Good Co(o)p or Bad Co(o)p? Redistribution Concerns and Competition in Credit Markets with Imperfect Information

2.1 Financial NPOs in Historical Perspective

Financial NPOs have a long and well-established tradition in the history of advanced economies (Butzbach and Mettenheim 2014, 2015). In the U.S. the number of banks has dramatically increased after the Second World War within a rapidly growing economy and a regulatory framework which strongly opposed the creation of monopoly rents in the banking industry. While this trend has almost reverted in the last decades, member-owned credit unions as well as small non-profit community lenders continue to operate in specific geographic areas and urban districts next to profit-oriented commercial banks. Given their strong links with local communities and institutions, community lenders typically offer financing and other services to business owners based on repeated interactions with their borrowers (relying on the reputation of the owners) and other relational lending practices, which help mitigate hidden information issues and thereby facilitate access to credit for under-served groups (e.g. Berger and Udell 1995, 2002; Petersen and Rajan 1994).

Originating in local areas at the turn of the 19th century, credit cooperatives and saving banks were founded to favor access to credit for the rural poor and working-class people along the industrialization process, e.g. the Raiffeisen and Schultz-Delitz credit cooperatives in German-speaking areas (Guinnane 2001, 2002); other public and cooperative credit associations pursuing mutualistic aims sprang up across francophone countries over the same years.

While still playing a role in overcoming financial exclusion of population groups who would otherwise have no access to affordable credit, in most advanced economies financial cooperatives compete vis-à-vis other types of financial institutions, e.g. commercial banks, in providing funding to retail customers and to small and medium-sized enterprises. Over the last decades, drastic regulatory changes and the process of financial innovation in the U.S. and most European countries allowed several types of financial NPOs to expand the scope of their operations across financial services and beyond local markets. Nowadays, cooperative banks and credit cooperatives make up a large share of the financial industry in several jurisdictions, oftentimes coordinating in federations and networks with shared solidarity schemes (Ayadi et al. 2010).^[3]

2.2 Banks, Information and Redistribution

Modern banking theory situates for-profit commercial banks within a market-based frame, according to which such financial institutions go well beyond collecting deposits and originating loans — i.e. intermediating financial resources; for they generally engage in a wide range of sophisticated operations (such as trading assets and offering insurance products) and spread and diversify risk invoking the law of large numbers in the presence of market imperfections (e.g. Battacharya and Thakor 1993). Credit cooperatives and other financial NPOs, by contrast, operate on alternative principles which make explicit reference to socially shared objectives, such as local project finance and public policies, savings for local communities, economic and social development. Financial cooperatives generally abide by statutory provisions according to which profits (surplus) are redistributed based on members’ participation. As a result, while redistribution within for-profit universal banks occurs because of information asymmetries and through the market (cross-subsidization), in the case of financial cooperatives redistribution concerns are explicitly stated and exogenous with respect to market forces (Fonteyne 2007).

Carrying unique features inherent to member ownership, the cooperative banking model does not rest on an exclusive notion of efficiency as measured by the ability to create value for its shareholders. Rather, it typically pursues distinctive member-related objectives — e.g. pooling resources to secure and improve access to credit to their members, that are also the cooperative’s clients, depositors and borrowers. Members of credit cooperatives typically benefit from surplus sharing in the form of e.g. reduced fees and dividends. Member ownership, originally inspired by the cooperative principles of democratic decision-making and participation (“one person, one vote”), social commitment and solidarity, also lies at the core of the redistribution mechanism within the supported community (Butzbach and Mettenheim 2014, 2015).

Strong focus on territorial economic needs and proximity to customers are distinctive traits that allow cooperatives to be perceived as local and trustworthy banks (Fonteyne 2007) and thus gathering soft information about their creditworthiness — cooperatives as information machines (Banerjee, Besley, and Guinnane 1994). By its very nature, relational lending practices largely rely on mutual trust and reputation rather than explicit collateral requirements in business transactions (e.g. Cosimano 2004), awarding an information-based advantage to local cooperatives (e.g. Sharpe 1990) while also enhancing their screening power over new loan applications (e.g. Agarwal and Hauswald 2010). In this case, the same sources of good information — e.g. social networking, trust-based personal relationships — are also at the root of the cooperative redistributive goals.

