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U.S. credit unions: survival, consolidation, and growth.

I. INTRODUCTION

In banking and financial services, industry structure characterized by the firm-size distribution is a key determinant of the nature of competition. Competition among financial service providers has, in turn, implications for consumer welfare, and for the stability or fragility of the financial system. In the U.S. credit union sector, as in banking and financial services generally, a tendency for concentration to increase was apparent in many developed countries throughout the 1980s, 1990s, and 2000s. (1)

This study examines the contribution of exit and the internally generated growth of established firms to changes in industry structure and the rise in concentration in the U.S. credit union sector. Changes to the membership of the population of firms through exit occurs as a result of corporate failure or a merger and acquisition (M&A) transaction in which an established firm is acquired by another industry member. Variation between firms in patterns of internally generated growth leaves the population membership unchanged, but alters the relative shares of firms in total industry assets. If firm-level growth rates are correlated with firm size, the link between internally generated growth and concentration is self-evident. According to the law of Gibrat (1931), also known as the Law of Proportionate Effect, even if growth and size are uncorrelated, and the factors that influence the firm's growth such as customer demand, managerial talent, innovation, or organizational structure, are randomly distributed across firms, there is a natural tendency for concentration to increase over time and for the firm size distribution to become increasingly skewed. (2)

Structural and conduct deregulation, technological and financial innovation, and changes in the economic environment, enabled many U.S. credit unions to expand their scale of operations significantly during the 1990s and 2000s. In 2010, credit unions accounted for around 10% of consumer savings and deposits in the United States, and provided financial services to more than 90 million members. (3) In common with commercial banking, the credit union sector has undergone large-scale consolidation. (4) The number of credit unions declined from 14,549 in 1990 to 7,335 in 2010. A few new credit unions were formed, while many more disappeared through either acquisition or failure. At the end of 2010, 167 U.S. credit unions reported assets in excess of $1bn and loan portfolios similar in structure to that of a medium-sized commercial bank. (5)

This study provides an integrated analysis of corporate demographics for the U.S. credit union sector for the period 1994-2010. There are several important insights with respect to the drivers of acquisition and failure. Smaller credit unions are at higher risk of acquisition or failure than their larger counterparts. Older credit unions that are similar in size to younger credit unions are more likely to be acquired, but the failure probability is not age-dependent. Credit unions holding a high proportion of liquid assets, those with low loans-to-assets ratios, and those with low profitability, are at increased risk of exit through acquisition or failure. Highly capitalized credit unions are at increased risk of acquisition.

This study also provides insights into the evolution of industry structure for the U.S. credit union sector. Consolidation through M&A has greatly reduced the population size, but the impact on concentration has been modest, owing to the relatively small average asset size of acquired credit unions. Internally generated growth is shown to be the main driver of the trend toward increased concentration. Interpreted as a descriptor of the dynamics of the size-growth relationship for each credit union individually, Gibrat's law accurately describes the growth of credit unions at the upper end of the asset size distribution; but for many of the smaller credit unions Gibrat's law is rejected in favor of a stationary alternative hypothesis. Interpreted as a descriptor of the cross-sectional size-growth relationship Gibrat's law is unequivocally rejected, with larger credit unions consistently experiencing faster average growth than their smaller counterparts. This divergence between the average growth of large and small credit unions is the principal cause of the increase in concentration.

In the previous literature on credit union failure, Smith and Woodbury's (2010) comparative study of U.S. banks and credit unions suggests credit unions are less exposed than banks to fluctuations in the business cycle. Elsewhere, it has been shown that small or weakly capitalized credit unions are among those most at risk of failure. Other factors that increase the failure hazard include poorly trained management, lax lending standards and weak collection operations, poor record-keeping, and the closure of sponsoring companies (Barron, West, and Hannan 1994; Gordon 1987; Kharadia and Collins 1981; Pille and Paradi 2002; U.S. Government Accountability Office 1991; Wilcox 2005). In respect of credit union M&A, Goddard, McKillop, and Wilson (2009) find the hazard of acquisition for U.S. credit unions during the period 2001-2006 is inversely related to asset size and profitability, and positively related to liquidity. Worthington (2004) finds asset size, asset management, liquidity, and regulatory variables influenced significantly the probability of Australian credit unions engaging in M&A during the period 1992-1995. (6)

Barron, West, and Hannan (1994) investigate the growth of state-chartered credit unions in New York City for the period 1914-1990, by analyzing the effects of organizational age, size, and population density on the rates of failure and growth. Old and small institutions were more likely to fail, while young and small institutions had the highest growth rates. Goddard, McKillop, and Wilson (2002) test Gibrat's law for U.S. credit unions, using data for the period 1990-1999. Larger credit unions grew faster than smaller ones. On average, credit unions with above-average growth in one period experienced below-average growth in the following period. Small credit unions exhibited more variable growth than large credit unions. More recently, Wheelock and Wilson (2011) report evidence of increasing returns to scale among U.S. credit unions of all sizes for the period 1989-2006. They anticipate that continued deregulation, allowing credit unions to expand their scale or scope of financial service provision, would encourage further growth at the upper end of the size distribution.

The econometric analysis reported in this study comprises a panel estimation of hazard functions for the determinants of acquisition or failure, and two sets of time-series and cross-sectional estimations of the relationship between asset size and internally generated growth. This study extends and integrates previous empirical analysis of credit union acquisition (Goddard, McKillop, and Wilson 2009), and the dynamics of credit union growth (Goddard, McKillop, and Wilson 2002). The study of disappearance through acquisition by Goddard, McKillop, and Wilson (2009) is extended by estimating a competing-risks model that comprises separate hazard functions for the incidence of firm disappearance through both acquisition and failure. The implications of population changes through acquisition and failure for the long-term trend in concentration are also explored.

The present analysis of growth also offers several improvements on the cross-sectional and panel analysis of credit union growth during the 1990s reported by Goddard, McKillop, and Wilson (2002). In order to focus exclusively on internally generated growth (as opposed to growth by means of acquisition) in the cross-sectional analysis, the lagged size and lagged growth covariates of any credit union that was an acquirer are adjusted by defining the lagged values for a "synthetic" credit union constructed using the aggregate assets of the acquirer and the acquired credit union as separate entities at the relevant data-points. Survivorship bias in the cross-sectional growth regressions is addressed by correcting for violation of the conditions for valid estimation and inference resulting from statistical dependence between growth and survival. The Heckman sample-selection model provides a framework for integrating the analyses of growth, and disappearance through acquisition or failure.

This article proceeds as follows. Section II describes the U.S. credit union sector. Section III reports an empirical analysis of the determinants of exit through acquisition or failure. Section IV reports an empirical analysis of patterns of survivorship and internally generated growth. Finally, Section V summarizes and concludes.

II. THE U.S. CREDIT UNION SECTOR

The U.S. credit union data are compiled from the "5300 Call Reports," published by the National Credit Union Association (NCUA). Semiannual data are available for the period June 1994 to December 2010. These data are augmented with information (provided by the NCUA in response to several Freedom of Information requests) on entrants and exits. Attrition is tracked to an exceptional degree of accuracy, with a cause of disappearance identified for 99.5% of all exits. The acquiring credit union is identified for 98.8% of credit unions that exited as a result of M&A, and acquisitions account for 89.9% of all exits.

Table 1 (panel A) reports the total number of U.S. credit unions at the end of December from 1994 to 2010, and an analysis of the evolution of the distribution of the population by asset size. In each year, the population is subdivided into five asset size classes, defined in real terms as follows: Class 1, assets below $2m in 1994 prices (all price conversions are based on the 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 that there has been a marked shift in the composition of the population by asset size, owing to a combination of consolidation through acquisition and failure, and differences between the average internally generated growth of small and large credit unions. In 1994, for example, Class 1 accounted for 31.6% of the entire population, and Class 5 accounted for 9.0%. In 2010, the corresponding figures were 16.6% for Class 1 (assets below $2.8m in current prices) and 22.6% for Class 5 (assets above $74.9m in current prices).

