credit unions and the common bond · credit unions and the common bond ... cooperative financial...

FEDERAL RESERVE BANK OF ST. LOU IS

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SEPTEMBER/OCTOBER 1999

Credit Unionsand theCommon BondWilliam R. Emmons andFrank A. Schmid

C ooperative financial institutions havetheir roots in 19th century Europe,appearing first in the United States

during the early 20th century. Cooperativefinancial institutions are ubiquitous inboth developed and developing countriestoday, posing something of a puzzle in theformer group of countries where onemight have expected corporate financialinstitutions with professional managementand sophisticated capital-market oversightto have displaced them. This has notoccurred, however, as some groups ofcooperative financial institutions in devel-oped countries are holding steady or evenincreasing their market shares. In theUnited States, the most prominent types ofcooperative financial institutions today aremutual savings and loans, mutual savingsbanks, mutual insurance companies, andcredit unions.

Credit unions are regulated and insuredfinancial institutions dedicated to the saving,credit, and other basic financial needs ofselected groups of consumers. By law,credit unions are cooperative enterprisescontrolled by their members—under theprinciple of “one-person one-vote.” Inaddition, credit union members must beunited by a “common bond of occupationor association, or (belong) to groups withina well-defined neighborhood, community, or rural district” (Supreme Court, 1998, p. 2, quoting from the Federal Credit Union Act of 1934).

Despite the rather low profile andmundane operations of the vast majority

of credit unions, these institutions havelong been a source of controversy in theUnited States. Public awareness of thislong-simmering debate was piqued recentlyby a Supreme Court case pitting commer-cial banks against credit unions and theirfederal regulator (Supreme Court, 1998).The Court found in favor of banks in thiscase, ruling that the federal credit-unionregulator, the National Credit UnionAdministration, must cease granting feder-ally chartered credit unions the right tocombine multiple common bonds (fieldsof membership) within a single institution.Less than six months later, however, President Clinton signed into law new legislation that essentially reversed theSupreme Court’s ruling.

This paper provides background oncredit unions and the debate they havespurred in the United States. In addition,we present new evidence relevant to thecredit-union debate concerning fields ofmembership (common bonds). Ouranalysis is based on a theoretical model of credit-union formation and consolidation.Using an extensive dataset and a nonlinearempirical approach, we find that credit-union participation rates generally declineas the group of potential members becomeslarger, holding all else equal. That is, the larger the pool from which a single-group credit union can draw, the lesseffective it is in attracting members.

We also provide new evidence on twomore general banking policy issues. First,we find evidence to support the structure-conduct-performance paradigm of localbanking competition. This is the prediction,derived from theoretical considerations,that more concentrated markets ultimatelylead to higher prices and lower quantities.Policymakers have used this paradigmextensively when justifying intervention in the market for corporate control infinancial services. Using the Herfindahlindex calculated for local bank depositmarket shares as a measure of local

William R. Emmons is a research economist and Frank A. Schmid is a senior research economist at the Federal Reserve Bank of St. Louis.Robert Webb and Marcela Williams provided research assistance.

market structure, we find that higher levelsof market concentration are associated withhigher participation rates at credit unions.This is consistent with the notion thatbanking competition is weaker in moreconcentrated markets, which increases the attractiveness of credit unions.

The second banking policy issue weaddress is that of possible scale economiesamong financial institutions. Our empir-ical results indicate that credit unionsgenerally encounter significant scaleeconomies, whether scale is measured bythe log of total assets or by the log of thenumber of credit-union members. The latterfinding, however, applies only to relativelylarge credit unions.

It is important to point out severallimitations of this study. As in allempirical investigations, we can describerelationships in the existing data but wecannot predict exactly how these relation-ships would appear under a different set ofoperating conditions. For example, anextended period of growth by many creditunions could alter the extent of scaleeconomies that exist. Similarly, significantchanges in credit-union regulation mightresult in different empirical regularitiesthan those identified here. It also isimportant to keep in mind that we abstractfrom managerial agency problems in creditunions in this article (see Emmons andSchmid, 1999, for an extensive discussionof this issue). Finally, it is hazardous todraw conclusions about public policytoward credit unions on the basis of thisrather narrowly focused investigation. Wehope to provide insights into the effects ofcommon-bond requirements, not toprovide a comprehensive framework forevaluating competition in the financial-ser-vices sector as a whole.

The paper is organized as follows: The first section provides some institutionaland historical background on creditunions, while the second section outlinesthe current credit-union debate in theUnited States. The third section developsa theoretical model of credit-union forma-tion and consolidation. The modelstresses the countervailing influences

on participation rates of (1) scale economiesin production, and (2) decreasing within-group membership affinity as a creditunion grows. The model provides intuitionfor why the number of common bondswithin a credit union might be importantfor their formation and growth. The thirdsection also describes a simulation of thetheoretical model that can be used to gen-erate some comparative-static results. Thefourth section briefly describes the datasetand the econometric methods we employin analyzing federally chartered occupationalcredit unions. The fifth section presentsour empirical results, and the sixth sectiondraws conclusions. An appendix describesthe data we use.

BACKGROUND ON CREDIT UNIONS

This section provides some institutionalbackground to help motivate the theoreticaland empirical analyses later in the article.The key points this section seeks to illumi-nate are the restrictions on credit-unionexpansion and the arguments that have beenmade to support or oppose these restrictions.The sections that follow investigate theextent to which the common-bond require-ment acts as a binding constraint oncredit-union operations.

Overview of Credit Unions in theUnited States

Credit unions numbered 11,392 atyear-end 1996, serving some 70 millionindividual members (U.S. Treasury, 1997,p. 15). At the same time, there were11,452 commercial banks and thrift insti-tutions (savings and loan associations andmutual savings banks). Credit-union assetswere only $327 billion, compared to$5,606 billion held by commercial banksand thrifts (U.S. Treasury, 1997, p. 21). Amore direct standard of comparison mightbe community banks and thrifts, however.At year-end 1996, there were 7,049community banks and thrifts (defined asall federally insured banks and thrifts withless than $100 million in assets) holding


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1 We concentrate on federallychartered credit unions becausethe NCUA does not vouch forthe accuracy of data providedby state-chartered credit unions,which report directly to theirstate's regulatory authorities.

2 The estimated 70 million current credit-union membersrepresent a bit more than 34 percent of the 1996 U.S.population over 16 years of age numbering 204 million(U.S. Census Bureau,<http://www.census.gov>).


combined assets of $324 billion (U.S. Trea-sury, 1997, p. 21). A comparison of creditunions and community banks and thrifts isparticularly meaningful becauseinstitutions of both types are relativelyfocused institutions, and hence, are unableto grow beyond certain limits. Forexample, a single-employer occupationalcredit union is authorized to serve only theemployees of the sponsoring firm and theirimmediate relatives, who may total nomore than a few hundred people. A com-munity bank or thrift may operate in onlyone geographical area. In addition, creditunions are restricted in the types of finan-cial services they may provide, withtraditional consumer financial services atthe core of virtually all credit unions’ activ-ities. Community banks and thrifts mayoffer a similar array of services.

Both federal and state agencies grantcredit-union charters. Regardless of thetype of charter they hold, the deposits (ortechnically, “shares”) of virtually all creditunions are now federally insured by theNational Credit Union Administration(NCUA). Federal credit unions are regulatedby the NCUA while state-chartered creditunions are regulated by an agency of thechartering state.

Of the 7,068 federally chartered institu-tions at year-end 1996, about three quarterswere occupational credit unions (U.S. Trea-sury, 1997, p. 19).1 In an occupationalcredit union, one or more firms sponsor acredit union, sometimes providing officespace, paid time off for volunteer workers,and perhaps other forms of support. Theremaining federal credit unions were eithersingle-group associational or communitycredit unions, or multiple-group creditunions with predominantly associational,community, or more than one type of mem-bership (i.e., several groups that span theusual classifications).

By size, most credit unions (65 percentof federally insured institutions) had lessthan $10 million in assets (U.S. Treasury,1997, p. 19). Large credit unions exist,however, and they are an important part ofthe sector. For example, the 11 percent ofcredit unions with more than $50 million

in assets (1,284 institutions) accounted for74 percent of total credit-union assets.

Credit unions play a limited role in theU.S. financial system, catering to the basicsaving, credit, and other financial needs ofwell-defined consumer groups. More than95 percent of all federal credit unions offerautomobile and unsecured personal loans,while a similar proportion of large creditunions (more than $50 million in assets)also offer mortgages; credit cards; loans topurchase planes, boats, or recreationalvehicles; ATM access; certificates ofdeposit; and personal checking accounts(U.S. Treasury, 1997, p. 23). Very smallcredit unions typically offer a limitedrange of services, are staffed by member-volunteers, and are likely to receive free orsubsidized office space. Larger creditunions offer a broader array of services.They may employ some full-time workers,including the manager, and are more likelyto pay a market-based rent for office space.

