How did bank holding companies prosper in
the 1990s?
Kevin J. Stiroh
*Federal Reserve Bank of New York, 33 Liberty Street, NY 10045, USA Received 14 July 1998; accepted 8 July 1999
Abstract
This paper examines the improved performance of US bank holding companies (BHCs) from 1991 to 1997. Analysis of cost and pro®t functions using several alter-native output speci®cations suggests that the gains were primarily due to productivity growth and changes in scale economies. Various econometric methodologies yield productivity growth of about 0.4% per year and the optimal size seems to have increased in the 1990s era of deregulation, technological change, and ®nancial innovation. Esti-mates of both productivity growth and economies of scale are robust across traditional and non-traditional output speci®cations. Despite the overall success, however, sub-stantial cost and pro®t ineciency existed for BHCs of all sizes in the 1990s. These eciency estimates are particularly sensitive to the output speci®cation and failure to account for non-traditional activities like o-balance sheet (OBS) items leads pro®t eciency, but not cost eciency, to be understated for the largest BHCs. Ó 2000 Elsevier Science B.V. All rights reserved.
JEL classi®cation:G21; D21
Keywords:Bank holding companies; Productivity; Eciency
www.elsevier.com/locate/econbase
*Tel.: +1-212-720-6633; fax: +1-212-720-8363. E-mail address:[email protected] (K.J. Stiroh).
1. Introduction
Fundamental changes in regulation, macroeconomic shocks, and ®nancial innovation have led to a major restructuring of the US commercial banking industry. Over the last decade, the number of FDIC-insured banking organi-zations declined by more than 35% even as total assets continued to grow and the banking industry emerged from the crisis of the 1980s with strong per-formance and record pro®ts in the 1990s.
This paper examines the behavior of 661 bank holding companies (BHCs) from 1991 to 1997 to identify the sources of success in the 1990s. Cost and pro®t function analysis from alternative output speci®cations that include both tra-ditional lending activities and non-tratra-ditional activities like fee income or o-balance sheet (OBS) items suggest that the improved performance re¯ects a combination of productivity growth and scale economies. Persistent ®rm-level ineciency, however, prevented even larger gains. The large literature on the eciency of ®nancial institutions has primarily focused on individual com-mercial banks and this study, as far as is known, represents the ®rst compre-hensive analysis of productivity and frontier eciency of US BHCs in the 1990s. Productivity growth was a steady force that contributed to the success of BHCs in the 1990s. Estimates from several dierent econometric methods ± a simple pooled cost analysis, panel data methods, and a cost decomposition ± yield productivity growth rates of about 0.4% per year in the 1990s. Although observed costs rose steadily over this period, the econometric evidence shows that this was primarily due to changes in size and business conditions, while improved productivity ± measured as a shift in the cost function ± prevented costs from rising even more quickly.
Estimates of scale economies, both ray scale economies and expansion path scale economies, show BHCs operating with economies of scale throughout the 1990s. Fundamental changes in the production process increased the optimal scale as the degree of unexploited scale economies increased from 1991 to 1994 while BHCs increased in size. After 1994, however, the degree of unexploited scale economies began to decline as continued growth moved the BHCs closer to the new optimal scale. The inclusion of non-traditional activities does not aect these estimates.
more dispersion in pro®t eciency than in cost eciency, implying that BHCs do a better job of minimizing costs through optimal resource allocation than maximizing pro®ts through output choices.
These results suggest that there is further room for improvement in the banking industry since there are still unexploited scale economies and sub-stantial BHC-speci®c ineciencies. If the current consolidation trend contin-ues, it is reasonable to expect both a reduction in unexploited scale economies (as more assets are held by BHCs near the optimal size) and a reduction in BHC-speci®c ineciency (as the most inecient BHCs are acquired and merged with more ecient ones). As a caveat, however, these results do not imply that large BHCs are always successful. Rather, BHCs of all sizes have been both successful and unsuccessful in the 1990s and there is little dierence in performance of the best BHCs across size classes.
2. The US banking industry
The US banking industry is in a period of dramatic evolution. After decades of relative stability, market, technological, and regulatory shocks in the 1980s led to the most severe banking crisis since the Great Depression.1 These shocks ± increased competition and disintermediation, loan problems from the severe regional recessions, ®nancial innovation and technological advances, and widespread deregulation of deposit rates, bank powers, and geographic restrictions ± contributed to rapid industry consolidation through a wave of bank failures and mergers. From 1980 to 1994, for example, more than 1600 FDIC-insured commercial banks closed or required FDIC assistance and the number of FDIC-insured banking organizations (BHCs and independent banks and thrifts) fell from 14,886 in 1984 to 8895 in 1997 (FDIC, 1998b).
A bene®cial consequence, however, is that the US banking industry emerged with a core of larger institutions that showed steady growth and improved performance in the 1990s. FDIC (1997) reports various accounting data, e.g., return on assets (ROA), return on equity (ROE), equity to assets ratios, etc., as well as ®nancial market data, e.g., price±earnings ratios, and concludes that the performance in the 1990s ``does not support earlier concerns that banking was a declining industry'' (p. 8). Rather, the banking industry as a whole seems to be strengthening in the current era of deregulation and consolidation. Indeed, FDIC (1998a) reports that industry ROA rose to a record 1.23% in 1997 with more than $15 billion in net income during the fourth quarter alone.
Over the same period, BHCs steadily increased their control of the US banking industry. From 1984 to 1997, the number of independent
FDIC-in-1See Berger et al. (1995) and FDIC (1997) for a thorough analysis of the commercial bank
sured bank and thrift institutions fell more than 60%, while the number of BHCs (both single- and multi-bank) declined less than 8% and the share of total FDIC-insured assets held by BHCs increased from 62% in 1984 to 83% in 1997 (FDIC, 1998b). The following subsections summarize the changing role of BHCs in the US banking system and describe the sample of BHCs used in the subsequent empirical analysis.
2.1. The evolving role of BHCs
A BHC is any ``company, corporation, or business entity that owns stock in a bank or controls the operation of a bank through other means'' (Spong, 1994, p. 36).2BHCs have existed since at least the turn of the century and the early popularity of multi-bank BHCs was in part due to the ability to operate throughout states with branching restrictions. These institutions, however, were not subject to substantial regulation until the Bank Holding Company Act of 1956. This law appointed the Federal Reserve System as the primary regulator of multi-bank BHCs, required interstate acquisitions to be consistent with state law,3and de®ned the permissible non-bank activities in Regulation Y. An important consequence of the Bank Holding Company Act was the eective elimination of interstate expansion since no state speci®cally autho-rized such acquisitions at that time. As part of the supervision process, BHCs are required to ®le the Consolidated Financial Statements for BHCs (FR Y-9C) with the Federal Reserve.
The restrictions on non-bank activities did not apply to single-bank BHCs, however, and these institutions grew rapidly in the 1960s. According to Spong (1994, p. 23), one-third of all commercial bank deposits were controlled by single-bank BHCs in 1970. This loophole was closed when Congress imposed the same regulatory structure on single-bank BHCs by amending the Bank Holding Company Act in 1970.
During the 1970s and 1980s, technological innovation, economic shocks, and deregulation fundamentally altered the banking environment and the move toward interstate banking began. In 1975, Maine became the ®rst state to allow interstate entry, eective in 1978 and conditional upon reciprocal entry. Increased competition from other ®nancial institutions and the removal of interest rate ceilings by the Depository Institutions Deregulation and Mone-tary Control Act of 1980 spurred additional consolidation as small banks that previously operated in protected markets were forced to adapt to a more
2
This subsection draws heavily from Spong (1994), Berger et al. (1995), Holland et al. (1996), and FDIC (1997, 1998a, 1998b).
