Directory UMM :Data Elmu:jurnal:J-a:Journal Of Banking And Finance:Vol24.Issue11.2000:
Journal of Banking & Finance 24 (2000) 1703±1745
www.elsevier.com/locate/econbase
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 alternative 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. Estimates of both productivity growth and economies of scale are robust across traditional
and non-traditional output speci®cations. Despite the overall success, however, substantial 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
*
Tel.: +1-212-720-6633; fax: +1-212-720-8363.
E-mail address: [email protected] (K.J. Stiroh).
0378-4266/00/$ - see front matter Ó 2000 Elsevier Science B.V. All rights reserved.
PII: S 0 3 7 8 - 4 2 6 6 ( 9 9 ) 0 0 1 0 1 - 6
1704
K.J. Stiroh / Journal of Banking & Finance 24 (2000) 1703±1745
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 organizations 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 performance 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 traditional lending activities and non-traditional activities like fee income or obalance 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 commercial banks and this study, as far as is known, represents the ®rst comprehensive 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.
Despite the overall improvements, these estimates suggest that BHCs operated with substantial ineciency throughout the 1990s. Roughly 10% of
costs during the 1990s can be attributed to cost ineciency and 30±40% of
potential pro®ts are foregone due to pro®t ineciency. A comparison of alternative output speci®cations shows that failure to account for non-traditional
activities leads pro®t eciency, but not cost eciency, to be substantially
understated for BHCs with more than $30 billion in assets. This suggests that
previous research that failed to include non-traditional activities likely understates pro®t eciency for large ®nancial institutions. Finally, there is much
K.J. Stiroh / Journal of Banking & Finance 24 (2000) 1703±1745
1705
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 substantial BHC-speci®c ineciencies. If the current consolidation trend continues, 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-in1
See Berger et al. (1995) and FDIC (1997) for a thorough analysis of the commercial bank
industry in the 1980s and early 1990s.
1706
K.J. Stiroh / Journal of Banking & Finance 24 (2000) 1703±1745
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). 2 BHCs 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, 3 and 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 authorized 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 Monetary 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).
3
Some BHCs that already owned subsidiary banks in multiple states were grandfathered and
allowed to remain in operation.
K.J. Stiroh / Journal of Banking & Finance 24 (2000) 1703±1745
1707
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 framework 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 restrictions, 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 restricted for individual banks, e.g., BHCs can own separately capitalized subsidiaries 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 operated continuously from 1991 to 1997 using data from the consolidated FR Y9C reports. 5 These 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
The analysis began with 746 BHCs that operated continuously between December 1991 and
December 1997. Since these data are measured with error, however, a procedure based on Berger
and Mester (1997a, p. 915) to drop questionable input price observations (more than 3.5 standard
deviations from the annual mean) was implemented. This left a core sample of 661 BHCs with
reasonable data for each year from 1991 to 1997.
1708
K.J. Stiroh / Journal of Banking & Finance 24 (2000) 1703±1745
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 continuously 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/A or average ROA for
1991±1997 to explore the dispersion of performance both across and within size
classes.
Fig. 1 graphs the mean C/A for the highest quintile, the entire size class, and
the lowest quintile for each size class, while Fig. 2 shows the same breakdown
for ROA. 6 These charts show wide dispersion within every size class for both
C/A and ROA, with a slight trend towards lower C/A for larger size classes,
except for the very largest BHCs, which show an increase in C/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 variation in performance and are suggestive of some scale economies for BHCs. The
question of economies of scale and more precise estimates of relative performance are addressed in the following sections.
6
Berger and Humphrey (1992) report substantial dispersion in costs per asset for commercial
banks in the 1980s.
Year
1991
1992
1993
1994
1995
1996
1997
a
Number of
Obs.
Total
assets
Equity
capital
Variable
costs
Variable pro®ts
P-1 and
P-4
P-2
P-3
661
661
661
661
661
661
661
2797.8
3097.6
3357.8
3692.8
4130.1
4728.1
5303.6
191.4
234.9
267.9
285.3
331.8
387.7
427.4
177.4
147.9
138.5
158.4
211.4
233.9
261.6
54.3
66.6
70.3
74.9
80.3
91.9
98.4
89.5
106.7
116.2
122.6
135.9
162.7
182.1
57.6
70.3
74.8
78.2
84.1
96.9
104.1
ROA
ROE
C/A
0.80
1.04
1.14
1.13
1.17
1.23
1.24
10.43
13.30
13.75
13.38
13.31
13.59
13.64
6.25
4.96
4.31
4.29
4.88
4.84
4.89
All 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/A is
variable costs divided by total assets. ROA, ROE, and C/A are percentages.
