive) bank finance to FinTech finance. This happens 4

5 because banks extract rents from entrepreneurs but is not necessarily the optimal way credit should be granted as it could be that overall the FinTech industry is less efficient for some of the entrepreneurs that switch. We show that the competitive intensity of the banking sector as well as the relative efficiency of the FinTech industry determine which force prevails. We want to highlight that the potential negative effects of more efficient FinTech companies in imperfectly competitive banking is more general than our model setup. We base our model on an existing safety net and the resulting need for capital regulation in order to analyze the effect of FinTech competition on optimal bank capital requirements. However, the effect of inefficient allocation of credit supply does not depend on these assumptions. We could also focus on other types of regulations in order to analyze how to reduce the effects of FinTech companies on welfare and regulation. For the ease of exposition, and in order to give an idea of the main driving forces of the model, we present the setup with capital requirements and deposit insurance as we consider them as the most discussed and therefore relevant aspects of banking regulation. The focus on understanding how the competitive structure of the banking sector affects the loan allocation and welfare as well as the optimal regulation is shared by a long standing literature in finance. A broad stream of literature argues that higher competition is supposed to have an adverse effect on bank stability as less bank rents increase the incentives for risk taking as discussed e.g. by Hellmann, Murdock, and Stiglitz 5

6 (2000), Repullo (2004) and Allen and Gale (2004)). Boyd and De Nicolò (2005) challenge this view by arguing that higher competition leaves more rents to borrowers and reduces therefore the risk of the bank s assets. Martinez- Miera and Repullo (2010) extend the Boyd and De Nicolò (2005) model and show that the impact of competition on banking stability is generally nonmonotonous. The effect of capital regulation on bank stability is also non-monotonous for similar reasons as pointed out by Martinez-Miera (2009). In fact, the level of competition among traditional banks may be an important moderator in how regulation is transmitted into bank stability as shown by Schliephake (2016). Our study is related to a more recent literature analyzing the impact of capital regulation and its interaction with unregulated entities. Plantin (2014) analyzes the effect of capital regulation on banks business models when they are able to create unregulated institutions (shadow banks). The optimal response to the regulatory arbitrage can be to tighten capital requirements. This makes banks that are not bypassing regulation by shadow banking activity very safe but at the same time stricter regulation triggers higher higher shadow banking activity. In contrast the regulator may prefer to relax regulatory capital requirements with the result of a more fragile banking sector but also less shadow banking. We deviate from the main setup of Plantin (2014) and analyze a setup in which unregulated banks are competitors of banks but are not necessar- 6

7 ily owned by the banks themselves. This allows us to understand different competitive pressures on the banking sector that come from non-banks and allows for novel insights regarding the welfare impact of such institutions. Moreover, we are focusing on the asset side of the bank and unregulated bank competition, thereby allowing unregulated institutions to fulfill an important role in the economy as they fill the void that banks may leave in the loan market when they are strictly regulated. Harris, Opp, and Opp (2014) analyze a general equilibrium model where competition from public market funding alters bank lending rents and can therefore push banks into higher risk lending. This effect induces a nonmonotonic relationship between regulatory capital requirements and banks risk taking. In an extension where we allow for bank risk shifting, our model yields similar results. However, our basic result: the non-monotonic relation between optimal capital regulation and non-bank competition however, is not based on higher risk taking but on constrained bank lending and lending efficiency. The idea that regulation restricts bank investments is also the starting point of a paper by Ordonez (2013). In this paper, however, the bank s future reputation as the main driver of his results. The idea is that shadow banks depend on market funding and therefore have to build up a good reputation, in contrast to deposit funded bank that rely on insured funds. In order to keep a good reputation shadow banks self-regulate and invest more efficiently. Therefore the appearance of shadow banks increases welfare. However, as 7

8 shadow banks highly depend on their reputations they are also very fragile to concerns about their reputation. Therefore, doubts about future prospects may lead to a collapse of shadow banking and a return to traditional banking. To our knowledge, this is the first study that tackles how regulation should react to the existence of new unregulated competitors taking into account the competitive intensity in the banking industry. 2 Model Setup We assume a static economy with two dates indexed by t = 0, 1. There are four types of risk neutral agents in the economy: investors, entrepreneurs, financial intermediaries and regulator. 2.1 Investors Investors are atomistic, have deep pockets and have the possibility of holding their endowment in cash, which yields 1 for each dollar invested. They can also decide to lend their money to financial intermediaries. For unmodelled frictions we assume that investors, however, cannot fund entrepreneurs directly. It should be noted that we could think that an investor can lend directly by converting himself into a FinTech which would capture direct or P2P lending platforms. For ease of exposition we leave this interpretation aside. 8