The shift in the asset size distribution has been encouraged by several developments in regulation and fiscal treatment, which have contributed to a tendency for the larger credit unions to offer portfolios of financial services resembling those of medium-sized commercial banks. (7) The NCUA revised the field of membership rules in 1994, diluting the common bond and permitting credit unions to add occupational groups of up to 100 persons without regulatory approval. The 1998 Credit Union Membership Access Act (CUMAA) permitted federal credit unions to add select employee groups (SEGs) to their fields of membership. In some cases, a credit union's common-bond designation makes it difficult to add SEGs, and some credit unions converted from occupational to residential common bonds in order to expand their membership base. (8)

Owing partly to the restrictions on their activities and their high capitalization, credit unions have, in general, withstood the current financial crisis better than many banks (Smith and Woodbury 2010). The crisis in the real-estate market has impacted on the credit union sector, primarily through the investment policies of a number of corporate credit unions, (9) which used cash deposits received from retail credit unions to purchase risky asset-backed securities, and realized large losses in several cases. The 2010 Dodd-Frank Act made radical changes to financial services regulation and supervision. For credit unions, deposit insurance was increased from $100,000 to $250,000 per account, and the supervision of corporate credit unions was strengthened. (10)

Table 2 reports a further analysis of the dynamics of change in the asset size distribution, in the form of a set of empirical yearly rates of transition between each size class and the nearest adjacent classes, and exit rates from each size class. The size classes are the same as those used to construct Table 1, and the computations follow closely the methodology used by Robertson (2001) in a similar analysis of transition rates between asset size classes for U.S. banks over the period 1960-2000. The numbers of credit unions moving by more than one size class in any year are negligible, and the corresponding rates of transition are not reported. Table 2 indicates that there is a high degree of stability in the asset size distribution from year to year. The propensities for credit unions to remain within the same asset size class are, in general, higher on average than those reported by Robertson (2001) for banks, particularly among the larger size classes. (11) The propensity to remain within the same class is an increasing function of size, and this relationship appears to be driven mainly by an inverse relationship between size and the propensity to exit. The exit rate in the two largest size classes appears to have risen significantly over the observation period. The year 2008-2009 witnessed unusually high rates of upward transition from each of Classes 1 to 4 to the next highest Class (2-5, respectively), apparently due to unusual patterns of consolidation at the height of the late-2000s financial crisis.

Consistent with the analysis presented by Robertson (2001), Table 1 (panel B) reports projections of future changes in the asset size distribution over the period 2011-2015, based on the assumption that the yearly entry, transition, and exit rates observed over the final year included in Table 2, 2009-2010, remain unchanged for the following 5 years. The projected size distribution for 2011 is obtained by multiplying a matrix containing the transition and exit rates for each size class by a vector containing the numbers of credit unions in each class in 2010, and adding five new entrants to Class 1 (equivalent to the actual number of entrants in 2010, all of which joined Class 1). The projections for subsequent years are then obtained iteratively, by multiplying the same matrix by a vector containing the projected numbers for the preceding year. The projections suggest further shrinkage in the population and shifts in the shape of the size distribution, with the projected number of credit unions in the smallest size class dropping by a further 23.4% over a 5-year period, while the projected number in the largest size class drops by only 2.2%.

Table 3 reports an analysis of changes in the population owing to entry and exit. Between December 1994 and December 2010, the total number of credit unions fell from 12,051 to 7,334. This decline in numbers reflects the net effect of entry (156 new credit unions) and exit (4,873 credit unions). A large majority of the credit unions that exited did so as a consequence of having been acquired (4,382 credit unions, or 89.9% of the total number that exited). The exit rate was remarkably stable throughout the 2000s (between 3% and 4% per year), and the exit rate does not appear to be sensitive to the economic cycle. Smith (2012) reports that on conservative estimates, credit union loan portfolios were around 25% less sensitive to macroeconomic shocks than bank loan portfolios.

III. EMPIRICAL ANALYSIS OF EXIT THROUGH ACQUISITION OR FAILURE

Section III reports an investigation of the determinants of credit union disappearance through acquisition or failure during the period 1994-2010.

A. Empirical Model for the Determinants of Acquisition or Failure

The hazard function estimations reported in this section are based on the method used by Wheelock and Wilson (2000) to model the hazards of failure and acquisition for U.S. banks. The empirical model is the Cox (1972) proportional hazard model with time-varying covariates. The probabilities of disappearance through events defined as failure and acquisition are modelled separately, using a competing-risks framework. The alternative modes of disappearance are treated as independent events, and the observations on a credit union that disappeared through each event are treated as fight-censored in the estimations of the hazard for disappearance through the other event.

The hazard function expressing the probability that credit union i disappears through event k between time t and time t+1 (k = 1 denotes acquisition; k = 2 denotes failure), conditional on a vector of covariates specific to credit union i at time t that influence the probability of event k, denoted [x.sub.k,i] (t), is modelled as follows:

(1) [[lambda].sub.k,i] (t|[x.sub.k,i](t), [[beta].sub.k]) = [bar.[lambda]](t)exp([x.sub.k,i](t)'[[beta].sub.k]).

In Equation (1), the baseline hazard is denoted [[bar.lambda]].sub.k](t), and [[delta].sub.k] is a vector of coefficients to be estimated. The time-index t is measured in calendar time elapsed since December 1994. [R.sub.t] denotes the set of credit unions that are in existence at time t and exposed to risk of disappearance between t and t+1, and [D.sub.k,t] denotes the set of [d.sub.k,t] credit unions that disappear through event k between time t and time t + 1. The contribution to the partial likelihood function of credit union i, which disappears through event k between t and t + 1, is:

(2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

The baseline hazard [[bar.[lambda].sub.k] (t) drops out of the partial likelihood function, and is not parameterized explicitly. The (semiparametric) log-partial likelihood function is:

(3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

The hazard function covariate definitions are as follows: [S.sub.i,t] = Total Assets; [K.sub.i,t] = capital-to-assets ratio = Net Worth / Total Assets; [Q.sub.i,t] = Liquid Assets / Total Assets; [N.sub.i,t] = Non-performing Loans / Total Assets; [L.sub.i,t] =

Loans / Total Assets; [E.sub.i,t] = Non-interest Expenses / Total Assets; [R.sub.i,t] =Return on Assets; and [A.sub.i,t] = Age. Table 4 reports the mean values of each of the covariates at the end of each year. In the empirical hazard functions, logarithmic transformations are applied to the total assets and age covariates.

B. Estimation Results

Table 5 reports the empirical hazard function estimation results. All members of the credit union population are included in the estimations (see the final column of Table 1). The acquisition hazard function is based on 4,471 credit unions reported in Table 3 as exits through either acquisition or purchase and assumption. The failure hazard function is based on 341 credit unions reported in Table 3 as exits through liquidation. Observations on credit unions that exited for reasons other than acquisition, purchase, and assumption or liquidation are treated as right-censored.

The anticipated inverse relationship between asset size and the hazard of disappearance is evident in both of the hazard function estimations, indicating that a smaller credit union was at significantly greater risk of disappearance through either acquisition or failure than a larger one. The coefficient on the age covariate in the M&A hazard is positive and significant, suggesting that an older credit union is more likely to be acquired than a younger credit union of the same size. The coefficient on the age covariate is insignificant in the failure hazard.

The coefficients on the capital-to-assets ratio covariate are negative and significant in the M&A hazard, and positive and significant in the failure hazard. These results are consistent with Hannan and Piloff's (2009) explanation for a negative relationship between the capitalization of U.S. banks and the hazard of acquisition: high capitalization is a proxy for efficiency, indicating limited scope for post-merger efficiency gains, while low capitalization reduces the purchase price and increases the attractiveness of the target. Contrary to results reported by Wilcox (2005), highly capitalized credit unions appear to be at greater risk of failure. Credit unions regarded as inadequately capitalized under Section 301 of CUMAA (1998) are subject to a range of mandatory actions, such as earnings retentions, lending restrictions, and the prohibition of increases in assets. (12) These actions impact on both the denominator and the numerator of the capital-to-assets ratio, sometimes causing the latter to spike for a distressed credit union immediately prior to failure. It is also the case that smaller credit unions maintain a higher capital-to-assets ratio on average than large credit unions, and small credit unions are at higher risk of failure. Although [x.sub.2,i] (t) includes a separate control for asset size, it is possible that the positive coefficient on [K.sub.i,t] in the failure hazard also reflects aspects of the strong association between asset size and failure.

The coefficients on the liquidity ratio covariate are positive and significant in both hazards. The coefficient on the loans-to-assets ratio covariate is insignificant in the M&A hazard, but the corresponding coefficient is negative and significant in the failure hazard. A credit union that hordes cash, or does not create a loans portfolio of a size commensurate with its deposits, may be either an attractive target for an acquirer that believes itself capable of earning a higher return by expanding the loans portfolio, or at risk of failure due to an inability to generate an adequate return.

The coefficient on the non-performing loans covariate in the M&A hazard is negative and significant, while the corresponding coefficient in the failure hazard is positive and significant. These coefficients suggest a lack of control over the quality of lending makes a credit union a less attractive target for acquisition, but increases the likelihood of disappearance through failure. The coefficient on the ratio of non-interest expenses to assets covariate in the M&A hazard is positive and significant. This appears consistent with the interpretation of the ratio of non-interest expenses to assets as a managerial inefficiency measure, and the hypothesis that inefficient credit unions are more vulnerable to either acquisition. The corresponding coefficient in the failure hazard is insignificant. Finally, the coefficients on the return on assets covariate are negative and significant in both hazards, indicating that the likelihood of disappearance through either acquisition or failure is reduced by an increase in profitability.