K.J. Stiroh / Journal of Banking & Finance 24 (2000) 1703±1745
Table 1
Trends in bank holding company performance, 1991±1997a
1709
1710
K.J. Stiroh / Journal of Banking & Finance 24 (2000) 1703±1745
Fig. 1. Mean C/A and Hi and Low C/A quintiles by size class, 1991±1997.
Fig. 2. Mean ROA and Hi and Low ROA quintiles by size class, 1991±1997.
3. General approach ± BHCs and production concepts
There is a large literature on productivity and eciency of ®nancial institutions and this paper does not attempt to summarize that work. 7 This papers
simply follows the general methodologies and utilizes panel and pooled
methods to estimate the rate of productivity growth, the degree of scale
7
Berger and Humphrey (1997) provide a comprehensive review of the empirical literature on
®nancial institutions.
K.J. Stiroh / Journal of Banking & Finance 24 (2000) 1703±1745
1711
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 important 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-management unit. Akhavein et al. (1997, p. 18) argue that managers will coordinate
activities and optimize production choices with respect to the overall institution. 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 meaningful. 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.
8
Other earlier research that examines BHCs includes Grabowski et al. (1993) and Newman and
Shrieves (1993).
1712
K.J. Stiroh / Journal of Banking & Finance 24 (2000) 1703±1745
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 standard 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
C f 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 outputs), 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
P f p; y; z; m; p; eP ; t;
2
where p is BHC-speci®c pro®t eciency and eP 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 evidence 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
9
Berger and Mester (1997a) present several additional arguments why the alternative pro®t
function may be preferable, e.g., quality dierences, semi-®xed outputs, imperfect markets, and
large errors in price measurement.
K.J. Stiroh / Journal of Banking & Finance 24 (2000) 1703±1745
1713
Third, all estimation was based on a parametric approach in general and the
translog functional form in particular. 10 For a cost function with I inputs, J
outputs, and two ®xed netputs, the basic translog speci®cation used is
ln C= z2 pI a0
Iÿ1
J
X
X
ai ln pi =pI
bj ln yj =z2
i1
J X
J
X
j1
/ij ln yj =z2 ln yj =z2
i1 j1
Iÿ1 X
Iÿ1
X
dij ln pi =pI ln pj =pI
i1 j1
Iÿ1 X
J
X
hij ln pi =pI ln yj =z2 c1 ln z1 =z2
i1 j1
2
c2 ln z1 =z2
Iÿ1
X
ki ln pi =pI ln z1 =z2
i1
J
X
2
uj ln yj =z2 ln z1 =z2 q1 ln v1 q2 ln v1
j1
lne;
3
where ln C= z2 p3 and ec are replaced by ln P= z2 p3 1
abs Pmin = p2 z3 and eP for the alternative pro®t function estimates. Note
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 additional 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.
10
See Bauer et al. (1998) for a detailed comparison of parametric and non-parametric
techniques.
1714
K.J. Stiroh / Journal of Banking & Finance 24 (2000) 1703±1745
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 /ji and dij dji ) of the cost
and pro®t functions are also imposed. Costs, pro®ts, and all quantities (variable 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 nontraditional outputs, which is discussed in detail below. Table 2 provides summary 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 (including 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'' activities are growing over time and concentrated in the largest institutions, failure to
account for them may lead to incorrect conclusions.
11
Berger and Mester (1997a, p. 918) discuss this transformation and the economic interpretation
of scaling by equity capital. Note also that predicted costs and pro®ts are calculated by
exponentiating the ®tted value from the log speci®cation and then multiplying by the scaling
factors. Since this adjustment is non-linear, average predicted values are multiplicatively adjusted to
equal actual mean values when needed.
