U.S. CREDIT UNIONS: SURVIVAL, CONSOLIDATION, AND GROWTH

U.S. CREDIT UNIONS: SURVIVAL, CONSOLIDATION, AND GROWTH

JOHN GODDARD, DONAL MCKILLOP and JOHN O. S. WILSON∗

This study uses hazard function estimations and time-series and cross-sectionalgrowth regressions to examine the impact of exit through merger and acquisition(M&A) or failure, and internally generated growth, on the firm-size distribution withinthe U.S. credit union sector. Consolidation through M&A was the principal cause ofa reduction in the number of credit unions, but impact on concentration was small.Divergence between the average internally generated growth of smaller and largercredit unions was the principal driver of the rise in concentration. (JEL G21)

I. INTRODUCTION

In banking and financial services, industrystructure characterized by the firm-size distribu-tion is a key determinant of the nature of com-petition. Competition among financial serviceproviders has, in turn, implications for consumerwelfare, and for the stability or fragility of thefinancial system. In the U.S. credit union sector,as in banking and financial services generally,a tendency for concentration to increase wasapparent in many developed countries through-out the 1980s, 1990s, and 2000s.1

This study examines the contribution of exitand the internally generated growth of estab-lished firms to changes in industry structure andthe rise in concentration in the U.S. credit unionsector. Changes to the membership of the popu-lation of firms through exit occurs as a result

*The authors are grateful to James MacGee (Editor) andtwo anonymous referees for many helpful comments on anearlier draft of this paper. We would like to thank LeonardNakomura, Bob DeYoung, and other participants at the FMAand SFA Annual Meetings in Denver and Charleston forhelpful comments and suggestions.Goddard: Professor, Bangor Business School, Bangor Uni-

versity, Bangor, Gwynedd LL57 2DG, UK. Phone +44-1248-383221, Fax +44-1248-383228, E-mail [email protected]

McKillop: Professor, Queen’s University ManagementSchool, Queen’s University Belfast, Belfast, North-ern Ireland BT9 5EE, UK. Phone +44-28-9097-4852,Fax +44-28-9097-4201, E-mail [email protected]

Wilson: Professor, School of Management, University of StAndrews, The Gateway, North Haugh, St Andrews, FifeKY16 9SS, UK. Phone +44-1334-462803, Fax +44-1334-462812, E-mail [email protected]

1. According to the World Bank Financial Structuredatabase (2010), the five-firm concentration ratio (CR5) forthe U.S. banking industry was 21% in 2003 and 37% in2009; for the UK: 86% (1993) and 88% (2009); for France:46% (1993) and 52% (2009); for Germany: 50% (1993) and77% (2009); and for Japan: 30% (1993) and 65% (2009).

of corporate failure or a merger and acquisi-tion (M&A) transaction in which an establishedfirm is acquired by another industry member.Variation between firms in patterns of internallygenerated growth leaves the population mem-bership unchanged, but alters the relative sharesof firms in total industry assets. If firm-levelgrowth rates are correlated with firm size, thelink between internally generated growth andconcentration is self-evident. According to thelaw of Gibrat (1931), also known as the Lawof Proportionate Effect, even if growth and sizeare uncorrelated, and the factors that influencethe firm’s growth such as customer demand,managerial talent, innovation, or organizationalstructure, are randomly distributed across firms,there is a natural tendency for concentration toincrease over time and for the firm size distri-bution to become increasingly skewed.2

2. According to Sutton (1997), Caves (1998), and Coad(2009), Gibrat’s law provides an accurate representationof the actual size distribution of firms in many industries.Empirical tests of Gibrat’s law have produced mixed results.A number of early studies, based on data up to andincluding the 1970s, report either no relationship or apositive relationship between firm size and growth. Severalrecent studies find a consistent tendency for small firms togrow faster than large firms.

ABBREVIATIONS

ADF: Augmented Dickey–FullerAIC: Akaike Information CriterionCUMAA: Credit Union Membership Access ActHHI: Herfindahl–Hirshman IndexIPS: Im, Pesaran, and ShinM&A: Merger and AcquisitionNCUA: National Credit Union AssociationNWRP: Net Worth Restoration PlanSEG: Select Employee Group

304

Economic Inquiry(ISSN 0095-2583)Vol. 52, No. 1, January 2014, 304–319

doi:10.1111/ecin.12032Online Early publication July 5, 2013© 2013 Western Economic Association International

GODDARD, McKILLOP & WILSON: U.S. CREDIT UNIONS 305

Structural and conduct deregulation, techno-logical and financial innovation, and changes inthe economic environment, enabled many U.S.credit unions to expand their scale of opera-tions significantly during the 1990s and 2000s.In 2010, credit unions accounted for around10% of consumer savings and deposits in theUnited States, and provided financial servicesto more than 90 million members.3 In commonwith commercial banking, the credit union sectorhas undergone large-scale consolidation.4 Thenumber of credit unions declined from 14,549in 1990 to 7,335 in 2010. A few new creditunions were formed, while many more disap-peared through either acquisition or failure. Atthe end of 2010, 167 U.S. credit unions reportedassets in excess of $1bn and loan portfoliossimilar in structure to that of a medium-sizedcommercial bank.5

This study provides an integrated analysisof corporate demographics for the U.S. creditunion sector for the period 1994–2010. Thereare several important insights with respect tothe drivers of acquisition and failure. Smallercredit unions are at higher risk of acquisitionor failure than their larger counterparts. Oldercredit unions that are similar in size to youngercredit unions are more likely to be acquired,but the failure probability is not age-dependent.Credit unions holding a high proportion of liquidassets, those with low loans-to-assets ratios, andthose with low profitability, are at increased riskof exit through acquisition or failure. Highlycapitalized credit unions are at increased risk ofacquisition.

3. Worldwide, more than 50,000 credit unions operate in100 countries, with a combined membership of 188 millionand assets under control of $1,460bn (World Council ofCredit Unions 2011). The credit union operating and busi-ness model is relatively homogeneous across countries. TheU.S. credit union movement is among the most developed inthe world, and the United States’ experience offers insightsfor cooperative movements in financial services worldwide.

4. During the 1990s and 2000s, financial deregulationalso eased many of the constraints on the business activ-ities of U.S. banks, increasing competition as barriers toentry into local or state banking markets were reduced oreliminated. An increasingly dominant group of large banks,operating a high-volume low-cost retail banking model, pur-sued aggressive growth strategies, including M&A on a largescale. Although similar trends toward deregulation and con-solidation have been operative for banks and credit unionsalike, analogies should be drawn cautiously in view of thedifference between the profit and non-profit orientation ofthe two types of institution.

