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TECHNICAL CHANGE, REGULATION, A N D
ECONOMIES OF SCALE F O R L A R G E C O M M E R C I A L
BANKS: A N APPLICATION O F A M ODIFIED VERSION
O F SHEPHARD'S L E M M A
Douglas D. Evanoff, Philip R. Israilevich
and Randall C. Merris
Working Paper Series
Issues in Financial Regulation
Research Department
Federal Reserve Bank of Chicago
June, 1989 (WP-89-11)
DRAFT
Technical Change, Regulation, and
Economies of Scale For Large Commercial Banks:
An Application of a Modified Version of Shephard's Lemma
by
Douglas D. Evanoff *
Philip R. Israilevich
and
Randall C. Merris
*The authors are economists at the Federal Reserve Bank of
Chicago. Individually they are also affiliated with DePaul
University, the University of Illinois-Urbana, and the Asian
Development Bank, respectively. Helpful comments and
suggestions were provided by Herbert Baer, Jeffrey Brown, and
Larry Mote. Betsy Dale provided helpful assistance in data
collection. The views expressed are those of the authors and
may not be shared by others, including the Federal Reserve Bank
of Chicago or the Federal Reserve System.
R e l a t i v e Price Efficiency, T e c h n i c a l Change, and
Economies of Scale For Large C o m m e r c i a l Banks
Recent
additions
to
the
c o m m e r c i a l b a n k i n g have
functional
forms
scale
bank
of the
economies
role
resu l t
studies
re c e n t
bank
neoclassical
that
this
Banking
facets
firms
ma y not
find that
levels.
The
should be
decisions
the basis
conce r n i n g
decis i o n s
the
for w e i g h i n g
may grant
Pot e n t i a l
a more
problems
perhaps
duality
theory
Mor e
to g e n e r a t e
e x t e nsive
evidence
to exten s i v e
regulation
the p o s s i b i l i t y
subject
a
in
exists
p r a c t i c e d by r e g u l a t e d
1
as a
a s s u m p t i o n of
However,
occur.
exists
specifically,
input pric e s
cost m i n i m i z a t i o n
s i g nificant
the m a j o r p r o b l e m with
to m a rket
raising
cost
e x c l u s i o n of r e l e v a n t
resp e c t
subj e c t
of operations,
consistent with
as
is m e t h o d o l o g i c a l .
the b e h a v i o r
are
cost
f u n c t i o n b a s e d on the m a i n t a i n e d
markets.
is not
generally
economies
However,
have u t i l i z e d
cost m i n i m i z a t i o n wit h
competitive
studies
of r e s trictions
are
s e l e c t i o n and
cost
costs
low output
literature
cost studies
studies
and scope,
at r e l a t i v e l y
than merited.
e x p l a n a t o r y variables.
previous
of scale
on b a n k
that
in
and expansion.
existing
of sample
effect
on p r o d u c t i o n
t h e o r y and flexible
in b a n k r e g u l a t o r y
in b a n k r e g u l a t o r y
to past
d uality
empirical
implications
acquisitions
Use
the
The
consideration
literature
e c onomies
are e x h a u s t e d
resulting policy
little
and
expansion.
economies
given
incorporated
to e v a l u a t e
c o m p e t i t i v e viability,
on g e o g r a p h i c
ex t e n s i v e
s u ggesting
firms.
in n e a r l y
all
that b e h a v i o r
to m a r k e t
input prices
2
The p u r p o s e
large b anks
of this
utilizing
standard neoclassical
g e n e r a l i z e d model
shadow
cost
is s u p e r i o r
there
is also
input p r ices
w h i c h may
a statistical
could r e sult
an d other
inappropriate
banks
and the more
suggest
that
for m o d e l i n g
The
to alter
Thus,
the
estim a t e s
results
traditional
found
neoclassical
We
altered.
the
to see
on shadow
factor
Each
of
role
these
of
shares,
found w h e n m i n i m i z i n g
cost
of
aspects
of b o t h
of
the
n e o c l a s s i c a l model.
the n e o c l a s s i c a l
cost
the p r o d u c t i o n b e h a v i o r
framework
of the
imposed by r e g ulation,
in p r e v i o u s
if
different measures
the co n t e x t
to shad o w
of the various
to
generalized
Behavior based
restrictive
subject
the
The
re s p e c t
test
generally neglected
constraints
cost m i n i m i z a t i o n
shown
The
those
subsumes
in the p r o d u c t i o n
of substitution,
is e v a l u a t e d w i t h i n
analyzed.
resulting
than
for
prices
or economic v i e w p o i n t
c ould also be
g e n e r a l i z e d m odel
results
distortions
elasticities
to m a r k e t prices.
bank production
that
case.
from m a r k e t
difference.
e conomic m e a s u r e s
The
deviate
in s i g n i f i c a n t l y
of scale,
change
function
to the n e o c l a s s i c a l model.
economies
technical
e s t i mates
for cost m i n i m i z a t i o n w i t h
F rom a t h e o r e t i c a l
model
cost
f u n c t i o n as a s pecial
of r e g u l a t i o n - i n d u c e d
process.
subject
is to generate
a g e n e r a l i z e d cost
allows
input prices
because
study
b ank cost
large
and the
input prices,
e l e ments
of b a n k
studies
f r a m e w o r k may be biased.
is
are
costs.
employing
the
3
The next
s tudies
and
section b r i e f l y
introduces
reviews
the l i t e r a t u r e
the m o t i v a t i o n
for the
introduces
the
g e n e r a l i z e d cost model,
app l y
are
discussed
this
detailed
in S e ction 4.
discusses
1.
the
in S e c t i o n
The
implic a t i o n s
final
of the
study.
and the
3.
The
on b a n k cost
data
Sect i o n 2
to w h i c h we
empirical
sect i o n draws
results
conclusions
are
and
findings.
B A C K G R O U N D AND M O T I V A T I O N
Many
of the
Cobb-Douglas
a ra t h e r
1965,
cost
Wit h
of recent
account
studies
range
the
development
the p o t e n t i a l
m u l t i -p r o d u c t production,
effects.
scale
These
output
are
(Benston,
Humphrey
1987,
and M a r s h a l l
found
studies
economies
laws
These
Hanweck,
1984).
studies
data
Analysis
(FCA)
Program.
include
a ver y
from the
average
of scope
significant
to p r o d u c e
Federal
W hile
1982,
1968,
cost
forms
a
into
curves,
as scale
any b e n e f i t s
low levels
Berger,
from
of
Hanweck,
and Gilligan,
diseconomies
at single
over
Benston
taking
as well
found that
1984,
Smirlock
have been
offices
by unit
and Humphrey).
analyzed relatively
utilized
samples
for U - s h a p e d
and H u m p h r e y
Hanweck,
economies
functional
e x h a u s t e d at r e l a t i v e l y
constrained
(Berger,
scale
r e e v a l u a t e d b a n k costs
and e c o nomies
In fact,
the
and M u r p h y
of flexible
g e n e r a l l y have
fully
utilized
found
(Bell
G i l l i g a n and S m i r l o c k
for banks
banking
of output
studies have
directly
of b a n k costs
f u n c t i o n and g e n e r a l l y
substantial
1972).
number
early
Rese r v e
rich
small banks
System's
in cost
l i m i t e d numb e r
and
in most
Functional
allocation
of banks
which
cases
Cost
detail,
are not
FCA
4
representative
of
insufficient
of the
size
multicollinearity
forms,
which
( H e g gestad and Mingo,
to g e n e r a t e
resulting
and exclude
are most
industry
results
the use
from
not
of f l e x i b l e
the v e r y banks
likely
to be
1978),
(those
involved
may be
d e t e r i o r a t e d by
over
function
$1 b i l l i o n
in a c q u i s i t i o n s
in assets)
and m a rket
e x p a n s i o n .1
Analyses
pr e v a l e n t .
of costs
Add i t i o n a l l y ,
the
role
the
significant
of technical
incorporated
(1984)
and H u n t e r
co u l d be
and Timme
and find s i g n i f i c a n t
of technical
important
Most
(1932)
change
of the b a n k cost
in d u a l i t y
and S h e p h a r d
functional
bank
there
costs,
still be
too
conditions
the
function.
the
shares
also
large
evaluated
the
it to be
scale
1980s hav e
duality
have p r o d u c e d
that
Duality
the
effects.
utilized
derived
in D i e w e r t
theory
and the
advances
functional
implies
is e q u i v a l e n t
Additionally,
can be
consider
and s u m m a r i z e d
f u n c t i o n pro v i d e s
production
HT
Shaffer
as d e v e l o p e d and r e f i n e d by H oteling
Wh i l e
forms
that
HT)
and to e n h a n c e
in the
1970),
is e v i d e n c e
cost
p r o d u c t i o n process
fact o r
theory
restrictive.
economies.
studies
(1986).