1715
K.J. Stiroh / Journal of Banking & Finance 24 (2000) 1703±1745
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 and P-4
P-2
P-3
98.4
182.1
104.1
394.2
827.1
434.1
)89.0
1.1
)41.7
4,958.0
1,007.0
5,650.0
Variable input prices
Purchased funds
Core deposits
Labor
4.68
3.29
37.70
0.77
0.59
7.73
0.03
1.00
3.79
8.99
4.89
78.76
Variable output quantities
Business loans
Consumer loans
Securities
Net non-interest income (Y-2)
O-balance sheet items (Y-3)
572.2
2774.1
1877.5
83.7
840.1
2609.7
11,674.3
10,268.5
466.7
6730.9
0.3
15.2
18.9
0.6
0.1
33,431.0
143,403.0
193,287.0
7937.2
137,607.1
Fixed netputs
Physical capital
Equity capital
O-balance sheet items (Y-4)
79.8
427.5
840.1
340.5
1807.4
6730.9
0.1
5.0
0.1
4147.9
21,742.0
137,607.1
5303.6
24,205.9
37.6
365,520.9
Total assets
a
Variable 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®cation Y-1 includes business loans, consumer
loans, and securities as outputs and physical capital and equity capital as ®xed netputs. Other
speci®cations include Y-1 plus the designated output quantity or ®xed netput.
One set of non-traditional activities includes the sources of non-interest
income, e.g., ®duciary activities, trading, and activities that generate other noninterest 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
12
See English and Nelson (1998) for a discussion of the importance of dierent types of
o-balance sheet items.
1716
K.J. Stiroh / Journal of Banking & Finance 24 (2000) 1703±1745
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 recently 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 traditional measures of bank outputs and de®nes the variable output vector to
include three outputs ± business loans, consumer loans, and securities (all assets 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 exchange and interest rate contracts) as a fourth output. 13 The ®nal speci®cation, Y-4, follows Berger and Mester (1997a) and uses the three traditional
outputs, but includes the credit equivalent of OBS items as a ®xed netput z. 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
The credit equivalent of o-balance sheet items are reported by risk category in Part II of
schedule HC-I of the FR Y-9C report. The transformation to credit equivalent values is described
in the Federal Reserve BoardÕs Capital Adequacy Guidelines for Bank Holding Companies. For
example, direct credit substitutes are converted at 100%, transaction related contingencies are
converted at 50%, and short-term, self-liquidating, trade-related contingencies are converted at
20%. If a BHC does not have all of these items, the minimum value of the credit equivalent sum for
each year is assigned to prevent taking logs of a zero value.
K.J. Stiroh / Journal of Banking & Finance 24 (2000) 1703±1745
1717
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 augments P-1
with net non-interest income de®ned above. P-3 augments P-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 to P-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 concentrated 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 mean C/A declined. A possible source of improvement 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 explanatory 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.
15
Note that both net non-interest income and OBS items cannot be included in the same
regression since the associated revenues overlap.
1718
K.J. Stiroh / Journal of Banking & Finance 24 (2000) 1703±1745
(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
lnC G X
2
X
i1
t 1991; . . . ; 1997;
1
ln pi =p3 sit t s1 t s2 t2 lne;
2
4
where the G(X) function includes all translog terms in Eq. (3) except the ®rstorder input price terms and t is a simple time trend that is set equal to 0 in 1991
and then grows linearly.
The s parameters capture the impact of changes in costs that are not explicitly 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
#
"
2
X
o ln C
ÿ
5
ln pi =p3 sit s1 s2 t ;
mt ÿ
ot
i1
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 of mt for 1991±1997.
Note that Eqs. (4) and (5) impose a very speci®c structure on the production
technology with the assumption that only the input price slopes and intercepts
vary over time. All other slope parameters are forced to be constant
throughout the 1990s. In addition, there is no explicit role for ineciency as all
K.J. Stiroh / Journal of Banking & Finance 24 (2000) 1703±1745
1719
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
lnC G X ai
2
X
i1
t 1991; . . . ; 1997:
1
ln pi =p3 sit t s1 t s2 t2 lne;
2
6
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 through ai , 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. 16 Berger (1993) discusses the potential bias in scale economy estimates if the unobserved variable is correlated to cost function regressors. For
example, if X-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 the ai terms. If ai is a ®xed parameter for each BHC that simply shifts
the common cost function, then a ``®xed eects'' methodology is appropriate
and ai can be estimated like any other parameter. 17 That is, persistent dierences across BHCs are re¯ected in dierences in the intercepts, which represent
the unobserved eects. This approach assumes that the ai are 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'' methodology, on the other hand, views ai as a random, though permanent, variable that
is drawn from a distribution and assumes that ai is uncorrelated with the other
explanatory variables. Under this interpretation, the sample is viewed as representative 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.
The ®xed eect estimator is equivalent to a ``within estimator'' from an ordinary least squares
regression of deviations from the mean for each BHC.
18
See Chamberlain (1984) for details.