5. Neither banks nor credit unions face restrictions onthe prices they charge for specific products. Credit unions,however, face some restrictions on their volumes of small-business lending, while banks are subject to limits on lendingconcentration.

This study also provides insights into theevolution of industry structure for the U.S.credit union sector. Consolidation through M&Ahas greatly reduced the population size, butthe impact on concentration has been mod-est, owing to the relatively small average assetsize of acquired credit unions. Internally gener-ated growth is shown to be the main driver ofthe trend toward increased concentration. Inter-preted as a descriptor of the dynamics of thesize-growth relationship for each credit unionindividually, Gibrat’s law accurately describesthe growth of credit unions at the upper end ofthe asset size distribution; but for many of thesmaller credit unions Gibrat’s law is rejectedin favor of a stationary alternative hypothe-sis. Interpreted as a descriptor of the cross-sectional size-growth relationship Gibrat’s lawis unequivocally rejected, with larger creditunions consistently experiencing faster averagegrowth than their smaller counterparts. Thisdivergence between the average growth of largeand small credit unions is the principal cause ofthe increase in concentration.

In the previous literature on credit union fail-ure, Smith and Woodbury’s (2010) comparativestudy of U.S. banks and credit unions suggestscredit unions are less exposed than banks tofluctuations in the business cycle. Elsewhere, ithas been shown that small or weakly capital-ized credit unions are among those most at riskof failure. Other factors that increase the fail-ure hazard include poorly trained management,lax lending standards and weak collection oper-ations, poor record-keeping, and the closure ofsponsoring companies (Barron, West, and Han-nan 1994; Gordon 1987; Kharadia and Collins1981; Pille and Paradi 2002; U.S. GovernmentAccountability Office 1991; Wilcox 2005). Inrespect of credit union M&A, Goddard, McKil-lop, and Wilson (2009) find the hazard of acqui-sition for U.S. credit unions during the period2001–2006 is inversely related to asset sizeand profitability, and positively related to liq-uidity. Worthington (2004) finds asset size, assetmanagement, liquidity, and regulatory variablesinfluenced significantly the probability of Aus-tralian credit unions engaging in M&A duringthe period 1992–1995.6

6. Several studies examine the impact of creditunion M&A on financial performance (Bauer, Miles, andNishikawa 2009; Fried, Lovell, and Yaisawarng 1999;Mcalevey, Sibbald, and Tripe 2010; Ralston, Wright, andGarden 2001; Wilcox and Dopico 2011).

306 ECONOMIC INQUIRY

Barron, West, and Hannan (1994) investi-gate the growth of state-chartered credit unionsin New York City for the period 1914–1990,by analyzing the effects of organizational age,size, and population density on the rates offailure and growth. Old and small institutionswere more likely to fail, while young andsmall institutions had the highest growth rates.Goddard, McKillop, and Wilson (2002) testGibrat’s law for U.S. credit unions, using datafor the period 1990–1999. Larger credit unionsgrew faster than smaller ones. On average, creditunions with above-average growth in one periodexperienced below-average growth in the fol-lowing period. Small credit unions exhibitedmore variable growth than large credit unions.More recently, Wheelock and Wilson (2011)report evidence of increasing returns to scaleamong U.S. credit unions of all sizes for theperiod 1989–2006. They anticipate that con-tinued deregulation, allowing credit unions toexpand their scale or scope of financial serviceprovision, would encourage further growth at theupper end of the size distribution.

The econometric analysis reported in thisstudy comprises a panel estimation of hazardfunctions for the determinants of acquisition orfailure, and two sets of time-series and cross-sectional estimations of the relationship betweenasset size and internally generated growth. Thisstudy extends and integrates previous empiricalanalysis of credit union acquisition (Goddard,McKillop, and Wilson 2009), and the dynam-ics of credit union growth (Goddard, McKillop,and Wilson 2002). The study of disappear-ance through acquisition by Goddard, McKillop,and Wilson (2009) is extended by estimating acompeting-risks model that comprises separatehazard functions for the incidence of firm dis-appearance through both acquisition and failure.The implications of population changes throughacquisition and failure for the long-term trend inconcentration are also explored.

The present analysis of growth also offersseveral improvements on the cross-sectional andpanel analysis of credit union growth duringthe 1990s reported by Goddard, McKillop, andWilson (2002). In order to focus exclusivelyon internally generated growth (as opposed togrowth by means of acquisition) in the cross-sectional analysis, the lagged size and laggedgrowth covariates of any credit union that wasan acquirer are adjusted by defining the laggedvalues for a “synthetic” credit union constructedusing the aggregate assets of the acquirer and

the acquired credit union as separate entities atthe relevant data-points. Survivorship bias in thecross-sectional growth regressions is addressedby correcting for violation of the conditions forvalid estimation and inference resulting fromstatistical dependence between growth and sur-vival. The Heckman sample-selection modelprovides a framework for integrating the analy-ses of growth, and disappearance through acqui-sition or failure.

This article proceeds as follows. Section IIdescribes the U.S. credit union sector. Section IIIreports an empirical analysis of the determinantsof exit through acquisition or failure. SectionIV reports an empirical analysis of patterns ofsurvivorship and internally generated growth.Finally, Section V summarizes and concludes.

II. THE U.S. CREDIT UNION SECTOR

The U.S. credit union data are compiledfrom the “5300 Call Reports,” published bythe National Credit Union Association (NCUA).Semiannual data are available for the periodJune 1994 to December 2010. These data areaugmented with information (provided by theNCUA in response to several Freedom of Infor-mation requests) on entrants and exits. Attritionis tracked to an exceptional degree of accu-racy, with a cause of disappearance identified for99.5% of all exits. The acquiring credit union isidentified for 98.8% of credit unions that exitedas a result of M&A, and acquisitions accountfor 89.9% of all exits.