of f l e x i b l e
Stud i e s by
hereafter
costs
In light of
the p o t e n t i a l
on p r o d u c t i o n and f o u n d
(1953,
and J o r g e n s o n
in recent y ears
(1986;
scale
costs.
of
t e c h n o l o g y w h i c h have been
substantial.2
in d e t e r m i n i n g b a n k
developments
1974)
in e l e c t r o n i c
are not nea r l y as
total n e g l e c t
on b a n k p r o d u c t i o n
into b a n k o p e r a t i o n s
on b a n k costs
effect
c o m m e r c i a l b anks
there has b e e n a n ear
change
advances
effect
banks
for large
that u n d e r
u s e d may
certain
of the
to that p r o v i d e d by
given
that
dire c t l y via
the
adopt i o n
in m o d e l i n g
forms
a description
(1971,
the
c o n d i t i o n s hold,
differentiation
from
5
the
cost
function--Shephard's
generate
the dual
cost
c o m p e t i t i v e markets
output
level,
behaved
It
cost
still
trend
is h e a v i l y
geographic
limitations,
perspective
alter
beca u s e
the
illustrative
the
purposes
that
as
to compete
additional
magnitude
Thus,
in m a r g i n a l
Other
For
The
of the d i s t o r t i o n s
laws,
loan
accounts,
are
likely
from the
firm's
an a d d i tional
from w hat
example,
it w ould
assume
for
in a m a r k e t where
on d e p o s i t s
role
are
limi t e d by
of p h y s i c a l
capital
Office p r o l i f e r a t i o n may occur
and the p e r c e i v e d
the
effective
in d e t e r m i n i n g
While
the
w ill
r e t u r n on
p rice
true
account
rest r i c t i o n s
behavior.
inputs
different
the b a n k m a n a g e r will
constraints.
adjustments
of
of u t i l i z i n g
and prices
or c o n v e r s e l y
capital
usuary
constraints
a b a n k operates
affected.
input prices
cost
for deposits
is o b v i o u s l y
on c e r t a i n d e p o s i t
o p t i m u m choice
expanded.
in
requirements,
regulatory
levels.
hold
the b a n k i n g
limitations,
constraints.5
significantly
effective
in
to p r o d u c e well
conditions
reserve
significantly
m a y now be
will be
The
is a l l o w e d
expenditures,
these
interest
the m a r g i n a l
to b e l o w - m a r k e t
capital,
to
the p r e d e t e r m i n e d
conditions
and p r o d u c t
regulation
these
that
include
additional
limited branching
a means
by
only
s u p e r v i s e d and b e h a v i o r
allowable
of an input may be
be w i t h o u t
required
firm cost m i n i m i z a t i o n
toward d e r e gulation,
entry barriers.
significantly
unit
the
Restrictions
requirements,
and m a r k e t
conditions
functions.3
restrained.4
to
constrained
The
and c e r t a i n r e g u l a r i t y
Despite
industry
size
f u n c t i o n are
is s e riously d o u b t f u l
banking.
Lemma.
of the
or
for
similarly
direction
p r o d u c e d by b a n k i n g
the
lead to
and
restrictions
are
6
not
obvious,
there
is little
A t k i n s o n and H a l v o r s e n
r e a s o n to b e l i e v e
(1980;
regulation-induced distortions
neoclassical
electric
produce
cost
utility
factor
HT d i r e c t l y
structure
cost
the
on the
role
in b a n k i n g
found by AH,
we b e l i e v e
of technology.
then H T 's use
This may p a r t i a l l y
to be
c ounter
regulation
In the next
in s l i g h t l y
(1971),
more
Lovell
g eneral
is
shown
Lemma
(1983),
is use d
to be
a special
on the cost
effect
of this
if cost m i n i m i z a t i o n
constraints
of the
neoclassical
role
of their
is n e e d e d
in the
of
results which
is a more
for d i s t o r t i o n s
i n duced by
in cost m i n i m i z i n g behavior.
a model w h i c h has b e e n u t i l i z e d
(1980,
1984),
and Toda
La u and Yo t o p o u l o s
(1976,
1977).
It is
a modified version
in w h i c h cost m i n i m i z i n g b e h a v i o r
These prices
c r e a t e d by regulation.
is not binding.
the
However,
What
allows
forms by AH
and Sickles
scale
of o r g a n i z a t i o n
e x p l a i n some
change
on shadow input prices.
distortions
effect
change
than the n e o c l a s s i c a l model b e c a u s e
Shephard's
based
analyzed
estimates
se c t i o n we p r e s e n t
different
case
of
shown to
of cost para m e t e r s ,
of the r e s t r i c t i v e
intuitive.
and the r e s u l t i n g
the costs
cost m odel was
is a l t e r e d by r e g u l a t o r y
g e n e r a l b a n k cost model w h i c h
of
the
f u n c t i o n may p r o d u c e b i a s e d
technology.
Evaluating
of technical
They
and
tr a d i t i o n a l
elasticities.
the role
elasticities
offsetting.
f ound that
of the
t r a d i tional
estim a t e s
of c o m m e r c i a l banks.
structure
behavior
r e n d e r e d use
and p rice
evaluated
on scale
manner
companies,
shares,
h e r e a f t e r AH)
inappropriate.
significantly biased
effects,
chan g e
function
they are
of the
account
for
The n e o c l a s s i c a l
general
model
is
cost
whe n
f unction
regulation
7
2.
The
A G E N E R A L I Z E D M O D E L OF B ANK C O S T S - - T H E
Theoretical
Model
AH d e r i v e d
the
p r o d u c t i o n under
industry.
directly
sha d o w pri c e
regulatory
In m o d e l i n g
apply
pertinent
their
model
constraint
SP model,
is s u m m a r i z e d
to
of the
in this
cost m odel
production
output;
From
function;
the
rate
equ a l
the
we
include v a r i a b l e s
inclu s i v e
of our
section.6
firms
are
assumed
function
to m i n i m i z e
g iven by:
(1)
of input p r ices
and quantities,
is a w e l l - b e h a v e d n e o c l a s s i c a l
Z is a v e c t o r
of exoge n o u s
variables;
Q is
and \ is a L a g r a n g i a n multiplier.
i
marginal
to
/(X,Z)
ele c t r i c power
- H[/(X,Z)-Q]
P and X are m x 1 v e c t o r s
respectively;
it to
of large banks,
SP m o d e l
in the L a g r a n g i a n - c o n s t r a i n e d cost
L - P'X
and a p p l i e d
in the U.S.
augmented
Derivation
In the n e o c l a s s i c a l
where
(SP)
the p r o d u c t i o n b e h a v i o r
to banking.
modifications
costs
SHADOW-PRICE MODEL
first-order
conditions
of tec h n i c a l
ratio
for cost m i n i m i z a t i o n ,
substitution between
of prices
of the
two
inputs.
inputs
That
the
i and j is
is,
8
i / j - 1 , . . .m,
where
is the m a r g i n a l
the price
level
of input
of output as
inputs
can be
Assume
now
i.
Gi v e n
the
only
derived
L = P'X
conditions
exist.
of the
two
/
M
- f > hRh(P,X)
hl
=
/j
(3)
aris i n g
the m a r g i n a l
inputs.
S
from regulation,
From
i and j is equal
P1 +
=
The
f u n c t i o n to be m i n i m i z e d becomes:
for cost m i n i m i z a t i o n ,
prices
c o m b i n a t i o n of
costs.
constraints
inputs
and Pj is
the o p t i m a l
are L a g r a n g i a n multip l i e r s .
substitution between
effective
are
i,
and the p r e d e t e r m i n e d
constraints
- |»[/(X,Z)-Q]
Rh (h— l,...,n)
Kh (h-l,...,n)
constraint,
that a d d i t i o n a l
cost
of input
input prices,
to m i n i m i z e
Lagrangian-constrained
where
product
(2)
W
That
3*!
___________ h = l __________________
the
rate
to the
and
first-order
of technical
ratio
of
is,
P *
=
Pj + i ^ R j / a x j
M
PJ*
(4)
i / j =
where
P } is the
*
effective
or
shadow
price
of input
i.
9
In the
reduces
absence
of b i n d i n g
to the n e o c l a s s i c a l
technical
regulatory constraints,
condition whereby
s u b s t i t u t i o n equals
the
ratio
of
equation
the m a r g i n a l
market
prices
(4)
rate
of
of
inputs;
Pi*
i
This
and
special
case
is r e f e r r e d
is n e s t e d w i t h i n
The
the more
sh a d o w prices
Th e r e f o r e ,
of the
kj is an input-
proportionality.
all
general
inputs
Shadow-Price
are not
and f i r m - s p e c i f i c
As n o t e d by AH,
first-order
shadow-price
s h a d o w prices
kj — 1 for all
neoclassical
to as the M a r k e t - P r i c e
(SP)
directly
(1971)
(MP)
Model
Model.
observable.
and AH
(1984),
the
i * 1, . . . ,m,
i n t e r p r e t e d as
arbitrary
(5)
are a p p r o x i m a t e d by
Pi* - k t
Pi
can be
.m
1,
J
fol l o w i n g Lau and Y o t o p o l o u s
s h a d o w prices
where
/
i,
cost
equal
functions.
the
and the
the
factor
of
shadow-price
Taylor's
series
When regulation
approximations
expansions
of
is nonbinding,
r e s p e c t i v e m a r k e t prices,
s h a d o w cost
function.