3.1 Entrepreneurs

The (expected) utility of the entrepreneur from accepting the contract offered by the type i bank is

Hence, entrepreneur q∈Q selects the contract offered by the type i bank if and only if

where u₀ > 0 denotes the (type-independent) entrepreneurs’ outside option.^[5]

3.2 Credit Organizations

Commercial banks are modeled as pure for-profit organizations, and thus aim at maximizing expected profits

where ρb is the uniform price (gross interest rate) and Q_b is the set of subscribing entrepreneurs.

As in standard models of credit markets with imperfect information (e.g. de Meza and Webb 1987; Mankiw 1986), separation of entrepreneurial types is not possible under individual lending arrangements in the absence of collateral or other observable characteristics of borrowers. The only solution is thus to offer a pooling (unsecured) debt contract providing all subscribing entrepreneurs with the required capital to start their own venture, and that has a fixed (type-independent) repayment ρb in non-bankruptcy states, whereas non-defaulting entrepreneurs retain full ownership rights over their project’s return net of repayment.^[6]

As discussed above, credit cooperatives rather operate on the basis of explicit redistribution concerns: they aim at maximizing the size — here, the measure — of their client base over which to redistribute the aggregate surplus flowing from funded (and successful) investment projects. The explicit cross-subsidization scheme adopted by credit cooperatives is restricted to enforce equal treatment of signing entrepreneurs: the aggregate surplus flowing to the banks is equally redistributed across served entrepreneurs of sufficiently high quality (where the quality threshold is endogenously determined), so as to provide them with the same level of expected utility.^[7] The surplus-sharing contract offered by cooperative banks, which is specifically designated for (and only available to) entrepreneurs of type q, thus stipulates an expected (constant) payoff πc for all signing entrepreneurs, for some share c∈(0,1), and entail a type-dependent repayment ρc(q) when the projects are successfully undertaken: an unsecured debt contract with type-dependent interest rates. Equal treatment must then be achieved by stipulating a type-increasing price function ρc(q), that explicitly enforces cross-subsidization from high-quality entrepreneurs to low-quality ones.^[8]

Surplus redistribution with equal treatment involves collecting all individual (project-specific) surpluses from subscribing entrepreneurs (members) q∈Qc, and granting them a constant expected utility

provided Q_c maximizes the measure μF(Qc)=∫QcdF(q) of the pool.^[9] When ρc(q) is restricted to be non-negative, we have

Notice that a negative priceρc(q)<0 would result for all projects of quality q < c — see relation (4): the payment (π−ρc(q)) for entrepreneurs of inferior quality with a successful project would in fact exceed the return on the latter; as a result, those holding the debt claim (the cooperatives) would need to subsidize some of their debtors in the good state of the world. As this provision would conflict with the structure of standard debt contracts, our entire analysis and the ensuing results are based on the restriction that debt repayments on termination ρc(q) be non-negative.^[10]

It is worth emphasizing that the choices of c and Q_c necessarily intertwine with each other, since the former shapes the boundaries of the pool of entrepreneurs that credit cooperatives can target. For any price ρbe that they expect their for-profit competitors to offer, credit cooperatives in fact set the lowest share c(q˜) inducing targeted entrepreneurs to self-select into the associated contract, where q˜≤1 identifies the marginal entrepreneur who finds herself just indifferent between the two borrowing possibilities; while no contract {ρc(q),1} is supplied to entrepreneurs endowed with projects of quality q<c(q˜) — see (4), any q≥q˜ will necessarily accept the commercial banks’ offer, for this grants subscribing entrepreneurs a type-increasing expected utility — see (1). If several couples (c(q˜),Qc) exist that support a balanced budget, credit cooperatives then select the one(s) yielding Q_c with maximal measure.

Formally, cooperatives solve the following problem: for any ρbe, let

from U(ρbe;q˜)=πc, and define the sets

then Q_c is optimally selected so as to maximize the measure μF(Φ(ρbe)).

4.1 Equilibrium Notion

The timing of the model is as follows. First, the distribution of projects F (q) is known to both credit organizations, only credit cooperatives know the realization q before entering the contracting stage. Then, all bank types (commercial banks and cooperatives) decide whether or not to enter the market and simultaneously offer contracts to the entrepreneurs (i.e. no offer corresponds to no entry). All banks hold correct expectations about both their rival’s pricing choices and the pool of entrepreneurs who will accept the contract. Entrepreneurs choose whether to implement the project and select the contract that yields the higher expected payoff, agreeing to make repayment subject to their terms. Once contracts are signed, the subset Q_j of funded projects by type j banks take place and each succeeds with own probability q.