9 2.2 Entrepreneurs Entrepreneurs have no own funds but have access to risky investment opportunities. If entrepreneurs receive outside funding they can invest one unit into a risky project. The project is successful with probability 1 p and returns in that case 1 + α, with probability p the project fails in which case only 1 λ can be extracted from the project. Entrepreneurs are limited liable. We assume that there exist two types of entrepreneurs in the market. Bad entrepreneurs have access to projects with success probability p = p l = 0. Good entrepreneurs have success probabilities p = p h > 0, i.e., their projects have positive net present values. In order to obtain funding, good borrowers have to convince investors that they are of good type with the help of banks or FinTech companies. Importantly we assume that the the type of the entrepreneur is private knowledge. 2.3 Financial Intermediaries Our model aims to capture three main differences between commercial banks and other financial intermediaries. First, both kinds of institutions use different sources of information and technologies to overcome asymmetric information between the lender and borrower. Second, both institutions have different sources of funding and accordingly different funding costs. Third, and closely related to the different funding sources, banks are capital regu- 9

10 lated while other financial intermediaries are not. Banks If the financial intermediary is a (commercial) bank it is allowed to collect insured deposits from investors and provides loans to entrepreneurs at a loan rate r. A bank is covered by limited liability. Hence, in case of insolvency the bank owners receive zero, but outstanding liabilities to depositors are covered by the deposit insurance fund with an deposit insurance premium normalized zero. Therefore, deposits are safe and investors are willing to lend to a bank if 1 + r D 1 r D 0. As investors have deep pockets, the supply of funds is perfectly elastic such that r D = 0. If a bank defaults, it is liquidated and the residual asset value of the bank s investment is collected by the deposit insurance. Banks are regulated with minimum capital requirements: at least a fraction ˆk of bank funding has to be bank equity. An investor that invests in banks equity receives positive cash flows only if the bank is not liquidated. Let p be the probability that the bank asset s default, then the indifference condition of an investor providing equity is the following: (1 p) (1 + r E ) (1 + r D ) = 1 (1) Banks, therefore have to promise the investors a return rate on equity of: r E = p 1 p (2) 10

11 Given the implied subsidy of deposit insurance, bank equity funding is dominated by deposit funding. Hence, in this simple setup, bank capital regulation will be binding k = ˆk. 1 In the basic setup, we take the amount of banks competing in the banking market, n as exogenous. It is in our research agenda to endogenize how such number would vary in equilibrium. One way to do so would be to acknowledge the fixed costs that creating a bank has. Unregulated intermediaries If the financial intermediary is not a bank it does not have access to deposit funding covered by deposit insurance but it is also not subject to bank regulations. Without any regulation or entry restriction in the FinTech sector, it is reasonable to assume that there is perfect competition among FinTech companies such that they make zero-profits. The financiers of FinTechs become residual claimants of the asset value in case of default. Informed investors foresee the risk of the loss given default and are willing to invest if their expected return equals their outside option of investing in deposits at a bank. Denote with µ F the cost of a FinTech to analyze data of a particular customer. The participation constraint of investors becomes (1 p)(1 + r M ) + p(1 λ) µ F 1 (3) 1 A fully equity funded bank would not face any default risk, such that the required return on equity would equal the return on safe deposits. In order to exclude fully equity funded banks we could assume different tax treatments of equity and debt. 11

12 Hence, we obtain that the minimum loan rate that a FinTech can offer and still break even would be r M = pλ µ F 1 p (4) 2.4 The Regulator The regulator in our setup sets capital requirements and provides deposit insurance to regulated banks. If banks fail, they cannot repay their liabilities to depositors and the deposit insurance has to step in. We do not model why the regulator wants to provide such a deposit insurance but rather take it as given. 2 In our simplified setup, the deposit insurance has to cover the bank s shortfall on liabilities (λ k) with probability p. We assume that the cost covering the bank s liabilities in case of bank default is costly ψ > 1 and proportional to the extent of bank failure. This could reflect the cost of raising a distortionary tax to cover for deposit insurance. Per unit of bank s failed asset investment the expected cost of covering the liabilities in case of failure are p Ψ(λ k). 2.5 Information Technology We assume that both good and bad entrepreneurs generate a random signal about their quality. This signal has (at least) two components: one com- 2 We could introduce introduce inefficient bank panic runs in the sense of Diamond and Dybvig (1983) to micro-found the safety net in a more complicated model. 12