17
1720
K.J. Stiroh / Journal of Banking & Finance 24 (2000) 1703±1745
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 prore
ductivity growth, mfe
t and mt , 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
Total cost change
ft1 X t1 ft1 X t ft1 X t
;
ft X t
ft1 X t ft X t
7
where Xt represents all components of the cost function in Eq. (3) and ft
represents the cost function available to BHCs, both at time t.
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 Xt 1 , for a given cost function, ft1 . The second term represents 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 second 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 and ft . The mean value of each variable in Eq. (3) for all BHCs in
each year was then used for Xt 1 and Xt . By combining the parameter estimates 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
Y-2 speci®cation. The annual point estimates and standard errors for each
1721
K.J. Stiroh / Journal of Banking & Finance 24 (2000) 1703±1745
Table 3
Average productivity growth rates, 1991±1997a
Output speci®cation
Pooled
analysis
Fixed
eects
Random
eects
Cost
decomposition
Y-1: business loans, consumer loans,
securities
Y-2: business loans, consumer loans,
securities,
net non-interest income
Y-3 and Y-4: business loans, consumer
loans, securities, o-balance sheet items
as an output or as a ®xed netput
0.44
0.47
0.45
0.32
0.42
0.50
0.47
0.05
0.44
0.46
0.45
0.31
a
All 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.
econometric method and each output speci®cation are reported in Tables 3a±
c. 19 Results for the Y-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 correspond 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 3a
Annual estimates of productivity growth, 1991±1997,
Y-1: business loans, consumer loans, securitiesa
Year
Pooled analysis
Fixed eect
Random eect
1992
0.242
(0.225)
0.596
(0.177)
0.614
(0.120)
0.280
(0.092)
0.426
(0.164)
0.473
(0.248)
)0.438
(0.114)
0.129
(0.083)
0.453
(0.052)
0.529
(0.049)
0.900
(0.083)
1.223
(0.125)
)0.302
(0.111)
0.214
(0.081)
0.472
(0.051)
0.466
(0.049)
0.781
(0.082)
1.041
(0.124)
0.438
0.466
0.445
1993
1994
1995
1996
1997
Mean
Cost decomposition
0.236
)0.771
0.016
1.979
0.348
0.089
0.316
a
Standard errors are in parentheses for the econometric estimates. Estimation details are given in
Section 4. All growth rates are percentages.
19
Note that productivity growth rate from the cost decomposition cannot be estimated for 1991
since that requires actual cost data for 1990. To be consistent, Tables 3a±c report the various
productivity growth rate estimates, mt , from 1992 onward.
1722
K.J. Stiroh / Journal of Banking & Finance 24 (2000) 1703±1745
Table 3b
Annual estimates of productivity growth, 1991±1997,
Y-2: business loans, consumer loans, securities, net non-interest incomea
Year
1992
1993
1994
1995
1996
1997
Mean
Fixed eect
Random eect
Cost decomposition
)0.683
(0.215)
0.024
(0.163)
0.414
(0.105)
0.474
(0.084)
0.951
(0.151)
1.351
(0.231)
Pooled analysis
)0.449
(0.111)
0.139
(0.081)
0.479
(0.050)
0.563
(0.048)
0.951
(0.081)
1.289
(0.123)
)0.418
(0.109)
0.158
(0.079)
0.472
(0.050)
0.516
(0.048)
0.886
(0.081)
1.201
(0.122)
)0.802
0.422
0.495
0.469
)1.784
)0.741
2.919
0.396
0.334
0.054
a
Standard 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 and Y-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
1992
0.219
(0.226)
0.587
(0.179)
0.615
(0.122)
0.288
(0.092)
0.446
(0.163)
0.504
(0.247)
)0.429
(0.114)
0.131
(0.083)
0.451
(0.052)
0.524
(0.049)
0.890
(0.083)
1.208
(0.125)
)0.289
(0.111)
0.221
(0.081)
0.475
(0.051)
0.465
(0.049)
0.774
(0.082)
1.029
(0.124)
0.443
0.463
0.446
1993
1994
1995
1996
1997
Mean
Cost decomposition
0.075
)0.727
0.126
2.005
0.348
0.061
0.315
a
Standard errors are in parentheses for the econometric estimates. Estimation details are given in
Section 4. All growth rates are percentages.
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
K.J. Stiroh / Journal of Banking & Finance 24 (2000) 1703±1745
1723
Fig. 3. Annual productivity growth for alternative econometric methods for Y-3 and Y-4,
1992±1997.