3Some BHCs that already owned subsidiary banks in multiple states were grandfathered and
competitive environment. The Financial Institutions Reform, Recovery, and Enforcement Act of 1989 further contributed to this trend by allowing BHCs to acquire any savings and loan, conditional on certain standards.4
The Riegle±Neal Interstate Banking and Branching Eciency Act of 1994 completed the consolidation trend by providing a consistent, national frame-work for interstate banking. Eective September 29, 1995, BHCs were allowed to acquire a bank in any state and eective 1 June 1997, banks were authorized to merge across state lines. While both activities were subject to certain re-strictions, e.g., deposit concentration ceilings and capital adequacy tests, the Riegle±Neal Act created a true national banking system. As Holland et al. (1996) point out, however, the Riegle±Neal Act did not create interstate banking, but rather broadened the scope of the consolidation trends that were already taking place under state laws.
The importance of BHCs in US banking has co-evolved over the last century with the regulatory structure and BHCs now are clearly the dominant form of bank ownership. As of year-end 1997, 67% of all FDIC-insured assets were held by multi-bank BHCs, single-bank BHCs held an additional 16%, and independent bank and thrift institutions held the remaining 17% (FDIC, 1998b). The BHC structure originally was attractive due to expanded non-bank powers and geographic advantages and then gained with the limited interstate expansion provided by reciprocal state agreements and compacts. Although the Riegle±Neal Act and interstate branching deregulation eliminated some of these advantages, the BHC structure remains advantageous for several reasons. BHCs are currently allowed to expand into activities that are partially re-stricted for individual banks, e.g., BHCs can own separately capitalized sub-sidiaries that provide discount brokerage services, investment advice, and certain securities underwriting. In addition, the BHC structure provides better access to funds, tax advantages, improved ¯exibility regarding bank-level constraints, and possible eciency gains (Berger et al., 1995, pp. 185±193).
2.2. The sample of BHCs
This paper examines a balanced panel of 661 top-tiered BHCs that oper-ated continuously from 1991 to 1997 using data from the consolidoper-ated FR Y-9C reports.5These 661 BHCs ranged in size from $38 million to $366 billion
4
Certain interstate acquisitions of troubled thrift institutions were allowed earlier under the Garn-St Germain Depository Institutions Act of 1982.
5
in assets in 1997 and cumulatively held $3,506 billion in assets or about 70% of all FDIC-insured assets held by BHCs. The analysis examines only con-tinuously operating BHCs to avoid the impact of entry and exit and to focus on the changing behavior of a core of healthy, surviving institutions during the 1990s.
Summary statistics for the sample, Table 1, show trends for 1991±1997 that are very similar to the trends for the aggregate industry±increasing mean assets, rising variable pro®ts (de®ned below), and improved ROA (net income over assets). Mean variable costs (de®ned below) have also been rising in absolute terms as the sample increased in average size, but mean variable costs per total assets (C/A) declined rapidly for 1991±1994 and then stabilized at a slightly higher level through 1997. Mean ROA and ROE showed a similar pattern with larger increases from 1991±1993 and small gains for 1994±1997.
Simply looking at overall means, however, can be misleading and hides substantial variation in the performance of individual BHCs. This sample, for example, covers a wide range of sizes, product mixes, and risk pro®les and all BHCs need not show the same average costs or returns to remain competitive. Large BHCs, for example, hold a dierent mix of assets with more business loans and fewer consumer loans. To examine these dierences, the 661 BHCs were broken down into 10 groups based on average assets for 1991±1997 to ensure roughly comparable product mixes. Each asset class was then further decomposed into quintiles based on either average C/Aor average ROA for 1991±1997 to explore the dispersion of performance both across and within size classes.
Fig. 1 graphs the meanC/Afor the highest quintile, the entire size class, and the lowest quintile for each size class, while Fig. 2 shows the same breakdown for ROA.6These charts show wide dispersion within every size class for both
C/Aand ROA, with a slight trend towards lower C/Afor larger size classes, except for the very largest BHCs, which show an increase inC/A. There is also a small upward trend in ROA for large BHCs and a narrowing of the ROA distribution within the largest size classes. These data show substantial varia-tion in performance and are suggestive of some scale economies for BHCs. The question of economies of scale and more precise estimates of relative perfor-mance are addressed in the following sections.
6Berger and Humphrey (1992) report substantial dispersion in costs per asset for commercial
Table 1
Trends in bank holding company performance, 1991±1997a
Year Number of Obs.
Total assets
Equity capital
Variable costs
Variable pro®ts ROA ROE C/A
P-1 and
P-4
P-2 P-3
1991 661 2797.8 191.4 177.4 54.3 89.5 57.6 0.80 10.43 6.25 1992 661 3097.6 234.9 147.9 66.6 106.7 70.3 1.04 13.30 4.96 1993 661 3357.8 267.9 138.5 70.3 116.2 74.8 1.14 13.75 4.31 1994 661 3692.8 285.3 158.4 74.9 122.6 78.2 1.13 13.38 4.29 1995 661 4130.1 331.8 211.4 80.3 135.9 84.1 1.17 13.31 4.88 1996 661 4728.1 387.7 233.9 91.9 162.7 96.9 1.23 13.59 4.84 1997 661 5303.6 427.4 261.6 98.4 182.1 104.1 1.24 13.64 4.89 aAll values are simple means. Variable costs and variable pro®ts are de®ned in Section 3.3. Total assets, equity capital, variable costs, and variable pro®ts are measured in millions of 1997 dollars. ROA is net income divided by average assets. ROE is net income divided by average equity.C/Ais variable costs divided by total assets. ROA, ROE, andC/Aare percentages.
Stiroh
/
Journal
of
Banking
&
Finance
24
(2000)
1703±1745
3. General approach ± BHCs and production concepts
There is a large literature on productivity and eciency of ®nancial insti-tutions and this paper does not attempt to summarize that work.7This papers simply follows the general methodologies and utilizes panel and pooled methods to estimate the rate of productivity growth, the degree of scale
Fig. 2. Mean ROA and Hi and Low ROA quintiles by size class, 1991±1997. Fig. 1. MeanC/Aand Hi and LowC/Aquintiles by size class, 1991±1997.
7Berger and Humphrey (1997) provide a comprehensive review of the empirical literature on
economies, and the relative eciency of BHCs in the 1990s. Berger et al. (1987) and Jagtiani and Khanthavit (1996) provide a framework for estimating scale economies; Berger and Mester (1997b) for productivity growth; Bauer et al. (1998), Berger and Mester (1997a), and Berger et al. (1993) for cost and pro®t eciency; and Berger and Humphrey (1997, 1992) provide a general discussion on interpretation and methodology.
3.1. Analyzing BHCs
This focus on BHCs is in contrast to much recent work that examines the behavior of individual commercial banks, e.g., Berger and Mester (1997a,b), Humphrey and Pulley (1997), Jagtiani and Khanthavit (1996), and Berger and Humphrey (1992), although there has been some work on BHCs. Akhavein et al. (1997) use BHC data to analyze the impact of large mergers on eciency; Rivard and Thomas (1997) examine the impact of interstate banking on pro®t volatility for 218 BHCs in the 1980s; Roland (1997) examines pro®t persistence in 237 BHCs; and Hughes et al. (1996) examine eciency and risk for 443 BHCs in 1994. This paper presents, as far as is known, the ®rst comprehensive analysis of productivity and frontier eciency of BHCs in the 1990s.8
The use of BHC data rather than individual bank data, however, presents a trade-o. On the advantage side, bank managers, particularly in the 1990s environment of rapid consolidation, presumably care about the performance of the institution as a whole, rather than the individual subsidiary banks. Berger et al. (1995) conclude that ``looking at the holding company rather than at an individual bank within an MBHC (multi-bank holding company) may give a more accurate description of the relevant economic entity'' (p. 66) since im-portant business decisions are typically made at the holding company level, holding company aliates often exchange portfolio items, and the current regulatory structure eectively makes the holding company the risk-manage-ment unit. Akhavein et al. (1997, p. 18) argue that managers will coordinate activities and optimize production choices with respect to the overall institu-tion. Finally, since the majority of previous research, particularly frontier ef-®ciency studies, analyze individual commercial banks it is worthwhile to compare the results of analysis at higher levels of business organization.