13 ponent is based on the daily bank activity of the entrepreneur and another component that has to do with the public information that the entrepreneur generates and that banks do not use. There could be another third component that could include all publicly known information to both types of financial intermediaries. For simplicity we are going to assume that there are only two components of the signal a bank intensive component and a Fin- Tech intensive component. This would be akin to stating that each borrower generates two types of signals. The crucial assumption is that some of those signals are deposit based and banks are specialized in receiving them. Other types of signals are non deposit based and FinTech companies are specialized in interpreting them. Bank Specific signal The signal that a good borrower i generates for a bank j is s i,j = g + ε i,j (5) Where ε i,j is a random variable with support [ε, ε]. A bad borrower generates a signal s i,j = δg + ε ij. (6) Where δ takes the value 1 with probability q and 0 with probability 1 q. As before ε i,j is a random variable with support [ε, ε]. We assume that the amount of bad borrowers in the economy is suffi- 13

14 ciently large so that it does not pay to give a loan to any entrepreneur if signals are not used. 3 Good borrowers have the possibility of exerting some private effort in order to improve the signal they generate s i,j (e) = g + e + ε i,j at a cost µ per unit of effort. We assume that this effort is unobservable by the financial intermediaries and investors but the borrower knows the signal he produces for each type of intermediary. In order for a borrower to signal that he is of type good, he has to exert an effort e i = g + ε (g + ε i,j ) = ε ε i,j. Hence entrepreneurs that have the luck of being correctly read by the bank have to exert no effort but in principle all firms have to exert some effort that is increasing in how bad the bank analyses it, this would be the distance of asymmetries of information. Considering the correlation of ε i,j across banks we will show that the optimal strategy of banks is to choose a technique that generates negatively correlated errors to the signals already present in the market. This choice of technology is optimal as it grants each bank the highest market power. Such a technology can then be depicted in a traditional spatial competition model in the spirit of Hauswald and Marquez (2006). In contrast to the aforementioned study, the entrepreneurs and not the banks have to bear the signaling cost in our model. This could reflect additional effort of the entrepreneur to convince his banker of his good project such as writing a 3 We could relax this assumption or assume that bad firms can loot a fraction of the money they receive and then there would be a different threshold than the one we will have. 14

15 detailed business plan or acquiring costly collateral. In particular, let the continuum of borrowers with mass normalized to 1 be uniformly distributed along a circle with circumference 1. The n banks are allocated equidistantly on this circle. We assume that the quality of the deposit based signal is decreasing in the borrower s distance x i to a particular bank. As a result, the effort that a (good) borrower has to exert in order to receive a loan is also increasing in its distance to the bank. This specification captures the idea of the comparative advantage that commercial banks have for their closest customers over other institutions: Due to a close or long term relationship with their customers they are able to produce better information at no additional cost. However, this informational advantage is reduced as banks seek to transact with customers located further away representing less frequent interactions with the customer or shorter relationships. We define ϑ i,j = ε ε i,j to be a parameter that represents the effort that the (good) borrower i has to spend in order to overcome the informational distance bank j. In order to qualify to receive a loan from bank j the borrower i therefore has to pay the cost µϑ i,j. FinTech Information Creation: Despite generating a signal for their relationship bank, entrepreneurs also generate signals by running their business that can be read by the financial market, i.e., FinTech companies specialized on analyzing these signals. However we assume that the FinTech companies 15