(6)
f u n c t i o n redu c e s
i mplying
to the
10
Differing
from the n e o c l a s s i c a l
i n p u t - p r i c e variables,
the
cost
s h a d o w cost
function
function
only
in the
is given by
CS - CS(kP,Q,Z),
w h e r e kP is a v e c t o r
Applying
Shephard's
functions
of s h a d o w prices
Lemma
(1970),
of inputs.
the set of d e r i v e d
input demand
can be obtained:
3C5
3(k,P,)-
L
1
Using
(7)
equation
(8),
the
firm's
(8)
total
actual
cost
is
3Cr
P'X - I Pi
i, M 3 ( W
t
The
shadow
differentiation
M
1
Rearranging
factor-cost
shares
(9)
are
o b t a i n e d by
logarithmic
of Cs:
31nCiS
ainCkiP,)
equation
M,SCS
k,Pi
kjPjX,
1 .....m .
(10)
(10),
l,...,m,
(ID
11
and s u b s t i t u t i n g e q u a t i o n
(11)
into e q u a t i o n
(9)
gives,
(12)
11
=
Taking
logarithms,
A
c
“ M,S
lnCA - l n C S + I n S
il K i
=
Using
also be
equations
(11)
PiX,
1
Comparison
combination
of
the
equivalent
to
are
optimal
in response
factor-cost
,m
shares
can
that
the
observed
and optimal
and are d e t e r m i n e d by
the
observed
and o p t i m a l
of the
firm.
the
w h i c h may cause
The
to differ.
Thus,
to the e f f e c t i v e
function
of costs
input
or s h adow
is a more
to be m i n i m i z e d
The
the
SP model
the
o bserved
costs
and o b s e r v e d b e h a v i o r by a l l o w i n g
constraints
shadow cost
(14)
Models
the b e h a v i o r
the p r o d u c t i o n process.
Cost
equal
A c c o r dingly,
input prices
representation
M P
it is a s s u m e d
of a d d i t i o n a l
resulting
and
and d e t e r m i n e
differentiates
effective
S P
of inputs
input prices.
adopted
actual
1, •
M , V
In the MP model
effect
(12),
obtained,
Mi
Intuitive
and
(13)
are
SP model
for the
o b s e r v e d and
combination
input prices.
is
The
comprehensive
and
is
also
the
appropriate
allows
one
to
dual
12
calculate
prices,
the
the optimal
P.
cost
This
combination
d i f f e rences
conditions
the
procedure
resulting
differences
inputs
combination
is r e l e v a n t
the
are
regulatory
represent
SP mod e l
constraints.
produces
C , and s h a d o w
different.
and are us e f u l
optimizing behavior
cost,
directly
an example.
eff e c t
increases,
determined
to that
ma y
the
behavior.
to be
found
a c t ually
but
this
shadow
in other
Bankers
may
share
consider
lower
than
the market
in
illustrated
observe
that as
Regulation
However,
is
a result
viewing
may be misleading.
on c a p i t a l
in the
actually
true,
the more
in e v a l u a t i n g
in b anking;
obsc u r e d
the
can be
and ma y
to economize
are
are
interested
and shares
which
relevant
increases.
using
are
Cs estimates
interested
industries.
effect ma y be
all
This
shares
quantities,
at t e m p t
is
may be
capi t a l
input prices
significantly
the capi t a l
input prices,
increases,
to be
Ban k r e g u l a t o r s
if one
of r e g u l a t i o n on factor
regulation
therefore
expressions
of Shephard's
on o b s e r v e d data
observable,
or i n f l u e n c i n g b a n k behavior.
is
this
of results.
o b s e r v e d behavior.
evaluating
It
empl o y
sets
are b a s e d
of the
Bankers
We
C , estimates
incorporating
a l t h o u g h not
two
two
meaningful
observed
constraints.
a modified version
CA results
for f o r e c a s t i n g
i n f o r m a t i o n and,
similar
co m p e t i t i v e
in CA c o m p u t e d w i t h P and P*
d e r i v e d by u s i n g
actual,
conceptually
the
for m e a s u r i n g
in S e ction 4.
Although both
with
given observed
from p r o d u c t i o n u n d e r
cost of the b i n d i n g
E s t i m a t i o n of the
Lemma,
of
input
and those u n d e r b i n d i n g
Correspondingly,
measure
(unobserved)
observed
data.
influencing
effective
price
as r e g u l a t i o n
as
cost
of capital
a direct
result
13
of regulation.
and
the
3.
saving.7
policies,
EMPIRICAL
following
Z is
based
the
specified
H - Holding
on the
T - A time
Banks
3.
The
4.
The
to
AND
DATA SOURCES
include
the
are
trend
the
fol l o w i n g vari a b l e s :
struc t u r e
(H — 1 for b a n k s
companies;
to acco u n t
a single
(L)
in
H * 0 for ban k s
and c apital
function
in o n e - b a n k
and kK w o u l d be
is s p e c i f i e d
the
services
of two
Total
form,
a
continuous
shadow
cost
is spe c i f i e d
in shadow prices.
i d entical
is b e y o n d
change.
in t r a n s l o g
to an a r b i t r a r y
factors,
input,
technological
(K).
function.
linearly homogeneous
shad o w price
for
output by u t i l i z i n g
approximation
s p e c i f i c but as
kj (i * L,K),
firm,
the
are
across b a n k i n g
and time
scope
specifed
firms.
specific,
of our e m p i r i c a l
The
sh a d o w price
factor
for
the
s h adow price
factor
for capital,
banks,
companies),
s h adow cost
generality
o b s e r v e d data may be misguided.
adopted:
twice - d i f f e r e n t i a b l e
as
a c t ually be
or an e v a l u a t i o n of
specifications
comp a n y
labor
convenient
r e g u l a t i o n may
used
of b a n k offices,
prod u c e
inputs:
of capital
to large U.S.
multi-bank holding
holding
i.e.,
quantity
S h a d o w - P r i c e Model
empirical
B — Number
2.
of the
Bank r e g u l a t o r y policies,
SPECIFICATIONS
In a p p l y i n g
1.
the p r o d u c t
shadow price may decline,
capital
those
Thus,
labor,
kL, is set
as
input
Ideally,
but
kL
such
estimation.8
equal
to unity;
kK , is a p a r a m e t e r
to be
14
estimated.
The
estimated,
given
factor
kK .
cost
absolute values
that
shares
Therefore,
but
can test
The
total
we
e q u a tions
are h o m o g e n e o u s
ca n n o t
test
for r e l a t i v e
shadow cost
lnCs -• pQ + PQlnQ +
+
the
of kL and kR cannot be
for
total
of degree
for a bsolute
price
efficiency
function
in tra n s l o g
actual
zero
p rice
cost and
in kL and
efficiency,
(kL
kK) .
form
is
(1/2) PQq ( I n Q ) 2 + S ^ l n Q l n d c ^ )
( l / 2 ) 2 i j i l n ( k 1 i)ln(kj
I y j
P
Pj) + $TlnT +
+ 0QTlnQlnT + S ^ l n (k,P,) InT + pglnB +
+ X^ln^P,)
( 1/2 )<> (InT )2
tu
(1/2 )PBB(I n B )2
+ y ^ l n Q l n B + y ^ l n T l n B + S i i ^n (ki
y B
Pj) InB + PhH
+ yHQH l n Q + yHTH l n T + y ^ H l n B + S ^ l n (k,P,) H
i - L ,K
where
y
implies
— y
the
.
j - L ,K
Linear h o m o g e n e i t y
following
adding-up
(15)
in shadow p r ices
restrictions
on p a r a m eters:
SjPi ” 1 > S,y1 ” S,y1 ” Sj^iT ~ ^iy i “ ®
Q
B
H
= SjVtj - S 1 j 1 “ 0
S yJ
Shadow
by
cost
logarithmic
shares
for
the
differentiation
i >j “ L ,K .
translog
of C
c
(16)
specification
in e q u a t i o n
are
de ri v e d
(15):
31nCs
M,S ■ ain(k1 1
"
P )
= P + I j i ln(kj
i
y J
PJ) + y iQlnQ
+ y iTlnT + y i lnB + y ( H
B
H
i,j
- L,K.