On the other hand, if input and output choices are actually made at the level of the individual subsidiary, the holding company data would be less mean-ingful. Nonetheless, the more aggregated BHC seems to be the proper unit of analysis and it is important to examine the performance of BHCs in todayÕs evolving banking environment.
8Other earlier research that examines BHCs includes Grabowski et al. (1993) and Newman and
3.2. Cost and pro®t functions
The basic econometric analysis examines a variable cost and a variable pro®t function for the sample of 661 BHCs. These two approaches are stan-dard in the literature on ®nancial institutions and are brie¯y described below. In particular, this analysis follows the ``intermediation'' or ``asset'' approach of Sealey and Lindley (1977) where ®nancial institutions transform deposits and purchased funds into loans and other assets.
A general variable cost function is
Cf p;y;z;m;l;ec;t; 1
where variable costs, C, depend on a vector of input prices, p, a vector of variable output quantities,y, a vector of ®xed netputs (either inputs or out-puts),z, a vector of environmental variables,m, BHC-speci®c cost ineciency,
l, random error, c, and time,t, which proxies for productivity growth.
Likewise, one can examine the relationship between variable pro®ts,P, and the same set of explanatory variables with a general variable pro®t function as
Pf p;y;z;m;p;eP;t; 2
wherepis BHC-speci®c pro®t eciency andeP is a random error term.
There are several important things to note about Eqs. (1) and (2). First, cost eciency and pro®t eciency need not be the same since a BHC, for example, can eciently choose inputs, yet make errors and be inecient in the choice of outputs. Berger and Mester (1997a), for example, ®nd cost and pro®t eciency to be negatively related and Akhavien et al. (1997) report that mergers improve pro®t eciency, but not cost eciency. Thus, this paper examines both measures.
Second, Eq. 2 is an ``alternative'' pro®t function that relates pro®ts to quantities of outputs, rather than a ``standard'' pro®t function that relates pro®ts to prices of outputs. Humphrey and Pulley (1997) derive this type of alternative pro®t function from a bankÕs pro®t maximization problem in the presence of market power in the output market and review the empirical evi-dence for this assumption. Since these assumptions are reasonable for BHCs and both types of pro®t functions led to similar results with this sample, only the results from the alternative pro®t function are reported here. Moreover, diculties in estimating prices for some assets make the alternative pro®t function more attractive.9
9Berger and Mester (1997a) present several additional arguments why the alternative pro®t
Third, all estimation was based on a parametric approach in general and the translog functional form in particular.10 For a cost function withIinputs,J
outputs, and two ®xed netputs, the basic translog speci®cation used is
ln C= z2pI a0
that the dependent variable in the pro®t function is transformed by adding a constant set equal to one plus the absolute value of the minimum observed pro®t to avoid taking the log of zero or a negative number. Subsequent speci®cations include either BHC-speci®c cost and pro®t ineciency terms or time parameters depending on the particular question.
Some authors have found that a more ¯exible functional form, e.g., a Fourier-¯exible functional form that includes trigonometric terms in addition to the standard translog terms, provide a better ®t. With regard to eciency estimates, however, there appears to be little economic gain from those addi-tional terms. Berger and Mester (1997a), for example, report that standard mean eciencies dier by less than 1% between the standard translog and Fourier-¯exible functional form and ®nd rank-order correlations are more than 99%. Since the Fourier approach requires additional truncations of data, the standard translog was used.
10See Bauer et al. (1998) for a detailed comparison of parametric and non-parametric
Finally, standard restrictions and transformations were incorporated to be consistent with economic theory. Costs, pro®ts, and all input prices are scaled by one arbitrarily chosen input price (pI) to impose linear homogeneity.
Symmetry restrictions in the quadratic terms (/ij/jianddijdji) of the cost
and pro®t functions are also imposed. Costs, pro®ts, and all quantities (vari-able outputs and ®xed netputs) are scaled by one ®xed netput, chosen as equity capital, to control for heteroskedasticity and reduce the scale bias that results from including BHCs of very dierent sizes in a single regression. That is, scaling by equity capital makes both the cost and pro®t dependent variables in the same range for all institutions.11
3.3. Variable de®nitions
An important decision in this analysis is the speci®cation of outputs and inputs. In the asset approach, ®nancial assets are treated as outputs and ®-nancial liabilities and physical factors are the inputs. Since there is some question about which variables to include, this analysis generally follows the variable de®nitions and speci®cations of the ``preferred model'' in Berger and Mester (1997a). One important departure, however, is the treatment of non-traditional outputs, which is discussed in detail below. Table 2 provides sum-mary statistics for the variables used in the cost and pro®t functions. All variables are measured in 1997 dollars.
On the input side, three inputs are included. The price vector,p, includes the interest rate on purchased funds (jumbo certi®cates of deposits (CDs), federal funds purchased, and liabilities except core deposits), the interest rate on core deposits (domestic deposits less jumbo CDs), and the price of labor. This is consistent with Akhavein et al. (1997), who include total deposit funds (in-cluding purchased funds) and labor as the inputs, and follows Berger and Mester (1997a).
On the output side, things are less clear since BHCs do much more than ``traditional'' banking activities like making loans and holding securities as in the standard speci®cation. BHCs earn a substantial portion of revenue from fee and service activities and OBS items like lines of credit, loan commitments, and derivatives are now important activities. Since these ``non-traditional'' activi-ties are growing over time and concentrated in the largest institutions, failure to account for them may lead to incorrect conclusions.
11
One set of non-traditional activities includes the sources of non-interest income, e.g., ®duciary activities, trading, and activities that generate other non-interest income like fee income from credit cards, mortgage servicing, mutual fund and annuity fees, and ATM surcharges. According to English and Nelson (1998), non-interest income has increased from 26% to 38% of total bank revenue since the mid-1980s as the bank product set expands. OBS items like loan commitments, letters of credit, derivatives, and loan securitization are another type of non-traditional activity that is increasing in importance.12 These items in particular are highly concentrated in the largest institutions, e.g., Berger et al. (1995) report that the notional value of derivatives was 11.5 Table 2
Cost and pro®t function variables, 1997a
Mean S.D. Minimum Maximum
Variable costs 261.6 1212.4 1.8 19,035.0
Variable pro®ts
P-1 andP-4 98.4 394.2 )89.0 4,958.0
P-2 182.1 827.1 1.1 1,007.0
P-3 104.1 434.1 )41.7 5,650.0
Variable input prices
Purchased funds 4.68 0.77 0.03 8.99
Core deposits 3.29 0.59 1.00 4.89
Labor 37.70 7.73 3.79 78.76
Variable output quantities
Business loans 572.2 2609.7 0.3 33,431.0
Consumer loans 2774.1 11,674.3 15.2 143,403.0
Securities 1877.5 10,268.5 18.9 193,287.0
Net non-interest income (Y-2) 83.7 466.7 0.6 7937.2 O-balance sheet items (Y-3) 840.1 6730.9 0.1 137,607.1 Fixed netputs
Physical capital 79.8 340.5 0.1 4147.9
Equity capital 427.5 1807.4 5.0 21,742.0
O-balance sheet items (Y-4) 840.1 6730.9 0.1 137,607.1
Total assets 5303.6 24,205.9 37.6 365,520.9
aVariable costs, variable pro®ts, variable output quantities, ®xed netputs, and total assets are
measured in millions of 1997 dollars. Price of purchased funds and core deposits are percentages. Price of labor is in thousands of 1997 dollars. Speci®cationY-1 includes business loans, consumer loans, and securities as outputs and physical capital and equity capital as ®xed netputs. Other speci®cations includeY-1 plus the designated output quantity or ®xed netput.
12See English and Nelson (1998) for a discussion of the importance of dierent types of
times assets for megabanks (BHCs with more than $100 billion in assets in 1994) and only 0.002 times assets for small banks (BHCs and banks with less than $100 million in assets in 1994).
These non-traditional activities are clearly increasing in importance, but the wide range of activities and imperfect data make analysis problematic. For example, it is straightforward to calculate the credit equivalent dollar value of OBS items from regulatory data, but it is dicult to consistently estimate the associated revenue for a pro®t function analysis. Nonetheless, there have re-cently been several innovative attempts to account for non-traditional activities in cost and pro®t function analysis.