Historically, members of credit unionswere drawn from groups that were under-served by traditional private financialinstitutions; these consumers tended tohave below-average incomes or were oth-erwise not sought out by banks. Whilecredit-union members today still mustshare a common bond to be eligible formembership, the demographic characteris-tics of credit-union members have becomemore like the median American. Whileonly 1 percent of the U.S. adult populationaged 18 or over belonged to a credit unionin 1935, some 33 percent of the adult pop-ulation had joined by 1989 (AmericanBankers Association, 1989, p. 29). Subse-quent strong growth of new credit-unioncharters has increased that proportion.2

According to a credit-union survey in1987, 79 percent of all Americans whowere eligible to join a credit union haddone so (American Bankers Association,1989, p. 29). Given the prominent role ofoccupational credit unions, a majority ofmembers are in the prime working ages of25-44 (American Bankers Association,1989, p. 30). Perhaps surprisingly, giventhe origins of credit unions, current mem-bers are overrepresented in upper-middle


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income strata, defined as householdincomes between $30,000 and $80,000 in 1987. Overall, it appears that creditunions, banks, and thrifts are more directcompetitors today than when credit unions first appeared.

A Brief Legislative History of CreditUnions in the United States

The predecessors of American creditunions were cooperative banking institutionsof various sorts in Canada and Europeduring the 19th century. The first creditunion in the United States was formed inManchester, New Hampshire, in 1909 (U.S.Treasury, 1997, p. 15). Soon thereafter,Massachusetts created a charter for creditunions. The credit-union movement sweptacross the United States from there,meeting with particular success in the NewEngland and upper Midwestern states.

These early cooperative financial insti-tutions often had a social, political, orreligious character in addition to theirexplicit economic function. While thesocial and political aspects of the coopera-tive movement were acknowledged andaccepted by the United States Congress,the Federal Credit Union Act (FCUA) of1934 was focused more narrowly on theeconomic potential of credit unions.

The legislation itself was modeledclosely on state credit-union statutes thathad appeared during the early decades ofthe 20th century in the Northeast andupper Midwestern states. The FCUAclearly reflected Congressional intent tocreate a class of federally chartered finan-cial institutions that would operate in asafe and sound manner:

… the ability of credit unions to“come through the depression withoutfailures, when banks have failed sonotably, is a tribute to the worth ofcooperative credit and indicates clearlythe great potential value of rapidnational credit union extension.”(Supreme Court, 1998, p. 17, citingthe FCUA, S.Rep. No. 555.)

The likelihood that federal creditunions would serve consumers not servedby banks was an additional element inCongressional deliberations:

Credit unions were believed to enablethe general public, which had beenlargely ignored by banks, to obtaincredit at reasonable rates. (SupremeCourt, 1998, p. 17.)

Partly because credit unions are mutual associations, they were not subjected to federal taxation as were share-holder-owned commercial banks and thriftinstitutions. Mutuality cannot be the onlyreason why credit unions are not taxed,however. Other mutually owned enterprisesare subject to taxation. As for the benefits of tax exemption, credit unions (or anyother firm) could avoid paying taxes bypaying out all “profits” to members in theform of lower borrowing rates or higherdeposit rates. The real importance of the tax exemption is that credit unions canretain earnings tax free. Advocates arguethat this is justified because credit unionscannot raise equity in a public offering, sothey must be able to build capital internally.

It is clear from the legislative historysurrounding the passage of the FCUA in1934 that Congress saw the common-bondrequirement as critical to the success ofcredit unions:

The common bond requirement “wasseen as the cement that united creditunion members in a cooperative venture,and was, therefore, thought importantto credit unions’ continued success. ...”

“Congress assumed implicitly that acommon bond amongst memberswould ensure both that those makinglending decisions would know moreabout applicants and that borrowerswould be more reluctant to default.”(Supreme Court, 1998, pp. 17-18,citing 988 F.2d, at 1276.)

The subsequent history of creditunions in the United States largely has fulfilled the promise envisioned by


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Congress in 1934. Credit unions havegrown and spread across the country.Although hundreds of individual creditunions failed during the 1980s and early1990s, the National Credit UnionInsurance Fund (NCUSIF, formed in 1970)avoided accounting insolvency—inmarked contrast to the Federal Savingsand Loan Insurance Corporation and theBank Insurance Fund of the FederalDeposit Insurance Corporation (Kane andHendershott, 1996). Credit unions controla small but growing share of householddeposits, and some of our empirical resultsindicate that they may play a role in main-taining a high level of retail bankingcompetition in some local markets.

THE CURRENT CREDIT-UNION DEBATE

The special status and comparativesuccess of credit unions in recent decades,coinciding as it has with a period of stresson thrift and commercial-banking institu-tions, has led to political conflicts betweenadvocates of credit unions and banks.This conflict reached its high point in aseries of court decisions culminating at theU.S. Supreme Court in October 1997. Theparticular case at issue involved the AT&TFamily Credit Union and the NCUA’sinterpretation of the 1934 FCUA allowingmultiple common bonds of membership.Brought by several banks and theAmerican Bankers Association, the casewas ultimately decided in February 1998(on a 5-4 decision) in favor of the bankswho sued to stop the NCUA from grantingmore multiple-group credit-union charters.The bankers’ victory was short-lived, however, as Congress almost immediatelydrafted new legislation that enables creditunions to continue growing much asbefore—including multiple commonbonds within a single credit union. The shaded insert summarizes the key provisions of the Act.

Attacks on credit unions have comefrom a wide range of viewpoints, the pro-ponents of which have wielded sometimescontradictory arguments. Some of the

arguments used in the recent SupremeCourt decision concerning the role of thecommon-bond requirement in creditunions reflect the unsettled nature of thedebate. We focus on two strands of thecredit-union debate here, namely the argu-ments stressing inefficient governancestructures on the one hand and unfaircompetition on the other.

Some have argued that credit unionsare inherently inefficient due to their one-member one-vote governance structure.One might expect decision-making in a credit union to be of poor quality due to a lack of professionalism (i.e., volunteermanagers and workers), free-riding ofmembers in monitoring the management,and weak incentives for members to intervene when action is needed to correct specific problems or deficiencies.3

According to this argument, credit unionsmay waste scarce resources and they mayeventually impose significant costs onindividual sponsoring firms or theeconomy as a whole.

The second prominent line ofargument aimed at credit unions takes a nearly opposite view of their organizationaleffectiveness. This view presumes thatcredit unions operate efficiently enough tooffer consistently better terms on savingsand credit services than those offered bycommercial banks and thrifts. Bank andthrift managers and owners often presentthis point of view in public discourse. To be sure, those arguing that creditunions represent unfair competitionascribe some or all of their competitiveadvantages to subsidies such as their tax-exempt status or sponsor subsidies ratherthan inherent efficiency.

Proponents of the first view—thatcredit unions are inherently inefficient—have a difficult time explaining why thenumber of credit unions and credit-unionmembers continues to grow, and whymembers express high levels of satisfactionwith the services they receive. If mostcredit unions were very inefficient, onemight expect their members to becomedisaffected and their role in the financialsystem to diminish over time.

3 Free-riding is when memberschoose not to exert monitoringeffort because they assumesomeone else will do it for them.



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On the other hand, proponents of thesecond view—that credit unions are unfaircompetitors due in part to subsidies—cannot explain easily why credit-union

sponsors and governments are such strongsupporters of credit unions. It is hard tounderstand how large net subsidies couldbe delivered to credit-union members over

THE CREDIT UNION MEMBERSHIP ACCESS ACTPresident Clinton signed the Credit Union Membership Access Act on August 7,

1998, following approval in the Senate on July 28 and in the House of Representativeson August 4. The act substantially reverses a Supreme Court ruling handed down onFebruary 25, 1998, that would have barred federally chartered credit unions fromaccepting multiple membership groups, each with its own common bond.

This landmark credit-union legislation represents a major defeat for the top lobbying group representing commercial banks, which had argued successfully at the Supreme Court that credit unions with multiple common bonds violated both the letter and the spirit of federal legislation dating from 1934. The subsequent legislative response in support of multiple common bonds at credit unions was swift and overwhelming, passing both chambers with large majorities.

The act contains three provisions upholding the rights of federal credit unions toserve membership groups encompassing multiple common bonds. First, all federalcredit unions that already included multiple common bonds before February 25, 1998,were allowed to continue operating without interruption. Second, all federal creditunions were given the right to accept additional membership groups with multiplecommon bonds so long as the relevant groups have fewer than 3,000 members. Third,the act gives the National Credit Union Administration the right to grant exemptions to the 3,000-member limit under certain circumstances, such as when the group inquestion could not reasonably support its own credit union.