(17)
15
F r o m equations
(13),
(15),
and
(17),
total
actual
lnCA - lnCS + I n { ^[P. + ^ ^ ^ ^ ( k j P j )
+ S v iTlnT + I V i lnB +
B
ln C s is given in e q u a t i o n
Using
are
e q u ations
(11),
}
(18)
- L,K,
(15).
(12),
(14),
and
(17),
actual
-
[Pt +
I jY ijl n ( k JP j)
2,[P,
+
+
y iQl n Q
ZjVijinCkjPj)
+
+
V 1Tl n T
Y 1Ql n Q
+
+
Y^lnB
Y 1Tl n T
+
Equation
with
(18)
classical
equations
because
err o r
a dditive
to be j o i n t l y
of the
terms
adding-up
for the
co n d i t i o n s
and actual
to
share
terms,
estimated.
One
shares
equation
(19),
constitute
share
share
equations.
equation
equations.
of share
the
We
esti m a t e
The
(19)
appended
the
set of
is dropped
matrix
from
the
and
of the
the
total
empirical
shadow-price
y 1HH ^
arbitrarily
equation deleted
labor
+
“ L,K.
system r e s u l t i n g
and j o i n t l y
labor-share
for
V ^ H l k , -1/
of the v a r i a n c e - c o v a r i a n c e
on the
kL — 1,
equ a t i o n s
disturbance
three - e q u a t i o n
the choice
normalization,
of the
singularity
c a p i t a l -share
invariant
and one
+
y iBl n B
i,j
cost
cost
g i v e n by
M t
A
the
are
+ V 1QlnQ
i,j
where
costs
actual
results
to the
factor.9
drop
are
16
Data
To
estimate
the years
the
banks
collected
in the U.S.
164 banks
The
data
additional
recent years
of data
in results
could be
consequences
e s t i m a t i o n methods,
The
Costs,
Fede r a l Re s e r v e
C, were
capital.
of
and
loans
of w h i c h
banking
was
are
were
accounted
price
for
also
PL, was
and a s s i g n e d
to each b a n k
Call
Report
measured
as
level wage
data as the
trend,
ratio
to p lant
sample
to the
capital,
data
source.
on labor
and
the dollar value
sheet
results,
The n u m b e r
some
of
Call R e p o r t
as was
Technical
the
progress
The
input
of Labor
collected
for each year
l o c a t i o n of its home
PR, was
of phys i c a l
and
specification.
similar
H.
and five
samples
T - 1,2,...,16.
trends were
is
differences
balance
from the B u r e a u
according
of p h y s i c a l
additions
Alternative
organization,
obtained
State
The price
de f i n e d as
taken from the
a time
Statis t i c s .
office.
was
in the a p p e n d i x . 1
0
company
for w i t h
labor,
Q,
c o n s i d e r e d and p r o d u c e d
B, was
of b a n k h o l d i n g
the m a j o r
some
c o n s i s t e d of
Therefore,
sum of e x p e n d i t u r e s
securities.
summarized
offices,
This
of d i f f e r e n t
the
eliminating
the d i f f e r e n t m o d e l
B a n k output,
inv e s t m e n t
output measures
as
the
after
set for
company
are more banks
included.
Call R e p o r t was
d e f i n e d as
physical
type
as well
set,
there
for
of a h o l d i n g
observations.
to that used by H T , a l t h o u g h
data
of data
in i n d i vidual years,
of 2,624
the
f u n c t i o n a pan e l
that c o n s i s t e d
final
of data p r o b l e m s
for a total
cost
w h i c h were m embers
entire period.
because
similar
generalized
1972-87 was
l a r g e s t banks
over
the
approximated
c a pital
and equipment,
from
expenditures
furniture,
and
17
physical
premises,
furniture
4.
r e p o r t e d b o o k value
of net b a n k premises,
equipment.
E M P I R I C A L RESULTS
section,
shadow-price
technical
Results
Basic
model
change,
and
Table
iterated
sample.1
1
for
in the
and OBHCs,
the c o e f f i c i e n t
and m a r k e t - p r i c e
sample
e s timates
(MP)
and for
for b o t h
models
imposed.
are met
While
for all
estim a t e s
that
the
general
SP m odel
are binding.
likelihood-ratio
the
test
strong r e j e c t i o n
quite
not
the
the p a r a m e t e r
globally
stable,
in our
similar.
are not
suggest
The
different
that b a n k m a n a g e r s
than
the
and g e n e r a l i z e d R 2
two models
less
the
e s t i m a t e d by
data po i n t s
reveals
is s i g n i f i c a n t l y
to be
indicates
(16)
appear
constraints
suggests
of scale,
respe c t i v e l y .
SP and MP m o dels
from the more
which
elasticities
Tests
condi t i o n s
the
the
de m a n d and s u b s t i t u t i o n are presented.
in MBHCs
The p a r a m e t e r
production
capital
and e s t i m a t e d
for all banks
in e q u a t i o n
scrutiny
sense,
input
nested within
seemingly unrelated regression method with
stability
.562,
hypotheses
tested,
Hypothesis
(SP)
restrictions
Results
and
1 contains
shadow-price
closer
are
of banks
Results
results
various
are r e p o r t e d
subsamples
the
the
and p h y s i c a l
In this
the
to
that
equivalent.
the
a d d i tional
e s t i m a t e d va l u e
from one
per c e i v e
price
of the MP model
for kK,
in a st a t i s t i c a l
the price
o b s e r v e d m a rket price.
of r elative
However,
Additio n a l l y ,
efficiency
relative
of phys i c a l
to
(kL k K-l)
the more
18
general
SP model,
T h e r efore,
as
except
sho w n by
for dir e c t
i n d i c a t i o n of the extent
c o m m o n l y u s e d MP model,
resu l t s
from
the
test results
c o m p a r i s o n of the
of the p o t e n t i a l bias
our
d i s c u s s i o n will
in Table
2.
two m o dels
p r o d u c e d by
concentrate
to get an
the
on the
the SP model.
S cale E c o n o m i e s
To
for returns
actual
total
test
cost w i t h
elasticity--was
to scale
respect
in the
to o u t p u t --i .e .,
d e r i v e d by d i f f e r e n t i a t i o n
the
the
actual
of e q u a t i o n
ztr'y i
Q
+ 0TQlnT + GgglnB + 9HqH
sha d o w cost m e a s u r e
equation
(20)
with
the
is given by
last
scale,
equal
model,
Table
then PQ * 1 and all
zero.
the r i g h t - s i d e
2.
Table
2 also
1 i k e 1 i h o o d -ratio
of h o m o g e n e i t y
eve r y w h e r e
other
and w i t h o u t
The h y p o t h e s i s
shows
the
test results
these
expression
constant
in
based
res t r i c t i o n s ,
returns
for
the
returns
in e q u a t i o n
to scale
r elevant p a r a m e t e r
stati s t i c s
and h o m o t h e t i c i t y
exhib i t s
coefficients
of c o n s t a n t
test
(20)
(21)
Likelihood-ratio
e s t i m a t e d wit h
rejected.
and
(18).
term deleted,
If the p r o d u c t i o n p r o c e s s
(20)
scale
i-L,K.
SE s _ 31nCs
01nQ
to
e l a s t i c i t y of
31nCA
' 'Q
P )
31nQ = Pq + PQQl n Q + 2 1> tl n (k 1 i
sea
The
SP model,
testing
of the p r o d u c t i o n
on the
are
SP
shown
in
is s t r ongly
restrictions
and r e j e c t i o n
function.
19
Estimated
scale
dat a points.
elasticities
Estimates
the
sample,
(2)
and
(3)
at the means
For
the
SP model,
elasticities,
As
shown
Tab l e
g r a n d means
of the
results
in Panel
less
returns
3 shows
for all
derived
data
(a)
observations
3,
on OBHCs
and for
cases,
displaying
decreasing
the m a j o r i t y
of them were
diseconomies
For
in states
comparative
located
coefficient
estimates
P anel
(c)
of Table
the
means
of the data
How e v e r ,
the
were
for all
to the
a test of the
two mo d e l s
(SE vs.
statistically
indicate
by H T .
0.69
close
The m e a n value
for OBHCs.
scale
and OBHCs.
were
of
than unity
three p e r c e n t
that
(b)
of the
to scale
studies
for
Panel
less
of the
r e v e a l e d that
states.
This
f o u n d greater
elasticities
scale
corresponding
for MBHCs,
e s timates
All
of these
economies
that
of SE r e p o r t e d by HT was
in
at the
and for OBHCs
f rom
the
the
SP model.
estimates
however,
than were
0.71
of
estimates
estimates,
of scale
shown
(SE)
of the r e s u l t i n g m e a n
SEA or SES) s u g g e s t e d
s m aller
calculated
As
elasticities
o bservations,
equality
were
from the MP model.
actual
different.
considerably
subsamples.