Table 1 (panel A) reports the total numberof U.S. credit unions at the end of Decemberfrom 1994 to 2010, and an analysis of the evo-lution of the distribution of the population byasset size. In each year, the population is subdi-vided into five asset size classes, defined in realterms as follows: Class 1, assets below $2m in1994 prices (all price conversions are based onthe U.S. GDP deflator); Class 2, assets between$2m and $6m; Class 3, between $6m and $18m;Class 4, between $18m and $54m; Class 5,assets above $54m. This analysis indicates thatthere has been a marked shift in the composi-tion of the population by asset size, owing toa combination of consolidation through acqui-sition and failure, and differences between theaverage internally generated growth of smalland large credit unions. In 1994, for example,Class 1 accounted for 31.6% of the entire pop-ulation, and Class 5 accounted for 9.0%. In2010, the corresponding figures were 16.6% for


TABLE 1Trends in the Size Distribution of the Population of U.S. Credit Unions, 1994–2010, and

Projections, 2011–2015

Number of Credit Unions by Asset Size Class

1 2 3 4 5 Total Number

Panel A: actualDecember 1994 3,805 2,919 2,586 1,657 1,085 12,052December 1995 3,648 2,812 2,506 1,661 1,120 11,747December 1996 3,429 2,715 2,473 1,656 1,170 11,443December 1997 3,275 2,638 2,442 1,669 1,222 11,246December 1998 3,047 2,522 2,438 1,690 1,295 10,992December 1999 2,784 2,415 2,395 1,705 1,329 10,628December 2000 2,659 2,314 2,300 1,700 1,342 10,315December 2001 2,370 2,111 2,317 1,731 1,454 9,983December 2002 2,147 1,955 2,305 1,738 1,542 9,687December 2003 1,938 1,832 2,256 1,764 1,578 9,368December 2004 1,788 1,777 2,143 1,713 1,594 9,015December 2005 1,732 1,705 2,061 1,614 1,580 8,692December 2006 1,671 1,656 1,919 1,570 1,544 8,360December 2007 1,602 1,584 1,850 1,516 1,545 8,097December 2008 1,458 1,475 1,801 1,503 1,563 7,800December 2009 1,308 1,351 1,729 1,494 1,666 7,548December 2010 1,221 1,281 1,707 1,466 1,660 7,335

Panel B: projectedDecember 2011 1,141 1,216 1,683 1,436 1,653 7,132December 2012 1,066 1,154 1,657 1,413 1,646 6,938December 2013 997 1,097 1,630 1,388 1,639 6,752December 2014 933 1,044 1,602 1,364 1,631 6,574December 2015 874 993 1,574 1,341 1,623 6,404

Notes: Asset size classes are defined in real terms, measured in 1994 prices, as follows: Class 1, assets below $2m; Class2, assets between $2m and $6m; Class 3, assets between $6m and $18m; Class 4, assets between $18m and $54m; Class 5,assets above $54m. All price conversions are based on the U.S. GDP deflator.

Class 1 (assets below $2.8m in current prices)and 22.6% for Class 5 (assets above $74.9m incurrent prices).

The shift in the asset size distribution hasbeen encouraged by several developments inregulation and fiscal treatment, which have con-tributed to a tendency for the larger creditunions to offer portfolios of financial servicesresembling those of medium-sized commer-cial banks.7 The NCUA revised the field of

7. With the exception of some securities investments,credit unions were originally distinguished from other finan-cial institutions by their emphasis on small value, unsecured,nonmortgage loans to individuals and households. Federalcredit unions gained the authority to make long-term (upto 30 years) mortgage real estate loans in 1977. At the endof 2010, first mortgages accounted for 39.3% of all loans,and second mortgages accounted for 7.6%. The 1994 figureswere 21.3% and 5.5%, respectively. Other changes to thetypical product mix of credit unions include growth in theimportance of credit-card lending. Around 53% of creditunions offered credit cards in 2010 (CUNA 2010). Unse-cured lending accounted for only 10.8% of all credit unionlending in 2010, down from 20.3% in 1994.

membership rules in 1994, diluting the com-mon bond and permitting credit unions to addoccupational groups of up to 100 persons with-out regulatory approval. The 1998 Credit UnionMembership Access Act (CUMAA) permittedfederal credit unions to add select employeegroups (SEGs) to their fields of membership.In some cases, a credit union’s common-bonddesignation makes it difficult to add SEGs, andsome credit unions converted from occupationalto residential common bonds in order to expandtheir membership base.8

8. For discussion of the background to CUMAA, seeFrame, Karels, and McClatchey (2002). CUMAA also intro-duced a capital regulation system of net worth requirementsand prompt corrective action, which came into force in 2000.Congressional hearings were held in 2005 to examine thetax-exempt status of credit unions, justified by its proponentsas a policy tool to tackle financial exclusion. Tax-reformproponents argue that credit unions should be subject tocorporate taxation (U.S. Government Accountability Office2005). Following the 2005 hearings the tax-exempt statusof credit unions was retained, despite intense lobbying bybanks for its abolition.


Owing partly to the restrictions on their activ-ities and their high capitalization, credit unionshave, in general, withstood the current finan-cial crisis better than many banks (Smith andWoodbury 2010). The crisis in the real-estatemarket has impacted on the credit union sector,primarily through the investment policies of anumber of corporate credit unions,9 which usedcash deposits received from retail credit unionsto purchase risky asset-backed securities, andrealized large losses in several cases. The 2010Dodd-Frank Act made radical changes to finan-cial services regulation and supervision. Forcredit unions, deposit insurance was increasedfrom $100,000 to $250,000 per account, andthe supervision of corporate credit unions wasstrengthened.10

Table 2 reports a further analysis of thedynamics of change in the asset size distribution,in the form of a set of empirical yearly rates oftransition between each size class and the near-est adjacent classes, and exit rates from each sizeclass. The size classes are the same as those usedto construct Table 1, and the computations fol-low closely the methodology used by Robertson(2001) in a similar analysis of transition ratesbetween asset size classes for U.S. banks overthe period 1960–2000. The numbers of creditunions moving by more than one size class inany year are negligible, and the correspondingrates of transition are not reported. Table 2 indi-cates that there is a high degree of stability inthe asset size distribution from year to year. Thepropensities for credit unions to remain withinthe same asset size class are, in general, higheron average than those reported by Robertson(2001) for banks, particularly among the largersize classes.11 The propensity to remain withinthe same class is an increasing function of size,and this relationship appears to be driven mainlyby an inverse relationship between size and thepropensity to exit. The exit rate in the twolargest size classes appears to have risen sig-nificantly over the observation period. The year

9. Corporate credit unions provide services for (retail)credit unions, including deposit of excess funds, paymentservices, and access to liquid funds (if required).

10. In addition, the NCUA has approved a new rulerequiring credit union directors to receive financial literacytraining, and opened a new office of Consumer Protection.

11. An analysis of churning in the rankings of U.S.credit unions at the top end of the asset size distribution alsoreflects a high level of stability in the size distribution. Thesame two credit unions, Navy Federal and State Employees,occupied the top two positions throughout this period; andseven of the ten largest credit unions in December 1995 alsofeatured among the ten largest in December 2010.

2008–2009 witnessed unusually high rates ofupward transition from each of Classes 1 to 4to the next highest Class (2–5, respectively),apparently due to unusual patterns of consoli-dation at the height of the late-2000s financialcrisis.