Rogers (1998) uses the revenue from non-traditional activities, de®ned as ``net non-interest income'', equal to total non-interest income less service charges earned on deposits, as a proxy for both the quantity and the revenue associated with non-traditional activities. Berger and Mester (1997a) cite the problems with estimating revenue from OBS items and include risk-weighted OBS items as a ®xed netput in both a cost and pro®t estimation. Jagtiani and Khanthavit (1996) estimate a cost function only, and thus avoid problematic revenue estimates, and include the risk-weighted, credit equivalent of OBS products as an output.
Since each of these approaches is imperfect, this paper de®nes and compares four alternative speci®cations. The ®rst speci®cation, Y-1, includes only tra-ditional measures of bank outputs and de®nes the variable output vector to include three outputs ± business loans, consumer loans, and securities (all as-sets except loans and physical capital). The second, Y-2, uses RogersÕ (1998) de®nition and expands the output vector to include net non-interest income (total non-interest income less service charges on deposits) as a fourth output. A third speci®cation,Y-3, follows Jagtiani et al. (1995) and includes the credit equivalent of OBS items (loan commitments, credit derivatives, foreign ex-change and interest rate contracts) as a fourth output.13 The ®nal speci®ca-tion, Y-4, follows Berger and Mester (1997a) and uses the three traditional outputs, but includes the credit equivalent of OBS items as a ®xed netputz. The other ®xed netputs, in all cases, include premises and ®xed assets, and total equity capital.
From these inputs and outputs, variable costs, C, and variable pro®ts,P, are de®ned as follows. For all speci®cations, variable costs are the interest
13
expense on purchased funds and on core deposits plus total salary and bene®ts expenditure. Variable pro®ts, however, depend on the output speci®cation. For the ®rst speci®cation of output, variable pro®ts, P-1, are de®ned as interest income from all loans and securities less the variable costs.P-2 augmentsP-1 with net non-interest income de®ned above.P-3 augmentsP-1 with total OBS trading income plus the impact on income from OBS derivatives held for purposes other than trading.14 Prior to 1995, however, these revenue items were not required to be reported so trading income, which equals only the trading portion, was used.P-4 is equal toP-1 since the OBS items are treated as a ®xed netput and thus do not have an associated revenue stream.15
As mentioned above, each speci®cation has certain weaknesses so it is useful to estimate all forms and examine the robustness of the results.Y-1 suers since it totally excludes non-traditional activities, which are growing and concen-trated in large BHCs. Y-2 is imperfect since it treats the revenue and the quantity of non-traditional activities as identical and does not account for price variation.Y-3 is a good speci®cation for the cost function, but is less reliable for the pro®t function due to the changing de®nition and imprecise revenue estimates for OBS items.Y-4 does not require revenue from OBS items, which is an advantage, but it treats OBS items as ®xed and thus aects the estimates of scale economies. Despite these limitations, a comparison of results across speci®cations should lead to a robust view of the behavior of BHCs in the 1990s.
4. Productivity growth in the 1990s
Table 1 shows that these BHCs improved their performance in the 1990s as mean ROA increased and meanC/Adeclined. A possible source of improve-ment is productivity growth, measured as a shift in the cost function, which lowers costs for a given set of input prices, output quantities, and other ex-planatory variables.
This section uses three related econometric methodologies to estimate rates of productivity growth in the 1990s. The ®rst approach simply pools the annual data into a single regression and estimates the shift in a common cost function. The second approach, following Lang and Welzel (1996), uses panel data methods to incorporate BHC-speci®c eects and again measures how the cost function shifts over time. The ®nal approach, based on Berger and Mester
14
These items are included as memorandum items M9-M10 of Schedule HI on the FR Y-9C report.
15Note that both net non-interest income and OBS items cannot be included in the same
(1997b), decomposes total cost changes into a portion due to changes in business conditions and a portion due to changes in BHC productivity.
Each productivity method is estimated using the four alternative output speci®cations,Y-1±Y-4. When applying these approaches with the translog cost function, however, it does not matter if a variable is labeled an output or a ®xed netput, so speci®cation Y-3 and Y-4 yield identical productivity results. Thus, results for only three output speci®cations are reported. Results from the three econometric methods yield a rate of productivity growth in the range of 0.4% for the 1990s and suggest that productivity growth played a role in the improved performance during the 1990s.
4.1. Productivity growth from a pooled analysis
The ®rst method pools the data for all years from 1991 to 1997 into a single function that explicitly varies with time as
lnCG X X
where theG(X) function includes all translog terms in Eq. (3) except the ®rst-order input price terms andtis a simple time trend that is set equal to 0 in 1991 and then grows linearly.
The sparameters capture the impact of changes in costs that are not ex-plicitly due to changes in the other exogenous variables and measure how the cost function evolves. The average rate of productivity growth,mt, can then be
de®ned as the percent reduction in costs, holding constant everything except the input price slopes, as
where mt>0 implies positive productivity growth (costs fall holding all else
equal) and mt<0 implies negative productivity growth (costs rise holding all
else equal).
To estimate the rate of productivity growth in this pooled analysis, the cost function in Eq. (4) is estimated with all 4627 observations (661 BHCs for 7 years). The parameter estimates and the mean input prices for each year are then used to evaluate Eq. (5) and generate estimates ofmt for 1991±1997.
BHCs are implicitly assumed to operate on a single cost frontier. This is clearly a restrictive speci®cation and the next two subsections generalize this.
4.2. Productivity growth from a panel analysis
A more general approach augments the pooled speci®cation in Eq. (4) with BHC-speci®c intercepts through a BHC-speci®c eect,ai, as
lnCG X ai
Eq. (6) maintains the assumptions that slopes coecients, except for the ®rst-order input price terms, are constant throughout the 1990s, but generalizes Eq. (4) by recognizing persistent cost dierences throughai, which raise costs
all else equal. This unobserved term accounts for all dierences ± location, management skills, or persistent X-ineciency ± that permanently raise the variable costs of a particular BHC relative to other BHCs that face similar conditions.16Berger (1993) discusses the potential bias in scale economy es-timates if the unobserved variable is correlated to cost function regressors. For example, ifX-ecient BHCs grow large, then the impact of eciency may be mislabeled as the impact of scale economies.
An econometric issue in this type of speci®cation is how to interpret and estimate theaiterms. Ifaiis a ®xed parameter for each BHC that simply shifts
the common cost function, then a ``®xed eects'' methodology is appropriate andai can be estimated like any other parameter.17That is, persistent
dier-ences across BHCs are re¯ected in dierdier-ences in the intercepts, which represent the unobserved eects. This approach assumes that theaiare non-random, but
correlated with the independent variables. Since the ®xed-eects are assumed to be permanent characteristics, strictly speaking, the results only apply to this sample and do not generalize to other BHCs. A ``random eects'' methodol-ogy, on the other hand, viewsaias a random, though permanent, variable that
is drawn from a distribution and assumes thataiis uncorrelated with the other
explanatory variables. Under this interpretation, the sample is viewed as rep-resentative of the entire population and statistical inference is possible. Since it is unclear a priori which approach is correct, both are used and speci®cation tests are reported along with the empirical results.18
16
The issue of ineciency is dealt with in more detail in Section 4.
17The ®xed eect estimator is equivalent to a ``within estimator'' from an ordinary least squares
regression of deviations from the mean for each BHC.
Estimates of productivity growth are then calculated in the same way as in the pooled analysis. A single regression with 4627 observations is used to estimate the generalized cost function in Eq. (6) using both the ®xed eect or the random eect methodology. The estimated parameters are then combined with mean values each year to generate two alternative estimates of pro-ductivity growth, mfet and mret , for the ®xed and random eect methodologies, respectively.
4.3. Productivity growth from a cost decomposition
The ®nal approach begins with the observation that costs rise if BHCs either face less favorable economic conditions, e.g., an increase in input prices, or if they become less productive in their operations. One can employ the cost framework to decompose observed cost changes into these two factors as
where Xt represents all components of the cost function in Eq. (3) and ft
represents the cost function available to BHCs, both at timet.