3.
in unit b a n k i n g
scale
the
quite
and OBHC
sample,
l i m i t i n g b a n k branching.
using
were
entire
in
indicating
of the
returns
earl i e r
purposes,
3,
observation
the
97 p e r c e n t
Clos e r v i e w i n g
institutions
at specific
the e s t i m a t e d a verages
elasticities
on MBHCs.
is c o n s i s t e n t w i t h
each
in Table
for both MBHCs
observations
finding
(1)
shadow and actual
in all
scale
calculated
the MBHC
reported
than u n i t y
that actual
for
for
of Table
to scale
also
of data for
for b o t h
SEs and SEA , are
S E s and SEA are
increasing
at the
were
were
reported
for MBHCs
and
20
In Panel
(c)
of Table
3, we have
model
of m e a n values
(ASE)
o r i g i n a t e d by Benston,
e m p l o y e d by H T .
direct
effect
ef f e c t
ar i s i n g
b a n k offices
of an i n c rease
from the
utilized
q -»
rA
estim a t e s
scale
is d e s i g n e d
(1982)
and also
the
indirect
on the number
of
is d e f i n e d as
, 31nC 31nB
+ 31nB 31nQ *
(22)
r e l a t i v e l y m inor
and i n s i g n i f i c a n t
the MP
economies
and the
output
ASE
for
to capture b o t h
on cost
of h i g h e r
in production.
indicate
for MBHCs
scale
and H u m p h r e y
in output
effe c t
estimates
of a u g m e n t e d
Hanweck,
The ASE m e a s u r e
ASE
Our
of a m e a s u r e
inc l u d e d
augmented
e c onomies
augmented economies
of
for
OBHCs.1
2
Impact
of
The
Technical
impact
examining
tcha
the
Change
of t e c hnical
elasticity
change
on b a n k
of cost w i t h
costs
resp e c t
to
is e x p l o r e d by
the
time
trend,
T.
31nC
81nT
- <> + #TTlnT + ZjV^lnCkjP,)
*T
+ 0QTlnQ + 0TBlnB +
The
t e c h n i c a l -change
the
right - side
S|k i'lyi
T
i = L ,K .
(23)
e l a s t i c i t y of shadow cost T C H S is given by
expression
for
the e l a s t i c i t y
of actual
cost
TCH
21
in e q u a t i o n
(23)
advancement
is g a uged by
less
our
with
than zero.
est i m a t e s
Panel
(a)
progress
of
within
suggest
Table
3,
for MBHCs
and suggests
the MBHC
p r o gress
observations
The
role
the
of the bias
previous
greater
economies
showed
from
of the role
dissemination
the
Once
of
again,
the more
is
the
an i n d i c a t i o n of
re s t r i c t i v e
shown
(TCHS— -0.338
of t e c hnical
is
91.6 p e r c e n t
to compare
to get
is s t a t i s t i c a l l y
finding
technology.
3 can be u s e d
change
in line with
E v a l u a t i o n of
that
the MP m odel
of t e chnical
is
for T C H S.
and SP models
SP model
This
from H T .
shown in
technical
However,
larger b e n e f i t s
in Table
As
of t e c h n o l o g y
form exists.
are
of the data,
progress.
than for OBHCs.
and the d i f f e r e n c e
estim a t e s
these m e a s u r e s
p r o d u c e d by u t i l i z i n g
to the
the effect
TCH~-0.306)
suggest
conclusion
in the MP
Technical
at the m e a n s
t e chnical
at each data point
presented
Relative
understate
to w h i c h
p r o d u c e d n e g a t i v e values
of t e c h n o l o g y
model.
the
found to realize
results
extent
that
organization
technical
were
extent
our results
conf l i c t wit h
MBH C s
the
term excluded.
significant
in di r e c t
the
last
B a s e d on c a l c u l a t i o n s
on average
our prio r s
the
to
and
significant.
Thus,
chan g e may be
misleading.
The
i n f luence
of t e c hnical
change
economies
e x a m i n e d by d i f f e r e n t i a t i n g
the
InT.
of InT on u n a u g m e n t e d
We
focus
elasticities.
to
InT,
on the
effect
Differentiating
and u sing
equation
(17)
scale
on scale
elasticity with
SEA in e q u a t i o n
gives,
is
re s p e c t
to
scale
(20)
wit h
respect
22
tchsea
3SEa
a2lnCA
” 31nT " 31nC31nT
(24)
Differentiating
SEs as d e f i n e d
in eq u a t io n
(21)
gives,
3SES
T C H S E s “ 31nT ” °QT»
the
(25)
first
term of T C H S E A in e q u a t i o n
Using
the grand m e a n data
es ti ma te s
in Table
from
3 imply
on averag e
flattened
time.
in wh ic h
important.
Th es e
re sults
actually
sug ge st s
Thus,
c o in ci des
to b r e a k
appears
en h a nc ed
it e s s e n t i a l l y
findings
it easier
1986),
given
over
of scale.
as a ba r r i er
cost
the
output
and make
size
d e c l in i n g price
particularly
that
as
curve has
from other
the p e r i o d
That
decreases
to pr od u c e
advances,
the HT findings
serves
ave ra ge
down scale b a rr i e r s
of t e ch ni cal
econ om ie s
the pa ra me t e r
led to m o de s t
the
with
re as on a b l e
( Br es na ha n
and
of T C H S E A and T C H S E S
change has
t ec hn o l o g y makes
co ntr as t with
advantageous.
our estimates
of scale.
This
This
te chn ol o gy
for all banks
te chn ica l
i n c r ea se d e ff ic i e n c y
computer
had
that
is u s ed as a means
less
and
SP model,
in ec onomies
over
in du st ri es
and
the
(24).
analyzed.
tech ni cal
is,
their
it makes
change
results
size more
23
Finally,
derived.
(19)
the effect of t e c hn o l o gy
For the
sh adow cost
on factors
can also be
differentiation
function,
shares
of equation
gives,
3M,S
3lnT ” y i
T
From Table
1,
labor
saving
Again,
this
and,
The
of
eq uivale ntly,
found
Demand
in other
and
ow n-p ri ce
constant,
e la s t i c i t y
the
is
re la t i ve
ex pe cta ti ons
to labor.
and coin ci des
with
industries.
of de mand for
the
input
i, h o l d i n g Q
elasticity
4 displays
and OBHC
Mi
S(M1 l ) + y f
Sl
£1
_ 3Xj Pj
= 3Pj X t -
gr an d means
the MBH C
capital using
in e qu a t i o n
cr os s- p ri ce
%
at
technology
is given by
u s i n g Xj as d ef in ed
Table
that
Substitution
_ 3X, P t
E 3P7 x;
The
suggesting
is in a gr eem en t wi t h
wha t has b e e n
Elasticities
* -0.012
*
(
(11)
of demand
for a c o n s t a n t
output
of the data
is
(28)
Mis
the results
subsamples.
(27)
for
these
elasticities
for all banks
Because
of the
in the
c a lc ula ted
sample
coefficient
and for
24
restriction
in our tw o - in p u t model,
elasticities
are equal
in ab so lut e value
Concentrating
on the
SP model,
we re
to two
de cimal
the
same
o w n - pr ic e
el ast ic i ty
in abs olu te value,
d e ma nd
the
of labor
cro s s - pr ic e
inputs
are
presented
mo d el
with
the
gross
Once
s ig ni f i c a n t l y
Estim at es
also
sho wn
same
ei t he r
the
Regulatory
The
Costs
inputs
that
are
g re ate r
are
tw o- in p u t
from
that
this
the more
case,
the
are
also
reje cte d
general model.
elasticities
of
are give n by
(29)
than zero,
substitutes,
and OBHCs b a s e d
and
effects
the
own-price
from the MP model
pa rtial
of the
as
and are v e r y n ea rly
on the c o ef f i c i e n t
estima te s
the
from
SP or MP model.
utilization
u n de r
than unity
MiSMjS
( * 0^)
=
for MBHCs
the
indicating
those usin g
4,
less
elasticity
the
the results
(1966)
The
1 +
estimated
for
Re sults
in Table
a
required
are positive,
from
but
than
for
estimates
and OBHCs.
o wn -pr ic e
greater
in sign.
elasticity
is ne ga t i ve
re q u i re d
ag ai n
for the A l l e n
sub sti tution,
The
As
substitutes.
in Table 4.
differ
input
relatively
e la st i ci ti e s
and op p o s it e
for MBHCs
estimated
demand.
and cr o ss - p r ic e
the own- pr ice
places
for each
for capital b e i n g
elasticity
the own-
are
Factor
Shares
of r e g u l a t i o n
on actual p r o d u c t i o n
i nv es t i g a t e d by
al ter na t iv e
co mp ar i n g
a ss u m p t io n s
results
of relative
costs
for
pric e
the
and factor
SP model
e f f ic i e n cy
and
25
ine fficiency.
un d er
Estimated
relativ e price
actual p r o d u c t i o n
efficiency
e s t i m a t e d p ar am ete rs
of the
are
Results unde r
us i n g
es t i ma te d c oe f f i c i e n t s
the
kK — 0.562.
shares,
means
The e st ima te s
shown
all banks,
re la ti ve
price
(and average)
r el at iv e
the
5,
of the
SP model,
MBHCs,
e s t i m a t e d re g ul a t o ry
efficiency.
are
ob ta ine d by
inclusive
and
of
factor
at the
grand
and OBHCs.
costs
a ri sin g
from
great er
total
than w o u l d have
This w o u l d
p r e v a i l e d under
tran sl ate
on b a n k returns
effects
the
to 1.8 p e r c e n t
amount
effect
regulation-induced
inefficiency
are b a s e d on c a lc u l a t i o n s
p r o d u c t i o n costs
greater
price
for all banks,
shares
except w i t h kR - kL - 1
of total p r o d u c t i o n costs
i n e f f i ci en c y
price
significantly
The
in Table
of the data sets
For
r e la ti ve
and factor
c a l c u l a t e d by us i ng
SP model,
imposed.
costs
are about
into
a
on e qu ity
the
same
or assets.
for MBHCs
and
OBHCs.