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. An F-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 assumption 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 uncorrelated 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 example, 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.
1724
K.J. Stiroh / Journal of Banking &
www.elsevier.com/locate/econbase
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 alternative 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. Estimates of both productivity growth and economies of scale are robust across traditional
and non-traditional output speci®cations. Despite the overall success, however, substantial 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
*
Tel.: +1-212-720-6633; fax: +1-212-720-8363.
E-mail address: [email protected] (K.J. Stiroh).
0378-4266/00/$ - see front matter Ó 2000 Elsevier Science B.V. All rights reserved.
PII: S 0 3 7 8 - 4 2 6 6 ( 9 9 ) 0 0 1 0 1 - 6
1704
K.J. Stiroh / Journal of Banking & Finance 24 (2000) 1703±1745
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 organizations 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 performance 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 traditional lending activities and non-traditional activities like fee income or obalance 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 commercial banks and this study, as far as is known, represents the ®rst comprehensive 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.
Despite the overall improvements, these estimates suggest that BHCs operated with substantial ineciency throughout the 1990s. Roughly 10% of
costs during the 1990s can be attributed to cost ineciency and 30±40% of
potential pro®ts are foregone due to pro®t ineciency. A comparison of alternative output speci®cations shows that failure to account for non-traditional
activities leads pro®t eciency, but not cost eciency, to be substantially
understated for BHCs with more than $30 billion in assets. This suggests that
previous research that failed to include non-traditional activities likely understates pro®t eciency for large ®nancial institutions. Finally, there is much
K.J. Stiroh / Journal of Banking & Finance 24 (2000) 1703±1745
1705
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 substantial BHC-speci®c ineciencies. If the current consolidation trend continues, 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-in1
See Berger et al. (1995) and FDIC (1997) for a thorough analysis of the commercial bank
industry in the 1980s and early 1990s.
1706
K.J. Stiroh / Journal of Banking & Finance 24 (2000) 1703±1745
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). 2 BHCs 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, 3 and 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 authorized 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 Monetary 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).
3
Some BHCs that already owned subsidiary banks in multiple states were grandfathered and
allowed to remain in operation.
K.J. Stiroh / Journal of Banking & Finance 24 (2000) 1703±1745
1707
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 framework 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 restrictions, 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 restricted for individual banks, e.g., BHCs can own separately capitalized subsidiaries 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 operated continuously from 1991 to 1997 using data from the consolidated FR Y9C reports. 5 These 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
The analysis began with 746 BHCs that operated continuously between December 1991 and
December 1997. Since these data are measured with error, however, a procedure based on Berger
and Mester (1997a, p. 915) to drop questionable input price observations (more than 3.5 standard
deviations from the annual mean) was implemented. This left a core sample of 661 BHCs with
reasonable data for each year from 1991 to 1997.
1708
K.J. Stiroh / Journal of Banking & Finance 24 (2000) 1703±1745
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 continuously 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/A or average ROA for
1991±1997 to explore the dispersion of performance both across and within size
classes.
Fig. 1 graphs the mean C/A for the highest quintile, the entire size class, and
the lowest quintile for each size class, while Fig. 2 shows the same breakdown
for ROA. 6 These charts show wide dispersion within every size class for both
C/A and ROA, with a slight trend towards lower C/A for larger size classes,
except for the very largest BHCs, which show an increase in C/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 variation in performance and are suggestive of some scale economies for BHCs. The
question of economies of scale and more precise estimates of relative performance are addressed in the following sections.
6
Berger and Humphrey (1992) report substantial dispersion in costs per asset for commercial
banks in the 1980s.
Year
1991
1992
1993
1994
1995
1996
1997
a
Number of
Obs.
Total
assets
Equity
capital
Variable
costs
Variable pro®ts
P-1 and
P-4
P-2
P-3
661
661
661
661
661
661
661
2797.8
3097.6
3357.8
3692.8
4130.1
4728.1
5303.6
191.4
234.9
267.9
285.3
331.8
387.7
427.4
177.4
147.9
138.5
158.4
211.4
233.9
261.6
54.3
66.6
70.3
74.9
80.3
91.9
98.4
89.5
106.7
116.2
122.6
135.9
162.7
182.1
57.6
70.3
74.8
78.2
84.1
96.9
104.1
ROA
ROE
C/A
0.80
1.04
1.14
1.13
1.17
1.23
1.24
10.43
13.30
13.75
13.38
13.31
13.59
13.64
6.25
4.96
4.31
4.29
4.88
4.84
4.89
All 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/A is
variable costs divided by total assets. ROA, ROE, and C/A are percentages.