Consistent with the analysis presented byRobertson (2001), Table 1 (panel B) reports pro-jections of future changes in the asset size distri-bution over the period 2011–2015, based on theassumption that the yearly entry, transition, andexit rates observed over the final year includedin Table 2, 2009–2010, remain unchanged forthe following 5 years. The projected size dis-tribution for 2011 is obtained by multiplying amatrix containing the transition and exit rates foreach size class by a vector containing the num-bers of credit unions in each class in 2010, andadding five new entrants to Class 1 (equivalentto the actual number of entrants in 2010, all ofwhich joined Class 1). The projections for sub-sequent years are then obtained iteratively, bymultiplying the same matrix by a vector con-taining the projected numbers for the precedingyear. The projections suggest further shrinkagein the population and shifts in the shape of thesize distribution, with the projected number ofcredit unions in the smallest size class droppingby a further 23.4% over a 5-year period, whilethe projected number in the largest size classdrops by only 2.2%.

Table 3 reports an analysis of changes in thepopulation owing to entry and exit. BetweenDecember 1994 and December 2010, the totalnumber of credit unions fell from 12,051 to7,334. This decline in numbers reflects the neteffect of entry (156 new credit unions) and exit(4,873 credit unions). A large majority of thecredit unions that exited did so as a consequenceof having been acquired (4,382 credit unions, or89.9% of the total number that exited). The exitrate was remarkably stable throughout the 2000s(between 3% and 4% per year), and the exit ratedoes not appear to be sensitive to the economiccycle. Smith (2012) reports that on conservativeestimates, credit union loan portfolios werearound 25% less sensitive to macroeconomicshocks than bank loan portfolios.

III. EMPIRICAL ANALYSIS OF EXIT THROUGHACQUISITION OR FAILURE

Section III reports an investigation of thedeterminants of credit union disappearance


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TABLE 3Entrants and Exits, 1995–2010

EntrantsAcqui-sition

Purchase&

Assump-tion

Liqui-dation

Conversionto Bank

Conversionto Privately

Insured

UnclassifiedDisappear-

anceTotalExits

ExitRate

NumberLive atEnd ofYear

1994 — — — — — — — — — 12,0521995 13 290 5 22 1 0 0 318 0.0264 11,7471996 20 293 11 17 1 1 1 324 0.0276 11,4431997 19 192 4 17 0 3 0 216 0.0189 11,2461998 8 215 5 28 3 11 0 262 0.0233 10,9921999 13 335 11 24 3 4 0 377 0.0343 10,6282000 13 292 13 18 3 0 0 326 0.0307 10,3152001 10 296 8 25 6 2 5 342 0.0332 9,9832002 7 265 7 23 1 4 3 303 0.0304 9,6872003 15 315 5 10 2 2 0 334 0.0345 9,3682004 3 332 6 11 3 0 4 356 0.0380 9,0152005 8 302 1 25 2 0 1 331 0.0367 8,6922006 10 313 2 23 1 0 3 342 0.0394 8,3602007 4 248 2 10 3 0 4 267 0.0319 8,0972008 4 275 1 19 1 1 4 301 0.0372 7,8002009 4 229 1 23 1 2 0 256 0.0328 7,5482010 5 190 7 19 0 0 2 218 0.0289 7,335

through acquisition or failure during the period1994–2010.

A. Empirical Model for the Determinantsof Acquisition or Failure

The hazard function estimations reported inthis section are based on the method used byWheelock and Wilson (2000) to model the haz-ards of failure and acquisition for U.S. banks.The empirical model is the Cox (1972) propor-tional hazard model with time-varying covari-ates. The probabilities of disappearance throughevents defined as failure and acquisition aremodelled separately, using a competing-risksframework. The alternative modes of disappear-ance are treated as independent events, and theobservations on a credit union that disappearedthrough each event are treated as right-censoredin the estimations of the hazard for disappear-ance through the other event.

The hazard function expressing the probabil-ity that credit union i disappears through eventk between time t and time t+1 (k = 1 denotesacquisition; k = 2 denotes failure), conditionalon a vector of covariates specific to credit unioni at time t that influence the probability of eventk, denoted xk,i(t), is modelled as follows:

λk,i (t |xk,i(t), βk) = λ̄k(t)exp(xk,i(t)′βk).(1)

In Equation (1), the baseline hazard isdenoted λ̄k(t), and δk is a vector of coefficients

to be estimated. The time-index t is measured incalendar time elapsed since December 1994. Rt

denotes the set of credit unions that are in exis-tence at time t and exposed to risk of disappear-ance between t and t+1, and Dk,t denotes the setof dk,t credit unions that disappear through eventk between time t and time t+1. The contributionto the partial likelihood function of credit unioni, which disappears through event k between tand t+1, is:

exp(xk,i(t)′δk)/

∑j∈Rt

exp(xk,j (t)′δk).(2)

The baseline hazard λ̄k(t) drops out of thepartial likelihood function, and is not parameter-ized explicitly. The (semiparametric) log-partiallikelihood function is:

ln[L(k)] =T∑

t=1

⎡⎣ ∑

i∈Dk,t

xk,i(t)′δk

(3)

− dk,t ln

⎧⎨⎩

∑j∈Rt

exp(xk,j (t)′δk)

⎫⎬⎭

⎤⎦ .

The hazard function covariate definitions are asfollows: Si,t = Total Assets; Ki,t = capital-to-assets ratio = Net Worth / Total Assets;Qi,t = Liquid Assets / Total Assets; Ni,t =Non-performing Loans / Total Assets; Li,t =


TABLE 4Descriptive Statistics: Mean Values of Key Variables, by Year

Si,t Ai,t Ki,t Qi,t Li,t Ni,t Ei,t Ri,t

December 1994 24.22 38.82 0.127 0.0384 0.615 0.00432 0.0200 0.0199December 1995 26.29 39.86 0.134 0.0403 0.643 0.00436 0.0208 0.0217December 1996 28.71 40.91 0.140 0.0377 0.651 0.00430 0.0216 0.0211December 1997 31.32 41.88 0.145 0.0380 0.651 0.00426 0.0223 0.0206December 1998 35.42 42.90 0.145 0.0397 0.617 0.00429 0.0218 0.0193December 1999 38.78 43.96 0.148 0.0994 0.625 0.00397 0.0179 −0.0113December 2000 42.55 44.97 0.145 0.1095 0.662 0.00387 0.0201 0.0039December 2001 50.32 46.00 0.138 0.1573 0.600 0.00411 0.0192 0.0022December 2002 57.91 47.03 0.135 0.1560 0.570 0.00419 0.0188 0.0033December 2003 65.55 48.03 0.133 0.1631 0.553 0.00408 0.0187 0.0021December 2004 72.26 49.08 0.136 0.1410 0.564 0.00385 0.0190 0.0020December 2005 78.61 50.20 0.143 0.1209 0.595 0.00389 0.0198 0.0021December 2006 85.53 51.21 0.151 0.1200 0.618 0.00310 0.0208 0.0023December 2007 93.64 52.23 0.155 0.1287 0.613 0.00314 0.0213 0.0021December 2008 104.3 53.36 0.151 0.1251 0.586 0.00364 0.0208 −0.0004December 2009 117.2 54.43 0.138 0.1410 0.552 0.00388 0.0199 −0.0025December 2010 124.6 55.50 0.134 0.1471 0.530 0.00402 0.0216 −0.0002