The act also:• Requires annual independent audits for insured credit unions with total assets of

$500 million or more.• Authorizes and clarifies a federally insured credit union’s right to convert to a

mutual savings bank or savings association without prior NCUA approval.• Limits business loans to members to 12.25 percent of total assets.• Establishes new capital standards for insured credit unions similar to those

enacted for banks and thrifts in 1991.• Gives the NCUA authority to base deposit-insurance premiums on the reserve

ratio of the insurance fund.• Directs the Treasury to report to Congress on differences between credit unions and

other federally insured financial institutions, including the potential effects ofapplying federal laws—including tax laws—to credit unions.

Hailing the new legislation, President Clinton said, “This bill ensures that con-sumers continue to have a broad array of choices in financial services….and [makes] iteasier for credit unions to expand where appropriate.” Meanwhile, a spokeswoman forthe American Bankers Association termed it “ironic” that the bill was presented as ameasure to protect credit unions because in the long run, she said, it will dilute them,turning them into larger and larger institutions.

Source: BNA Banking Report, “House Passes Credit Union Bill; Clinton Wastes NoTime Signing It,” August 10, 1998, Vol. 71, No. 6.

time without more opposition arising from constituencies that might be payingthe subsidies, such as shareholders oremployees who do not belong to theirfirm’s occupational credit union, ortaxpayers who belong to no credit union.In fact, the most vocal complaints aboutalleged subsidies for credit unions areheard from banks and thrifts, whoseresentment of credit-union competitioncould be expected even if there were nosubsidies flowing to credit unions.

Ironically, the juxtaposition of thesetwo lines of attack against credit unionsappeared in the argumentation of theSupreme Court majority that decided the AT&T Family Credit Union case infavor of commercial banks. At one pointin its opinion, the majority cited thelegislative history surrounding the 1934Federal Credit Union Act as support for the view that credit unions are afragile—even flawed—type of institution,reasoning that:

Because, by its very nature, a coopera-tive institution must serve a limitedmarket, the legislative history ofSection 109 demonstrates that one ofthe interests “arguably…to beprotected” by Section 109 is an interestin limiting the markets that federalcredit unions can serve. (SupremeCourt, 1998, footnote 6, pp. 8-9.)

Thus, a credit union would become ineffi-cient if it grew beyond its “limited market,”as defined by its common bond.

At a different point in its opinion,however, the majority accepted theargument that credit unions with multiplegroups of members would be more formi-dable competitors to banks and thriftsthan single-group institutions. Themajority argued that an expansiveinterpretation of the 1934 Act “wouldallow the chartering of a conglomeratecredit union whose members included theemployees of every company in the UnitedStates (1998, p. 4).” In other words, creditunions would overwhelm banks and thriftsunless otherwise constrained.

The irony is, of course, that the argumentation based on the reductio adabsurdum of a hypothetical “conglomeratecredit union” did not mention the legisla-tive history of the 1934 Act, which hadessentially predicted that such a hugecredit union would not have been a safeand sound financial institution, nor conse-quently a viable one in the long run.

THE MODEL ANDSIMULATION

How should policymakers think aboutcredit unions? Are they relics of a bygoneera, propped up by subsidies anddistorting financial-sector competition?Or, are they efficient and focused financialinstitutions that could, if unleashed, even-tually dominate some or all of the retailfinancial landscape? We do not seek toanswer these emotionally charged questionsdirectly. Instead, we focus on the morelimited question of what effect thecommon-bond restriction exerts on credit-union formation and consolidation. In asense, we are merely attempting to answerthe question, “Does the common-bondrequirement constrain the existence orgrowth of credit unions?” We hope thatour insights may contribute to a betterunderstanding of the larger policyquestions mentioned above.

In this section we present a model ofcredit-union formation and consolidation.We then describe the results of a simulationof the model. Subsequent sections of the paper discuss testable hypothesesemerging from the model, the data weexamine, and empirical results.

The ModelWe take for granted that credit unions

typically are small; that they encounteroperating economies of scale as they expandfrom a very small base of members andassets; and that they face direct competitionfrom banks. The key trade-off we model is between decreasing affinity amongmembers as the potential membershipgrows (i.e., as a given common bond is



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extended to more people)—making acredit union less effective—versus theincreasing scale economies that come witha larger base of members and assets—making a credit union more effective. Weshow that the ability of credit unions toexpand by adding multiple common bondsto their membership affects this trade-offin an important way.

We examine a Hotelling (1929)economy consisting of a “city” that lies ona straight line of unit length. The city’slength is covered by a continuum ofhouseholds. The location of eachhousehold corresponds to its preferencesfor banking services. In particular, eachhousehold demands exactly one unit ofbanking services but the nature of desiredservices differs among households. Prefer-ences in the real world are, of course,multidimensional, encompassing tastes fordifferent menus of financial services,different levels of service, or different loca-tional preferences. We assume for the sakeof simplicity, however, that a household’spreferences for banking services can berepresented in terms of a single index run-ning from zero to one. Figure 1 depictsthe linear-city model.

Because we are interested only in theformation and consolidation of creditunions, we assume that credit unions arescarce (or differentiated) while commercialbanks are ubiquitous (or uniform). In otherwords, consumption of credit-union-provided financial services takes place atthe point on the unit interval where a credit

union is located, while commercial-bankservices are available at a fixed price at anypoint on the line. This assumption makeshousehold preferences critical for the exis-tence of and participation in credit unionswhile maintaining the realistic assumptionthat commercial banks provide an alterna-tive to credit unions (and vice versa).

We assume that the entire city (i.e.,every point on the line) is covered by at leastone household and at most two households.Without loss of generality, we assume thatall points covered by two households arearrayed continuously from zero upwardtowards, but potentially short of, one on theunit interval. For expositional purposes, wewill refer to the households that inhabit thecompletely covered zero-to-one interval asbeing above the line and all others as belowthe line. Thus, two households that possessidentical locations (preferences) are said tobe “back-to-back” households.

Households are further grouped byaffinity, or common bonds. For tractability,we discuss occupational common bondsand limit the number of employers in theeconomy to three. Each household locatedabove the line contains an employee ofeither firm A or firm B (but not both).Because all households in employee groupA share a common bond, they are located ina contiguous segment of the line that doesnot overlap the domain of employee groupB. All households below the line containemployees of firm C. Each employer maysponsor a credit union, although, as we will see, not all will do so.

We examine two periods (or regimes),differentiated according to the permissibilityof forming credit unions with multiplecommon bonds. All households are bornat the start of period 1 and live through theend of period 2. Each household needs toconsume one unit of banking services ineach period. These services can be providedby an occupational credit union or by abank in either period.

At the beginning of the first period,households find themselves arrayed alongthe city’s unit interval. The lengths of the firm-A and firm-C segments aredistributed as uniform random variables



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Figure 1

Linear City with Three Common Bonds of Occupation

Preferences for Banking Services

AAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBB

CCCCCCCCCCCCCCCCCCCCCCCC

Households employed by firm A Households employed by firm B

Households employed by firm C

0 1

on the [0, 1] interval. The length of thefirm-B segment is one minus the length ofthe firm-A segment.

Suppose, first, that each of the threeemployers sponsors a credit union (in thesimulation below, not all firms necessarilysponsor a credit union). All credit unionsare restricted to a single employee groupduring the first period. Each credit unionhas a life span of one period. The creditunions have idiosyncratic technologies forproducing banking services. In particular,each credit union i operates with fixedcosts fi = fa + fbei , where fa and fb are commonto all credit unions and ei is an i.i.d. uniformrandom variable. In addition, each creditunion faces constant marginal costs of v perunit of banking services provided. Thus,the cost function of credit union i is C(mi) = fa + fbe i + vmi , where mi is thenumber of actual members in the creditunion, and i = A, B, or C. An importantfeature of this cost function is that averagecosts, C(mi)/mi , are declining in thenumber of members the credit union isable to attract.

At the beginning of period 1, householdsvote on the credit-union management teamfor that period. Voting is costless, the one-household one-vote principle applies, andside payments among households are per-mitted (to allow those with strongly heldpreferences to “buy” the votes of those withweaker preferences). This implies, by virtueof the “value maximization principle,” thatthe competitive outcome maximizes socialwelfare (Milgrom and Roberts, 1992, pp.36-37). The potential members choose amanagement team that locates the creditunion to minimize the sum of member“travel costs” (which are described in thefollowing paragraph). It is clear that thecredit union will locate in the center of the preference spectrum of all potentialmembers because we assume that travelcosts are quadratically increasing in the distance between member households and the credit union.