Let us restrict the model’s parameters Γ={F,π,Rb,Rc,u0} to satisfy R_c + u₀ < π, which creates room for profitable bank-borrower relationships and implies that the set of efficient projects

is non-empty.^[11] The following notion of a competitive equilibrium in the presence of redistribution concerns is next adopted:

Part (i) is the expected zero profit condition for the commercial banks. Parts (ii) and (iii) jointly state that the redistribution process undertaken by credit cooperatives must be consistent with their maximal measure objective, cannot violate their balanced budget requirement, and must enforce equal treatment of subscribing entrepreneurs — see Eqs. (4)–(6); whereas uniform pricing within the for-profit sector involves type-increasing utility for their pool of borrowers. Part (iv) stipulates that the allocation of projects to the two types of credit organizations must be consistent with the self selection incentives faced by the entrepreneurs. Notice that the borrower pools QjM served by either type of banks is endogenously determined. We focus attention on competitive equilibria in which both bank types are active in the marketplace and have positive market shares; i.e. the sets QjM must be of non-zero measure — part (v).

4.2 Benchmark Equilibrium

How would credit be allocated in a free entry market populated by for-profit banks only, which compete for investment projects whose quality is entrepreneurs’ private information? Since type-increasing (expected) utility emerge in entrepreneurship relative to a constant outside option — i.e. U(ρb;q) increases with q for any given ρb — favorable selection occurs, with good entrepreneurs drawing bad ones in (de Meza and Webb 1987).^[12] The zero (expected) profit conditions will settle the market (uniform) price consistent with individuals’ sorting into entrepreneurship. A competitive equilibrium is thus a set Qbb and a price ρbb such that

Then the following holds true:

A key feature of such ‘too much investment’ outcome is that all loan applicants endowed with efficient projects are approved and thus can start their own ventures. Which role, if any, may then redistribution-concerned credit organizations play in market environments in which no rationing occurs, and where their for-profit peers operate in the absence of market power? We address this question in the next section.

6.1 Heterogeneity of Credit Organizations

Either kind of credit organization in our model values loans to entrepreneurs in a risk neutral way, yet they explicitly differ in terms of refinincing costs and available information at the contractual stage. Specifically, credit cooperatives enjoy an informational advantage (they have perfect information about entrepreneurial types) over their for-profit peers, while facing a higher funding cost per loan (i.e. R_c > R_b). Such a cost disadvantage may be due to an unbalanced access to different sources of funding (e.g. deposits versus wholesale debt or bonds issued on international financial markets), heterogeneity in underwriting costs, varying costs for asset holdings and collateral-based loans from central banks (as occurs in e.g. the euro area) or rather to the peculiar cooperative feature of gathering information on opaque projects vis-à-vis universal banks’ specialization on providing ancillary services to fund owners. As discussed in the Background Section, there exists an extensive literature exploring the reasons why lenders may specialize in different tasks and operate their business more on relational lending rather than on anonymous trade (see for example, Berger and Udell 1995; Guinnane 2002).

Assuming Rc≤Rb in the model would grant credit cooperatives an overwhelming advantage in terms of both information and cost. If these credit organizations were pure profit-seeking entities, they would capture all the efficient borrowers and thereby force their imperfectly informed, high-cost competitors out of the market.^[16] In principle, the presence of redistribution concerns and of the maximal coverage objective may still sustain competitive equilibria in which uninformed, high-cost banks retain a positive market share; intuitively, given the equal treatment principle they enforce, credit cooperatives may optimally decide to refrain from offering debt contracts to top quality entrepreneurs, which would self-select into the credit relationship with for-profit banks, as it engenders type-increasing expected utility. Being able to attract efficient projects, for-profit banks would in turn be able to break even on a pool formed by good and bad entrepreneurs, provided the cost gap Rb/Rc is not too large. In this very specific situation, credit cooperatives would find themselves enforce surplus sharing across projects of intermediate quality — see Proposition 2, part (ii).