Note: Variable definitions are as follows: Si,t = Total Assets; Ai,t = age; Ki,t = capital-to-assets ratio = Net Worth /Total Assets; Qi,t = Liquid Assets / Total Assets; Li,t = Loans / Total Assets; Ni,t = Non-Performing Loans / Total Assets;Ei,t = Non-Interest Expenses / Total Assets; Ri,t = Return on Assets = Net Income / Total Assets.

Loans / Total Assets; Ei,t = Non-interest Exp-enses / Total Assets; Ri,t = Return on Assets;and Ai,t = Age. Table 4 reports the mean val-ues of each of the covariates at the end of eachyear. In the empirical hazard functions, loga-rithmic transformations are applied to the totalassets and age covariates.

B. Estimation Results

Table 5 reports the empirical hazard func-tion estimation results. All members of thecredit union population are included in theestimations (see the final column of Table 1).The acquisition hazard function is based on4,471 credit unions reported in Table 3 asexits through either acquisition or purchase andassumption. The failure hazard function is basedon 341 credit unions reported in Table 3 asexits through liquidation. Observations on creditunions that exited for reasons other than acqui-sition, purchase, and assumption or liquidationare treated as right-censored.

The anticipated inverse relationship betweenasset size and the hazard of disappearance is evi-dent in both of the hazard function estimations,indicating that a smaller credit union was at sig-nificantly greater risk of disappearance througheither acquisition or failure than a larger one.The coefficient on the age covariate in the M&Ahazard is positive and significant, suggesting

TABLE 5Estimation Results: M&A and Failure Hazard

Functions

M&A Hazard Failure Hazard

si,t−1 −0.3892 −0.3733(−47.5) (−13.1)

ai,t−1 0.2232 −0.0689(6.57) (−0.81)

Ki,t−1 −3.2013 2.1939(−15.8) (6.40)

Qi,t−1 0.8537 1.4142(8.26) (5.28)

Li,t−1 0.1354 −1.2614(1.74) (−4.32)

Ni,t−1 −0.5707 1.8707(2.12) (4.40)

Ei,t−1 1.3732 −0.3604(6.38) (−0.83)

Ri,t−1 −4.5576 −3.5482(−20.9) (−5.47)

No. of observations 311,637 311,637No. of disappearances 4,471 341Log-likelihood −39,325.3 −2,652.0

Note: Variable definitions are as follows: si,t−1 =logarithm of total assets at the 6-monthly data-point priorto disappearance; ai,t−1 = Log Age; Ki,t−1 = capital-to-assets ratio = Net Worth / Total Assets; Qi,t−1 = LiquidAssets / Total Assets; Li,t−1 = Loans / Total Assets; Ni,t−1= Non-Performing Loans / Total Assets; Ei,t−1 = Non-Interest Expenses / Total Assets; Ri,t−1 = Return on Assets= Net Income / Total Assets.


that an older credit union is more likely to beacquired than a younger credit union of thesame size. The coefficient on the age covariateis insignificant in the failure hazard.

The coefficients on the capital-to-assets ratiocovariate are negative and significant in theM&A hazard, and positive and significant inthe failure hazard. These results are consis-tent with Hannan and Piloff’s (2009) expla-nation for a negative relationship between thecapitalization of U.S. banks and the hazard ofacquisition: high capitalization is a proxy forefficiency, indicating limited scope for post-merger efficiency gains, while low capitalizationreduces the purchase price and increases theattractiveness of the target. Contrary to resultsreported by Wilcox (2005), highly capitalizedcredit unions appear to be at greater risk of fail-ure. Credit unions regarded as inadequately cap-italized under Section 301 of CUMAA (1998)are subject to a range of mandatory actions, suchas earnings retentions, lending restrictions, andthe prohibition of increases in assets.12 Theseactions impact on both the denominator and thenumerator of the capital-to-assets ratio, some-times causing the latter to spike for a distressedcredit union immediately prior to failure. It isalso the case that smaller credit unions maintaina higher capital-to-assets ratio on average thanlarge credit unions, and small credit unions are athigher risk of failure. Although x2,i (t) includes aseparate control for asset size, it is possible thatthe positive coefficient on Ki,t in the failure haz-ard also reflects aspects of the strong associationbetween asset size and failure.

The coefficients on the liquidity ratio covari-ate are positive and significant in both haz-ards. The coefficient on the loans-to-assets ratiocovariate is insignificant in the M&A hazard,but the corresponding coefficient is negative andsignificant in the failure hazard. A credit unionthat hordes cash, or does not create a loans port-folio of a size commensurate with its deposits,may be either an attractive target for an acquirerthat believes itself capable of earning a higherreturn by expanding the loans portfolio, or atrisk of failure due to an inability to generate anadequate return.

12. The CUMAA specifies mandatory actions for creditunions that do not meet capital adequacy standards. Theseinclude: annual earnings retentions of at least 0.4% oftotal assets; the submission and adherence to a net worthrestoration plan (NWRP); lending restrictions; and theprohibition of increases in assets until net worth is restored.The CUMAA allows the NCUA to use 14 supervisoryactions to supplement the mandatory actions.

The coefficient on the non-performing loanscovariate in the M&A hazard is negative andsignificant, while the corresponding coefficientin the failure hazard is positive and significant.These coefficients suggest a lack of control overthe quality of lending makes a credit union a lessattractive target for acquisition, but increases thelikelihood of disappearance through failure. Thecoefficient on the ratio of non-interest expensesto assets covariate in the M&A hazard is positiveand significant. This appears consistent withthe interpretation of the ratio of non-interestexpenses to assets as a managerial inefficiencymeasure, and the hypothesis that inefficientcredit unions are more vulnerable to eitheracquisition. The corresponding coefficient inthe failure hazard is insignificant. Finally, thecoefficients on the return on assets covariateare negative and significant in both hazards,indicating that the likelihood of disappearancethrough either acquisition or failure is reducedby an increase in profitability.