Credit-union services are offered at theprice pi to all potential members of a creditunion (i.e., employees of the relevantfirm). The price equals the credit union’s

average costs (ACi) because credit unionsare not-for-profit institutions. Householdsface marginal costs of t 3 r per unit of dis-tance r when travelling to a credit union witht being a travel-cost parameter. This isbecause the credit union’s banking services are(in general) not identical to a given house-hold’s preferences (i.e., location on theline). The cost of using credit union i at adistance rj from household j ’s location is(t/2)r j

2. Each household also can accessbanking services from a commercial bankat a constant price c. Together, theseassumptions imply that the membership ofcredit union i will comprise all households jwithin the potential membership for whichthe following inequality holds (see Figure 2):

In particular, the marginal—i.e., mostdistant—households will be the ones (oneither side of the credit union) for whichthe expression holds at equality:

As Figure 2 illustrates, not everypotential member joins the credit union.A household relatively far from the creditunion (at a distance greater than r*) buysbanking services from a commercial bankinstead. The number of members credit

tr c pi2

* .2 = −

tr c pj i2

2 ≤ − .



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Figure 2

Travel Costs Facing Households Employed by Firms A and B

Travelcosts

Marginal HHs

CreditUnion B

a

r*

1Credit

Union A

Households employed by firm A Households employed by firm B

O

c - p

union i attracts is therefore 2r*, which we denote m*.

Because the average cost as a functionof the number of credit-union members,m, is (f + vm)/m, and price must be equalto average cost, we now obtain an expres-sion relating the distance between themarginal member and the credit union, r*,and the optimal number of members in thecredit union, m*:

(1)

But we know that r* = m*/2, so we cansubstitute in equation 1 for r* to obtain a

cubic expression that determines theoptimal number of credit-union members,m*, expressed in terms of the demand-sideparameters c and t (price of commercial-banking services and the travel-costparameter, respectively), as well as thesupply-side parameters f and v (fixed andmarginal costs of credit-union productionof financial services, respectively):

(2)

The economic interpretation of Equation 2, the optimality condition, is straightforward. The left-hand side rep-resents the demand curve for credit-unionservices, while the right-hand side representsthe average-cost curve of a credit union.Credit unions are not-for-profit institutions,so their average-cost curves also are theirsupply curves. A downward-sloping supplycurve indicates that scale economies existin the range we consider (see Figure 3). Formpot > m*, where mpot is the potential mem-bership of the credit union, we obtain aninterior solution. In other words, the parti-cipation rate—the fraction of the potentialmembership that chooses to join the creditunion—is lower than one. For mpot ≤ m*,on the other hand, the participation rate isequal to one because all potential memberschoose to join.

Notice that, if the domain of potentialmembers of a credit union is too small, the supply and the demand curves maynot intersect. In this case, the credit unioncannot operate because there is no positivenumber for m* that satisfies equation 2(see Figure 4).

The second period of the model corre-sponds to a regime in which the law allowscredit unions to serve groups of householdsunited by different common bonds (e.g.,employees of both firms A and B). A newmanagement team must be selected at thebeginning of period 2 to operate each creditunion. New credit unions may be formedin which multiple occupational groups areincluded. In addition to single-employercredit unions, we now might see fourother combinations of common bonds—

ct m f vm

m−

= +2 2

* *

*.

2

ct

rf vm

m− = +

2*

*

*.2



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Figure 3

Demand and Supply Curves for Credit-Union Services

ACc – t/2 X (m/2)2 Supply

Demand

mm*m 1pot m

2pot

Figure 4

A Case in Which No Credit Union Exists

ACc – t/2 X (m/2)2

Supply

Demand

m

a multiple-group credit unionencompassing employees of firms:

• A and B (what we term an “A&B”credit union) plus a single-group creditunion serving employees of firm C;

• A and C (an “A&C” credit union) plusa single-group credit union servingemployees of firm B;

• B and C (a “B&C” credit union) plus a single-group credit union servingemployees of firm A; and

• A, B, and C (an “A&B&C” credit union).

As in period 1, none of these credit unions necessarily exists; the particularconfiguration of parameters will determinethe outcome.

We allow for side payments so there isno path dependence as we go from period1 to period 2 (i.e., period-2 results do notdepend on period-1 outcomes). As inperiod 1, the socially optimal combinationof occupational groups is chosen. Also,the new credit unions will again be locatedin the center of the preference spectrumsof their potential members. Before voting,all potential members of the various creditunions observe the (random) technologythe new credit unions possess. These aredrawn anew at the beginning of period 2.We allow the fixed costs of a multiple-group credit union to deviatesystematically from the fixed costs of asingle-group credit union. The fixed costsof a multiple-group credit union i amountto fi = fa(1+a) + fbei , with a>–1–fbei / fa.

After the new credit unions have beenestablished, each household either purchasesone unit of banking services from the creditunion or it buys them from a commercialbank. The economy ends after period 2.

Finally, we point out several compara-tive-static features of the model that followstandard intuition despite the existence ofa downward-sloping supply curve. The twoimportant demand-side parameters are t,the households’ travel-cost parameter, and c, the cost of alternative bankingservices as provided by a commercial bank. Recalling Figure 3, which shows the supply curve of the credit union andthe demand curve for its services, it is clear

that as a household’s travel costs rise, thedemand for credit-union services declines.We interpret rising travel costs as anincrease in the strength of a household’spreferences for its ideal bundle of bankingservices. Such an increase causes thedemand curve to shift downward,decreasing m*. That is, the optimal size of the credit union declines. On the otherhand, an increase in the price of commer-cial-bank provided financial services, c,shifts the demand curve up. This has theopposite effect on the optimal size of thecredit union, increasing m*.

The important supply-side parametersof the model are f, the credit union’s fixedcost, and v, the credit union’s marginal costof providing banking services. An increasein f pushes up the supply curve of credit-union services, with the sharpest increase atlow levels of membership. An increase inthe marginal cost of credit-union productionalso translates into an upward shift of thesupply curve. In both cases, the size of thepotential membership required to achievefull participation increases.

Simulation of the ModelWe simulate the model by drawing

repeatedly (10,000 times) a set of five uni-formly distributed random numbers fromthe [0, 1] interval. The first draw determinesthe length of the segment containinghouseholds with an employee of firm A.Recall that the length of the segmentcontaining firm-B households equals oneminus the length of the firm-A segment.The second draw determines the length ofthe segment containing households withan employee of firm C. This determinesthe length of the line segment that is cov-ered by two households. The last threerandom numbers enter the three (potential)credit unions’ cost functions as stochasticelements of their fixed costs (denoted ei inthe model description above, i = A, B, C).These random elements in the credit unions’cost functions ensure that a “conglomerate”credit union consisting of the employees ofall three firms is not degenerate—i.e., existingwith probabilities of either zero or one.



51

Recall that in the first period, all creditunions must consist of a single commonbond. The first step in the formation of a credit union is a vote by the potentialmembership on the management team.Since side payments are allowed, the teamthat minimizes the sum of the travel costsof all potential members—i.e., which picksthe most central location—will win. In asecond step, all households decide whetherto become members or to purchase financialservices from a commercial bank.

We calculate the preferred outcome for each group of households in turn (A, B, and C). The equilibrium solutionfor each employee group must be one ofthree possibilities: the credit union existsat a corner solution, in which all householdsparticipate; the credit union achieves aninterior solution with a participation rateless than one; or the credit union does notexist. To compare the various outcomes,we calculate a welfare index for each groupof households that is simply the sum of theproduction costs of the credit union (if itexists), the travel costs incurred by house-holds that use credit unions, and theexpenditures of households that obtainfinancial services from a bank, allmultiplied by negative one (to maintainthe convention that a higher index valuesignifies higher social welfare):

(3)

In the second period, multiple-groupcredit unions are allowed. We iteratethrough the possible combinations by firstallowing mergers between two given creditunions and forcing the third to operateindependently (if it exists). Then we allowall three credit unions to merge. In eachregime, households vote on the managementteam (i.e., choose the credit union’slocation). In particular, householdschoose between a team that would operatethe credit unions independently and ateam that would merge them. Becausebribing is allowed, the team thatmaximizes the welfare index over allpotential members will win. It is possible

that a stand-alone credit union that couldnot exist on its own becomes part of amultiple-group credit union. The reason is that the post-merger credit union is ableto spread its fixed costs over a larger mem-bership. It also is possible that a creditunion that could not exist on its own alsois not viable as part of a multiple-groupcredit union. On the other hand, anyemployee group that is served by a creditunion in period 1 also will be served by acredit union in period 2 because allmergers must be welfare-enhancing. Thatis, all options for operating credit unionswith single common bonds available inperiod 1 still are possible after permittingmultiple common bonds in period 2.