K.J. Stiroh / Journal of Banking & Finance 24 (2000) 1703±1745
Table 1
Trends in bank holding company performance, 1991±1997a
1709
1710
K.J. Stiroh / Journal of Banking & Finance 24 (2000) 1703±1745
Fig. 1. Mean C/A and Hi and Low C/A quintiles by size class, 1991±1997.
Fig. 2. Mean ROA and Hi and Low ROA quintiles by size class, 1991±1997.
3. General approach ± BHCs and production concepts
There is a large literature on productivity and eciency of ®nancial institutions and this paper does not attempt to summarize that work. 7 This papers
simply follows the general methodologies and utilizes panel and pooled
methods to estimate the rate of productivity growth, the degree of scale
7
Berger and Humphrey (1997) provide a comprehensive review of the empirical literature on
®nancial institutions.
K.J. Stiroh / Journal of Banking & Finance 24 (2000) 1703±1745
1711
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 important 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-management unit. Akhavein et al. (1997, p. 18) argue that managers will coordinate
activities and optimize production choices with respect to the overall institution. 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 meaningful. 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.
8
Other earlier research that examines BHCs includes Grabowski et al. (1993) and Newman and
Shrieves (1993).
1712
K.J. Stiroh / Journal of Banking & Finance 24 (2000) 1703±1745
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 standard 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
C f 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 outputs), 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
P f p; y; z; m; p; eP ; t;
2
where p is BHC-speci®c pro®t eciency and eP 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 evidence 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
9
Berger and Mester (1997a) present several additional arguments why the alternative pro®t
function may be preferable, e.g., quality dierences, semi-®xed outputs, imperfect markets, and
large errors in price measurement.
K.J. Stiroh / Journal of Banking & Finance 24 (2000) 1703±1745
1713
Third, all estimation was based on a parametric approach in general and the
translog functional form in particular. 10 For a cost function with I inputs, J
outputs, and two ®xed netputs, the basic translog speci®cation used is
ln C= z2 pI a0
Iÿ1
J
X
X
ai ln pi =pI
bj ln yj =z2
i1
J X
J
X
j1
/ij ln yj =z2 ln yj =z2
i1 j1
Iÿ1 X
Iÿ1
X
dij ln pi =pI ln pj =pI
i1 j1
Iÿ1 X
J
X
hij ln pi =pI ln yj =z2 c1 ln z1 =z2
i1 j1
2
c2 ln z1 =z2
Iÿ1
X
ki ln pi =pI ln z1 =z2
i1
J
X
2
uj ln yj =z2 ln z1 =z2 q1 ln v1 q2 ln v1
j1
lne;
3
where ln C= z2 p3 and ec are replaced by ln P= z2 p3 1
abs Pmin = p2 z3 and eP for the alternative pro®t function estimates. Note
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 additional 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.
10
See Bauer et al. (1998) for a detailed comparison of parametric and non-parametric
techniques.
1714
K.J. Stiroh / Journal of Banking & Finance 24 (2000) 1703±1745
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 /ji and dij dji ) of the cost
and pro®t functions are also imposed. Costs, pro®ts, and all quantities (variable 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 nontraditional outputs, which is discussed in detail below. Table 2 provides summary 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 (including 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'' activities are growing over time and concentrated in the largest institutions, failure to
account for them may lead to incorrect conclusions.
11
Berger and Mester (1997a, p. 918) discuss this transformation and the economic interpretation
of scaling by equity capital. Note also that predicted costs and pro®ts are calculated by
exponentiating the ®tted value from the log speci®cation and then multiplying by the scaling
factors. Since this adjustment is non-linear, average predicted values are multiplicatively adjusted to
equal actual mean values when needed.
1715
K.J. Stiroh / Journal of Banking & Finance 24 (2000) 1703±1745
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 and P-4
P-2
P-3
98.4
182.1
104.1
394.2
827.1
434.1
)89.0
1.1
)41.7
4,958.0
1,007.0
5,650.0
Variable input prices
Purchased funds
Core deposits
Labor
4.68
3.29
37.70
0.77
0.59
7.73
0.03
1.00
3.79
8.99
4.89
78.76
Variable output quantities
Business loans
Consumer loans
Securities
Net non-interest income (Y-2)
O-balance sheet items (Y-3)
572.2
2774.1
1877.5
83.7
840.1
2609.7
11,674.3
10,268.5
466.7
6730.9
0.3
15.2
18.9
0.6
0.1
33,431.0
143,403.0
193,287.0
7937.2
137,607.1
Fixed netputs
Physical capital
Equity capital
O-balance sheet items (Y-4)
79.8
427.5
840.1
340.5
1807.4
6730.9
0.1
5.0
0.1
4147.9
21,742.0
137,607.1
5303.6
24,205.9
37.6
365,520.9
Total assets
a
Variable 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®cation Y-1 includes business loans, consumer
loans, and securities as outputs and physical capital and equity capital as ®xed netputs. Other
speci®cations include Y-1 plus the designated output quantity or ®xed netput.