16 have a cost µ F of processing the information. 4 Hence, parameter µ F determines the relative efficiency of the FinTech sector compared to the banking sector. The signal that a good borrower i generates for a FinTech j is h i,j = g h + ε i,j where ε i,j is a random variable with support [ε, ε]. A bad borrower generates a signal h i,j = δg h + ε i where δ takes the value 1 with probability q and 0 with probability 1 q. As before ε i,j is a random variable with support [ε, ε]. The borrower can receive finance from the FinTech sector by exerting an effort e i = ε ε i,j. We assume that FinTech companies are perfectly competitive, and there exist an infinite number of them. Hence, the good entrepreneur does not need to exert any effort to signal his quality as he receives offers from at least one FinTech company. Although the assumption of perfectly competitive FinTech companies is extreme, we conjecture that the main trade-offs of the model are not qualitatively altered by this assumption. We could relax the assumption and allow for imperfect competition due to some infinite number of FinTech companies. This would imply positive effort cost for borrowers but not fundamentally alter our core findings. Figure 1 provides a summary of the model setup. Note that the asymmetric information on the type of entrepreneur induces a cost for both ways of borrowing. Bank lending requires borrowers to spend additional effort to convince their relationship bank of their good type. FinTech lending requires 4 We could also assume that banks have a cost µ B which we normalize to 0. 16

17 Figure 1: Commercial Bank Lending in competition with FinTech lending to scan and analyze huge amounts of data. We are able to differentiate between commercial lending and FinTech lending in a crucial way by capturing this asymmetric nature of competition between these different business models. Banks possess an informational advantage over their closest relationship customers compared to FinTech companies. But this advantage fades with the distance to their customers. Hence, banks enjoy only local market power over their closest customers and compete for further away customers increasingly intensively. FinTech companies on the other hand do not have this informational advantage. However their information technology does not depend on the distance to the customer but rather on the efficiency information acquisition technology. 17

18 3 Equilibrium In equilibrium good borrowers either receive a loan from a bank, from a FinTech or no loan at all if their utility from borrowing is negative. 5 If entrepreneur i receives a loan from a bank j his utility depends on the rate r j and the effort he has to exert to signal that he is a good borrower which can be interpreted as his distance ϑ i to the bank: U B (r, ϑ i ) = (1 p)((1 + α) (1 + r)) µϑ i (7) Alternatively, the same borrower can borrow from the FinTech sector at r M defined in equation (4) and obtain: U F = (1 p)(α r M ) = (1 p)α pλ µ F (8) As banks have market power they set the loan rates in order to maximize their own profits under the constraint of the competitive pressures from other banks and the FinTech sector. In particular, banks maximize the following objective function: Π(r) = l(r, n, µ F ) [(1 p)r kp.] (9) Where l(r, n) is the demand from good entrepreneurs that want to borrow from the bank at interest rate r. The one sided loan demand for bank j 5 Based on our assumptions only good entrepreneurs are able to obtain financing. 18

19 implicitly defined by the borrower at a distance ˆϑ that makes him indifferent between borrowing from bank j and his highest outside option : [ U i (ϑ i ) = max U B (r y, 1 ] n ϑ i), U F, 0 (10) Given the relative efficiency of the FinTech sector µ F, the level of bank competition n then determines three different market structures in which the efficiency of FinTech competition has different effects. 3.1 Low bank Competition: With very low levels of competition among banks i.e., n <n = µ (1 p)α some borrowers would get negative utility from bank loans and therefore not borrow from a bank. If FinTechs become more efficient in providing loans it becomes an attractive alternative for all potential borrowers that are not provided with bank loans. Moreover, non-bank lending also becomes attractive to a proportion of the most distant borrowers to the banks. With low bank competition, the indifferent borrower for bank j is determined by: ˆϑ(µ F ) = (1 p) (α r) µ [ ] UF max µ, 0 (11) The bank then chooses an interest rate to maximize its objective function, 19

20 taking regulation k and FinTech efficiency µ F as given. Π(r) = 2ˆϑ(µ F )) [(1 p)r kp] (12) The loan rate that maximizes this objective function is respectively: r (k) = 1 ( ) (δ + p) α + k 2 (1 p) [ 1 max 2 ] U F (1 p), 0 (13) Accordingly, the commercial bank with local market power makes the following profits: [ ] 1 Π(µ F, k) = 2ˆϑ F (rf (k)) 2 ((1 p)α k p) max(1 2 U F, 0) (14) The increase in FinTech efficiency in the low bank competition setup has several effects on borrowers. The borrowers that stay with the bank gain from the increased competition since they receive better loan conditions than before, while overall less borrowers demand a loan from commercial banks. This decreases also the aggregate effort that borrowers spend on receiving loans. The aggregate utility of borrowers that obtain loans from banks is: 2 ˆϑ(µF ) 0 ( ) 1 U B (r (µ F ), ϑ i )dϑ = 2ˆϑ(µ F ) 2 ((1 p)α k p + U F 2 ˆϑ(µF ) 0 (15) µϑ dϑ In case of default of the bank s assets the deposit insurance has to step 20