The ®rst term on the right-hand side of Eq. (7) represents the change in costs that result from the change in economic conditions, e.g., changes in Xt to Xt1, for a given cost function, ft1 . The second term
rep-resents the change in cost that result from a change in the cost function,
ft to ft1 , holding economic conditions constant at Xt. Thus, the ®rst
term captures the impact of changing business conditions, while the sec-ond term captures the impact of changing production techniques or productivity.
To implement this approach, parameter estimates from a separate cost function regression for each year between 1991 and 1997 are used to estimate
ft1 andft . The mean value of each variable in Eq. (3) for all BHCs in
each year was then used forXt1 and Xt. By combining the parameter
esti-mates and mean values for dierent annual periods, one can calculate each element in the cost decomposition in Eq. (7).
4.4. Estimates of productivity growth
Table 3 reports the estimated annual rate of productivity growth for the entire period 1991±97 for the four methods described above ± pooled data, ®xed eects, random eects, and cost decomposition ± for each of three output speci®cations. The estimates are very close, typically falling between 0.31% and 0.59% per year. An obvious outlier, however, is the cost decomposition for the
econometric method and each output speci®cation are reported in Tables 3a± c.19Results for theY-4 speci®cation, which is similar to other speci®cations, is graphed in Fig. 3.
It should be made clear that these estimates of productivity growth corre-spond to multi-factor productivity. That is, the econometric approach controls for changes in inputs and output size, so mt measures the shift in the cost Table 3
Average productivity growth rates, 1991±1997a
Output speci®cation Pooled
Y-1: business loans, consumer loans, securities
0.44 0.47 0.45 0.32
Y-2: business loans, consumer loans, securities,
net non-interest income
0.42 0.50 0.47 0.05
Y-3 andY-4: business loans, consumer loans, securities, o-balance sheet items as an output or as a ®xed netput
0.44 0.46 0.45 0.31
aAll estimates are from cost function regressions for 1991±1997 as a whole. Estimation details are
given in Section 4. All values are percentages and simple means of average annual growth rates.
Table 3a
Annual estimates of productivity growth, 1991±1997, Y-1: business loans, consumer loans, securitiesa
Year Pooled analysis Fixed eect Random eect Cost decomposition
1992 0.242 )0.438 )0.302 0.236
(0.225) (0.114) (0.111)
1993 0.596 0.129 0.214 )0.771
(0.177) (0.083) (0.081)
aStandard errors are in parentheses for the econometric estimates. Estimation details are given in
Section 4. All growth rates are percentages.
19Note that productivity growth rate from the cost decomposition cannot be estimated for 1991
function over time. In this context, 0.4% growth is very respectable when compared to the economy as a whole. BLS (1998), for example, estimates multi-factor productivity growth of 0.3% per year for the private business economy and 1.9% for manufacturing for 1990±1996. Since manufacturing is a Table 3b
Annual estimates of productivity growth, 1991±1997,
Y-2: business loans, consumer loans, securities, net non-interest incomea
Year Pooled analysis Fixed eect Random eect Cost decomposition
1992 )0.683 )0.449 )0.418 )0.802
(0.215) (0.111) (0.109)
1993 0.024 0.139 0.158 )1.784
(0.163) (0.081) (0.079)
1994 0.414 0.479 0.472 )0.741
(0.105) (0.050) (0.050)
aStandard errors are in parentheses for the econometric estimates. Estimation details are given in
Section 4. All growth rates are percentages.
Table 3c
Estimates of productivity growth, 1991±1997,
Y-3 andY-4: business loans, consumer loans, securities, o-balance sheet items as an output or as a ®xed netputa
Year Pooled analysis Fixed eect Random eect Cost decomposition
1992 0.219 )0.429 )0.289 0.075
(0.226) (0.114) (0.111)
1993 0.587 0.131 0.221 )0.727
(0.179) (0.083) (0.081)
substantial share of output, this implies that estimated BHC productivity growth far exceeded multi-factor productivity for the non-manufacturing sectors of the US economy.
When comparing the alternative methods, econometric tests strongly reject the pooled analysis in favor of a panel approach that incorporates persistent ®rm dierences. AnF-test of identical intercepts for all BHCs is rejected at the 1% level in the ®xed eects model and a Breusch±Pagan test rejects the as-sumption of equal random eects at the 1% level in the random eects model. A Hausman speci®cation test, however, rejects the null hypothesis that the random eects are uncorrelated with the other right-hand side variables. This implies either that the cost function is misspeci®ed or the assumption of un-correlated random eects is violated.
As a whole, these results are quite consistent with the simple ROA and C/A means presented in Table 1 since the econometric estimates control for changes in all right-hand side variables, including BHC size. For 1991±1997, for ex-ample, mean costs rose 6.5% per year, but mean BHC size grew even faster as assets increased at 10.7% per year and mean equity (the scaling factor in the cost regressions) increased 13.4% annually. Since these productivity estimates are derived from predicted changes in costs, ceteris paribus, the relatively slow increase in costs partially represents real productivity growth.
This can also be seen from the details of the cost decomposition from Eq. (7) that are shown in Table 4. For the entire period 1991±1997, the average actual cost increase was 6.47% per year (the weighted average column) while predicted costs increased 6.99 per year. This predicted cost change is decomposed into a 7.0% to 7.3% annual increase due to changing business conditions and a 0.05± 0.32% annual decrease due to productivity growth. This implies that had the business and operating environment, e.g., size and input prices, stayed at the
Table 4
Comparison of actual cost change to estimated cost decomposition, 1991±1997a
Year Actual cost change Estimated cost decomposition Mean Weighted
Y-1: Business loans, consumer loans, securities
1991±1992 )17.62 )18.25 )6.95 )0.24 )6.71
1992±1993 )9.32 )6.52 )7.91 0.77 )8.68
1993±1994 5.37 13.41 6.44 )0.02 6.46
1994±1995 20.80 28.87 23.47 )1.98 25.45
1995±1996 7.13 10.09 17.15 )0.35 17.50
1996±1997 9.50 11.22 9.74 )0.09 9.83
Mean 2.64 6.47 6.99 )0.32 7.31
Y-2: Business loans, consumer loans, securities, net non-interest income
Y-3 andY-4: Business loans, consumer loans, o-balance sheet items
aTotal cost change is de®ned as ln(f
1991 levels, then total costs would have fallen about 2.0% in 1997 relative to 1991.
These results show that productivity growth was a source of the improved performance of BHCs in the 1990s. The results, however, are quite dierent from Berger and Mester (1997b) who report 10% cost increases per year for 1989±1995 after accounting for changes in business conditions. This might re¯ect the dierent samples, i.e., relatively large BHCs vs. smaller individual banks, or the dierent set of control variables used in each speci®cation. Compared with the raw data that show asset growth of 11% per year and cost increase of 7% per year, however, the ®nding of 0.4% annual productivity growth for BHCs seems reasonable.
5. Economies of scale for BHCs in the 1990s
Scale economies ± intuitively described as a decrease in average costs as size increases ± has been an important topic in the empirical study of commercial banks. Perhaps surprisingly, most early research found little evidence of economies of scale beyond a relatively modest overall size. Recent evidence from the 1990s, however, suggests sizable economies of scale that increase with bank size. Hughes and Mester (1998), for example, ®nd the largest quartile of commercial banks in 1990 have the largest degree of scale economies, Berger and Mester (1997a) report that an average bank would have to be 2±3 times as large to maximize cost scale eciency, and Hughes et al. (1996) ®nd that BHCs with assets greater than $50 billion have the largest degree of scale economies in 1994. Moreover, Berger and Mester (1997a) test several speci®cations and conclude ``the 1990s are indeed dierent'' (p. 928) with regard to scale economies.