C. Impact of Consolidation on Industry Structure

Table 6 reports a descriptive analysis of the trend in concentration over the period 1994-2010. The first five columns report 5-, 10-, and 20-firm concentration ratios, together with the Herfindahl--Hirshman Index (HHI) and the HHI numbers equivalent. Consistent with the patterns reported in Table 1, these data indicate a trend toward increased concentration that has been remarkably steady and consistent over time.

The final two columns of Table 6 provide an indication of the contribution of consolidation through M&A to the trend in concentration, in the form of a "counterfactual" HHI based on hypothetical population data. For the purposes of calculating the counterfactual HHI, each acquired credit union is assumed to have continued to operate as a separate entity to the end of 2010. A proportion of the combined assets of the acquirer at each data-point after the merger took place are reallocated to the (counterfactually surviving) acquired credit union. The proportion of the assets reallocated is based on the relative asset sizes of the acquirer and the acquired at the data point immediately preceding the merger: the final data point at which separate assets data are available for both institutions.

The large number of credit union mergers notwithstanding, the analysis reported in Table 6 suggests that the contribution of M&A to the rise in concentration was modest. The counterfactual 2010 HHI of 43.8 is only slightly smaller than the observed HHI of 46.5; and the observed drop in the HHI Numbers Equivalent from 520.9 in 1994 to 215.2 in 2010 would have been mitigated only marginally, to a counterfactual figure of 228.5 in 2010, had no credit unions mergers taken place between 1994 and 2010. The disparity between the large effect of M&A on the population size, and the much smaller effect on concentration, is attributed to the majority of acquired credit unions having been drawn from the lower end of the asset size distribution.

IV. EMPIRICAL ANALYSIS OF INTERNALLY GENERATED GROWTH

The empirical analysis reported in Section III suggests that while consolidation through M&A accounts for most of the large decline in the number of U.S. credit unions over the period 1994-2010, the effect on industry structure was small. With the sector also having experienced modest rates of entry and failure, it appears that internally generated growth was the main driver of the trend toward increased concentration over the same period. Section IV reports an empirical analysis of the relationship between credit union size and growth, using Gibrat's law as a benchmark.

A. Empirical Analysis of the Relationship Between Firm Size and Growth

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

(4) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

In Equation (4), logarithmic growth over a 1-year period is the dependent variable, and log size at the start of the period and growth over [m.sub.i,t] previous 1-year periods are the explanatory variables.

Clearly, estimation requires the imposition of restrictions on the coefficients of Equation (4). Below, two sets of restrictions are considered. Under the first set, it is assumed that the coefficients are constant over time, but variable over all surviving i for which a complete set of time-series observations is available, so that [[phi].sub.1,i,t] = [[alpha].sub.1,i] for all t (with similar restrictions imposed on the other coefficients, and [m.sub.i,t] = [m.sub.i]). These restrictions are embodied in a set of individual Dickey--Fuller time-series regressions (for each i = 1, ..., N, where N is the number of surviving credit unions), defined as follows:

(5) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Each regression in Equation (5) has t = 1, ..., T observations. The focus is on the dynamics of the size-growth relationship for each credit union individually. As the credit union grows in size (possibly relative to a deterministic time-trend or drift component), either growth might tend to decline ([[alpha].sub.1,i] < 0), or growth might be independent of attained size ([[alpha].sub.1,i] = 0). (13) The latter case [[alpha].sub.1,i] = 0 represents Gibrat's law, interpreted as a descriptor of the dynamics of the size-growth relationship for each credit union individually.

Under the second set of restrictions, it is assumed that the coefficients are the same for all i but variable over time, so that [[phi].sub.1,it,] = [[beta].sub.1,t] for all i (with similar restrictions imposed on the other coefficients, and [m.sub.i,t] = 1 for all i, t). A series of cross-sectional regressions (for each t = 1, ..., T) is defined as follows:

(6) ([S.sub.i,t] - [S.sub.i,t-1]) = [[beta].sbu.0,t] + [[beta].sub.1,t] [S.sub.i,t-1] + [[beta].sub.2,t] ([S.sub.i,t-1] - [S.sub.i,t-2]) + [u.sub.i,t].

Each regression in Equation (6) has i = 1, ..., [N.sub.t] observations (where [N.sub.t] is the number of credit unions live in year t). The focus is on the cross-sectional size-growth relationship, which might be either positive ([[beta].sub.1,t] > 0), neutral ([[beta].sub.1,t] = 0), or negative ([[beta].sub.1,t] < 0). The nature of this relationship is permitted to vary over time. The case [[beta].sub.1,i] = 0 represents Gibrat's law, interpreted as a descriptor of the cross-sectional size-growth relationship.

In order to focus solely on growth that is internally generated, rather than growth that is achieved by means of M&A, the lagged size and lagged growth covariates in Equation (6) of any credit union that was an acquirer are adjusted by defining the lagged values for a "synthetic" credit union constructed using the aggregate assets of the acquirer and the acquired credit union as separate entities at the relevant data-points. (14) The cross-sectional size-growth regressions are estimated using the Heckman (1979) sample-selection model, to mitigate potential survivorship bias. (15) The latter might arise because the probability that a credit union survives, and therefore appears in the data set for the estimation of the growth regression, might be related to the credit union's propensity for growth. The direction of any association between growth and survival might be either positive or negative: on the one hand, reckless growth in lending might increase the risk of disappearance as a consequence of financial distress; but on the other hand, sluggish growth in lending might reflect operational inefficiency or underperforming management. The sample-selection model comprises Equation (6), and the following survivorship regression observed for all credit unions live at t - 1:

[Z.sup.*.sub.i,t] = [[gamma].sub.0,t] + [[gamma].sub.1,t] [S.sub.i,t-1] + [[gamma].sub.2,t] ([S.sub.i,t-1] - [S.sub.i,t-2]) + [[gamma].sub.3,t'] [X.sub.i,t-1]

(7) [Z.sub.i,t] = 1 if [z.sup.*.sub.i,t] + [[epsilon].sub.i,t] > 0; [z.sub.i,t] = 0 if [z.sup.*.sub.i,t] + [[epsilon].sub.i,t] < 0

where [[gamma].sub.3,t] is a vector of coefficients, and [x.sub.i,t-1] = ([s.sub.i,t-1] [s.sub.i,t-1] [s.sub.i,t-1] - [s.sub.i.t-2] [K.sub.i,t-1] [Q.sub.i,t-1] [L.sub.i,t-1] [N.sub.i,t-1] [E.sub.i,t-1] [R.sub.i,t-1]). See Section III for covariate definitions. Equation (6)is observed only for those credit unions that were live at t - 1 and survived to t, for which [z.sub.i,t] = 1 in Equation (7). The disturbances [u.sub.i,t] in Equation (6) and [[epsilon].sub.i,t] in Equation (7) are assumed to be bivariate normal, with var([[epsilon].sub.i,t]) = 1, var([u.sub.i,t]) = [[sigma].sup.2.sub.u,t], corr([[epsilon].sub.i,t], [u.sub.i,t]) = [[rho].sub.[epsilon]u,t]. The covariates that appear in the survivorship regression are the same as those in the acquisition and failure hazard functions reported in Section II, with the sole exception of the age covariate, which was generally insignificant in preliminary estimations of the sample-selection model.

B. Estimation Results: Time-Series Regressions

Table 7 reports summary results from augmented Dickey--Fuller (ADF) unit root tests on the log assets series (Dickey and Fuller 1979), together with the associated Ira, Pesaran, and Shin (2003) (IPS) panel unit root tests, based on estimations of Equation (5) for each of the 7,247 surviving credit unions that reported assets data in every December call report from 1994 to 2010 (inclusive). The summary results for the ADF tests are the proportions of rejections of the unit root null hypothesis ([[alpha].sub.1,i] = 0 in Equation (5)) in favor of the stationarity alternative ([[alpha].sub.1,i] < 0) at the 0.01, 0.05, and 0.1 significance levels. These proportions are reported for the full cohort of 7,247 surviving credit unions, and for the same cohort subdivided by rank based on December 1994 assets as follows: size band (i) comprises rank 1-250; (ii) 251-500; (iii) 500-1000; (iv) 1001-2000; (v) 2001-7247 (rank 1 denotes the largest credit union in December 1994). Akaike Information Criterion (AIC) is used to determine [m.sub.i], the lag-length for the first-difference terms in log assets on the right-hand side of Equation (5), for each credit union individually. The IPS procedure tests the null hypothesis of a unit root for all panel constituents ([[alpha].sub.1,i] = 0 for all i in Equation (5)) against the alternative of stationarity for one or more panel constituents ([[alpha].sub.1,i]< 0 for some i).