21 in. The expected deposit insurance costs per bank vary with the size of the banking sector and the competition of FinTechs and can be summarized as: DI = p 2 ˆϑ(µ F ) Ψ(λ k) (16) The welfare in our economy with low bank competition can be summarized as: W (k) = 2 n ˆϑ(r (k) ((1 p)α k(p + δ)) }{{} Ψp(λ k) }{{} successful production net bank default cost [( ) ] + max 1 2 n ˆϑ(r (k)) U F, 0 } {{ } FinTech borrowing ˆϑ(r (k) µϑ i dϑ 0 } {{ } traveling cost (17) (18) A regulator that aims to maximize welfare has to set optimal capital requirements. He thereby considers that a marginal increase in capital requirement reduces negative externalities of bank default but also reduces the production if FinTech are not competitive. In contrast, an increase in capital requirements with efficient FinTech competition decreases bank profits and the proportion of production funded by FinTech companies but not the overall production. 21

22 Equilibrium with n = 1 Figure 2: With low bank competition, welfare and optimal capital regulation are monotonically increasing in FinTech efficiency (lower µ F ). k (Ψ) = 0 if Ψ < Ψ min F k λ if Ψ min F if Ψ > Ψ max Ψ Ψ max (19) With k = λ µ SB( 3 2 ψ) p(2ψ 3 2 ) (20) pλ+µ F Where Ψ min 3 and 2 (2pλ+µ F ) Ψmax 3 define the social cost of bank failure 2 that result in corner solutions for the welfare optimal capital requirement given the reasonable constraint of k [0, 1]. Proposition 1 If bank competition is low, FinTech competition increases welfare. 22

23 Proof [tba] The intuition is the following: for low n not all borrowers receive a bank loan such that the welfare maximizer trades-off more lending versus higher bank default cost. When FinTechs appear, non-bank lending extends production. Therefore, the welfare maximizer can set higher capital requirements without fearing a decrease in production. Welfare increases as a result because at the same level of production is reached at lower cost of bank failure. 3.2 High Bank Competition If bank competition is sufficiently high i.e., n > n = µ µ F all borrowers receive an attractive loan offers from the closest bank for any level of capital requirements. As a result, each bank now competes with the neighboring bank or a FinTech for the customers allocated between them. As all borrowers receive a bank loan the welfare becomes: W (k) = ((1 p)α k(p + δ)) }{{} Ψp(λ k) }{{} successful production net bank default cost 1 2n 2 n µϑ i dϑ } 0{{ } traveling cost In this case a marginal increase in capital requirement reduces the social cost of bank failure without reducing production. Therefore, the regulator does not face a trade-off and sets capital requirements optimally at the highest level necessary to minimize the deposit insurance cost to zero: k (Ψ) = λ (21) 23

24 The pressure of FinTech competition, when banks are fairly competitive, puts an additional constraint on the profits of banks as it increases the outside option of borrowers. In particular, more efficient FinTechs put an upper bound on the loan rate banks could charge to borrowers and thus decreases the price setting power of banks. This reduces bank profits and increases the borrower surplus but the welfare remains unaffected as long as n > n = µ µ F. Note however, that the reduction in bank profits may have an impact on bank s endogenous risk choices that we have neglected so far but will be discussed in further analysis. 3.3 Medium Bank Competition For the number of banks in the interval between the identified critical values n (n, n) some entrepreneurs do not receive a loan when regulation is too high. The regulator now faces the following trade-off: ( ( 1 2n ˆϑ(µ ) ) 1 ( 2n F ) µ F 2n µϑ dϑ 1 2n ˆϑ(µ ) F ) [(Ψ 1) p (λ k) ] ˆϑ(µ F ) }{{}}{{} DI Costs InformationAcquisitionCost (22) If FinTech lending inherits substantial information production costs compared to the marginal bank loan, the welfare maximizer would like to preserve bank lending despite banks inherent failure cost. He can secure that 24