As
sta te d earlier,
misleading
el e men ts
w hi c h
seen w h e n
Viewing
e va lu a ti ng
share
regulation when
considered.1
3
increases,
based
to parti es
the
effect
in Table
s i g n i f i c a n t l y with
the
in te re s t e d
of capital
whil e
ba n k ma n a ge rs
constraints.
in e v a l u a t i n g
of r e g u l a t i o n
a c tu al ly
of this
on factor
shares.
share
the
decreases
ac tu al l y
econom iz e
of capital,
is
of capital
to 25 percent.
with
shadow cost
o b ser ve d capital
cost
examp le
r e g u l a t i o n - -from 17
the more me a n i n g f u l
Thus,
in s i g n i fi c an tl y
A r e ve a l i n g
5 for CA the
on their p e r c e i v e d price
regulatory
CA could result
in fluence behavior.
the results
in cr ea s es
However
i n f o r m at io n
a n al y z i ng
shares
are
share
on p h ys i c a l
i n cl u d i n g
the
capital
costs
of
26
Potential
Explanations
The
labor,
be
for Price
es t i ma te d v alu e
ba nk e rs
this
alters
obviou s
pr ic e
the
q u es t io n exists:
of capital
c u s t om er s
e xp la na tio ns
that
Why
may
s pe nd
sums
theory"
co incides wi t h
f in a n c i a l
w o u l d be
capital
r ais ed
expenditures
r e su lt
b as is
this
the
for p hy si c al
on offic es
cu rrent
1989,
increase
di sc us s ed how
effective
ex pl anations
and v ia ble
structure.
This
ratio may
equity
Kolari
service
f r eq ue ntl y
co mpete
and Zardkoohi).
and teller machines.
oc cu rre d
as a direct
on a no n- pri ce
One means
through a d di ti on al
capital
in
ca pital wh ic h w o u l d not have
ba nk ers
if
requirement.
result
Finally,
and plush
Second,
then more
the
The
"c om mitment
architecture
ge n e r at e d w i t h o u t
requirement.
alternative
b a n k m a n a g e m e n t may
com me rci al banks.
are b i nd i n g
An
and po t e n ti a l
long-haul,
debt-equity
r e g ul at e d capital
(Evanoff
to
large
to
Although
te nt at i v e
o b s e r v e d ornate
than w o u l d be
sub opt im al
the
an imposing p h y s i c a l
r eq ui r em e n ts
of regulation,
is
the
found at ma ny
resulting
without
p e r c e i ve
three
to
of b a n k management.
is part of a long run st rategic plan.
surroundings
The
to ge nerate
the
capital
We have
is a credible
over
relative
inexpen si ve?
to co nv inc e
in the m ar k e t
behavior
exist,
institution
and will be
large
that,
of p h ys i c a l
do ban ke rs
relatively
First,
the
price
true
and the b e ha v i o r
as b e i n g
of f e r e d here.
suggests
than the m a rk e t price.
cost elements
alternative
are
less
in B a n k i n g
of kK».562
p er cei ve
significantly
Inefficiency
capital
of doing
ex penditures
27
5.
S U MM AR Y AND C ON CL US ION S
Re s ea r c h e r s
m ak in g
l i t e r a t u r e have
alternative
scale
the
data sources,
cost
contribution
st ructures
is more basic.
in these
c o m p e t i t i v e markets
the
We
into
the
influ enc es
of She p ha rd 's
Lemma.
which
"shadow"
pri c es
because
based
on this
mod e l
as a special
neoclassical
i.e.,
Using
sampl e
in the b a n k i n g
the v a l i d i t y
costs
of banks
indicated
inf l ue nce
Our
that
wh ic h may
of re g ul a t o ry
in co ntr a s t
te chnical
there
is
shares,
The
taking
empirical
a m o d i f i e d ve rsi on
scale
to past
pr o g r es s
subs um es
from m arket
The
the n e oc l as s ic al
su gg e s t
that use
for
sample
our
of
is rejected.
economies
Te ch ni c a l
of costs
cons tr ain ts .
in ap p r op r i a te
is
assumption.
d e via te
results
in
efficiency.
is b a se d on m i n i m i z a t i o n
efficiency
considered.
but,
in co rpo ra tes
e mp iri ca l
specification
price
of the
a n e oc l a s s i c a l
industry,
and factor
s had ow price b e h a vi o r
relative
Our
c r iti qu e
pr i ce
of this
are
found
for
pr og res s
was
found
findings,
the
results
tended
of
for differen ces
of techni ca l progress.
the new methodo lo gy,
su b st ant ia l,
Each employs
input prices
case.
of economies
a s s u m p t i o n of cost m i n i m i z a t i o n
The mo de l
of the
mod e l
banks,
is a fu n da m e n ta l
are b a s e d on a mod el w h i c h
re fl e ct
to ac co u n t
c h a r a c t e r i z e d by relative
rea son to doubt
acc o u nt
measures
and b r an c h banks.
studies.
es ti mat e ba n k p r o d u c t i o n
re sul ts
the
It
extent of r e g u l a t i o n
significant
means
of unit
to the b a n k cost
efforts by u t i l i z i n g
out pu t measures,
fr a m e w o r k b as ed on the
Given
their
and a l t e r n a t i v e
m e t h o d o l o g y us ed
cost
c o n t r i bu t i o ns
distinguished
and scope,
in the
rec en t
to d e c r e a se
scale
the
to be
of
28
ec on om ie s
R e su lt s
and was most b e n e f i c i a l
from the a lt er n at i v e
efficiency
(the
(the MP model)
SP model)
elasticities
of demand
subst itu tio n.
inf lu en ce
modeling
re ve a le d
and e s t i ma t io n
the MP model was
The
ban k s
results
on average
studies
regulation,
the
attempt
implications,
reducing
the
pric e
in own-
that
the
results
to me as u r e
indicate
should be
and cro ss -p ric e
the
that
the
input
costs,
into
the
given that
the
test.
sample
Future bank
i n du c e d by
of the
the
for
costs.
i n e f f i c ie n c y
to p o l i c y m a k e r s
al te rin g
the
l i k e l i h o o d ratio
of actual
extent
of
incorporated
in ef fi c i e nc i e s
costs w i t h o u t
relative price
in ef fi c ie n cy
cost of r e g u l a t i o n
2 percent
for the
companies.
and A l l e n e l as t i c i t i e s
r e j e c t e d under
and pr ov id e
re gu la t or y
industry.
input
u n de r
of l a r g e - b a n k p r o d u c t i o n
is about
should account
relative
d if fer en ces
c o ns t r a in t s
st ron gl y
suggest
es ti ma t io n s
and under
Ne vertheles s,
of re gu la t or y
mode l
small
for
to m u l t i b a n k h o l d i n g
and
c o n c er n e d with
saf et y
of the
29
FOOTNOTES
Shortcomings
M in go
(1978),
M c Nu l ty
2See La wr e nc e
di s c u s s i o n s
fi na nc ia l
ac c ou nt
3The
of the
(1983)
and Shay
of the
impact
industry.
for
FCA data are d i s c u ss e d
Bell
the effect
in H e g g e s t a d and
and G i ll i g a n and S m i r l o ck
(1986),
and Solom on
(1987),
of t e le c o m m u n i c a t i o n s
and M u r p h y
of te c hn o l o gy
st a n da rd r e g u l a r i t y
(1968)
con di tio ns
advances
to
effects
include
(1)
(2) hom og en ei t y,
(3) m o n o t o n i c i t y , and
Jorgenson
on the
indirectly
in banking.
positivity,
for a d i s c u s s i o n of the conditions.