According to Table 7, the proportions of rejections of the unit root null hypothesis in the ADF tests are higher than the proportions that should be expected due to type 1 error (equivalent to the significance level) if the null hypothesis were true in every case. For example, the proportion of rejections at the 0.05 level for the entire cohort of surviving credit unions is 0.153. The IPS test rejects decisively the null hypothesis of a unit root for every credit union, with a p value of .000. Across size bands (i)-(v), however, there is some variation in this pattern. At the 0.05 level, the propensity for the ADF test to reject the unit root null hypothesis is lowest for the largest December 1994 asset size band (i). This propensity increases (and is therefore inversely related to asset size) over bands (i)to (iii). Between bands (iii) and (v)there is little or no relationship between size and the propensity for the ADF test to reject. A similar pattern is obtained from the IPS test, which fails to reject the null for bands (i) and (ii). For band (iii), the result of the IPS test is borderline, with a p value of .0379. For bands (iv) and (v), the null is rejected decisively. (16)

Overall, the time-series estimations indicate that Gibrat's law, interpreted as a descriptor of the dynamics of the size-growth relationship for each credit union individually, cannot be rejected for surviving credit unions at the upper end of the asset size distribution. For smaller credit unions the pattern is mixed. Gibrat's law is rejected as a descriptor of the dynamics

of the size-growth relationship for all of the smaller credit unions: in some cases log assets is stationary in relation to a deterministic time trend. At the 0.05 level, the percentage rejection rate of the unit root null among the smaller credit unions is slightly below 16% in the ADF tests. With a maximum sample size of T = 17, however, the ADF test has limited power, suggesting that the true proportion of smaller credit unions departing from Gibrat's law might be substantially larger than the ADF test rejection rates indicate.

C. Estimation Results: Cross-Sectional Regressions

Table 8 reports the estimation results for the cross-sectional sample-selection model of survivorship and growth. A separate set of equations is reported for growth rates defined over yearly intervals (ending in December) for the period 1996 to 2010 inclusive. The survivorship regressions include the same set of covariates as the hazard functions reported in Section IV with the exception of the age covariate, for which the coefficients were small and insignificant in preliminary estimations of the survivorship regressions. A lagged growth covariate is included in the cross-sectional survivorship regressions. The latter, which are dominated by disappearances owing to M&A, are similar to the M&A hazard function reported in Table 5, with a reversal of signs on all coefficients because survival, rather than disappearance, is coded 1, and disappearance coded 0.

The coefficients on the size, lagged growth, capitalization, and return on assets covariates are predominantly positive and significant. The coefficients on the liquidity covariate are predominantly negative, and several are significant. These coefficients may be interpreted in the same way as the corresponding coefficients in the hazard function estimations reported in Section III. The coefficients on the loans-to-assets covariate are predominantly positive and several are significant prior to the late-2000s financial crisis; but several negative coefficients are obtained from t = 2007 onward. The change in sign might be linked to the fact that a significant share (around 50% on average) of a credit union's loan book takes the form of "first mortgage real estate" and "other real estate." This aspect of the loan book came under significant pressure during the financial crisis of the late-2000s, when a low loans-to-assets ratio may have increased the probability of survival. The coefficients on the non-performing loans covariate are varied in sign, but predominantly insignificant. The coefficients on the non-interest expenses covariates are predominantly negative and significant.

The estimates of the correlation coefficient between the stochastic components of the survivorship and growth regressions are varied in sign, but negative and significant in the estimations that correspond to the economic downturns of the early- and late-2000s. A plausible interpretation is that rapid expansion of a financial-service provider's balance sheet correlates negatively with survival during a downturn.

In the growth regressions, the coefficients on the lagged asset size covariate are all positive and significant; and the coefficients on the lagged growth covariate are likewise positive and significant. These results are indicative of a pattern of divergence in the size distribution, with the larger institutions growing faster on average than their smaller counterparts. In the cross-sectional dimension, accordingly, Gibrat's law is unequivocally rejected. A pattern of positive persistence in growth has tended to increase the pace of divergence.

Differences in product and service mix, product delivery mechanisms, and operational characteristics of large and small credit unions can help explain the pattern of divergence in growth. For example, at the end of 2010 unsecured lending for large credit unions (assets greater than $500m) accounted for 10.8% of all loans; the corresponding figure for small credit unions (assets less than $10m assets) was 21.1%. The average loan size was $14,173 for large credit unions, and $5,624 for small credit unions; 84.2% of large credit unions provided business loans, while only 7.0% of small credit unions did so. Technological capability in service delivery was size-dependent: 100% of large credit unions provided web-based home banking, while only 48% of small credit unions did so. Large credit unions used 0.26 full-time equivalent employees per million of assets; the corresponding figure for small credit unions was 0.45.

V. CONCLUSION

This study examines the impact of exit and internally generated growth on the firm-size distribution of the U.S. credit union sector for the period 1994-2010. This period represents the most recent stage of a longer-term phase of consolidation that has seen the number of credit unions reduced from a peak of 23,866 in 1969 to 7,335 in 2010.

The econometric analysis reported in this study comprises a panel estimation of hazard functions for the determinants of exit through acquisition or failure, and two sets of time-series and cross-sectional regressions for the relationship between asset size and internally generated growth. The cross-sectional estimations include a control for survivorship bias. The empirical hazard functions indicate that smaller credit unions are at greater risk than larger ones of disappearance through either acquisition or failure. After controlling for asset size older credit unions are at higher risk of acquisition, but the failure probability is not age-dependent. The empirical relationship between capitalization and the probability of acquisition is negative as anticipated, but highly capitalized credit unions appear to be at higher risk of failure. This latter pattern might be driven by a size effect (smaller institutions are more highly capitalized on average, and at higher risk of failure); or it might reflect balance-sheet adjustments on the part of distressed credit unions shortly prior to liquidation. Credit unions holding a high proportion of their assets in liquid form, and credit unions with low loans-to-assets ratios, and low profitability are at higher risk of exit through acquisition or failure. While consolidation through M&A has had a large impact on the size of the credit union population, the impact of consolidation on concentration is modest, owing to the majority of the acquired credit unions having been small in terms of asset size.

Consistent with the trend in the population size distribution and concentration revealed in descriptive tabulations, the growth regressions are indicative of a pattern of divergence in the population size distribution that is highly consistent over time, with the larger institutions having grown faster, on average, than their smaller counterparts. Interpreted as a descriptor of the dynamics of the size-growth relationship for each credit union individually, Gibrat's law accurately describes the growth of credit unions at the upper end of the asset size distribution, but is rejected in favor of a stationary alternative for many smaller credit unions. Interpreted as a descriptor of the cross-sectional size-growth relationship, Gibrat's law is unequivocally rejected. The inclusion of a control for survivorship bias in the cross-sectional growth regressions suggests that rapid expansion of a credit union's balance sheet correlates negatively with survival during an economic downturn. Divergence in the average rate of internally generated growth between the smaller and larger institutions is identified as the principal factor driving the observed increase in concentration.

ABBREVIATIONS

ADF: Augmented Dickey-Fuller

AIC: Akaike Information Criterion

CUMAA: Credit Union Membership Access Act

HHI: Herfindahl-Hirshman Index

IPS: Im, Pesaran, and Shin

M&A: Merger and Acquisition

NCUA: National Credit Union Association

NWRP: Net Worth Restoration Plan

SEG: Select Employee Group

doi: 10.1111/ecin.12032

Online Early publication July 5, 2013

REFERENCES

Barron, D. N., E. West, and M. T. Hannan. "A Time to Grow and a Time to Die: Growth and Mortality of Credit Unions in New York City, 1914-1990." American Journal of Sociology, 100(2), 1994, 381-421.

Bauer, K., L. Miles, and T. Nishikawa. "The Effect of Mergers on Credit Union Performance." Journal of Banking and Finance, 33(12), 2009, 2267-74.

Caves, R. E. "Industrial Organization and New Findings on the Turnover and Mobility of Firms." Journal of Economic Literature, 36(4), 1998, 1947-82.

Coad, A. The Growth of Firms: A Survey of Theories and Empirical Evidence. Cheltenham: Edward Elgar, 2009.

Cox, D. R. "Regression Models and Life Tables." Journal of the Royal Statistical Society Series B, 34(2), 1972, 187-220.

CUNA. Credit Union Report, 2010. Madison, WI: CUNA, 2010.