25 all lending is provided by banks with capital requirements lower or equal to: k crit = µ F + pλ µ n p (23) If the bank failure cost is low compared to the FinTech cost of data production the welfare maximizer sets capital requirements up to the point in which k = k crit. However, if the failure cost of banks is high, the welfare maximizer prefers to increase capital requirements and allows thereby some FinTech lending. The optimal regulation with intermediate bank competition is k (Ψ) = k crit if Ψ < Ψ crit = k 3µ 2(2µ µ F n) if Ψ crit Ψ Ψ max λ if Ψ > Ψ max = 3 2 (24) Proposition 2 For intermediate bank competition, the welfare effects of FinTech companies is non- monotonic and depends on the level of bank n and the relative efficiency µ F. dw (k ) dµ F 0 (25) Proof [tba] If banks are relatively efficient but bank competition is not high enough, the competition from FinTech companies can actually decrease welfare. Borrowers may want to switch to FinTech despite paying higher 25

26 Equilibrium with n = 3 Figure 3: With medium bank competition, welfare and optimal capital regulation are not monotonically increasing in FinTech efficiency. information acquisition costs µ F instead of µϑ i because they pay lower loan rates that compensate for the switch. This harms welfare as loan rates are just allocating welfare while higher information acquisition cost reduce welfare in the aggregate. We illustrate our key result in Figure 3. The less efficient the FinTech is relative to bank information acquisition, the more inefficient borrower switches harm welfare. However, if FinTech lending is very inefficient then FinTechs are not able to attract borrowers and therefore do not affect welfare. 3.4 Policy Implications The presence of FinTechs alters the optimal capital regulation as it alters the trade-offs faced by the regulator. This is depicted in Figure 4. On the one hand, FinTech competitors allow the regulator to tighten capital 26

27 Figure 4: The optimal regulation in dependence of FinTech efficiency and bank competition. requirements as an increase in capital requirements is less detrimental for the economy s level of production. By increasing capital requirements some loans are not granted by banks but in the presence of competitive FinTechs these loans are granted by FinTechs instead, which reduces the social cost of higher capital requirements. This intuition is the driving force in a setup in which the banking sector is characterized by high market power of banks. In such setting, welfare increases when competitive FinTechs enter the economy and how capital requirements increase as a response to such entry. However, when banks are fairly competitive this intuition does no longer hold as the banking sector is already granting a high amount of loans (even full production can be reached). In such cases the appearance of competitive 27

28 Figure 5: The welfare effects of higher FinTech efficiency depending on the level of bank competition. FinTechs makes some borrowers shift to FinTech. If banks are not highly competitive, the switch of borrowers may be inefficient as borrowers do not only consider the cost of information generation, but also the pricing schedule offered by banks and FinTechs. In this situation it can be that the higher prices of banks given their market power (and their regulation) could off-set the higher information generation cost that some borrowers face if they go to FinTechs. In such situation the welfare maximizer can find it optimal to reduce capital requirements, so that banks lower their price and borrowers find it less tempting to take a loan from the FinTechs. In this case, competitive FinTechs entering the economy result in lower capital requirements and 28

29 lower welfare. We show how this situation is most prone to arise for medium bank competition. These results are depicted in Figure Further Analysis Endogenous entry In an extension, we aim to show how the number of banks competing depends on a certain fixed cost and the level of regulation. We can think that such fixed cost is the cost of complying with regulation, e.g., hiring lawyers that make sure that you comply and paying them some wages. This cost would therefore not decrease welfare as it would be a transfer. In the long run, where banks can enter and exit the market, the appearance of FinTech companies that decreases the profits of banks, would decrease the number of competitors active in the market. The negative impact on the bank market could then push the market structure from high to medium or low competition. If the FinTech competition pushes the number of banks from the high competition to the medium competition, welfare could be harmed by the lowering of bank competition despite the increased competition of FinTech companies. 29