C. Impact of Consolidation on IndustryStructure

Table 6 reports a descriptive analysis ofthe trend in concentration over the period1994–2010. The first five columns report 5-,10-, and 20-firm concentration ratios, togetherwith the Herfindahl–Hirshman Index (HHI) andthe HHI numbers equivalent. Consistent withthe patterns reported in Table 1, these data indi-cate a trend toward increased concentration thathas been remarkably steady and consistent overtime.

The final two columns of Table 6 providean indication of the contribution of consolida-tion through M&A to the trend in concentra-tion, in the form of a “counterfactual” HHIbased on hypothetical population data. For thepurposes of calculating the counterfactual HHI,each acquired credit union is assumed to havecontinued to operate as a separate entity tothe end of 2010. A proportion of the com-bined assets of the acquirer at each data-pointafter the merger took place are reallocated tothe (counterfactually surviving) acquired creditunion. The proportion of the assets reallocated isbased on the relative asset sizes of the acquirerand the acquired at the data point immediatelypreceding the merger: the final data point atwhich separate assets data are available for bothinstitutions.

The large number of credit union mergersnotwithstanding, the analysis reported in Table 6


TABLE 6Trends in Industry Concentration Measures, 1994–2010

Concentration Ratios Actual Counterfactual (No M&A)

CR5 CR10 CR20 HHI Numbers Equivalent HHI Numbers Equivalent

December 1994 6.2 8.8 12.2 19.2 520.9 19.2 521.8December 1995 6.1 8.8 12.4 19.2 520.3 19.1 523.9December 1996 6.1 8.8 12.5 19.0 525.9 18.8 530.9December 1997 6.3 8.9 12.8 19.7 506.6 19.5 513.1December 1998 6.5 9.2 13.2 20.5 486.8 20.2 494.3December 1999 6.5 9.4 13.4 20.8 480.9 20.4 489.8December 2000 6.7 9.6 13.8 21.9 457.3 21.4 467.2December 2001 7.0 10.2 14.4 23.9 418.5 23.4 428.2December 2002 7.4 10.7 15.0 25.8 388.2 25.1 397.9December 2003 7.6 10.9 15.2 27.1 368.3 26.4 378.8December 2004 8.1 11.4 15.8 29.7 337.1 28.8 347.3December 2005 8.5 11.9 16.5 31.4 318.2 30.4 328.7December 2006 9.0 12.4 17.3 34.3 291.9 32.9 303.7December 2007 9.9 13.3 18.4 40.1 249.5 38.5 259.7December 2008 10.1 13.7 18.8 41.9 238.6 40.2 248.7December 2009 10.2 13.6 18.4 42.2 237.1 40.3 248.0December 2010 10.8 14.3 19.1 46.5 215.2 43.8 228.5

suggests that the contribution of M&A to the risein concentration was modest. The counterfactual2010 HHI of 43.8 is only slightly smaller thanthe observed HHI of 46.5; and the observeddrop in the HHI Numbers Equivalent from 520.9in 1994 to 215.2 in 2010 would have beenmitigated only marginally, to a counterfactualfigure of 228.5 in 2010, had no credit unionsmergers taken place between 1994 and 2010.The disparity between the large effect of M&Aon the population size, and the much smallereffect on concentration, is attributed to themajority of acquired credit unions having beendrawn from the lower end of the asset sizedistribution.

IV. EMPIRICAL ANALYSIS OF INTERNALLYGENERATED GROWTH

The empirical analysis reported in Section IIIsuggests that while consolidation through M&Aaccounts for most of the large decline in thenumber of U.S. credit unions over the period1994–2010, the effect on industry structure wassmall. With the sector also having experiencedmodest rates of entry and failure, it appears thatinternally generated growth was the main driverof the trend toward increased concentrationover the same period. Section IV reports anempirical analysis of the relationship betweencredit union size and growth, using Gibrat’s lawas a benchmark.

A. Empirical Analysis of the RelationshipBetween Firm Size and Growth

The empirical analysis of the firm size-growth relationship is based on the followinggeneral model specification:

(si,t − si,t−1) = φ0,i,t + φ1,i,t si,t−1

(4)

+mi,t∑j=1

φ2,j,i,t (si,t−j − si,t−j−1)

+ φ3,i,t t + ui,t .

In Equation (4), logarithmic growth over a1-year period is the dependent variable, and logsize at the start of the period and growth overmi,t previous 1-year periods are the explanatoryvariables.

Clearly, estimation requires the imposition ofrestrictions on the coefficients of Equation (4).Below, two sets of restrictions are considered.Under the first set, it is assumed that the coeffi-cients are constant over time, but variable overall surviving i for which a complete set of time-series observations is available, so that φ1,i,t =α1,i for all t (with similar restrictions imposedon the other coefficients, and mi,t = mi). Theserestrictions are embodied in a set of individualDickey–Fuller time-series regressions (for each


i = 1, . . . ,N , where N is the number of surviv-ing credit unions), defined as follows:

(si,t − si,t−1) = α0,i + α1,isi,t−1

(5)

+mi∑j=1

α2,j,i (si,t−j − si,t−j−1)

+ α3,i t + ui,t .

Each regression in Equation (5) has t = 1, . . . ,Tobservations. The focus is on the dynamicsof the size-growth relationship for each creditunion individually. As the credit union grows insize (possibly relative to a deterministic time-trend or drift component), either growth mighttend to decline (α1,i < 0), or growth mightbe independent of attained size (α1,i = 0).13

The latter case α1,i = 0 represents Gibrat’s law,interpreted as a descriptor of the dynamics of thesize-growth relationship for each credit unionindividually.

Under the second set of restrictions, it isassumed that the coefficients are the same forall i but variable over time, so that φ1,i,t = β1,t

for all i (with similar restrictions imposed onthe other coefficients, and mi,t = 1 for all i, t).A series of cross-sectional regressions (for eacht = 1, . . . ,T ) is defined as follows:

(si,t − si,t−1) = β0,t + β1,t si,t−1

(6)

+ β2,t (si,t−1 − si,t−2) + ui,t .

Each regression in Equation (6) has i = 1, . . . ,Nt observations (where Nt is the number ofcredit unions live in year t). The focus ison the cross-sectional size-growth relationship,which might be either positive (β1,t > 0), neutral(β1,t = 0), or negative (β1,t < 0). The natureof this relationship is permitted to vary overtime. The case β1,i = 0 represents Gibrat’s law,interpreted as a descriptor of the cross-sectionalsize-growth relationship.