Dickey, D. A., and W. A. Fuller. "Distribution of the Estimators for Autoregressive Time Series with a Unit Root." Journal of the American Statistical Association, 74(366), 1979, 427-31.

Frame, W. S., G. V. Karels, and C. A. McClatchey. "The Effect of the Common Bond and Membership Expansion on Credit Union Risk." Financial Review, 37(4), 2002, 613-36.

Fried, H. O., C. A. K. Lovell, and S. Yaisawarng. "The Impact of Mergers on Credit Union Service Provision." Journal of Banking & Finance, 23(2-4), 1999, 237-386.

Gibrat, R. Les Inegalities Economiques. Paris: Sirey, 1931.

Goddard, J., D. McKillop, and J.O.S. Wilson. "The Growth of US Credit Unions." Journal of Banking & Finance, 22(12), 2002, 2327-56.

--. "Which Credit Unions Are Acquired?" Journal of Financial Services Research, 36(2-3), 2009, 231-52.

Gordon, D. Causes of Credit Union Failures 1981-85. NCUA Office of the Chief Economist, Research Study Number 4. Washington: National Credit Union Administration, Washington, DC, 1987.

Hannan, T. H., and S. J. Pilloff. "Acquisition Targets and Motives in the Banking Industry." Journal of Money, Credit and Banking, 41 (6), 2009, 1167-87.

Heckman, J. "Sample Selection Bias as a Specification Error." Econometrica, 47(1), 1979, 153-61.

Im, K. S., M. H. Pesaran, and Y. Shin. "Testing for Unit Roots in Heterogeneous Panels." Journal of Econometrics, 115(1), 2003, 53-74.

Kharadia, V. C., and R. A. Collins. "Forecasting Credit Union Failures." Journal of Economics and Business, 33, 1981, 147-52.

Mcalevey, L., A. Sibbald, and D. Tripe. "New Zealand Credit Union Mergers." Annals of Public and Cooperative Economics, 81(3), 2010, 423-44.

Pille, P., and J. C. Paradi. "Financial Performance Analysis of Ontario (Canada) Credit Unions: An Application of DEA in the Regulatory Environment." European Journal of Operational Research, 139(2), 2002, 339-50.

Ralston, D., A. Wright, and K. Garden. "Can Mergers Ensure the Survival of Credit Unions in the Third Millennium?" Journal of Banking & Finance, 25(12), 2001, 2277-304.

Robertson, D. D. "A Markov View of Bank Consolidation 1960-2000." Working Paper 2001-4, Office of the Comptroller of the Currency, 2001.

Smith, D. M. Commercial Lending During the Crisis: Credit Unions vs. Banks. Madison, WI: Filene Research Institute, 2012.

Smith, D. M., and S. A. Woodbury. Withstanding a Financial Firestorm: Credit Unions vs. Banks. Madison, WI: Filene Research Institute, 2010.

Sutton, J. "Gibrat's Legacy." Journal of Economic Literature, 35(1), 1997, 40-59.

U.S. Government Accountability Office. Credit Unions: Reforms for Ensuring Future Soundness. Washington, D.C.: Government Accountability Office, 1991.

--. Financial Institutions: Issues Regarding the Tax Exempt Status of Credit Unions. Washington, D.C.: Government Accountability Office, 2005.

Wheelock, D. C., and P. W. Wilson. "Why Do Banks Disappear? The Determinants of US Bank Failures and Acquisitions." Review of Economics and Statistics, 82(1), 127-38.

--. "Are Credit Unions Too Small?" Review of Economics and Statistics, 93(4), 2011, 1343-59.

Wilcox, J. A. "Credit Union Failures and Insurance Losses: 1971-2004." Federal Reserve Bank of San Francisco Economic Letter, 2005-20, 2005.

Wilcox, J. A., and L. G. Dopico. "Credit Union Mergers: Efficiencies and Benefits." Federal Reserve Bank of San Francisco Economic Letter, 2011-28, 2011.

World Bank Financial Structure Database, 2010. Available at: http://econ.worldbank.org/WBSITE/EXTE RNAL/EXTDEC/EXTRESEARCH/0,,contentMDK: 20696167~pagePK:64214825~piPK:64214943~the SitePK:469382,00.html.

World Council of Credit Unions. Statistical Report. Madison, WI: World Council of Credit Unions, 2011.

Worthington, A. C. "Determinants of Merger and Acquisition Activity in Australian Cooperative Deposit Taking Institutions." Journal of Business Research, 57(1), 2004, 47-57.

JOHN GODDARD, DONAL McKILLOP and JOHN O. S. WILSON *

* The authors are grateful to James MacGee (Editor) and two anonymous referees for many helpful comments on an earlier draft of this paper. We would like to thank Leonard Nakomura, Bob DeYoung, and other participants at the FMA and SFA Annual Meetings in Denver and Charleston for helpful comments and suggestions.

Goddard: Professor, Bangor Business School, Bangor University, Bangor, Gwynedd LL57 2DG, UK. Phone +44-1248-383221, Fax +44-1248-383228, E-mail j.goddard@bangor.ac.uk

McKillop: Professor, Queen's University Management School, Queen's University Belfast, Belfast, Northern Ireland BT9 5EE, UK. Phone +44-28-9097-4852, Fax +44-28-9097-4201, E-mail dg.mckillop@qub.ac.uk

Wilson: Professor, School of Management, University of St Andrews, The Gateway, North Haugh, St Andrews, Fife KYI6 9SS, UK. Phone +44-1334-462803, Fax +44-1334-462812, E-mail jsw7 @st-and.ac.uk

(1.) According to the World Bank Financial Structure database (2010), the five-firm concentration ratio ([CR.sub.5]) for the U.S. banking industry was 21% in 2003 and 37% in 2009; for the UK: 86% (1993) and 88% (2009); for France: 46% (1993) and 52% (2009); for Germany: 50% (1993) and 77% (2009); and for Japan: 30% (1993) and 65% (2009).

(2.) According to Sutton (1997), Caves (1998), and Coad (2009), Gibrat's law provides an accurate representation of 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 and including the 1970s, report either no relationship or a positive relationship between firm size and growth. Several recent studies find a consistent tendency for small firms to grow faster than large firms.

(3.) Worldwide, more than 50,000 credit unions operate in 100 countries, with a combined membership of 188 million and assets under control of $1,460bn (World Council of Credit Unions 2011). The credit union operating and business model is relatively homogeneous across countries. The U.S. credit union movement is among the most developed in the world, and the United States' experience offers insights for cooperative movements in financial services worldwide.

(4.) During the 1990s and 2000s, financial deregulation also eased many of the constraints on the business activities of U.S. banks, increasing competition as barriers to entry into local or state banking markets were reduced or eliminated. An increasingly dominant group of large banks, operating a high-volume low-cost retail banking model, pursued aggressive growth strategies, including M&A on a large scale. Although similar trends toward deregulation and consolidation have been operative for banks and credit unions alike, analogies should be drawn cautiously in view of the difference between the profit and non-profit orientation of the two types of institution.

(5.) Neither banks nor credit unions face restrictions on the 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 lending concentration.

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

(7.) With the exception of some securities investments, credit unions were originally distinguished from other financial institutions by their emphasis on small value, unsecured, nonmortgage loans to individuals and households. Federal credit unions gained the authority to make long-term (up to 30 years) mortgage real estate loans in 1977. At the end of 2010, first mortgages accounted for 39.3% of all loans, and second mortgages accounted for 7.6%. The 1994 figures were 21.3% and 5.5%, respectively. Other changes to the typical product mix of credit unions include growth in the importance of credit-card lending. Around 53% of credit unions offered credit cards in 2010 (CUNA 2010). Unsecured lending accounted for only 10.8% of all credit union lending in 2010, down from 20.3% in 1994.

(8.) For discussion of the background to CUMAA, see Frame, Karels, and McClatchey (2002). CUMAA also introduced a capital regulation system of net worth requirements and prompt corrective action, which came into force in 2000. Congressional hearings were held in 2005 to examine the tax-exempt status of credit unions, justified by its proponents as a policy tool to tackle financial exclusion. Tax-reform proponents argue that credit unions should be subject to corporate taxation (U.S. Government Accountability Office 2005). Following the 2005 hearings the tax-exempt status of credit unions was retained, despite intense lobbying by banks for its abolition.

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

(10.) In addition, the NCUA has approved a new rule requiring credit union directors to receive financial literacy training, 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 also reflects a high level of stability in the size distribution. The same two credit unions, Navy Federal and State Employees, occupied the top two positions throughout this period; and seven of the ten largest credit unions in December 1995 also featured among the ten largest in December 2010.