30 Financial Stability: Endogenous Risk Choice and Imperfect Correlation The basic model setup considers only one role of regulatory capital: the reduction of loss given bank default as a burden to the deposit insurance and negative externalities from raising tax-holders money in order to cover these losses. However, equity has a much more fundamental role for bank stability: higher equity funding increases the stability of banks by reducing the states of nature in which the bank becomes insolvent. Martinez-Miera and Repullo (2010) show that this has important implications for the relationship of bank competition and stability without considering the competition of unregulated institutions. In the simple setup of our model this role of equity is not reflected because there are only two states of nature. We can extend our model and assume that banks can diversify idiosyncratic risks but are subject to systemic risk. In particular, we can assume that each bank faces a certain share x of defaulting loans in its portfolio. This share x is a random variable distributed in [0, 1] with a cumulative probability function F, which may depend on idiosyncratic risk p and systemic risk factors. 6 6 The relationship between idiosyncratic and systemic risk and the role of correlation of asset defaults are usually modeled in a Single- Risk factor copula model. However, since we are not interested in the role of correlation nor in the particular idiosyncratic risk choice we assume that asset defaults are random and exogenous. See Martinez-Miera (2009) and Schliephake (2016) for a detailed discussion of capital requirements and bank failure risk with imperfectly correlated assets and endogenous idiosyncratic risk choices. In a general model, the idiosyncratic risk would shift the distribution in such a way that distributions of x with lower probabilities of defaults p should stochastically dominate those with higher idiosyncratic risk. However, to keep the model simple and the results tractable we assume 30

31 Given a certain realization of x a particular bank is insolvent if the returns from non-defaulting loans does not suffice to repay outstanding liabilities ((1 x)(1 + r) + x(1 λ)) l(r) < (1 k)l(r) (26) The aggregate share of defaults that a bank can survive is: ˆx(k, r) = r + k (r + λ) (27) For k [0, λ) this critical default rate is increasing in the capital requirement and the loan interest rate. In such an extension, the welfare effect of FinTech competition is, again, non-monotonic and depends on µ F compared to the bank sector competition. However, the additional negative effect of the entrance of FinTech on bank profits implies that the efficiency of FinTech companies must be higher than in the benchmark model to increase welfare. 4 Conclusion This paper undergoes an analysis of bank capital regulation in the presence of competition between banks and unregulated entities. We show that when competition from unregulated entities increases, optimal capital requirements can increase or decrease. that x is exogenous and uniformly distributed in [0, 1]. 31

32 On the on hand, in contradiction to common wisdom, an increase in competition from unregulated entities can result in a decrease of social welfare if the level of competition in the banking market is high enough. In order to limit this loss of welfare bank regulators should reduce capital regulation. On the other hand, if the level of competition among banks is low an increase in competition from unregulated entities leads to higher optimal capital requirements and results in higher welfare. This non-monotonic results highlights the need of a better understanding of the underlying trade-offs regarding bank capital regulation, regulatory arbitrage and social welfare. References Allen, F., and D. Gale (2004): Competition and Financial Stability, Journal of Money, Credit and Banking, 36(3,2), Boyd, J. H., and G. De Nicolò (2005): The Theory of Bank Risk Taking and Competition Revisited, The Journal of Finance, 60(3), Diamond, D. W., and P. H. Dybvig (1983): Bank Runs, Deposit Insurance, and Liquidity, Journal of Political Economy, 91(3), Harris, M., C. Opp, and M. Opp (2014): Macroprudential bank capital regulation in a competitive financial system, Unpublished working paper, 32

33 University of Chicago, University of Pennsylvania, and University of California, Berkeley. Hauswald, R., and R. Marquez (2006): Competition and strategic information acquisition in credit markets, Review of Financial Studies, 19(3), Hellmann, T. F., K. C. Murdock, and J. E. Stiglitz (2000): Liberalization, Moral Hazard in Banking, and Prudential Regulation: Are Capital Requirements Enough?, The American Economic Review, 90(1), Martinez-Miera, D. (2009): Capital Requirements and Bank Failure, CEMFI-UIMP PhD Dissertation. Martinez-Miera, D., and R. Repullo (2010): Does Competition Reduce the Risk of Bank Failure?, The Review of Financial Studies, 23(6669), Ordonez, G. (2013): Sustainable shadow banking, Discussion paper, National Bureau of Economic Research. Plantin, G. (2014): Shadow banking and bank capital regulation, Review of Financial Studies, p. hhu055. Repullo, R. (2004): Capital Requirements, Market Power, and Risk- Taking in Banking, Journal of Financial Intermediation, 13(2),

34 Schliephake, E. (2016): Capital Regulation and Competition as a Moderator for Banking Stability, Journal of Money, Credit and Banking, 48(8),