Table 1 displays a summary of the simulation results. The table presents two measures of credit-union activity: the fraction of all employee groups servedby a credit union and the fraction ofhouseholds served by a credit union.When only single-employer credit unionsare allowed (period 1), only 6 percent ofthe 30,000 simulated employers (A, B, andC in each of 10,000 simulations) actuallysponsor a credit union and only 4 percentof households actually belong to creditunions. Among households that areeligible to join a credit union, some 50percent do so. All other households usecommercial banks to obtain financial ser-vices. We have chosen parameter values toreflect the fact that single-group creditunions are relatively small and may not beviable for many employee groups.

The bottom part of Table 1 presentsresults when multiple-group credit unionsare allowed (period 2). It is clear that thepermissibility of multiple common bondsdramatically increases the viability ofcredit unions. This is a general result inthe sense that restricting credit unionmembership to one employee group is abinding constraint, the relaxation of whichmay increase the beneficial role of creditunions for employees. When two employeegroups may be combined in a single creditunion (A and B, A and C, or B and C), thefraction of employee groups in the economyserved by a credit union rises to between

− + − − −∫∫( ) ( ) .**

f mv tr m m cpotrr

dr dr00



52

14 and 50 percent, while the fraction ofhouseholds served by a credit union risesto between 4 and 37 percent, dependingon the combination. When all threeemployee groups are allowed to combinein a single credit union (A and B and C),the fraction of employee groups served by a credit union jumps to 49 percent,although only 30 percent of householdsare still served.4

Examination of column 6 indicatesthat multiple-group credit unionscomprising groups A and B or A, B, and Care characterized by relatively low partici-pation rates. This reflects the fact thatmany members of employee groups A andB are located far from any multiple-groupcredit union, reducing their incentive tojoin. The credit union formed by employee

groups A and C alone, on the other hand—which are located back-to-back—ischaracterized by a very high participationrate (77 percent of those eligible actuallyjoin). This is because the preferences ofthese two groups overlap.

In general, how likely households areto join credit unions does not depend pri-marily on whether multiple-group creditunions are allowed (see column 7, wherethe exception is the credit union com-prising groups A and C, the back-to-backcase). In other words, participation ratesin multiple-group credit unions are notnecessarily higher. Rather, it is the factthat more credit unions are viable whenmultiple common bonds are allowed thatis responsible for the expanded role ofcredit unions in the economy. A comparison

4 Household segments notinvolved in a merger during thesecond-period simulations facethe same economic situation asin the first period. Consequently,they come to the same decisionduring the second period ofwhether to operate a creditunion as they did during thefirst period.



53

Simulation Results (1)Fraction of employee groups Participation rates as served by… a fraction of… 1

Credit Unions in the Economy

Period 1 Welfare index

Only single-group credit unions –23,951.89 0.06 0.06 ---- 0.04 0.50 ---- 0.50

Period 2 Increase in welfare index

A&B, C 53.09 0.14 0.04 0.10 0.04 0.50 0.31 0.40

A&C, B 1,048.20 0.50 0.03 0.47 0.37 0.48 0.77 0.74

B&C, A 523.49 0.34 0.04 0.30 0.16 0.45 0.60 0.46

A&B&C 1,123.34 0.49 0.01 0.48 0.30 0.58 0.41 0.42

Optimal Combination 1,590.32 0.94 0.02 0.93 0.43 0.54 0.56 0.56

Parameter values: fa = 0.1; a= 0; fb= 0.1; t = 22; c = 1.6; v = 1.1 Participation rate is the fraction of eligible households that belongs to a credit union. Rates are weighted by segment lengths.

Table 1

(1)Any Credit

Union

(2)A Single-

Group CreditUnion

(3)A Multiple-

Group CreditUnion

(4)All

Households

(5)Those

HouseholdsEligible to

Join a Single-Group Credit

Union

(6)Those


Join aMultiple-

Group CreditUnion

(7)Those


Join a CreditUnion

(weightedaverage of 5 and 6)

of columns 1 and 3 shows that newlyviable multiple-group credit unions areindeed the key to greater credit-unionaccess by households, as the lion’s share of all credit unions in every possible con-figuration in period 2 include multiplecommon bonds.

The final row of Table 1 presents the social optimum, which is the welfare-maximizing combination of single-and multiple-group credit unions that isfeasible in the economy. Multiple-groupcredit unions serve 93 percent of allemployee groups in the social optimum,while single-group credit unions serveonly 2 percent. Average household partici-pation rates are similar across the twotypes of credit unions, with the multiple-group average slightly higher.

The averages presented in Table 1 conceal two important features of creditunions in our model, however. Figure 5 is a scatterplot showing the participationrates of all the (optimally formed) creditunions from our 10,000 runs as a functionof potential membership. The horizontalscale runs from about 0.1 (the minimumsegment length needed to support a creditunion under our baseline parameterization)to 2.0 (the sum of two unit-length segments,corresponding to the maximum potentialmembership of any multiple-group creditunion). The two distinct downward-curving sets of points represent the

declining participation rates of single-group (the gray points in the lower curve,ending at 1.0) and multiple-group creditunions (the blue points), respectively. Ifwe were to show each type of credit unionplotted in Figure 5 in a separate chart, twoimportant features would be obvious from the average participation rates shown in Table 1.

The first feature is that participationrates of multiple-group credit unions tendto lie above those of single-group creditunions for a given number of potentialmembers. This points to the fact that mul-tiple-group credit unions can be closer tothe average member’s preferences due tothe existence of back-to-back households(i.e., households with different employersbut identical preferences for bankingservices). This effect is due entirely to thehouseholds in employee group C in ourmodel, whose preferences overlap those of some households in other employeegroups, most importantly group A.

Figure 5 also shows the second impor-tant feature of the model that is notrevealed in the table—the downward slopeof both main sets of points. Greater poten-tial membership tends to generate lowerparticipation rates. This always holds for single-group credit unions and for multiple-group credit unions that comprise“horizontally neighboring” membershipgroups only (i.e., groups A and B). Giventhe travel costs that represent preferenceheterogeneity among the potential mem-bership, it is not surprising that creditunions that span a more heterogeneous setof households are able to attract propor-tionately fewer of them. For credit unionsthat comprise segments B and C, participa-tion rates initially fall with an increase inthe membership base, then rise and laterfall again. Credit unions that unite allthree employee groups (A&B&C creditunions) exhibit a similar pattern in termsof participation rates. For A&B&C creditunions, a rise in the potential membershipis due solely to an increase in the intervalspanned by group C, which means anincrease in the fraction of householdslocated back-to-back. For back-to-back



54

Figure 5

1.11.00.90.80.70.60.50.40.30.20.10.0

0.1 0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1

Participation Rates as a Function of Potential MembershipParticipation Rate

Length of Household Continuum

credit unions of the type A&C, the participation rate increases with a growingmembership base if (and only if) the overlapof the intervals spanned by the two segmentsincreases. If (and only if) the overlapshrinks with an increase in the potentialmembership, the participation rates shrink,too. To sum up, the overall effect of thesize of potential membership on the partic-ipation rates depends on the relativeimportance of the various types ofmultiple-group credit unions.

Table 2 presents comparative-staticresults for changes in the parameters t, c,and a (the travel cost parameter, the priceof banking services of commercial banks,and the parameter in the multiple-groupcredit unions’ fixed costs, respectively).The first row restates the results of thebenchmark simulation summarized in thelast row of Table 1. Columns 1-5 show the number of times in the 10,000 runs ofthe simulation that each configuration ofcredit unions was optimal. The most fre-quently preferred configuration was atwo-group credit union comprisingemployee groups A and C (column 3), the back-to-back solution. In this configuration, employees of firm B weresometimes served by a credit union andsometimes not; the feasibility of a credit

union for employee group B depends onthe size of the membership base and therandom technology of the potential creditunion. The next most frequently preferredconfiguration involved a three-group creditunion. Across all simulations, almost 27percent of employee groups were leftunserved by credit unions even though all mergers were chosen optimally (thisfigure is calculated from column 6, whichis divided by the total number of employeegroups in the simulation, 30,000). It isapparent that participation rates of multiple-group credit unions (column 10) aredragged down primarily by the relativelylow participation rates in the credit unionswith horizontally neighboring groups (i.e.,credit unions A&B and A&B&C; recall theresult from column 6 of Table 1).