(12.) The CUMAA specifies mandatory actions for credit unions that do not meet capital adequacy standards. These include: annual earnings retentions of at least 0.4% of total assets; the submission and adherence to a net worth restoration plan (NWRP); lending restrictions; and the prohibition of increases in assets until net worth is restored. The CUMAA allows the NCUA to use 14 supervisory actions to supplement the mandatory actions.

(13.) The case [[alpha].sub.1,i] > 0, in which growth tends to increase with size, is usually disregarded because it implies unstable or explosive growth. The possibility that large firms tend to grow more rapidly than small firms can be accommodated, however, through suitable variation over i in the trend coefficients [[alpha].sub.3,i] (in the case [[alpha].sub.1,i] < 0, where log size is stationary relative to a deterministic time trend), or the drift coefficients [[alpha].sub.3,i] (in the case [[alpha].sub.1,i] = [[alpha].sub.3,i] = 0, where log size is non-stationary).

(14.) For the observation following an acquisition that took place between t - 1 and t, the acquirer's "synthetic" growth rate is [s.sub.i,t]-[s.sub.i,t-l]*, [s.sup.*.sub.i,t-1], where [s.sup*.sub.i,t-1] is the logarithm of the sum of the assets of the acquirer and the acquired as separate entities at t - 1, and the lagged "synthetic" growth is [s.sup.*.sub.i,t-1] - [s.sup.*.sub.i,t-2] with [s.sup.*.sub.i,t-2]. defined in the same manner at t - 2. Where the acquisition took place between t - 1 and t - 2, the lagged "synthetic" growth is [s.sub.i,t-1] - [s.sup.*.sub.i,t-2].

(15.) An inverse empirical size-growth relationship may be a manifestation of survivorship bias. Small firms are less likely to survive than large firms, but fast-growing small firms are likelier to survive than slow-growing ones. As a consequence, studies using samples of firms that survive over the entire period of the analysis are subject to a form of survivorship bias, because firms that failed to achieve rapid growth and exited would not have been recorded.

(16.) The power of the IPS test is dependent on the number of panel constituents. However, the observed pattern of rejection and non-rejection is not a feature of variation in the power of this test. A similar pattern is obtained if the cohort is subdivided into equal-sized quintiles based on June 1994 assets (with each quintile containing either 1,449 or 1,450 credit unions). The IPS test fails to reject the null for the largest assets-size quintile (p value = .7447); but the IPS test rejects the null for each of the four smaller size quintiles (p value = .0000 in each case).
TABLE 1
Trends 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
                                                             Total
                       1       2       3       4       5     Number

Panel A: actual
  December 1994      3,805   2,919   2,586   1,657   1,085   12,052
  December 1995      3,648   2,812   2,506   1,661   1,120   11,747
  December 1996      3,429   2,715   2,473   1,656   1,170   11,443
  December 1997      3,275   2,638   2,442   1,669   1,222   11,246
  December 1998      3,047   2,522   2,438   1,690   1,295   10,992
  December 1999      2,784   2,415   2,395   1,705   1,329   10,628
  December 2000      2,659   2,314   2,300   1,700   1,342   10,315
  December 2001      2,370   2,111   2,317   1,731   1,454    9,983
  December 2002      2,147   1,955   2,305   1,738   1,542    9,687
  December 2003      1,938   1,832   2,256   1,764   1,578    9,368
  December 2004      1,788   1,777   2,143   1,713   1,594    9,015
  December 2005      1,732   1,705   2,061   1,614   1,580    8,692
  December 2006      1,671   1,656   1,919   1,570   1,544    8,360
  December 2007      1,602   1,584   1,850   1,516   1,545    8,097
  December 2008      1,458   1,475   1,801   1,503   1,563    7,800
  December 2009      1,308   1,351   1,729   1,494   1,666    7,548
  December 2010      1,221   1,281   1,707   1,466   1,660    7,335
Panel B: projected
  December 2011      1,141   1,216   1,683   1,436   1,653    7,132
  December 2012      1,066   1,154   1,657   1,413   1,646    6,938
  December 2013        997   1,097   1,630   1,388   1,639    6,752
  December 2014        933   1,044   1,602   1,364   1,631    6,574
  December 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; Class 2, 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.

TABLE 2
Yearly Rates of Transition Between Asset Size Classes, 1994-2010

                                            Year, t
Size       Size Class,
Class, t      t + 1      1994    1995    1996    1997    1998    1999

1               1        0.922   0.915   0.934   0.917   0.898   0.919
                2        0.016   0.024   0.025   0.033   0.022   0.014
              Exit       0.062   0.061   0.041   0.050   0.081   0.067
2               1        0.043   0.026   0.021   0.014   0.015   0.036
                2        0.911   0.916   0.922   0.908   0.914   0.909
                3        0.026   0.035   0.039   0.058   0.043   0.022
              Exit       0.020   0.023   0.018   0.019   0.029   0.032
3               2        0.035   0.020   0.020   0.009   0.018   0.033
                3        0.924   0.940   0.937   0.931   0.930   0.922
                4        0.033   0.029   0.036   0.050   0.037   0.025
              Exit       0.007   0.011   0.007   0.011   0.014   0.020
4               3        0.024   0.011   0.010   0.005   0.011   0.021
                4        0.947   0.952   0.952   0.936   0.951   0.955
                5        0.026   0.033   0.034   0.051   0.031   0.018
              Exit       0.004   0.004   0.004   0.008   0.007   0.006
5               4        0.006   0.003   0.004   0.004   0.006   0.009
                5        0.993   0.995   0.995   0.989   0.985   0.987
              Exit       0.002   0.003   0.001   0.007   0.008   0.003

                                            Year, t
Size       Size Class,
Class, t      t + 1      2000    2001    2002    2003    20114   2005

1               1        0.881   0.890   0.883   0.893   0.902   0.902
                2        0.046   0.041   0.038   0.016   0.010   0.010
              Exit       0.073   0.070   0.079   0.091   0.088   0.088
2               1        0.008   0.015   0.015   0.030   0.064   0.059
                2        0.854   0.869   0.886   0.906   0.875   0.883
                3        0.106   0.085   0.054   0.020   0.014   0.014
              Exit       0.032   0.031   0.045   0.044   0.048   0.045
3               2        0.005   0.011   0.007   0.039   0.062   0.065
                3        0.899   0.914   0.927   0.917   0.899   0.891
                4        0.079   0.055   0.047   0.018   0.014   0.012
              Exit       0.017   0.021   0.019   0.027   0.026   0.032
4               3        0.003   0.005   0.007   0.022   0.065   0.036
                4        0.911   0.930   0.949   0.940   0.905   0.932
                5        0.074   0.054   0.031   0.024   0.018   0.017
              Exit       0.012   0.011   0.012   0.013   0.013   0.014
5               4        0.001   0.001   0.003   0.008   0.021   0.025
                5        0.990   0.994   0.988   0.983   0.972   0.959
              Exit       0.010   0.004   0.008   0.009   0.006   0.016

                                    Year, t
Size       Size Class,
Class, t      t + 1      2006    2007    2008    2009

1               1        0.922   0.893   0.884   0.910
                2        0.010   0.023   0.037   0.023
              Exit       0.069   0.083   0.079   0.067
2               1        0.035   0.016   0.010   0.019
                2        0.905   0.886   0.868   0.899
                3        0.023   0.046   0.091   0.038
              Exit       0.037   0.051   0.031   0.042
3               2        0.036   0.018   0.009   0.021
                3        0.919   0.919   0.881   0.937
                4        0.020   0.039   0.084   0.027
              Exit       0.025   0.023   0.026   0.016
4               3        0.031   0.016   0.006   0.023
                4        0.929   0.933   0.888   0.934
                5        0.023   0.030   0.083   0.024
              Exit       0.018   0.020   0.023   0.019
5               4        0.013   0.009   0.004   0.014
                5        0.977   0.981   0.985   0.975
              Exit       0.010   0.010   0.010   0.011

Notes: Asset size classes are defined in real terms, measured in 1994
prices. as follows: Class 1, assets below $2m; Class 2, 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.