This section reports estimates of economies of scale for the BHCs for 1991 to 1997. The estimates complement the earlier work of and Hughes and Mester (1998), Berger and Mester (1997a), and Jagtiani and Khanthavit (1996) on commercial banks rather than BHCs and Hughes et al. (1996), which examines a smaller subset of BHCs for only 1994. This broader analysis of BHCs allows an investigation of how scale economies vary across size classes, possibly changed during the period of deregulation and heavy consolidation in the 1990s, and contributed to the success of BHCs in the 1990s.
5.1. Measures of economies of scale
estimates and reports two well-known measures ± ray scale economies and expansion path scale economies ± for the sample of BHCs for 1991±1997. The four alternative speci®cations, Y-1 through Y-4, are used to estimates each measure.
Ray scale economies (RSE) measures the elasticity of cost with respect to a proportional increase in all outputs and is de®ned as
RSEX J
j1
olnC
olnyj; 8
where yj is the jth output from the y output vector with J assets. RSE<1
implies economies of scale (costs increase proportionally less than output in-creases) and RSE>1 implies diseconomies of scale.
This de®nition, however, measures the change in costs as a BHC increases all outputs proportionally. This implicitly assumes the same output mix over all BHC size classes, an assumption that is not consistent with the observed asset portfolios of BHCs. Larger BHCs, for example, hold fewer securities and more business loans than smaller BHCs.
To avoid this unrealistic assumption, Berger et al. (1987) developed the concept of expansion path scale economies, EPSCE(yA,yB), which measures
the proportional change in costs as a bank moves along the observed expansion path from output bundleyA to output bundleyB whereyB is the larger BHC. EPSCE(yA,yB) is de®ned as
whereCBandCAare the mean of the predicted variable costs for the large and
the small BHC, respectively.
EPSCE yA; yB<1 implies scale economies (costs increase proportionally
less than outputs) and EPSCE yA; yB>1 implies scale diseconomies (costs
increase proportionally more than outputs). EPSCE yA; yBis a more useful
measure of scale economies since it compares the cost change as BHCs increase in size and change their output mix in way that is consistent with the observed behavioral choices of BHCs.
5.2. Estimates of scale economies
EPSCE(yA, yB) and RSE were calculated from 1991 to 1997 for the 661
to determine changes in the optimal size. In all cases, the cost function in Eq. (3) with each of the four speci®cations was estimated separately for each year and the parameter estimates and mean values from each size class were used to evaluate Eqs. (8) and (9). Note also that since these estimates are based on a cost function, the same dependent variable is in each regression regardless of the output speci®cation.
The scale economy results, along with mean C/A for each group, are re-ported in Tables 5a, b, c, d. The estimates are very similar across the four speci®cations with modest economies of scale during the 1990s, i.e., the ma-jority of EPSCE(yA,yB) and RSE estimates are signi®cantly below 1.0. The $200m to $300m group is an exception with signi®cant EPSCE(yA, yB) dis-economies of scale for all years.
The degree of scale economies is typically stronger for the largest BHCs, especially using the preferred EPSCE(yA,yB) measure, and there is a de®nite
downward trend in both EPSCE(yA,yB) and RSE in the early 1990s and an
increase thereafter. Both of these ®ndings are consistent with the raw data on
C/A and ROA presented earlier. Table 1, for example, shows C/Adeclining from 1991 to 1994 and mean ROA rising throughout the 1990s, while Figs. 1 and 2 show a slight decline inC/Aand a small upward trend in ROA across size classes in 1997.
The ®nding that larger banks show more unexploited scale economies is perhaps surprising, but consistent with recent research that found signi®cant scale economies in the 1990s, e.g., Hughes and Mester (1998), Berger and Mester (1997a), Hughes et al. (1996), and Jagtiani and Khanthavit (1996). These results also suggest that the optimal scale of BHCs increased in the early 1990s and then stabilized. From 1991 to 1994, mean BHC size grew steadily while unexploited scale economies increased, which implies that op-timal size must have been increasing. After 1994, BHCs continued to grow, but there was a decrease in the degree of unexploited scale economies as the continued growth during the mid-1990s moved the BHCs closer to the new optimal size and left less potential gains from unrealized scale economies. Both of these results likely re¯ect the impact of deregulation, e.g., interstate banking and expanded bank powers, and technological advances, e.g., in-formation and communications equipment, that improved the relative posi-tion of large BHCs.
Table 5a
Estimates of returns to scale: EPSCE (yA, yB), RSE, andC/Aby size class, 1991±1997,Y-1: business loans, consumer loans, securitiesa
Asset size class Year
1991 1992 1993 1994 1995 1996 1997
EPSCE(yA, yB)
A< $200 million
$200 <A< $300 million 1.056 1.104 1.067 1.042 1.024 1.050 1.069 (0.013) (0.019) (0.024) (0.026) (0.020) (0.022) (0.024) $300 million <A< $500 million 1.032 0.960 0.905 0.887 0.935 0.887 0.889
(0.012) (0.015) (0.025) (0.027) (0.018) (0.018) (0.018) $500 million <A< $1 billion 0.985 1.001 0.973 0.934 0.934 0.924 0.950
(0.014) (0.018) (0.026) (0.024) (0.016) (0.018) (0.015) $1 billion <A< $5 billion 0.999 0.955 0.911 0.916 0.955 0.957 0.959
(0.012) (0.016) (0.025) (0.022) (0.017) (0.017) (0.015)
A> $5 billion 0.979 0.950 0.863 0.908 0.968 0.948 0.942 (0.022) (0.028) (0.044) (0.038) (0.028) (0.028) (0.025)
RSE
A< $200 million 0.994 0.983 0.957 0.942 0.965 0.976 0.973 (0.010) (0.013) (0.017) (0.016) (0.016) (0.017) (0.018) $200 <A< $300 million 0.998 0.969 0.944 0.919 0.937 0.938 0.930
(0.011) (0.015) (0.019) (0.021) (0.016) (0.017) (0.019) $300 million <A< $500 million 0.992 0.968 0.927 0.908 0.933 0.916 0.927
(0.011) (0.015) (0.023) (0.026) (0.017) (0.019) (0.019) $500 million <A< $1 billion 0.995 0.960 0.911 0.909 0.937 0.923 0.935
(0.013) (0.017) (0.025) (0.025) (0.017) (0.018) (0.016) $1 billion <A< $5 billion 0.991 0.961 0.913 0.923 0.952 0.938 0.943
(0.012) (0.017) (0.026) (0.023) (0.017) (0.017) (0.015)
A> $5 billion 0.981 0.953 0.865 0.909 0.973 0.954 0.946 (0.023) (0.029) (0.044) (0.038) (0.028) (0.028) (0.025)
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A< $200 million 6.29 5.12 4.42 4.42 4.99 5.01 5.03 (0.52) (0.46) (0.49) (0.40) (0.42) (0.45) (0.42) $200 <A< $300 million 6.32 4.99 4.34 4.25 4.84 4.82 4.89
(0.55) (0.55) (0.48) (0.43) (0.47) (0.44) (0.44) $300 million <A< $500 million 6.16 4.98 4.42 4.34 4.84 4.81 4.89
(0.71) (0.89) (0.97) (0.92) (0.50) (0.49) (0.53) $500 million <A< $1 billion 6.20 4.83 4.14 4.18 4.87 4.85 4.89
(0.60) (0.52) (0.46) (0.47) (0.90) (0.83) (0.77) $1 billion <A< $5 billion 6.19 4.90 4.27 4.22 4.82 4.75 4.81
(0.53) (0.44) (0.63) (0.48) (0.55) (0.62) (0.55)
A> $5 billion 6.25 4.84 4.20 4.35 5.11 4.94 4.89
(0.48) (0.40) (0.43) (0.42) (0.46) (0.51) (0.51) a
EPSCE(yA, yB) and RSE are estimated from a separate cost function for each year and evaluated with means from each size class. Standard errors are
in parentheses.C/Ais variable costs per assets multiplied by 100 and the standard deviation for each size class is in parentheses.