The first comparative-static exercisewe performed is summarized in the secondrow of Table 2. When the price of financialservices offered by commercial banks rises,the fraction of employee groups as well asthe fraction of households served by creditunions increases, as expected. Fromcolumn 6 we know that only 16 percent of employee groups have no credit unionafter the higher cost of bank-provided services is imposed, while only 46 percentof households use a commercial bank



55

Simulation Results (2)Column Parameter Number of times this configuration of Participation rates as a fraction of… 2

Values credit unions was optimal:1

(1) 0 22 1.6 746 168 4,452 1,168 3,466 7,959 0.43 0.56 0.54 0.56(2) 0 22 1.7 302 394 4,580 1,223 3,501 4,782 0.54 0.61 0.64 0.61(3) 0 24 1.6 926 99 4,436 1,169 3,370 8,793 0.40 0.55 0.50 0.55(4) 0.05 22 1.6 895 111 4,489 1,148 3,357 8,436 0.43 0.57 0.54 0.57

1 Based on 10,000 runs.2 Weighted by segment lengths.

Table 2

(1)A, B, C

(2)A&B, C

(3)A&C, B

(4)B&C, A

(5)A&B&C

(6)Number ofemployeegroups notserved by acredit union

(7)All House-

holds

(8)All House-

holdsEligible to

Join a CreditUnion

(9)Those


Join aSingle-Group

Credit Union

(10)Those


Join aMultiple-

Group Credit Union

a t c

(down from 57 percent in the benchmarkcase; see column 7). Interestingly, all of themultiple-group credit unions increasinglyare preferred when banking servicesbecome more costly, while only the single-group credit unions become less likely to be optimal. A higher price for bank-provided services is predicted by higherbanking concentration in the structure-conduct-performance paradigm, and ourcomparative-static result demonstrates thatcredit unions are indeed likely to benefitfrom more concentrated banking markets.

The second comparative-static resultwe computed is summarized in the thirdrow of Table 2. When the cost of travellingto a credit union is increased—intuitively,when preferences for banking servicesbecome more idiosyncratic or stronglyheld—both the fraction of employeegroups served by credit unions and theparticipation rate of households decline(columns 6 and 7-10, respectively). Com-pared to the benchmark case, the numberof single-group credit unions in optimalconfigurations increases (column 1). On the other hand, multiple-group creditunions appear somewhat less attractive(columns 2-5).

The last row of Table 2 displays ourthird comparative-static result. When thefixed costs of production are systematicallyhigher for multiple-group credit unionsthan for single-group credit unions, theformation of multiple-group credit unionsis less advantageous. Relative to thebenchmark case displayed in row 1, fewergroups of employees are served by creditunions (column 6). When they exist,credit unions with multiple-group chartershave higher participation rates than in thebenchmark case (column 10), which isdue mainly to the higher representation ofpure back-to-back credit unions (column3). This leaves the overall household par-ticipation rate unchanged at the reportedtwo-digit level of precision (column 7).

Taken together, the comparative-staticresults in Table 2 indicate that the optimalconfiguration of credit unions in theeconomy is sensitive to model parameterssuch as the market price of bank-provided

financial services, the intensity ofpreferences for specific bundles of bankingservices, and the potential extra costs asso-ciated with multiple-group charters.

HypothesesWe are now able to state several

testable hypotheses that involve the determinants of the participation rate andthe average operating costs (i.e., the costratio). First, we focus on participationrates at credit unions. Our maintainedhypothesis is that a credit union is moresuccessful in providing services to its constituency the less heterogeneous is its membership. This leads to our firsttestable hypothesis:

• HYPOTHESIS 1. A credit union’s participation rate falls with thenumber of its potential members, all else held constant.

Another hypothesis concerns theeffects of local banking-market conditionson credit-union participation rates:

• HYPOTHESIS 2. A credit union’s participation rate rises with the levelof concentration in the local bankingmarket, all else held constant.

Next we investigate the validity of ourmaintained assumption that credit unionsface scale economies in production:

• HYPOTHESIS 3a. A credit union’scost ratio falls with the number of itspotential members, all else heldconstant.

• HYPOTHESIS 3b. A credit union’scost ratio falls with its level of totalassets, all else held constant.

Related questions include the effect of multiple-group charters on the cost ratio and the participation rate. Neither the model nor the simulation address therelationship between multiple commonbonds and the cost ratio. As for the impact



56

of multiple common bonds on the participa-tion rate, the model and simulation resultsare ambiguous. Consequently, it is purelyan empirical question how multiple-groupcredit unions affect operating costs and par-ticipation rates, holding all else constant.

DATA AND EMPIRICALMETHODS

We examine a subset of all federallychartered and federally insured occupationalcredit unions in 1996 (see the appendixfor details on construction of the datasetand the variables we use). Table 3 providesa breakdown of our sample according tothe type of membership group characterizingeach credit union. The table distinguishesbetween credit unions with a single commonbond and those with multiple commonbonds. Credit unions sponsored by asingle educational institution, for example,numbered 299 in our sample. Creditunions with a membership comprisingmultiple common bonds, most of whichwere educationally oriented, numbered469, and so on for the other membershiptypes. Overall, 1,980 credit unions in oursample had a single common bond (41.8percent of the sample) while 2,753 creditunions had multiple common bondsamong the membership (58.2 percent).

In addition to data on individual creditunions, we collected three types ofenvironmental variables. To control fordifferences in local economic conditions,we gathered levels and computed growthrates of real gross state product for eachstate. Measures of economic activity maycapture systematic differences in demandfor credit union services that we have notmodeled explicitly. We also calculated theHerfindahl index of concentration of bankdeposit shares in each credit union’s localbanking market, since concentration measures often are used to control for differences in the competitiveness of localmarkets. The index is calculated as thesum of the squared market shares of allparticipants in each local market. Third,we collected data on population density by county, which might be another factor

in credit unions’ competition withcommercial banks.

We use a semiparametric model to allowthe influence of the number of membersand total assets on the dependent variableto be nonlinear. The parametric part ofthe model contains independent variableswhose effects may be approximately linear,such as the Herfindahl index. In particular,we use a semiparametric model of a creditunion’s participation rate of the form:

(4)

where yi is the i-th observation of thedependent variable; xpi is a row vector consisting of the i-th observation of theexplanatory variables of the linear(parametric) part of the model; bp is acolumn vector of the parameters of thelinear part of the model; xi is a vector consisting of the i-th observation of theexplanatory variables in the nonparametricpart of the model; and (εi is the i-th realiza-tion of the error term. For details on thiseconometric approach, see the appendix in Emmons and Schmid (1999).

Our hypotheses are framed in terms oftwo different dependent variables, namely:1) PARTICIPATION, the participation rateof those eligible to join the credit union,

y x f x i ni pi p i i= × + ( ) + =β ε , , , ,1 K



57

Distribution of Credit Unions by Type Of Membership (TOM)

Number of TOM Credit Unions Codes 1 Type of Membership

299 4 Educational37 5 Military392 6 Federal, state, local government744 10-15 Manufacturing508 20-23 Services469 34 Multiple group – primarily educational124 35 Multiple group – primarily military621 36 Multiple group – primarily federal, state, local government821 40-49 Multiple group – primarily manufacturing718 50-53 Multiple group – primarily services

Total: 4,733

1 National Credit Union Association (NCUA), Instruction No. 6010.2, July 28, 1995.

Table 3

defined as the number of actual membersdivided by the number of potential mem-bers as specified in the credit union’scharter; and 2) COST, the credit union’stotal operating expenses divided by totalassets. There are four independentvariables of interest: the number of mem-bers (or the number of potential memberswhen we examine participation rates);total assets (for the COST regression); theHerfindahl index of local bank-depositconcentration (HERF); and the indicatorvariable MULTGROUP, which is equal toone if the credit union has a multiple-group charter and zero otherwise.

Membership (or potential membership)and total assets are included in thenonparametric part of both regressionapproaches. They are in logarithmic formand—to avoid simultaneity problems—arelagged by one period. The parametric partof the model includes the other two variablesof interest, HERF and MULTGROUP. Theparametric part also contains the followingcontrol variables: the credit union’s homestate’s real gross state product per capita(REALGSPPC) in the PARTICIPATIONregression; the log growth rate of realgross state product (GRREALGSP) in theCOST regression; and indicator variablescorresponding to the credit union’s primaryfield of membership (in both regressionapproaches). Fields of membership includeeducational, military, government,

manufacturing, and services. Because thereis a constant included in the nonparametricpart of the regression equation, we mustdrop one of the membership indicator variables; we chose the educationalindicator variable for exclusion.

The variable REALGSPPC in the PARTICIPATION regression controls forpreferences for banking services as theymay vary with real income. In the COSTregression, GRREALGSP serves as a measurefor real growth, which is a main factor inthe capacity utilization of credit unions.In the PARTICIPATION regression, theHerfindahl index is lagged to avoid simul-taneity problems that may arise from theinteraction between credit-union participa-tion rates and concentration in the localbanking market.