TABLE 3
Entrants and Exits, 1995-2010

                                 Purchase
                                    &                      Conversion
       Entrants   Acquisition   Assumption   Liquidation    to Bank

1994      --          --            --           --            --
1995      13          290           5            22            1
1996      20          293           11           17            1
1997      19          192           4            17            0
1998      8           215           5            28            3
1999      13          335           11           24            3
2000      13          292           13           18            3
2001      10          296           8            25            6
2002      7           265           7            23            1
2003      15          315           5            10            2
2004      3           332           6            11            3
2005      8           302           1            25            2
2006      10          313           2            23            1
2007      4           248           2            10            3
2008      4           275           1            19            1
2009      4           229           1            23            1
2010      5           190           7            19            0

                                                       Number
        Conversion                                     Live at
       to Privately   Unclassified    Total    Exit    End of
         Insured      Disappearance   Exits    Rate     Year

1994        --             --          --       --     12.052
1995        0               0          318    0.0264   11.747
1996        1               1          324    0.0276   11.443
1997        3               0          216    0.0189   11.246
1998        11              0          262    0.0233   10.992
1999        4               0          377    0.0343   10.628
2000        0               0          326    0.0307   10.315
2001        2               5          342    0.0332    9.983
2002        4               3          303    0.0304    9.687
2003        2               0          334    0.0345    9.368
2004        0               4          356    0.0380    9.015
2005        0               1          331    0.0367    8.692
2006        0               3          342    0.0394    8,360
2007        0               4          267    0.0319    8,097
2008        1               4          301    0.0372    7.800
2009        2               0          256    0.0328    7,548
2010        0               2          218    0.0289    7.335

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

                [S.sub.i,t]   [A.sub.i,t]   [K.sub.i,t]   [Q.sub.i,t]

December 1994      24.22         38.82         0.127        0.0384
December 1995      26.29         39.86         0.134        0.0403
December 1996      28.71         40.91         0.140        0.0377
December 1997      31.32         41.88         0.145        0.0380
December 1998      35.42         42.90         0.145        0.0397
December 1999      38.78         43.96         0.148        0.0994
December 2000      42.55         44.97         0.145        0.1095
December 2001      50.32         46.00         0.138        0.1573
December 2002      57.91         47.03         0.135        0.1560
December 2003      65.55         48.03         0.133        0.1631
December 2004      72.26         49.08         0.136        0.1410
December 2005      78.61         50.20         0.143        0.1209
December 2006      85.53         51.21         0.151        0.1200
December 2007      93.64         52.23         0.155        0.1287
December 2008      104.3         53.36         0.151        0.1251
December 2009      117.2         54.43         0.138        0.1410
December 2010      124.6         55.50         0.134        0.1471

                [L.sub.i,t]   [N.sub.i,t]   [E.sub.i,t]   [R.sub.i,t]

December 1994      0.615        0.00432       0.0200         0.0199
December 1995      0.643        0.00436       0.0208         0.0217
December 1996      0.651        0.00430       0.0216         0.0211
December 1997      0.651        0.00426       0.0223         0.0206
December 1998      0.617        0.00429       0.0218         0.0193
December 1999      0.625        0.00397       0.0179        -0.0113
December 2000      0.662        0.00387       0.0201         0.0039
December 2001      0.600        0.00411       0.0192         0.0022
December 2002      0.570        0.00419       0.0188         0.0033
December 2003      0.553        0.00408       0.0187         0.0021
December 2004      0.564        0.00385       0.0190         0.0020
December 2005      0.595        0.00389       0.0198         0.0021
December 2006      0.618        0.00310       0.0208         0.0023
December 2007      0.613        0.00314       0.0213         0.0021
December 2008      0.586        0.00364       0.0208        -0.0004
December 2009      0.552        0.00388       0.0199        -0.0025
December 2010      0.530        0.00402       0.0216        -0.0002

Note: Variable definitions are as follows: [S.sub.i,t] = Total
Assets; [A.sub.i,t] = age; [K.sub.i,t] = capital-to-assets
ratio = Net Worth / Total Assets; [Q.sub.i,t] = Liquid Assets / Total
Assets; [L.sub.i,t] = Loans / Total Assets; [N.sub.i,t] =
Non-Performing Loans / Total Assets; [E.sub.i,t] = Non-Interest
Expenses / Total Assets; [R.sub.i,t] = Return on Assets = Net
Income / Total Assets.

TABLE 5
Estimation Results: M&A and Failure Hazard
Functions

                        M&A Hazard   Failure Hazard

[s.sub.i,t-1]             -0.3892       -0.3733
                        (-47.5)       (-13.1)
[a.sub.i,t-1]              0.2232       -0.0689
                          (6.57)       (-0.81)
[K.sub.i,t-1]             -3.2013        2.1939
                        (-15.8)         (6.40)
[Q.sub.i,t-1]              0.8537        1.4142
                          (8.26)        (5.28)
[L.sub.i,t-1]              0.1354       -1.2614
                          (1.74)       (-4.32)
[N.sub.i,t-1]             -0.5707        1.8707
                          (2.12)        (4.40)
[E.sub.i,t-1]              1.3732       -0.3604
                          (6.38)       (-0.83)
[R.sub.i,t-1]             -4.5576       -3.5482
                        (-20.9)        (-5.47)
No. of observations      311,637        311,637
No. of disappearances     4,471           341
Log-likelihood          -39,325.3       -2,652.0

Note: Variable definitions are as follows: [s.sub.i,t-1] =
logarithm of total assets at the 6-monthly data-point prior
to disappearance; [a.sub.i,t-1] = Log Age; [K.sub.i,t-1] = capital-to
assets ratio = Net Worth / Total Assets; [Q.sub.i,t-1] = Liquid
Assets / Total Assets; [L.sub.i,t-1] = Loans / Total Assets;
[N.sub.i,t-1] = Non-Performing Loans / Total Assets; [E.sub.i,t-1] =
Non Interest Expenses / Total Assets: [R.sub.i,t-1] = Return on
Assets = Net Income / Total Assets.

TABLE 6
Trends in Industry Concentration Measures, 1994-2010

                         Concentration Ratios

                [CR.sub.5]   [CR.sub.10]   [CR.sub.20]

December 1994       6.2          8.8          12.2
December 1995       6.1          8.8          12.4
December 1996       6.1          8.8          12.5
December 1997       6.3          8.9          12.8
December 1998       6.5          9.2          13.2
December 1999       6.5          9.4          13.4
December 2000       6.7          9.6          13.8
December 2001       7.0         10.2          14.4
December 2002       7.4         10.7          15.0
December 2003       7.6         10_9          15.2
December 2004       8.1         11.4          15.8
December 2005       8.5         11.9          16.5
December 2006       9.0         12.4          17.3
December 2007       9.9         13.3          18.4
December 2008      10.1         13.7          18.8
December 2009      10.2         13.6          18.4
December 2010      10.8         14.3          19.1

                         Actual              Counterfactual (No M&A)

                HHI    Numbers Equivalent   HHI    Numbers Equivalent

December 1994   19.2         520.9          19.2         521.8
December 1995   19.2         520.3          19.1         523.9
December 1996   19.0         525.9          18.8         530.9
December 1997   19.7         506.6          19.5         513.1
December 1998   20.5         486.8          20.2         494.3
December 1999   20.8         480.9          20.4         489.8
December 2000   21.9         457.3          21.4         467.2
December 2001   23.9         418.5          23.4         428.2
December 2002   25.8         388.2          25.1         397.9
December 2003   27.1         368.3          26.4         378.8
December 2004   29.7         337.1          28.8         347.3
December 2005   31.4         318.2          30.4         328.7
December 2006   34.3         291.9          32.9         303.7
December 2007   40.1         249.5          38.5         259.7
December 2008   41.9         238.6          40.2         248.7
December 2009   42.2         237.1          40.3         248.0
December 2010   46.5         215.2          43.8         228.5

TABLE 7
Estimation Results: Time-Series Growth Regressions

                    Rank by December 1994 Assets Size

                1-250    251-500   501-1,000   1,001-2,000

ADF tests: proportion of rejections of the unit root null hypothesis

[alpha] = .01   0.040     0.060      0.080        0.063
[alpha] = .05   0.108     0.116      0.156        0.144
[alpha] = .1    0.196     0.172      0.220        0.218
IPS panel unit root test

[Z.sub.tbar]     5.35     2.26      -1.775       -4.883
p value         1.0000    .9881      .0379        .0000

                  Rank by December
                  1994 Assets Size

                2,001-7,247     All

ADF tests: proportion of rejections of the unit root null hypothesis

[alpha] = .01      0.075       0.072
[alpha] = .05      0.159       0.153
[alpha] = .1       0.230       0.225

IPS panel unit root test
[Z.sub.tbar]      -18.005     -16.185
p value            .0000       .0000

TABLE 8
Estimation Results: Cross-Sectional Survivorship and Growth
Regressions

                 Growth Regression dep.
           var. = ([s.sub.i,t]--[s.sub.i,t-1])

t      [s.ub.t-1]    [s.sub.i,t1]--[s.sub.i,t-2])