Let us first consider the case R_c = R_b. It is easy to see that there cannot be any competitive equilibrium with vertical separation where for-profit banks attract the most capable while coops attract less capable entrepreneurs: the competitive equilibrium (if it exists) either is in the disconnected form described above, or rather complies with the vertical separation result emphasized in D’Amato, Di Pietro, and Sorge (2020) (cooperatives above, for-profit banks below). Further decreasing R_c strictly below R_b would all else equal definitely push up the measure of the pool of entrepreneurs served by the cooperatives, possibly causing a new market configuration to replace a former one: in fact, the specific way cooperative banks will decide to use this extra surplus under equal treatment depends on the underlying probability distribution of quality. In the market disconnection case, it might induce coops to target higher quality projects or, in the opposite case, to start serving low-quality ones. As a consequence, when R_c falls to a sufficient extent, the disconnected form vanishes, and a new equilibrium separation of the market might arise, where for-profit banks find themselves at the top end of the quality spectrum with coops covering the residual. In the vertical separation case, a falling R_c induces coops to extend their offers to inferior quality projects. This would at some point result in the competition for borrowers being unsustainable for the type of credit institution facing a double disadvantage: perfectly informed, low-cost credit cooperatives would then become the sole external financiers active in the market.

6.2 Financial Contracts

Our analysis of mixed credit markets abstracts from characterizing optimal financial arrangements: the only possible contracts between borrowers and lenders are either pure debt with fixed repayment (for-profit banks) or a debt contract with type-dependent repayments enforcing equal treatment (cooperative banks). As argued, this working assumption allows us to highlight what we consider the two essential features of a cooperative credit institutions: mutualistic statutory objectives and their informational advantage. The two aspects are separated in our analysis in the sense that we only allow redistribution concerns within the cooperative banks to interact with the features of the credit relationship only through the budget constraints and not the terms of the contract which, also in the case of a cooperative credit institution is taken to be a standard debt contract (more details on this point below). Faced with the alternative of choosing between a mutualistic credit institution and a standard commercial bank the entrepreneurs, in our model, choose between contracts with similar features issued by the two lenders. Only the terms of the contract (the interest rate) can differ. This assumption is made to simplify the analysis of the competitive forces emerging in mixed environments and their role in shaping the market equilibrium configuration.

Careful scrutiny of the literature on ex ante informational asymmetries suggests that confining attention to entrepreneurs raising outside finance rather than issuing equity is less restrictive than it may appear. In fact, de Meza and Webb (1987) as well as subsequent work (e.g. Innes 1993) have already shown that in asymmetric information models of credit markets in which entrepreneurial returns are ranked by increasing (expected) returns, the equilibrium requires that all ventures be debt financed. For example, in a model related to our banks-only setting, Boadway and Keen (2006) show that screening is prevented in the presence of inside equity on the part of entrepreneurs, for a pooling equilibrium always occurs as the only admissible outcome. This result carries over to more general settings in which investment projects feature variable size, and project returns increase with their own size, provided entrepreneurs differ by their probability of success, as our model assumes; under a mild monotonicity condition on the lenders’ payoff function, debt financing also emerges as the unique equilibrium contractual form when allowing for arbitrary distributions of returns to entrepreneurial ventures (Innes 1993).^[17]

It is in general true that, by conditioning financial contracts on some observables (e.g. collateral, inside equity, size of the investment) or alternatively envisioning a collective, incentive-compatible lending mechanism (e.g. Daripa 2008) would allow forms of screening of entrepreneurial types (e.g. through borrowers’ self-revealing choices from the menu of offered contracts), and it would reduce or, under certain conditions, even eliminate inefficiencies arising from informational frictions. However, to the extent that cross subsidization among projects is a feature of the equilibrium contract, the basic point we raise in our model would still hold, i.e. that the inclusion in the analysis of better informed banks (here, credit cooperatives) will impact the specific features of cross-subsidizing debt contracts (in our case the amount of overlending).