(1986)
^Empirical
pr o bl e m s
r e s u lt in g
requirement
in du st ri e s
discussed
to
em b e dd ed
e.g.,
recognized
ac co unt
generalized
ig n o r ed
the p o t e nt i a l
but
ignored
and St anley
studies
(1974),
( 19 88) -- onl y
r e cen tl y has
marke ts
Studies
problem
(1988)
cost m o d e l - -At kinson and H a l v o r s e n
in
and C h r i s t e n s e n and
have
in the use
(1983),
this b e en
in other
and
the p r o b l e m
of re g u l at e d u t i l i t i e s
N el s o n and Wohar
See
the po t e n ti al
of the c o m p e t i t i v e
for r e g u l a t i o n - i n d u c e d di st ort io ns
i n p u t s - -Joskow
Kowalewski
McMullen
While
concavity.
in the n e oc l a s s i c a l model.
the r es u l t i n g biases,
(1976).
of b a n k costs have
from v i o l a t i o n
e xp li c i t l y
estimati on ,
Green
studies
(4)
for
attempted
on scale
(1984).
and
a t te mpt ed
of
Is r ai l e v ic h
incorporated
(1980,
1984).
into
and
a
30
5The
idea
that r e g u l a t i o n
inputs has most
regulation
fuel
the
c om mon ly b e e n
limited
AH me n t io n
ad j us t m e n t
in v a l id it y
prices.
to
to the
f ina nc ial
studies,
we
entirely
to r e g ul at o ry
occur
sa tis ficing,
attribute
of the
are
d i s c u s s i n g pr ivate
dealing w i t h
the u n a v o i d a b l e
of b a n k
see AH
(1984,
Lau and Y ot op o l o u s
7 The
fi nd w h e n
to ma rk e t
that
errors
input
other
cost of
could account
If r e g u l a t i o n
wh i ch
of m i n i m i z i n g
are not
that we
is
taken
m a rk e t
the
factors
such as
emphasized
r e su l t i n g pr iv a t e
events
p p . 648-54).
(1971)
d is c u s s e d
the more
mode l
in this
into
ineffic ien cy
total
The AH mo d el bu ilds
of rela ti ve
example
g e n e r a l i z e d model
to
and sh adow prices
It is p o s s ib l e
efficiency.
cost
in leading
social
cost
operations.
6 1 so
A
the
of m a rk e t
ex t e r n a l i t i e s
pr iv a te
company
the p o t e nt i a l
It shou ld also be
the
For
C o n s i s t e n t with previous
data m e a s u r e m e n t
m ar k e t
utility
r e gu l a t i o n s
respe ct
is
restriction.
of n o n c o m p e t i t i v e b e h a v i o r
difference.
of return
its u s e f u l n e s s
discuss
industry.
effects.
a cc ou nt by b a n k managers,
is
(1971)
c o m b i n a t i o n of
rate
of e l ec t r i c
L em ma wi th
d i v er g e n ce
or co ns is t en t
some
effectively
the
as a result
for
role
and e n v i r o n m e n t a l
of She pha rd 's
the
form of r e g u l a t o r y
G r e e n b a u m and H a y w o o d
regulation
which
this
However,
the p o te n t i a l
clauses
the op t im a l
associated with
of public utilities.
o b v i o u s l y not
example,
di storts
price
upon
efficiency.
are p r e c i s e l y what we
is estimated.
31
8T o
the
re s p e c t
extent
to
their
9T o check
and MP models
r e le va n t
with
the cost
e v a l ua t e d
in the
equations.
s p e c if i c a ti o n s
case
r e s t ri c t io n s
the
Obviously,
The
can be
the
share
imply s y m m e t ry
the
two -i np ut
for
the
invar ian ce
their model.
1 The
0
studies
as
the
of results
are
d ep osi t
and H u m ph re y
(1965).
o u tp ut
assets,
Se a l e y
Others
as
the
sums
value
c om b i n a t i o n
and Li nd le y
(1977),
the
coef fi cie nt s)
case
fully
of
in
accounts
ex pl a i n
for
159.
controversy
or cre di t
deposits,
of these ba la nce
of recent
output
card
(1982),
and Bi nk ley
(1981,
A nu mb e r
and m e a s u r e d
"i nt er m ed i a r y
Shaff er
share
t w o - i n pu t
and H u mp h r e y
of loans,
tw o- eq u at io n
of the
accounts,
an
for
that all
s u b s t i t u t i o n m a tr i x
of ba n k output.
Pavel
have u t i l i z e d
dollar
or some
(1987),
fact
across
in pu t-price
of the
Hanweck
SP
invariant.
imposed on the
have u t i l i z e d a " p r o d u ct i o n approach"
of loans,
the
of the
9, p.
a pp ro pr iat e m e a s ur e s
number
were
that HT could not
fully aware
a c c o u n t s --e .g ., Benston,
Hanweck
of
property
See H T , footn ot e
authors
concerning
This
matrix
reestimated
from the
row and column
(i.e.,
case.
the
e q ua ti ons --i .e . , with
r e st r i c t i o n
s u b s t i t u t i o n mat rix
equations
we
results
follows
sy m m e tr y
zero
with
is appropriate.
and c a p i t a l -share
tw o-i np ut
including
are h o m o g e n e o u s
the b u r d e n of regulation,
eq ua t io n deleted.
p a r a me t er
subsystem,
and
te chn ol o gy
the e st i m a t i o n
l a b o r - sh ar e
In v ar i a n c e
firms
the
of identical k. v al ues
restriction
the
that
(1987)
Berger,
and Bensto n
appr oa ch"
me as ur in g
securities,
sheet
1984,
iterns--e .g .,
1985),
HT
(1986),
32
and Ko l a r i
and Za rdkoohi
t a k e n a m ul t i p r o d u c t
(1987).
approach
p r o d u c t i o n using va rio us
output.
the
The
assets
H T , we
that
separable.
The
ev en more
com ple x
value
of
in t an gib le s
(e.g.,
see
measure
bank
issue.
follow
in ba nk
Evano ff
output
1988).
large
progress.
are
em phasis
banks.
is actually
of service
cost
structure
d i s t or t i o n s
we use
evaluating
is
the presence
levels
in the
like
or dollar
e x a c e r b a t e d by
For c o m p a r i s o n purp os es
As
Also
funds
unit
on r e g u l a t o r y
to that u s ed by others
for using
output m e a s u r e
i n t e re s t e d
and
approach.
of r a i s i n g
such as d i f f e r in g
We
special
further
case
of
"production
than de c i d in g b e t w e e n p h y s ic a l
is
in
renders
Sealey
this
the
it for
of an a p pr o p r ia t e
The p r o b l e m
si milar
of b a n k i n g
a compelling
to use
pr e c l ud e
studies have
for jo i n t ne s s
theory
the p r o d u c t i o n pr ocess
of large banks with
t e c h ni ca l
to be
rec en t
and d ol lar val ue me asures
on the
if one w a n t e d
choice
measures.
unit
Like HT we
data li mit at ion s
assume
tested
an u n s e t t l e d
co ns i d er
as outputs.
in H T , even
approach",
ph y s i c a l
output m e a s ur e
L i n d l e y make what many
discussed
and have
lack of a c on se ns us
appropriate
earning
A d di ti ona ll y,
and
an output
these
aspects
of
costs.
nThe
first
s a t i s f i e d by
re q ui r e s
condition
prices.
p ri ce
that
two r eg u l a r i t y
all
the
requires
In the
two
factor
that
the
input
(footnote
imp os ed
the r e s t ri c ti o n s
elasticity
c on dit io ns
(16).
in
case
fu nc tio n be
this
is n on ne gat ive ,
c o n d i ti o n
i.e.,
are
Monotonicity
shares be positive.
cost
3)
The
co nc a v e
is met
sec on d order
in the
input
if the Allen
33
i
j
1 +
The m a x i m u m value
> 0
for M^l-Mj)
- 0.25,
satisfaction
of the
Yj
£ -0.25.
From our results,
in
(16),
- -y^ = -.033.
condition
occurs
is met
ca p it al
to
imagine
share
greater
that
the
SP model
this
requirement
1
2
It shou ld be
scale
se rvi ce
co u l d
e co no my
d ema nd
simp ly
Benston,
d InB/ d InQ
regression
Using
elasticity
the
ef fe ct
auxiliary
HT
r e g r es s io n
rea li sti ca lly ,
It is
to have
a labor
observations
that
this
only
a l t e r n a ti v e
to note
wh i ch violate
to the e xt ent
dispersed;
operations
estimated
for
mea su re
that ba nk
o t h er w i s e
at one
coeffic ie nts
InQ,
of
of an a u xi li ary
HT obtai ne d an e s ti ma te
wi th
respect
to output.