1996     0.006 ***             0.253 ***
       (12.0)                (29.4)
1997     0.009 ***             0.282 ***
       (17.9)                (27.4)
1998     0.011 ***             0.256 ***
       (21.5)                (29.3)
1999     0.002 ***             0.243 ***
        (4.38)               (24.2)
2000     0.011 ***             0.120 ***
       (19.2)                (12.3)
2001     0.011 ***             0.164 ***
       (20.5)                (15.7)
2002     0.004 ***             0.236 ***
        (8.38)               (24.2)
2003     0.008 ***             0.295 ***
       (15.1)                (29.2)
2004     0.007 ***             0.242 ***
       (16.0)                (25.8)
2005     0.012 ***             0.280 ***
       (22.6)                (26.9)
2006     0.009 ***             0.271 ***
       (17.9)                (24.7)
2007     0.007 ***             0.279 ***
       (15.7)                (26.7)
2008     0.009 ***             0.056 ***
       (15.4)                 (8.52)
2009     0.009 ***             0.275 ***
       (13.0)                (21.9)
2010     0.001 **              0.146 ***
        (2.26)               (12.1)

        Survivorship Regression dep. var. = 1 for Credit Unions
         that Survived from t--1 to t, 0 for Credit Unions that
                              Disappeared

t        Constant     [s.ub.t-1]    [s.sub.i,t1]--[s.sub.i,t-2])

1996     -0.060 ***     0.195 ***             1.71 ***
        (-8.17)       (10.2)                 (7.59)
1997     -0.125 ***     0.133 ***             2.26 ***
       (-15.1)         (6.08)                (7.47)
1998     -0.113 ***     0.131 ***             1.56 ***
       (-14.7)         (6.54)                (5.95)
1999     -0.013 *       0.144 ***             2.59 ***
        (-1.66)        (7.89)                (9.53)
2000     -0.155 ***     0.191 ***             2.65 ***
       (-17.4)        (10.1)                 (9.48)
2001     -0.079 ***     0.129 ***             1.34 ***
        (-9.20)        (7.13)                (6.46)
2002     -0.025 ***     0.106 ***             2.47 ***
        (-2.96)        (5.20)                (8.31)
2003     -0.091 ***     0.114 ***             1.76 ***
       (-10.6)         (5.58)                (6.44)
2004     -0.117 ***     0.153 ***             1.06 ***
       (-15.4)         (8.43)                (3.95)
2005     -0.203 ***     0.149 ***             2.16 ***
       (-24.1)         (7.81)                (7.11)
2006     -0.163 ***     0.087 ***             1.85 ***
       (-18.8)         (4.74)                (6.66)
2007     -0.108 ***     0.073 ***             2.43 ***
       (-13.7)         (3.51)                (7.31)
2008     -0.095 ***     0.124 ***             2.14 ***
       (-10.4)         (6.22)                (6.12)
2009     -0.085 ***     0.126 ***             1.46 ***
        (-7.63)        (5.95)                (5.07)
2010     -0.008         0.009                 2.37 ***
        (-0.80)        (0.41)                (6.80)

          Survivorship Regression dep. var. = 1 for Credit Unions
           that Survived from t--1 to t, 0 for Credit Unions that
                                Disappeared

t      [K.sub.i,t-1]   [Q.sub.i,t-1]   [L.sub.i,t-1]   [N.sub.i,t-1]

1996     1.27 ***       -0.272           0.421 **        3.58 *
        (3.18)         (-0.66)          (2.55)          (1.78)
1997    -0.109          -0.516           0.187           1.09
       (-0.26)         (-1.03)          (0.90)          (0.55)
1998     0.139          -0.502           0.229          -0.911
        (0.35)         (-1.10)          (1.19)         (-0.40)
1999     1.15 ***       -1.58 ***        0.549 ***       0.674
        (3.31)         (-4.10)          (3.13)          (0.32)
2000     1.88 ***        0.085           0.176          -2.29
        (5.05)          (0.40)          (1.14)         (-1.32)
2001     0.587          -0.420 **        0.529 ***      -2.16
        (1.57)         (-2.12)          (3.46)         (-0.98)
2002     1.52 ***       -0.514 ***       0.130          12.8 ***
        (3.45)         (-2.70)          (0.73)          (4.52)
2003     1.18 ***       -0.322 *         0.791 ***      -2.86
        (2.88)         (-1.87)          (4.51)         (-1.46)
2004     1.14 ***       -0.230           0.293 *        -1.69
        (2.81)         (-1.34)          (1.81)         (-0.69)
2005     1.90 ***       -0.426 **        0.110           2.68
        (4.33)         (-2.26)          (0.66)          (0.98)
2006     0.514          -0.104           0.774 ***      -0.321
        (1.32)         (-0.50)          (5.00)         (-0.12)
2007     0.355          -0.190          -0.217          -9.74 ***
        (0.80)         (-0.71)         (-1.22)         (-2.94)
2008     2.01 ***       -0.723 ***       0.075          -2.81
        (4.56)         (-3.05)          (0.46)         (-0.86)
2009     1.51 ***       -0.436 *        -0.089          17.49 ***
        (3.24)         (-1.67)         (-0.50)          (5.35)
2010     1.69 ***       -0.873 ***      -0.176           0.845
        (3.63)         (-3.48)         (-0.86)          (0.42)

       Survivorship Regression dep. var. = 1 for
        Credit Unions that Survived from t--1 to
        t, 0 for Credit Unions that Disappeared

t      [E.sub.i,t-1]   [R.sub.i,t-1]   Constant

1996    -7.10 ***       -0.746          -1.01 ***
       (-3.82)         (-0.35)         (-3.09)
1997    -5.32 **         4.18            0.129
       (-2.33)          (1.50)          (0.34)
1998    -4.74 **         4.63 *         -0.025
       (-2.31)          (1.86)         (-0.07)
1999    -5.00 **         5.04 **        -0.769 **
       (-2.52)          (2.12)         (-2.46)
2000    -5.89 ***        5.29 ***       -1.20 ***
       (-4.09)          (8.80)         (-3.94)
2001    -9.74 ***        8.58 ***       -0.122
       (-6.35)          (6.34)         (-0.38)
2002    -2.47           19.48 ***       -0.098
       (-1.32)         (10.0)          (-0.28)
2003    -5.39 ***       10.65 ***       -0.373
       (-3.26)          (6.53)         (-1.11)
2004    -6.33 ***       10.80 ***       -0.684 **
       (-4.42)          (6.97)         (-2.13)
2005    -5.50 ***       13.14 ***       -0.575 *
       (-3.56)          (7.03)         (-1.68)
2006    -7.07 ***       10.41 ***        0.218
       (-4.86)          (7.91)          (0.66)
2007    -4.38 ***       15.88 ***        1.08 ***
       (-4.17)          (9.28)          (2.74)
2008    -1.97 *         15.57 ***       -0.346
       (-1.93)          (9.61)         (-0.94)
2009     3.26 ***       19.98 ***       -0.434
        (4.73)         (12.0)          (-1.12)
2010     0.147          17.92 ***        1.71 ***
        (0.13)         (11.6)           (4.17)

t      atanh([[rho].sub.[epsilon]u])

1996              0.031
                 (1.13)
1997             -0.008
                (-0.18)
1998              0.022
                 (0.72)
1999             -0.047
                (-1.11)
2000             -0.033
                (-0.39)
2001             -0.097 **
                (-2.25)
2002             -0.253 ***
                (-5.26)
2003             -0.273 ***
                (-3.73)
2004             -0.062
                (-1.37)
2005              0.060
                 (1.26)
2006             -0.070
                (-1.01)
2007             -0.052
                (-1.04)
2008             -0.117 ***
                (-3.44)
2009             -0.358 ***
                (-6.30)
2010             -0.692 ***
               (-13.5)

Note: Variable definitions are as follows: [s.sub.i,t-1] = logarithm
of Total Assets at the data point at the start of the 2-year interval
over which growth is measured; ([s.sub.i,t] - [[s.sub.i,t-1]) =
logarithmic growth in assets from t--1 to t; ([s.sub.i,t-1] -
[s.sub.i,t-2]) = logarithmic growth in assets from
t - 1 to t - 2; [K.sub.i,t-1] = capital-to-assets ratio = Net Worth /
Total Assets; [Q.sub.i,t-1] = Liquid Assets / Total Assets;
[L.sub.i,t-1] = Loans / Total Assets; [N.sub.i,t-1] = Non-Performing
Loans / Total Assets; [E.sub.i,t-1] = Non-Interest Expenses / Total
Assets, [R.sub.i,t-1] = Return on Assets = Net Income / Total Assets.
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Author:Goddard, John; McKillop, Donal; Wilson, John O.S.
Publication:Economic Inquiry
Article Type:Abstract
Geographic Code:1USA
Date:Jan 1, 2014
Words:12400
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