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1703±1745
Table 5b
Estimates of returns to scale: EPSCE(yA,yB) and RSE by size class, 1991±1997,Y-2: business loans, consumer loans, securities, net non-interest
in-comea
Asset size class Year
1991 1992 1993 1994 1995 1996 1997
EPSCE(yA,yB)
A< $200 million
$200 <A<$300 million 1.062 1.129 1.118 1.067 1.023 1.053 1.065 (0.013) (0.019) (0.023) (0.022) (0.020) (0.023) (0.022) $300 million <A< $500 million 1.048 0.979 0.947 0.934 0.944 0.888 0.887
(0.012) (0.015) (0.019) (0.017) (0.016) (0.017) (0.016) $500 million <A< $1 billion 0.988 1.003 0.999 0.944 0.936 0.928 0.952
(0.015) (0.017) (0.021) (0.019) (0.015) (0.016) (0.015) $1 billion <A< $5 billion 0.999 0.952 0.926 0.933 0.953 0.959 0.961
(0.013) (0.016) (0.020) (0.018) (0.016) (0.018) (0.016)
A> $5 billion 0.967 0.921 0.853 0.926 0.959 0.951 0.954 (0.021) (0.029) (0.036) (0.034) (0.028) (0.030) (0.026)
RSE
A< $200 million 1.005 0.997 0.988 0.955 0.959 0.968 0.965 (0.010) (0.014) (0.016) (0.016) (0.016) (0.018) (0.017) $200 <A< $300 million 1.007 0.986 0.980 0.940 0.936 0.931 0.921
(0.011) (0.015) (0.018) (0.016) (0.016) (0.018) (0.017) $300 million <A< $500 million 1.000 0.976 0.959 0.934 0.932 0.913 0.921
(0.012) (0.015) (0.019) (0.018) (0.015) (0.018) (0.017) $500 million <A< $1 billion 1.001 0.968 0.946 0.933 0.936 0.922 0.932
(0.014) (0.016) (0.020) (0.018) (0.015) (0.016) (0.015) $1 billion <A< $5 billion 0.989 0.957 0.927 0.939 0.949 0.939 0.945
(0.013) (0.017) (0.021) (0.019) (0.016) (0.018) (0.015)
A> $5billion 0.969 0.922 0.853 0.926 0.963 0.956 0.956 (0.021) (0.029) (0.036) (0.035) (0.028) (0.031) (0.026) a
EPSCE(yA, yB) and RSE are estimated from a separate cost function for each year and evaluated with means from each size class. Standard errors are
Estimates of returns to scale: EPSCE(yA, yB) and RSE by size class, 1991±1997,Y-3: business loans, consumer loans, securities, o-balance sheet items
as an outputa
Asset size class Year
1991 1992 1993 1994 1995 1996 1997
EPSCE(yA, yB)
A< $200 million
$200 <A< $300 million 1.055 1.108 1.063 1.045 1.032 1.045 1.076 (0.013) (0.021) (0.025) (0.027) (0.020) (0.023) (0.028) $300 million <A< $500 million 1.031 0.959 0.907 0.891 0.937 0.885 0.889
(0.012) (0.016) (0.025) (0.028) (0.017) (0.018) (0.018) $500 million <A< $1 billion 0.986 0.997 0.974 0.936 0.931 0.924 0.950
(0.014) (0.018) (0.026) (0.024) (0.016) (0.018) (0.016) $1 billion <A< $5 billion 1.001 0.951 0.922 0.919 0.949 0.962 0.957
(0.014) (0.019) (0.027) (0.025) (0.018) (0.018) (0.016)
A> 5 billion 0.984 0.947 0.881 0.909 0.953 0.958 0.937 (0.025) (0.030) (0.047) (0.040) (0.029) (0.031) (0.027)
RSE
A< $200 million 0.992 0.986 0.950 0.943 0.968 0.966 0.968 (0.011) (0.015) (0.017) (0.017) (0.015) (0.019) (0.020) $200 <A< $300 million 0.998 0.967 0.946 0.922 0.939 0.932 0.928
(0.011) (0.015) (0.019) (0.021) (0.015) (0.017) (0.020) $300 million <A< $500 million 0.992 0.966 0.929 0.911 0.931 0.912 0.925
(0.011) (0.015) (0.023) (0.026) (0.017) (0.019) (0.019) $500 million <A< $1 billion 0.995 0.959 0.912 0.912 0.934 0.922 0.934
(0.013) (0.017) (0.025) (0.025) (0.017) (0.018) (0.016) $1 billion <A< $5 billion 0.993 0.957 0.924 0.926 0.946 0.941 0.941
(0.014) (0.019) (0.028) (0.025) (0.018) (0.019) (0.016)
A> $5 billion 0.987 0.949 0.884 0.910 0.958 0.965 0.941 (0.025) (0.031) (0.047) (0.041) (0.029) (0.031) (0.027) a
EPSCE(yA, yB) and RSE are estimated from a separate cost function for each year and evaluated with means from each size class. Standard errors are
Table 5d
Estimates of returns to scale: EPSCE(yA, yB) and RSE by size class, 1991±1997,Y-4: business loans, consumer loans, securities, o-balance sheet items
as a ®xed netputa
Asset size class Year
1991 1992 1993 1994 1995 1996 1997
EPSCE(yA, yB)
A< $200 million
$200 <A< $300 million 1.057 1.109 1.066 1.043 1.030 1.046 1.076 (0.014) (0.022) (0.025) (0.027) (0.020) (0.023) (0.028) $300 million <A< $500 million 1.033 0.959 0.909 0.890 0.931 0.885 0.888
(0.012) (0.016) (0.025) (0.028) (0.018) (0.019) (0.018) $500 million <A< $1 billion 0.988 0.998 0.978 0.934 0.924 0.923 0.947
(0.014) (0.019) (0.026) (0.024) (0.017) (0.019) (0.016) $1 billion <A< $5 billion 1.003 0.950 0.925 0.917 0.941 0.958 0.953
(0.015) (0.019) (0.028) (0.025) (0.019) (0.019) (0.016)
A> $5 billion 0.986 0.945 0.887 0.906 0.940 0.949 0.930 (0.026) (0.031) (0.047) (0.041) (0.031) (0.032) (0.029)
RSE
A< $200 million 0.991 0.988 0.949 0.943 0.967 0.967 0.969 (0.011) (0.015) (0.017) (0.017) (0.015) (0.019) (0.020) $200 <A< $300 million 0.998 0.967 0.948 0.921 0.937 0.932 0.928
(0.011) (0.016) (0.019) (0.021) (0.015) (0.017) (0.019) $300 million <A< $500 million 0.993 0.966 0.931 0.910 0.927 0.912 0.924
(0.012) (0.016) (0.024) (0.026) (0.017) (0.019) (0.019) $500 million <A< $1 billion 0.996 0.959 0.915 0.911 0.928 0.921 0.931
(0.013) (0.018) (0.025) (0.025) (0.017) (0.018) (0.016) $1 billion <A< $5 billion 0.995 0.956 0.927 0.923 0.938 0.938 0.938
(0.014) (0.020) (0.028) (0.025) (0.019) (0.019) (0.016)
A> $5 billion 0.989 0.948 0.889 0.907 0.946 0.956 0.935 (0.026) (0.031) (0.048) (0.041) (0.031) (0.032) (0.029) aEPSCE(
yA, yB) and RSE are estimated from a separate cost function for each year and evaluated with means from each size class. Standard errors are
scale economies measures in Y-3, but not in Y-4. Since OBS items are con-centrated in the large BHCs, the biggest dierence in scale economies between
Y-3 and Y-4 occurs for BHCs with assets greater than $5 billion. After controlling for size through other assets, equity capital, and physical capital, there may not be enough independent variation in the non-traditional mea-sure to materially eect the scale estimates. Alternatively, these non-tradi-tional activities could be primarily a pro®t and revenue phenomenon and not a cost-side scale phenomenon. While suggestive, more work is needed to substantiate these results.
6. Eciency of BHCs in the 1990s
This section examines the relative eciency of BHCs in the 1990s. Relative eciency, both in terms of costs and pro®ts, is estimated using the ``distribu-tion-free'' methodology in Berger (1993) and details on the actual estimation process can be found in Berger and Mester (1997a, particularly pp. 916±920). This framework uses data for the entire period to isolate persistent ineciency from random shocks. This approach, therefore, is not suitable for determining if changes in eciency contributed to the success of the 1990s, although Berger and Mester (1997a) report that both cost eciency and (alternative) pro®t eciency changed little in the 1990s relative to the 1980s.