One set of non-traditional activities includes the sources of non-interest
income, e.g., ®duciary activities, trading, and activities that generate other noninterest 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
12
See English and Nelson (1998) for a discussion of the importance of dierent types of
o-balance sheet items.
1716
K.J. Stiroh / Journal of Banking & Finance 24 (2000) 1703±1745
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 recently 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 traditional measures of bank outputs and de®nes the variable output vector to
include three outputs ± business loans, consumer loans, and securities (all assets 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 exchange and interest rate contracts) as a fourth output. 13 The ®nal speci®cation, Y-4, follows Berger and Mester (1997a) and uses the three traditional
outputs, but includes the credit equivalent of OBS items as a ®xed netput z. 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
The credit equivalent of o-balance sheet items are reported by risk category in Part II of
schedule HC-I of the FR Y-9C report. The transformation to credit equivalent values is described
in the Federal Reserve BoardÕs Capital Adequacy Guidelines for Bank Holding Companies. For
example, direct credit substitutes are converted at 100%, transaction related contingencies are
converted at 50%, and short-term, self-liquidating, trade-related contingencies are converted at
20%. If a BHC does not have all of these items, the minimum value of the credit equivalent sum for
each year is assigned to prevent taking logs of a zero value.
K.J. Stiroh / Journal of Banking & Finance 24 (2000) 1703±1745
1717
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 augments P-1
with net non-interest income de®ned above. P-3 augments P-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 to P-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 concentrated 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 mean C/A declined. A possible source of improvement 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 explanatory 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.
15
Note that both net non-interest income and OBS items cannot be included in the same
regression since the associated revenues overlap.
1718
K.J. Stiroh / Journal of Banking & Finance 24 (2000) 1703±1745
(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
lnC G X
2
X
i1
t 1991; . . . ; 1997;
1
ln pi =p3 sit t s1 t s2 t2 lne;
2
4
where the G(X) function includes all translog terms in Eq. (3) except the ®rstorder input price terms and t is a simple time trend that is set equal to 0 in 1991
and then grows linearly.
The s parameters capture the impact of changes in costs that are not explicitly 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
#
"
2
X
o ln C
ÿ
5
ln pi =p3 sit s1 s2 t ;
mt ÿ
ot
i1
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 of mt for 1991±1997.
Note that Eqs. (4) and (5) impose a very speci®c structure on the production
technology with the assumption that only the input price slopes and intercepts
vary over time. All other slope parameters are forced to be constant
throughout the 1990s. In addition, there is no explicit role for ineciency as all
K.J. Stiroh / Journal of Banking & Finance 24 (2000) 1703±1745
1719
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
lnC G X ai
2
X
i1
t 1991; . . . ; 1997:
1
ln pi =p3 sit t s1 t s2 t2 lne;
2
6
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 through ai , 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. 16 Berger (1993) discusses the potential bias in scale economy estimates if the unobserved variable is correlated to cost function regressors. For
example, if X-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 the ai terms. If ai is a ®xed parameter for each BHC that simply shifts
the common cost function, then a ``®xed eects'' methodology is appropriate
and ai can be estimated like any other parameter. 17 That is, persistent dierences across BHCs are re¯ected in dierences in the intercepts, which represent
the unobserved eects. This approach assumes that the ai are 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'' methodology, on the other hand, views ai as a random, though permanent, variable that
is drawn from a distribution and assumes that ai is uncorrelated with the other
explanatory variables. Under this interpretation, the sample is viewed as representative 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.
The ®xed eect estimator is equivalent to a ``within estimator'' from an ordinary least squares
regression of deviations from the mean for each BHC.
18
See Chamberlain (1984) for details.