In order to focus solely on growth that isinternally generated, rather than growth that

13. The case α1,i > 0, in which growth tends to increasewith size, is usually disregarded because it implies unstableor explosive growth. The possibility that large firms tend togrow more rapidly than small firms can be accommodated,however, through suitable variation over i in the trendcoefficients α3,i (in the case α1,i < 0, where log size isstationary relative to a deterministic time trend), or the driftcoefficients α0,i (in the case α1,i = α3,i = 0, where log sizeis non-stationary).

is achieved by means of M&A, the laggedsize and lagged growth covariates in Equation(6) of any credit union that was an acquirerare adjusted by defining the lagged values fora “synthetic” credit union constructed usingthe aggregate assets of the acquirer and theacquired credit union as separate entities atthe relevant data-points.14 The cross-sectionalsize-growth regressions are estimated using theHeckman (1979) sample-selection model, tomitigate potential survivorship bias.15 The lattermight arise because the probability that a creditunion survives, and therefore appears in the dataset for the estimation of the growth regression,might be related to the credit union’s propensityfor growth. The direction of any associationbetween growth and survival might be eitherpositive or negative: on the one hand, recklessgrowth in lending might increase the risk ofdisappearance as a consequence of financialdistress; but on the other hand, sluggish growthin lending might reflect operational inefficiencyor underperforming management. The sample-selection model comprises Equation (6), and thefollowing survivorship regression observed forall credit unions live at t − 1:

z∗i,t = γ0,t + γ1,t si,t−1 + γ2,t (si,t−1 − si,t−2)

+ γ3,t′xi,t−1

zi,t =1 if z∗i,t + εi,t >0; zi,t =0 if z∗

i,t + εi,t <0(7)

where γ3,t is a vector of coefficients, andxi,t−1 = (si,t−1 si,t−1 − si,t−2 Ki,t−1 Qi,t−1Li,t−1 Ni,t−1 Ei,t−1 Ri,t−1). See Section III forcovariate definitions. Equation (6) is observedonly for those credit unions that were liveat t − 1 and survived to t , for which zi,t =1 in Equation (7). The disturbances ui,t inEquation (6) and εi,t in Equation (7) are assumed

14. For the observation following an acquisition thattook place between t − 1 and t , the acquirer’s “synthetic”growth rate is si,t − si,t−1

∗, s∗i,t−1, where s∗

i,t−1 is thelogarithm of the sum of the assets of the acquirer andthe acquired as separate entities at t − 1, and the lagged“synthetic” growth is s∗

i,t−1 − s∗i,t−2, with s∗

i,t−2 defined inthe same manner at t − 2. Where the acquisition took placebetween t − 1 and t − 2, the lagged “synthetic” growth issi,t−1 − s∗

i,t−2.15. An inverse empirical size-growth relationship may

be a manifestation of survivorship bias. Small firms are lesslikely to survive than large firms, but fast-growing smallfirms are likelier to survive than slow-growing ones. As aconsequence, studies using samples of firms that surviveover the entire period of the analysis are subject to a formof survivorship bias, because firms that failed to achieverapid growth and exited would not have been recorded.


TABLE 7Estimation Results: Time-Series Growth Regressions

Rank by December 1994 Assets Size

1–250 251–500 501–1,000 1,001–2,000 2,001–7,247 All

ADF tests: proportion of rejections of the unit root null hypothesisα = .01 0.040 0.060 0.080 0.063 0.075 0.072α = .05 0.108 0.116 0.156 0.144 0.159 0.153α = .1 0.196 0.172 0.220 0.218 0.230 0.225IPS panel unit root testZtbar 5.35 2.26 −1.775 −4.883 −18.005 −16.185p value 1.0000 .9881 .0379 .0000 .0000 .0000

to be bivariate normal, with var(εi,t ) = 1,var(ui,t ) = σ2

u,t , corr(εi,t , ui,t ) = ρεu,t . The co-variates that appear in the survivorship regres-sion are the same as those in the acquisition andfailure hazard functions reported in Section II,with the sole exception of the age covariate,which was generally insignificant in preliminaryestimations of the sample-selection model.

B. Estimation Results: Time-Series Regressions

Table 7 reports summary results from aug-mented Dickey–Fuller (ADF) unit root tests onthe log assets series (Dickey and Fuller 1979),together with the associated Im, Pesaran, andShin (2003) (IPS) panel unit root tests, based onestimations of Equation (5) for each of the 7,247surviving credit unions that reported assets datain every December call report from 1994 to 2010(inclusive). The summary results for the ADFtests are the proportions of rejections of the unitroot null hypothesis (α1,i = 0 in Equation (5)) infavor of the stationarity alternative (α1,i < 0) atthe 0.01, 0.05, and 0.1 significance levels. Theseproportions are reported for the full cohort of7,247 surviving credit unions, and for the samecohort subdivided by rank based on December1994 assets as follows: size band (i) comprisesrank 1–250; (ii) 251–500; (iii) 500–1000; (iv)1001–2000; (v) 2001–7247 (rank 1 denotes thelargest credit union in December 1994). AkaikeInformation Criterion (AIC) is used to determinemi , the lag-length for the first-difference termsin log assets on the right-hand side of Equation(5), for each credit union individually. The IPSprocedure tests the null hypothesis of a unit rootfor all panel constituents (α1,i = 0 for all i inEquation (5)) against the alternative of station-arity for one or more panel constituents (α1,i < 0for some i).

According to Table 7, the proportions ofrejections of the unit root null hypothesis in

the ADF tests are higher than the proportionsthat should be expected due to type 1 error(equivalent to the significance level) if thenull hypothesis were true in every case. Forexample, the proportion of rejections at the0.05 level for the entire cohort of survivingcredit unions is 0.153. The IPS test rejectsdecisively the null hypothesis of a unit rootfor every credit union, with a p value of .000.Across size bands (i)–(v), however, there issome variation in this pattern. At the 0.05level, the propensity for the ADF test to rejectthe unit root null hypothesis is lowest for thelargest December 1994 asset size band (i). Thispropensity increases (and is therefore inverselyrelated to asset size) over bands (i) to (iii).Between bands (iii) and (v) there is little orno relationship between size and the propensityfor the ADF test to reject. A similar pattern isobtained from the IPS test, which fails to rejectthe null for bands (i) and (ii). For band (iii),the result of the IPS test is borderline, with ap value of .0379. For bands (iv) and (v), thenull is rejected decisively.16

Overall, the time-series estimations indicatethat Gibrat’s law, interpreted as a descriptorof the dynamics of the size-growth relationshipfor each credit union individually, cannot berejected for surviving credit unions at the upperend of the asset size distribution. For smallercredit unions the pattern is mixed. Gibrat’s lawis rejected as a descriptor of the dynamics

16. The power of the IPS test is dependent on thenumber of panel constituents. However, the observed patternof rejection and non-rejection is not a feature of variationin the power of this test. A similar pattern is obtained ifthe cohort is subdivided into equal-sized quintiles based onJune 1994 assets (with each quintile containing either 1,449or 1,450 credit unions). The IPS test fails to reject the nullfor the largest assets-size quintile (p value = .7447); butthe IPS test rejects the null for each of the four smaller sizequintiles (p value = .0000 in each case).