6.1. Cost eciency
The basic approach behind the ``distribution-free'' methodology is to esti-mate a separate cost function for each year that explicitly accounts for per-sistent ineciency as
lnCf X ef X lnlilnec; 10
wheref(X) includes all variables in Eq. (3),eis a composite error term, li is
relative cost ineciency for a particular BHC, andec is random error.20
It is assumed that li measures persistent cost ineciency, while ec is a
transitory cost-shock that averages to zero over time. A simple average of the residuals, e, for each BHC from the seven annual regressions then approxi-mates li, the ineciency term for a given BHC. A cost-inecient BHC ± a
relatively largeli ± will incur higher costs than a cost-ecient BHC ± a
rela-20Note that Eq. (10) can be interpreted as an unconstrained version of the ®xed and random
tively smallli± holding constant variation in input prices, output choices, and
other explanatory variables.21
The BHC with the smallest ineciency term for 1991±1997,lmin, is labeled the ``best cost-practice'' BHC since it incurs the lowest costs, conditional on the other variables. Every other BHC can then be compared to the best cost-practice BHC by asking the following counter-factual question ± what costs would a particular BHC incur if it were as ecient as the best cost-practice BHC? This measure of relative cost eciency is de®ned as
C-EFF expf X explnl
min
expf X explnli l
min
li
; 11
wherelminis the smallest observed ineciency term from the best cost-practice BHC.
This measure of eciency ranges between 1.0 for the most ecient BHC and approaches 0 for a BHC with maximum ineciency. C-EFF represents the proportion of costs that are eciently employed, e.g., if C-EFF0.75 for a particular BHC, then 25% of its costs are attributed to cost ineciency.
6.2. Pro®t eciency
One can examine pro®t eciency in a similar way by estimating the fol-lowing pro®t function:
ln Ph f X ef X lnpilneP; 12
wherehis a constant set equal to one plus the absolute value of the minimum pro®ts each year to avoid taking logs of a negative number as described above for Eq. (3). Again, the regression is run separately for each year and the mean residual for each BHC is interpreted as an estimate of persistent pro®t e-ciency,pi.
The BHC with the largestpifor 1991±1997 is then labeled the ``best
pro®t-practice BHC'' since it earns the most pro®ts, conditional on all other vari-ables. To measure relative pro®t ineciency, ask the following counter-factual question ± how much pro®t could a particular BHC earn if it were as ecient as the best pro®t-practice BHC? This measure of relative pro®t eciency is de®ned as
P-EFF expf X expln pi ÿh
expf X expln pmax ÿh; 13
21The truncation process of Berger and Mester (1997a) is used to assign less extreme values for
wherepmaxis the pro®t eciency for the best pro®t-practice BHC. Each ®tted value is evaluated using parameters estimated for each year and the right-hand side variables of a given bank in that year. The ®tted values are then averaged for each BHC to generate a single estimate for each BHC.22
This measure of pro®t eciency ranges from 1 for the most pro®t ecient bank to )1 for an in®nitely pro®t inecient bank. P-EFF represents the proportion of potential pro®ts that are earned, e.g., ifP-EFF equals 0.75, then the BHC is losing about 25% of potential pro®ts to ineciency.
6.3. Estimates of cost and pro®t eciency
This procedure yields a single measure of relative cost eciency, C-EFF, and relative pro®t eciency, P-EFF, for reach of the BHCs in the sample. Again,C-EFF andP-EFF were estimated using each of the four alternative speci®cations. Since true eciency likely varies for a given BHC over time as business conditions and the operating environment change, these eciency terms should be interpreted as the average eciency of a given BHC relative to the best practice BHC for the entire period 1991±1997.
6.3.1. Mean and variation in eciency
Table 6 presents weighted averages ofC-EFF andP-EFF across all BHCs for each of the four output speci®cations. In all cases, weights equal the de-nominator of the eciency ratios so that the estimates re¯ect the proportion of resources lost to ineciency. Note thatC-EFF is the same in theY-3 andY-4 speci®cation since it is irrelevant if OBS items are treated as an output or a Table 6
Average cost and pro®t eciency, 1991±1997a
Output speci®cation C-EFF P-EFF
Y-1: Business loans, consumer loans, securities 0.909 0.606 (0.049) (0.165) Y-2: Business loans, consumer loans, securities, net non-interest
income
0.887 0.720 (0.043) (0.101) Y-3: Business loans, consumer loans, securities, o-balance sheet
items as an output
0.911 0.659 (0.048) (0.129) Y-4: Business loans, consumer loans, securities, o-balance sheet
items as a ®xed netput
0.911 0.634 (0.048) (0.150)
aAll eciency measures are weighted averages for all 661 BHCs with weights equal to the
de-nominator of the eciency ratio.C-EFF1 for the ``best cost-practice'' BHC andp-EFF1 for the best pro®t-practice BHC. Standard deviations are in parentheses.
22Note that this does not reduce to the ratio of ineciency terms as in the cost function due to
®xed netput in the cost function analysis, butP-EFF varies since the depen-dent variable is dierent.
The weighted average C-EFF for all 661 BHCs ranges from 0.89 to 0.91, which implies that about 10% of incurred costs in the 1990s can be attributed to cost ineciency relative to the best cost-practice BHC. The weighted average of
P-EFF ranges from 0.61 for Y-1, the traditional output speci®cation, to 0.72
Fig. 4. Distribution of cost eciency (Y-4), 1991±1997.
forY-2, which includes net non-interest income as an output. This implies that ineciency forces BHCs to forego about one-third of the potential pro®ts that the best pro®t-practice BHC could earn. An important conclusion is that that failure to account for non-traditional activities understates pro®t eciency.
A second notable ®nding is that the distribution ofC-EFF is narrow relative to the distribution ofP-EFF, i.e., the standard deviation ofC-EFF far exceeds the standard deviation ofP-EFF for all speci®cations. As an example, Figs. 4 and 5 plot the distribution ofC-EFF andP-EFF from theY-4 speci®cation. This suggests that BHCs are more comparable in their ability to choose cost-minimizing inputs mixes and there is much more heterogeneity with respect to pro®t eciency. Although both distributions are roughly bell-shaped, the Shapiro±Wilk and Shapiro±Francia tests formally reject the null hypothesis of a normal distribution for all speci®cations exceptP-EFF forY-2. Finally, the skewness coecient, de®ned asl3/r3wherel3 is the third andr2is the second
moment about the mean, is less than zero for all distributions (exceptP-EFF forY-2), indicating that those distributions are skewed left.
These results are similar to earlier estimates that examined commercial banks. Berger and Humphrey (1997), for example, report mean cost eciency of 0.84 across 110 studies of US banks. In a comprehensive comparison of alternative measurement techniques, Bauer et al. (1998) estimate mean e-ciency of 0.83 across seven parametric models for 683 large banks (assets greater $100 million) for 1977±1988. Likewise, Berger and Mester (1997a) re-port average cost eciency of 0.87 and (alternative) pro®t eciency of 0.46 for a sample of 5946 individual banks. Rogers (1998), which includes net non-interest income as a bank output, reports cost-eciency of 0.71 and pro®t eciency of 0.71 in states with statewide branching. These results suggest that BHCs as an aggregate entity are much more cost ecient and slightly more pro®t ecient than the individual subsidiary banks.23
One interesting hypothesis concerning these ®ndings concerns the role of information technology. Prasad and Harker (1997) argue that information technology may not provide real bene®ts in retail banking, but rather is a ``strategic necessity'' that merely allows a bank to remain competitive. If this is primarily a cost-side phenomenon, one would expect relatively equal costs since all banks have access to the same fundamental technology. Consistent with these ®ndings, pro®tability would then vary more and would be largely dependent on the idiosyncratic ability of bank managers. Since ®nancial
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