17
1720
K.J. Stiroh / Journal of Banking & Finance 24 (2000) 1703±1745
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 prore
ductivity growth, mfe
t and mt , 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
Total cost change
ft1 X t1 ft1 X t ft1 X t
;
ft X t
ft1 X t ft X t
7
where Xt represents all components of the cost function in Eq. (3) and ft
represents the cost function available to BHCs, both at time t.
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 Xt 1 , for a given cost function, ft1 . The second term represents 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 second 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 and ft . The mean value of each variable in Eq. (3) for all BHCs in
each year was then used for Xt 1 and Xt . By combining the parameter estimates 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
Y-2 speci®cation. The annual point estimates and standard errors for each
1721
K.J. Stiroh / Journal of Banking & Finance 24 (2000) 1703±1745
Table 3
Average productivity growth rates, 1991±1997a
Output speci®cation
Pooled
analysis
Fixed
eects
Random
eects
Cost
decomposition
Y-1: business loans, consumer loans,
securities
Y-2: business loans, consumer loans,
securities,
net non-interest income
Y-3 and Y-4: business loans, consumer
loans, securities, o-balance sheet items
as an output or as a ®xed netput
0.44
0.47
0.45
0.32
0.42
0.50
0.47
0.05
0.44
0.46
0.45
0.31
a
All 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.
econometric method and each output speci®cation are reported in Tables 3a±
c. 19 Results for the Y-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 correspond 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 3a
Annual estimates of productivity growth, 1991±1997,
Y-1: business loans, consumer loans, securitiesa
Year
Pooled analysis
Fixed eect
Random eect
1992
0.242
(0.225)
0.596
(0.177)
0.614
(0.120)
0.280
(0.092)
0.426
(0.164)
0.473
(0.248)
)0.438
(0.114)
0.129
(0.083)
0.453
(0.052)
0.529
(0.049)
0.900
(0.083)
1.223
(0.125)
)0.302
(0.111)
0.214
(0.081)
0.472
(0.051)
0.466
(0.049)
0.781
(0.082)
1.041
(0.124)
0.438
0.466
0.445
1993
1994
1995
1996
1997
Mean
Cost decomposition
0.236
)0.771
0.016
1.979
0.348
0.089
0.316
a
Standard errors are in parentheses for the econometric estimates. Estimation details are given in
Section 4. All growth rates are percentages.
19
Note that productivity growth rate from the cost decomposition cannot be estimated for 1991
since that requires actual cost data for 1990. To be consistent, Tables 3a±c report the various
productivity growth rate estimates, mt , from 1992 onward.
1722
K.J. Stiroh / Journal of Banking & Finance 24 (2000) 1703±1745
Table 3b
Annual estimates of productivity growth, 1991±1997,
Y-2: business loans, consumer loans, securities, net non-interest incomea
Year
1992
1993
1994
1995
1996
1997
Mean
Fixed eect
Random eect
Cost decomposition
)0.683
(0.215)
0.024
(0.163)
0.414
(0.105)
0.474
(0.084)
0.951
(0.151)
1.351
(0.231)
Pooled analysis
)0.449
(0.111)
0.139
(0.081)
0.479
(0.050)
0.563
(0.048)
0.951
(0.081)
1.289
(0.123)
)0.418
(0.109)
0.158
(0.079)
0.472
(0.050)
0.516
(0.048)
0.886
(0.081)
1.201
(0.122)
)0.802
0.422
0.495
0.469
)1.784
)0.741
2.919
0.396
0.334
0.054
a
Standard 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 and Y-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
1992
0.219
(0.226)
0.587
(0.179)
0.615
(0.122)
0.288
(0.092)
0.446
(0.163)
0.504
(0.247)
)0.429
(0.114)
0.131
(0.083)
0.451
(0.052)
0.524
(0.049)
0.890
(0.083)
1.208
(0.125)
)0.289
(0.111)
0.221
(0.081)
0.475
(0.051)
0.465
(0.049)
0.774
(0.082)
1.029
(0.124)
0.443
0.463
0.446
1993
1994
1995
1996
1997
Mean
Cost decomposition
0.075
)0.727
0.126
2.005
0.348
0.061
0.315
a
Standard errors are in parentheses for the econometric estimates. Estimation details are given in
Section 4. All growth rates are percentages.
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
K.J. Stiroh / Journal of Banking & Finance 24 (2000) 1703±1745
1723
Fig. 3. Annual productivity growth for alternative econometric methods for Y-3 and Y-4,
1992±1997.
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. An F-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 assumption 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 uncorrelated 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 example, 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.
1724
K.J. Stiroh / Journal of Banking &