Table 4 presents descriptive samplestatistics for the dependent and some ofthe independent variables. The participationrate among sample credit unions rangedfrom 3 percent to 100 percent, with themedian at 62 percent. The median costratio was 3.90 percent, with a range of0.63 to 41.70 percent of assets. Althoughthis range may contain some extremevalues, we retain all observations becauseall of them contain information. Inaddition, our locally weighted regressionapproach is somewhat robust to outliers.Total assets ranged from $43,000 to $8.92 billion, with the median credit



58

Descriptive Statistics1

StandardMinimum Median Mean Maximum Deviation

Participation Rate (PARTICIPATION) 3.050 3 10–2 6.246 3 10–1 6.142 3 10–1 1 2.139 3 10–1

Cost Ratio (COST) 6.268 3 10–3 3.897 3 10–2 4.088 3 10–2 4.169 3 10–1

1.739 3 10–2

Total Assets 4.300 3 104 6.231 3 106 3.300 3 107 8.922 3 109 1.652 3 108

Number of Members 4.500 3 101 1.865 3 103 6.833 3 103 1.601 3 106 2.860 3 104

Number of Potential Members 7.500 3 101 3.193 3 103 1.432 3 104 2.032 3 106 5.540 3 104

Herfindahl Index 5.346 3 10–2 1.966 3 10–1 2.080 3 10–1 1 9.469 3 10–2

1 4,733 observations.

Table 4

union holding $6.23 million in assets. The number of actual and potential mem-bers ranged from 45 to 1.6 million and 75to 2.03 million, respectively, while medianactual and potential membership countswere 1,865 and 3,198, respectively.Finally, Herfindahl indexes in relevantbanking markets ranged from 0.0535 to 1.00 with a median value of 0.1966(recall that the index is defined on theinterval ((0,1]).

EMPIRICAL RESULTSOur results are presented in two

sections corresponding to the dependentvariable used. The first section discussesresults from regressions using creditunions’ participation rate while the secondsection reports results from regressionsusing credit unions’ cost ratio.

Participation RatesHypothesis 1 relates the size of a

credit union’s potential membership to itsparticipation rate. Regressions includingPARTICIPATION use (the lagged value ofthe log of) potential members instead ofactual members. Potential members arerelevant for evaluating participation ratesbecause all individuals eligible to join consti-tute the predetermined economic potentialthat each credit union seeks to exploit.

The series of plots presented inFigures 6-8 are “conditioning plots.” The solid lines in Figures 6-8 are pointestimates and the dashed lines indicate 90-percent confidence bounds. In eachplot, one variable is held at its medianvalue while the other variable (identifiedon the horizontal axis) is allowed to vary.The graph displays the impact of this independent variable on the level of the dependent variable. In other words,the slope of the graph at a particular pointreflects the marginal impact of the indepen-dent variable at that point. The interceptis not identified in regressions of this type, so only vertical distances aremeaningful (not the level itself). In sum,the key to interpreting these graphs is



59

Figure 6

8

6

4

2

0

–2

–4

–6

–84 6 8 10 12 14 16

Participation Rate – Number of Potential MembersPartial Impact

Log of Number of Potential Members

Figure 7

–2

–4

–6

–8

–10

–12

–14

–16

–1842 6 8 10 12 14 16

Cost Ratio – Number of Members

Partial Impact

Log of Number of Members

Figure 8

0

–2

–4

–6

–8

–10

–12

–14

–1618 20 22 2410 12 14 16

Cost Ratio – Total Assets

Partial Impact

Log of Total Assets

to focus on the slope of the curve and on the vertical differences moving along the horizontal axis.5

Figure 6 provides evidence supportingHypothesis 1 (a negative relationshipbetween participation rates and potentialmembership). The plot supports Hypoth-esis 1 because the lower confidence boundat small credit unions (small number ofpotential members) lies above the upperconfidence bound for large credit unions,except for the very smallest and very largestcredit unions, where the small number of observations widens the confidenceintervals. This confirms our findingswhen we simulated the theoretical model(recall Figure 5) and is consistent with theidea that larger membership pools containgreater heterogeneity of preferences forbanking services. This leads to greater differences in the most preferred bundle of banking services between the medianmember and members in the tails of thepreference distribution.

An existing single-group credit unionthat adds one or more membership groupsto its common bond encounters both ben-efits and costs of expansion. On the onehand, adding membership groups whosepreferences are close to those in the existingfield of membership (the back-to-backcase) may increase the participation rate.This outcome would be predicted as a

result of a reduction in average operatingcosts and hence in the credit union’s priceof banking services. On the other hand, for a given credit-union charter, a highernumber of potential members typicallymeans more heterogeneity and thus a lowerparticipation rate as the travel distance ofthe members located in the tails of the preference distribution increases.

Table 5 presents results from the parametric part of the model. The resultsprovide evidence on the question ofwhether credit-union participation ratesdiffer when comparing credit unions with a single common bond to those withmultiple common bonds, holding all elseequal. Recall from Tables 1 and 2 thatcredit unions with multiple-group charterswill (on average) have higher participationrates than single-group credit unions ifback-to-back membership combinationsdominate (i.e., if there is a significantoverlap of banking preferences amongemployees of different firms). Table 5indicates that multiple-group credit unionsin our sample indeed have higher partici-pation rates, perhaps reflecting the abilityof multiple-group credit unions to capitalizeon similar preferences among employees of different firms.

Another interesting result in Table 5 is the positive and significant coefficienton the lagged Herfindahl index of bankdeposit concentration in credit unions’local markets (Hypothesis 2). Thisindicates that, the more concentrated itslocal banking market is, the higher a creditunion’s participation rate will be. In otherwords, credit unions may provide anattractive alternative for consumers whoface a relatively uncompetitive localbanking market.

Cost RatioHypotheses 3a and 3b refer to tests

of an important maintained assumption of our model, namely, that a credit union’soperating expenses should decline with anincrease in its scale of operation. We alsowould like to know whether serving mul-tiple-group memberships is costly.

5 See Cleveland and Devlin(1988).



60

Participation Rate

Independent Variable Coefficient t-statistic

MULTGROUP 8.684 3 10–2 2.834 ***

HERF (lagged) 3.628 3 10–1 2.535 **

REALGSPPC –1.820 –1.090

POPDENS –3.743 3 10–6 –1.002

TOM: Military 2.266 3 10–1 3.004 ***

TOM: Government 6.205 3 10–2 1.496

TOM: Manufacturing –2.123 3 10–2 –0.560

TOM: Services 1.304 3 10–1 3.284 ***

Number of Observations 4,691

**/*** Significant at the 5/1 percent level (two-tailed tests).

Table 5

Figure 7 plots COST against thenumber of members, while holding thelevel of total assets constant at its medianvalue in the sample. The plot shows thatCOST decreases sharply beyond a certainthreshold level of membership. For smallcredit unions, average costs seem to increaseslightly with the number of members.While wide confidence intervals indicatethat in this range the relationship betweenaverage costs and number of members isestimated imprecisely, an initial increase inthe average operating costs actually mightbe supported by the data. For small creditunions, subsidies (such as rent-free officespace, volunteer workers, etc.) tend to berelatively more important than for largeunits. As these subsidies become lessimportant for credit unions with highernumbers of members, measured operatingcosts might approach shadow operatingcosts. Overall, the findings support ourmaintained assumption of decliningaverage costs as the scale of operationsincreases. Similar evidence is provided inFigure 8, which is generated by the sameregression that produced Figure 7. Figure8 plots the influence of another measure of the size of operations, total assets, onthe credit union’s average operating costs(Hypothesis 3b) while holding the numberof members constant at its median value in the sample.

Table 6 presents results from the parametric part of the model. The resultsindicate that there is a positive relationshipbetween the existence of multiple member-ship groups in a credit union and COST.One might think that multiple-group creditunions would have high cost ratios due to agency costs. According to this line ofreasoning, as membership groups try tofree-ride on each other’s monitoring, super-vision of management might be inefficientlylow. As Emmons and Schmid (1999) show,however, there is no evidence of multiple-group charters causing agency costs.

Finally, the significantly negative coef-ficient on the Herfindahl index in Table 6implies that higher levels of bank concentra-tion in a local market lead to lower levels ofthe cost ratio reported by credit unions.

One possible explanation is that lessintense competition from banks allowscredit-union managers to enjoy a “quietlife.” For example, credit unions may be able to attract or retain members withlower marketing efforts or lower qualityservices than would be the case in a morecompetitive market. On the other hand,the quiet life that comes with less competi-tive markets might allow greater scope for managerial agency costs. If the latterwere the case, however, it would generatepredictions opposite to our empirical find-ings of lower average operating expenses.