There in principle exist alternative deals that credit cooperatives can offer in order to equally redistribute surplus over their client base while standing on a clear path to budget balance. In general, by virtue of the risk-neutrality assumption, any arrangement entailing cross subsidies and/or unconditional transfers that provide entrepreneurs with a constant level of utility πc would do the job. One of such surplus-sharing contract — let us call it Scq — stipulates the following: entrepreneurs are granted πc for some share c∈(0,1)whatever the underlying state — that is, Scq(0)=Scq(π)=πc for all q∈Qc — in exchange for the residual claim to the net project’s return — that is, π (1 − c).^[18]

Under the specified conditions, the cooperatives’ budget would read as

where Qˆc⊆Q is the set of signing entrepreneurs. Notice that (13) is in the same form as the one dictated by the debt contract with price ρc(q) i.e.

and yet Q_c is possibly different from Qˆc because of the restriction ρc(q)≥0. In fact, the arrangement Scq involves subsidizing the cooperatives’ members (also) in the bad state of the world, while placing no restriction on the set of entrepreneurs participating in the credit relationship: credit cooperatives can serve as a source of financing for entrepreneurial ventures of inferior quality q < c, who are expected negative contributors to the aggregate cooperative surplus; both of these features (positive payments to all failed entrepreneurs and negative contributions from some of the subscribing entrepreneurs) are precluded in our environment where standard (unsecured) debt contracts are traded.

For the purpose of our analysis, let us assume here that credit cooperatives offer the surplus-sharing contract Scq. Then

We start noticing that studying setup in which credit cooperatives offer the surplus-sharing arrangement Scq rather than the debt contract Dcq is equivalent (up to features of market outcomes) to removing the restriction ρc(q)≥0. Since the price function ρc(q), whether positive or negative, proves strictly increasing over Q, the content of Lemma 2 carries over to the set Qˆc, which must be then convex in any competitive equilibrium; under any admissible model’s parameterization (in particular, the assumed cost disadvantage for the cooperatives) it is then easy to establish the following:

Proposition 5 allows us to argue that lifting the debt financing assumption does not affect the main findings of our analysis (about e.g. the conditions for existence of competitive equilibria in mixed credit markets and the nature of the associated market failure); yet, it may alter their interpretation in terms of e.g. the mitigating role played by cooperatives in otherwise standard markets with imperfect information (as discussed next).

We would finally like to emphasize that a competitive equilibrium with analogous features would also arise in a more sophisticated setting where imperfectly informed banks are allowed to invest in a screening, quality-revealing technology and yet the cost of acquiring information is so high as to induce banks to rather pool all entrepreneurs together with a uniform debt contract (e.g. Gormley 2014). Even in that case, relative to the efficient allocation, over-provision of credit to low-quality, inefficient projects would be enforced in equilibrium.

6.3 Coops-Only World and Market Failures

One of our main results concerns the mitigation of excessive lending due to the coexistence of credit cooperatives and for-profit banks, as opposed to a world populated by equally uninformed, profit-seeking banks whose uniform price contract pools efficient and inefficient types together. This suggests that cooperatives have a potential role in mitigating market failures.

We next show that, while the emergence of financial NPOs in a world of for-profit banks never produces an expansion of credit to riskier borrowers, the introduction of imperfectly informed, for-profit competitors into a market reserved for credit cooperatives may under some circumstances increase, rather than decrease, the intensity of excessive lending. And more generally, this prediction is ambiguous, for it depends on the specific parameterization of the model.

To see this, let us first explore the nature of equilibrium in a world made by credit cooperatives only, that offer the surplus-sharing debt contract Dcq described above and raise funds at the cost R_c (without loss of generality we let this latter equal the socially efficient one). A coops-only equilibrium consists of a set Qc°, a non-negative price ρc°(q)=π(1−c°q) and a share c°∈(0,1) such that

1. Qc°∈arg max μF(Qc) s.t. ∫Qc°(ρc°(q)⋅q−Rc)dF=0 ;

2. U(ρc°(q);q∈Qc°)=(π−ρc°(q))⋅q=πc° ;

3. Qc°={q∈[c°,1] |πc°≥u0} .

We next show that a coops-only equilibrium (i) always exists and (ii) it does not necessarily generate over-lending. First, notice that in any coops-only equilibrium Qc° must be a convex set with max(Qc°)=1. Suppose not, then it must be the case that Qc°=Qc′∪Qc″ where:

Then there exists an Qc‴ such that μF(Qc‴)=μF(Qc″) and:

This in turn implies that there exists a nonzero measure set Q‾c such that

which contradicts the fact that Qc° is measure-maximizing. Hence, Qc° must be convex to be part of a market equilibrium. By the same token, since for any Qc⊂Q one has

any Q_c with max (Q_c) < 1 cannot be measure-maximizing for the coops: there exists room for boosting membership by raising surplus from the best entrepreneurs.