316 ECONOMIC INQUIRYT

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2006

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of the size-growth relationship for all of thesmaller credit unions: in some cases log assetsis stationary in relation to a deterministic timetrend. At the 0.05 level, the percentage rejectionrate of the unit root null among the smallercredit unions is slightly below 16% in theADF tests. With a maximum sample size ofT = 17, however, the ADF test has limitedpower, suggesting that the true proportion ofsmaller credit unions departing from Gibrat’slaw might be substantially larger than the ADFtest rejection rates indicate.

C. Estimation Results: Cross-SectionalRegressions

Table 8 reports the estimation results forthe cross-sectional sample-selection model ofsurvivorship and growth. A separate set ofequations is reported for growth rates definedover yearly intervals (ending in December) forthe period 1996 to 2010 inclusive. The survivor-ship regressions include the same set of covari-ates as the hazard functions reported in SectionIV with the exception of the age covariate, forwhich the coefficients were small and insignifi-cant in preliminary estimations of the survivor-ship regressions. A lagged growth covariateis included in the cross-sectional survivorshipregressions. The latter, which are dominatedby disappearances owing to M&A, are simi-lar to the M&A hazard function reported inTable 5, with a reversal of signs on all coef-ficients because survival, rather than disappear-ance, is coded 1, and disappearance coded 0.

The coefficients on the size, lagged growth,capitalization, and return on assets covariatesare predominantly positive and significant. Thecoefficients on the liquidity covariate are pre-dominantly negative, and several are signifi-cant. These coefficients may be interpreted inthe same way as the corresponding coefficientsin the hazard function estimations reported inSection III. The coefficients on the loans-to-assets covariate are predominantly positive andseveral are significant prior to the late-2000sfinancial crisis; but several negative coefficientsare obtained from t = 2007 onward. The changein sign might be linked to the fact that a sig-nificant share (around 50% on average) of acredit union’s loan book takes the form of “firstmortgage real estate” and “other real estate.”This aspect of the loan book came under sig-nificant pressure during the financial crisis ofthe late-2000s, when a low loans-to-assets ratio

may have increased the probability of survival.The coefficients on the non-performing loanscovariate are varied in sign, but predominantlyinsignificant. The coefficients on the non-interestexpenses covariates are predominantly negativeand significant.

The estimates of the correlation coefficientbetween the stochastic components of the sur-vivorship and growth regressions are varied insign, but negative and significant in the estima-tions that correspond to the economic downturnsof the early- and late-2000s. A plausible inter-pretation is that rapid expansion of a financial-service provider’s balance sheet correlates neg-atively with survival during a downturn.

In the growth regressions, the coefficients onthe lagged asset size covariate are all positiveand significant; and the coefficients on thelagged growth covariate are likewise positiveand significant. These results are indicative ofa pattern of divergence in the size distribution,with the larger institutions growing faster onaverage than their smaller counterparts. In thecross-sectional dimension, accordingly, Gibrat’slaw is unequivocally rejected. A pattern ofpositive persistence in growth has tended toincrease the pace of divergence.

Differences in product and service mix, prod-uct delivery mechanisms, and operational char-acteristics of large and small credit unions canhelp explain the pattern of divergence in growth.For example, at the end of 2010 unsecuredlending for large credit unions (assets greaterthan $500m) accounted for 10.8% of all loans;the corresponding figure for small credit unions(assets less than $10m assets) was 21.1%. Theaverage loan size was $14,173 for large creditunions, and $5,624 for small credit unions;84.2% of large credit unions provided businessloans, while only 7.0% of small credit unions didso. Technological capability in service deliverywas size-dependent: 100% of large credit unionsprovided web-based home banking, while only48% of small credit unions did so. Large creditunions used 0.26 full-time equivalent employeesper million of assets; the corresponding figurefor small credit unions was 0.45.

V. CONCLUSION

This study examines the impact of exit andinternally generated growth on the firm-sizedistribution of the U.S. credit union sector forthe period 1994–2010. This period representsthe most recent stage of a longer-term phase of


consolidation that has seen the number of creditunions reduced from a peak of 23,866 in 1969to 7,335 in 2010.

The econometric analysis reported in thisstudy comprises a panel estimation of hazardfunctions for the determinants of exit throughacquisition or failure, and two sets of time-series and cross-sectional regressions for therelationship between asset size and internallygenerated growth. The cross-sectional estima-tions include a control for survivorship bias. Theempirical hazard functions indicate that smallercredit unions are at greater risk than larger onesof disappearance through either acquisition orfailure. After controlling for asset size oldercredit unions are at higher risk of acquisition,but the failure probability is not age-dependent.The empirical relationship between capitaliza-tion and the probability of acquisition is nega-tive as anticipated, but highly capitalized creditunions appear to be at higher risk of failure.This latter pattern might be driven by a sizeeffect (smaller institutions are more highly capi-talized on average, and at higher risk of failure);or it might reflect balance-sheet adjustments onthe part of distressed credit unions shortly priorto liquidation. Credit unions holding a highproportion of their assets in liquid form, andcredit unions with low loans-to-assets ratios,and low profitability are at higher risk of exitthrough acquisition or failure. While consolida-tion through M&A has had a large impact on thesize of the credit union population, the impact ofconsolidation on concentration is modest, owingto the majority of the acquired credit unions hav-ing been small in terms of asset size.

Consistent with the trend in the populationsize distribution and concentration revealed indescriptive tabulations, the growth regressionsare indicative of a pattern of divergence inthe population size distribution that is highlyconsistent over time, with the larger institu-tions having grown faster, on average, than theirsmaller counterparts. Interpreted as a descrip-tor of the dynamics of the size-growth rela-tionship for each credit union individually,Gibrat’s law accurately describes the growthof credit unions at the upper end of the assetsize distribution, but is rejected in favor of astationary alternative for many smaller creditunions. Interpreted as a descriptor of the cross-sectional size-growth relationship, Gibrat’s lawis unequivocally rejected. The inclusion ofa control for survivorship bias in the cross-sectional growth regressions suggests that rapid

expansion of a credit union’s balance sheetcorrelates negatively with survival during aneconomic downturn. Divergence in the averagerate of internally generated growth between thesmaller and larger institutions is identified as theprincipal factor driving the observed increase inconcentration.

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U.S. CREDIT UNIONS: SURVIVAL, CONSOLIDATION, AND GROWTH

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