CONCLUSIONSContinued expansion of credit unions

has been accompanied by public debateand courtroom confrontations. Advocatesargue that credit unions provide neededcompetition to banks and thrifts in localmarkets for retail financial services. Oppo-nents, including most notably the banksand thrifts themselves, point to various subsidies to credit unions that create anunlevel playing field. Previous researchfindings do not provide unambiguous conclusions favorable to either camp, whilerecent federal legislation favorable to credit-union expansion merely has intensified thedebate. More research into the fundamentaloperation of credit unions is needed.



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Cost Ratio

Independent Variable Coefficient t-statistic

MULTGROUP 7.509 310–2 6.847 ***

HERF –1.813 310–1 –3.427 ***

GRREALGSP –8.448 3 10–1 –2.377 **

TOM: Military 1.038 3 10–1 4.533 ***

TOM: Government 1.149 3 10–1 8.043 ***

TOM: Manufacturing 1.036 3 10–1 7.444 ***

TOM: Services 8.915 3 10–2 6.019 ***

Number of Observations 4,733

**/*** Significant at the 5/1 percent level (two-tailed tests).

Table 6

In this article, we investigate therelationships between several features of credit unions, namely the number ofmembers in a credit union, the amount oftotal assets on its balance sheet, and theexistence of single and multiple commonbonds among its membership, on the onehand, and two measures of credit-unioneffectiveness, on the other. We also examinethe effect of several environmental variables,including economic conditions and bankingconcentration in the local market, on credit-union operations.

We find that a larger potential credit-union membership translates into lowercredit-union participation rates. Creditunions with multiple common bonds,holding all else constant, have higher par-ticipation rates. We also find evidence thatcredit unions in more concentratedbanking markets exhibit higher participa-tion rates.

While greater asset size appears to beassociated with lower average operatingcosts, holding all else equal, we find that a larger number of members is associatedwith a lower cost ratio only for larger creditunions. Thus, asset size and the size of themembership are distinct aspects of credit-union operations. Multiple-group creditunions have higher costs on average, allelse equal. We also find that credit-unioncost ratios are lower in more concentratedbanking markets, perhaps indicating thatcredit unions can economize on marketingor service provision when competitionfrom banks is less intense.

Our findings are particularly interestingin light of the recent AT&T Family CreditUnion case decided by the Supreme Courtin February 1998, and its sequel in theU.S. Congress that culminated in theCredit Union Membership Access Act ofAugust 1998. This new federal legislationupholds the right of federally charteredcredit unions to grow under an expansivedefinition of the common-bond requirement.The new law allows multiple groups ofmembers to belong to a single credit unionas long as the members of each group areunited by a common bond. This statutetherefore upholds regulatory actions taken

in recent years and overturns the SupremeCourt’s narrow reading of the 1934 FederalCredit Union Act restricting a federalcredit union to a single common bond.

REFERENCES

American Bankers Association. The Credit Union Industry: Trends,Structure, and Competitiveness (Washington, D.C., 1989).

BNA Banking Report. “House Passes Credit Union Bill; Clinton Wastes No Time Signing It,” August 10, 1998, Vol. 71, No. 6.

Cleveland, William S., and Susan J. Devlin. “Locally WeightedRegression: An Approach to Regression Analysis by Local Fitting,”Journal of the American Statistical Association (September 1988), pp. 596-610.

Emmons, William R., and Frank A. Schmid. “Wages and Risk-Taking inOccupational Credit Unions: Theory and Evidence,” this Review(March/April 1999), pp.13-31.

Hotelling, Harold. “Stability in Competition,” Economic Journal,(March 1929), pp. 41-57.

Kane, Edward J., and Robert Hendershott. “The Federal DepositInsurance Fund that Didn’t Put a Bite on U.S. Taxpayers,” Journal of Banking and Finance (September 1996), pp. 1305-27.

Milgrom, Paul, and John Roberts. Economics, Organization andManagement, Prentice Hall, 1992.

Supreme Court. “National Credit Union Administration, Petitioner, v. FirstNational Bank & Trust Co., et al.; AT&T Family Federal Credit Union,et al., Petitioners, v. First National Bank and Trust Co., et al.” DecidedFeb. 25, 1998. Nos. 96-843, 96-847. 118 S. Ct. 927.

U. S. Treasury Department. Credit Unions, U.S. Government Printing Office, 1997.



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DATASET AND VARIABLESThe Dataset

We analyze a dataset comprising allfederally chartered and federally insuredcredit unions during the year 1996. Thedataset was obtained from the Report ofCondition and Income for Credit Unions(NCUA 5300, 5300S), produced by theNational Credit Union Administration(NCUA). These reports are issued semian-nually in June and December. We used the December data. The flows in theDecember income statements include the entire year of 1996.

We concentrate on the following TypesOf Membership (TOM) groups amongoccupationally based credit unions: educa-tional; military; federal, state, and localgovernment; manufacturing; and services.This means that we do not includecommunity credit unions, associationalcredit unions, or corporate credit unions.Lists of TOM classification codes are fromthe NCUA (Instruction No. 6010.2, July28, 1995).

We excluded observations for any ofthe following reasons:

• Missing TOM codes.• Activity codes other than “active.”• Number of members or of potential

members not greater than one; appliesto actual and to lagged values.

• Nonpositive values for total assets or lagged total assets.

• Zero number of employees.• Zero value for “employee

compensation and benefits.”Total assets, number of members,

potential number of members, and theHerfindahl index were all lagged one year(i.e., 1995 values). All other observationsare from year-end 1996.

We calculated county-specificHerfindahl indexes as measures of concen-tration of the local banking market. AHerfindahl index is defined as the sum ofsquared market shares. We measuredmarket shares by the fraction of total bank

deposits (as of June 30) within a countybased on FDIC Summary of Deposits data.These data are available online at<http://www2.fdic.gov/sod/>.

We used either the log level of Real GrossState Product (REALGSP) or its log growthrate to control for cross-sectional differencesin macroeconomic conditions facing creditunions. The REALGSP data are in millionsof chained 1992 dollars. We obtained thedata from the U.S. Department ofCommerce, Bureau of Economic Analysis,Regional Economic Analysis Division. Thedata are available online at <http://www.bea.doc.gov/bea/regional/data.htm>.

Population density at the county levelwas calculated by dividing the total countypopulation by the total land area of thecounty (in square miles). Both the countypopulation and land area data wereobtained from the U.S. Census Bureau<http://www.census.gov>. The populationdata are Census Bureau estimates as of July 1, 1996. The land area measurementsare from the 1990 census.

Definition of VariablesWe transformed the dependent

variables in some cases to ensure that theyare not bounded. These transformationsare necessitated by the assumption ofnormally distributed error terms. Forvariables that are restricted to the positiveorthant of real numbers, we substitute theirnatural logarithms. For variables expressedas fractions (i.e., restricted to the interval[0,1]), we applied the logit transformationlog(y/(1–y)), with log being the natural log-arithm. In this case, observations equal toone were eliminated from the set of obser-vations; there were no cases in which thetransformed variable equaled zero.

Definitions of variables and underlyingdata sources are listed below. For datataken from the Report of Condition andIncome for Credit Unions, produced bythe National Credit Union Administration,the relevant item numbers are in brackets.



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Appendix

Dependent Variables. We employed twodependent variables in the regressions:1) Participation Rate (PARTICIPATION):

Number of actual credit-unionmembers [CUSA6091] divided by the number of potential members[CUSA6092]. In the regressions, we use the logit transformationlog(y/(1–y)). No zero values for thenumber of members occurred. Forty-two cases of full participation (y= 1)were eliminated from the dataset forthese regressions only.

2) Cost Ratio (COST): Total operatingexpenses [CUSA4130] divided by totalassets [CUSA2170]. In the regression,we use log values.

Independent Variables. When total assets(measured in units of one dollar), thenumber of members, or the number of potential members served as regressors,they were lagged by one period and trans-formed into natural logarithms.1. MULTGROUP: equal to one if the

credit union has multiple groups; zero otherwise.

2. HERF: Sum of squared market shares of commercial banks within a countybased on total bank deposits. By defi-nition, the Herfindahl index is greaterthan zero; its maximum value is one.

3. REALGSPPC: Real gross state productper capita (chained 1992 dollars).

4. GRREALGSP: Logarithmic changes inthe real gross state product (chained1992 dollars).

5. POPDENS: Population Density, people per square mile in each local banking market.

6. TOM code variables: equal to one ifthe credit union is of a specific type(educational, military, government,manufacturing, or services). Becausewe use an intercept in (the nonpara-metric part of) the regression, theTOM code variable for the educationalcredit union was dropped.



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