Second, notice that for any c≥u0/π entrepreneurs prefer the cooperative contract over their outside option, yet only entrepreneurs with projects of sufficiently high quality q≥c will receive an offer. An immediate consequence is that full market participation can never occur. Furthermore, it is straightforward to show that a coops-only equilibrium is always supported by any set of parameters (F,π,Rc,u0). To this end, let us denote the least efficient project as q⋆=u0+Rcπ. Consider first the case where the unconditional average quality project EQ=∫QqdFq is inefficient, i.e. if EQ<q⋆, then pricing at ρc°=π(1−u0πq) for c°=u0π delivers an equilibrium with Qc°=[qc°,1] with qc∘ solving

or equivalently

if and only if Eq|q∈u0π,1≥q⋆ (if equality holds, then qc°=c°). In words, when the average project is of sufficiently low quality, cooperatives can offer the highest price ρc°(q) (or equivalently, the lowest surplus share c°) consistent with participation of both efficient and inefficient entrepreneurs into the credit relationship; notice that qc°≥u0π implies ρc°(q)≥0 for all q∈Qc°, while the balanced-budget Eq. (23) suggests that qc°<q⋆ (over-lending).

Consider now the case where Eq|q∈u0π,1>q⋆ (and a fortiori where EQ≥q⋆). Then c° — and thereby ρc°(q) and Qc°=[c°,1] — is determined by the balanced-budget equation

or equivalently

Notice that such a c° always exists by continuity of the conditional expectation operator and the limiting behavior of the left- and right-hand side of (25) when c°→u0π and c°→1; it also is unique.^[19] The key point here is that, conditional on the selection (F,π,Rc,u0), the coops-market equilibrium can entail either over- or under-provision of credit, or even entail the socially efficient level of investment. To show this, let us take quality to be uniformly distributed on the unit support Q; when parameters are such that

relation (25) is the relevant one to pin down the share c°>u0π, delivering

thus over-lending would require

Hence, under-investment can occur in such a coops-only world when the projects’ return π is sufficiently high relative to cooperatives’ funding cost Rc, all else equal.^[20]

Finally, let us explore the the case where credit cooperatives offer the above described surplus-sharing arrangement Scq rather than the debt contract Dcq. Recall that in this case a coops-only equilibrium would be characterized by the following

1. Qˆc°∈arg max μF(Qˆc) s.t. ∫Qˆc∘(πq−(πc+Rc))dF(q)=0 ;

2. U(πc°;q∈Qˆc°)=πc° ;

3. Qˆc°={q∈Q|πc°≥u0} .

Notice that q<c° can belong to Qˆc° (as it would occur if ρc(q) were allowed to be negative). If the unconditional average quality project is efficient, i.e. if EQ≥q⋆, then full market coverage Qˆc°=Q arises with c°≥u0π.^[21]. This is of course an instance of over-lending.

In any other equilibrium with partial coverage, a convex Qˆc°=[q‾°,1]⊂Q of course maximizes participation when c°=u0π. Again, over-lending is bound to arise. Suppose not, i.e. suppose q⋆<q‾°. Then by the balanced budget constraint one has

from which one has Eq|q∈q⋆,1<q⋆, which cannot hold true. It can be also shown that q‾°<q‾b, where q‾b is the lower bound of the pool Q^b that would be served in for-profit banks-world only, where funds can be raised at cost R_b = R_c (so that the efficient threshold q^⋆ stays the same between the setups); in fact, recalling that in the banks-only equilibrium it holds ρbb⋅E[q|q∈[q‾b,1]]=Rb (see Proposition 1), one has

and since q‾b=u0π−ρbb one has

i.e. a contradiction. As a result, a coops-only world in which the contractScqis traded always generates a higher degree of over-lending than the corresponding banks-only environment. It follows that mixed credit markets, in which both types of credit organizations co-exist, necessarily entail a reduction in excess lending relative to either of the two worlds. As mentioned above, this prediction is not warranted when the debt contracts Dcq are traded instead.