We
from the c o e f f i c i e n t
In B - a0 + ajlnQ + a2lnT.
correlation
of the
in the au xi lar y
of 0.725
for
es ti ma te d
on InQ
in the
This
s p e c i f i c a t i o n was m o t i v at e d by co nc ern s
term
Follow ing
+ OijlnQ + o 2(1/2 ) (InQ) 2.
t
on br a nc h e s
error
the ba nk
site.
alternative
it is
or
i n te r e s t i n g
ob t a i ne d an estimate
of br a n ch es
of output
and,
This
is the MP model.
InB — a 0
g r a n d - m e a n data
the
likel y
i n d e p e n de n t
given by
.97.
com me rci al ba n k w i t h
is g e o g r a p h i c a l l y
from the
than ~
in our sample
is a pp r o p r i a t e
et aL (1982),
second order
is less
emphasized
set up
the
than 97 percent.
is less
than
co n d i ti o n r e qu ir es
Thus
a large
global
and the r e s t r i c ti o n s
so long as
for each data point
difficult
of
s ec on d order
therefore,
over
regression.
serial
Our
34
estimated
the
e la sti ci ty
el a s t i c i t y was
a ss um e d
^Alt ernatively,
shares
with
For
can be
re s p e ct
the
which,
seen by
respect
to be
eff ec t
to Q was
—
differentiation
(SPS) function,
-y^,
de cl in es wi th
from one.
As
in H T ,
of r e g ul a t i on on fa ctor
of e q ua ti ons
with
(17)
regulation
and
(19)
regulation.
d i f f e r e n t i a t i o n of
- k«
i
since y
0.70.
constant.
to k t- -r ec o g n i z i n g kK decreases
as kR de c rea se s
the
sha dow cost
3k<
of B w i t h
(17)
generates
35
Table
1.
E st im a ti on Re sult s
Coefficient
MP Model
-0.930
00
(0.97)
SP Mode l
-1.104
(1.16)
0.321
(11.1)**
(4.06)”
0.573
(4.04)”
(1.88)
0.020
(1.87)
(30.6)”
0.033
(10.2)”
0.0075
^LQ
(38.1)”
0.048
yL
L
(23 .4 )”
0.020
Pqq
0.679
0.577
Pq
(45.4)”
0.456
Pk
yLH
( kK l )
' ^
the MP and SP Mod el s
0.544
Pl
^IB
for
(8.31)”
0.0051
(6.5 6) ”
-0.0003
(0.52)
-0.00005
(0.11)
-0.0034
(1.88)
-0.0020
(1.53)
-0.018
0BB
-0.012
(2.49)*
0.106
(1.75)
0.033
%
(14.0)”
0.151
yn
(8. 56 )”
(4.30)”
0.025
(3.28)”
0.070
(0.39)
0.072
(0.40)
-0.078
(0.59)
-0.132
(1.01)
-0.253
(11.4)**
PH
-0.237
*TT
(10.7)”
®QB
-0.0090
(1.75)
-0.0044
(0.86)
®QH
0.023
(1.63)
0.021
(1.44)
®BH
-0.062
(6.27)”
-0.056
(5 .5 7 )”
0QT
0.024
(10.7)”
0.027
(2. 62 )”
®TB
0.0018
(0.29)
9th
-0.084
(4.50)"
1.00
kK
Generalized R2
Note:
-0.0012
-0.085
0.562
.947
P a re n t h e t i c a l entries are
r a t i o s - ■* (**) in di c a ti n g
(0.19)
(4.55)**
(7.77)**
.948
absolute va lues of a s ym pt oti c tsi gn i f ic a n c e at the 5% (1%) level.
36
Table
2.
Results
of H y p ot h e si s
Tests
Numb er of
R es t r i c t i o n s
Null
Hypothesis
Market-Price
Model
Shadow-Price
(J)
R e st r i c t i o n s
LR
X2(J)
1
kK = 1
27.30
6.63
Model
6
PQ * 1
27.30
16.81
7
QT
0
138.69
15.09
®B
Q
127.65
13.28
with:
(a)
C on s ta n t Returns
to
S ca le
y L< r
“
(b)
Homogeneity
5
p q<
t
0QB“
y Lq“
Homotheticity
4
®QH “
PQ
Q
®QB=
(c)
V
®QH:
0QT”
0
= 0
Note:
the
LR denotes
the
l ik el i h o o d - r a t i o
l o g - l i k e l i h o o d ratio);
for J de grees
of freedom,
X2(J)
at the
test
denotes
the
on e- pe r ce n t
st at i s ti c
c h i - s qu a r e
(-2
times
value
significance
level.
37
Ta ble
3.
Panel
a.
Scale
E la st i ci ti es
and Measu re s
of T e c h n i c a l
Change
Sh ado w- Pri ce Model _________________________________________
Number
SES
Banks
of Obs .
All banks
2624
0.924
MBHC s
1685
(7.47)"
0.935
OBHCs
939
(5.87)"
0.906
TCHS
TCH a
0.921
-0.338
-0.329
0.931
( 2 3. 8 7 ) ”
-0.392
-0.384
0.902
(2 3.71)"
-0.241
-0.232
SE a
(6.81)"
Panel b . S ha do w- Pri ce
O b s . such
Number
Banks
(1 4.20)"
Model
that SES < 1
Perce nt
O b s . such
Number
that T C H S < 0
P e rce nt
All bank s
2580
98.3%
2404
91.6%
MBHC s
1651
98.0%
1596
94.7%
OBHCs
939
100.0%
808
86.0%
ASE
TCH
Panel
c . Ma rk e t -Price Model
Number
of O b s .
Banks
SE
All banks
2624
0.916
(8 . 37 ) ”
MBHCs
1685
0.928
(6.52)"
OBHCs
939
0.895
(7.67)"
Note:
0.978
(2.34)*
-0.306
(22.67)"
0.972
(2.66)**
-0.359
(2 2.53)"
0.991
(0.74)
-0.210
(12.73)"
Esti mat es are d er iv e d u s in g the g r a n d - m e a n value s of the
obs er va ti o ns (Obs.) for all banks, m u l t i - b a n k h o l d i n g
compa ni es (MBHCs), and o n e- ba nk h o l d i n g co mp an i e s (OBHCs).
Pa re n th e t i c a l entries are absolute value s of asymp to tic
t-ratios.
Tests of the eq uality of the e s t i m a t e d scale
c
el as t i c i t y me as u re (SE vs SE ) and effect of technical
change (TCH vs TCH ) in the two models were rejected;
the ca l c ul at e d t-ratios were 8.5 and 6.1, respectively.
38
Table
4
E st ima te d E la st i c i t i e s
Price
Elasticity
of D em and and S u b s t i t u t i o n
Re lative Price E f f i c i e n c y
Not Im posed in E s t i m a t i o n
(S h a d o w - P r i ce Model)
R e l a t i v e Price Effici enc y
I m p o s e d in E s t i m a t i o n
( M ar ke t-P ri ce Model)
All banks
-0.1123
-0.5601
0.1123
0.1774
0.6284
0.5601
-0.1114
-0.1763
-0.6280
-0.5603
-0.1139
-0.1794
-0.6292
1K
fK
*
-0.1774
-0.6284
T
\l
-0.5597
MBHCs
\
k
OBHCs
%
E l a s t i c i t y of
Substitution
OBHCs
°LK
%
0.7375
( 4 2. 7 1 ) ”
0.7393
0.7366
(8.48)”
MBHCs
°IK
0.7407
(8.65)’
*
All banks
( 4 1. 9 3 ) ”
0.7431
(8. 95) ”
Note:
E sti ma tes are
for all banks
0.7391
( 4 4. 0 5 ) ”
de ri v e d usin g gr a n d -m e a n v a lu e s of the
and the MBHC and OBHC subsamples.
data
39
Tab l e
5.
Es ti ma t ed Costs
and Fa ctor
Shares
Fitte d value wi t h
F i t t e d value with
r el at i v e - p r i c e i n ef f i c i e n c y
r e l a t i v e - p r i c e effici enc y
_________ kK » .562_________________________ k = 1 ________
All
banks
Tot a l
cost
Lab o r
sh are ML
A
75.91%
82.92%
MLS
84.84%
82.92%
share MKA
24.09%
17.08%
M kS
15.16%
17.08%
Ca pi tal
CA
$77 ,84 4.3 5
$ 76 ,45 2. 69
M B H C s
$7 1 , 23 3 . 44
Total
cost
La bor
share M L
A
76.05%
m ls
$6 9, 94 8 . 1 1
84.93%
Cap i ta l
CA
share MKA
23.95%
M s
nK
83.01%
15.07%
16.99%
OB HC s
Total
cost
Lab o r
share ML
A
75.66%
m ls
84.67%
Ca pi ta l
CA
$89 ,70 7.3 6
24.34%
M s
nK
Note:
share MRA
$8 8, 12 4 . 9 1
82.74%
15.33%
17.26%
Esti mat es are de ri v e d from the g r a n d - m e a n v al ues of the
data for all banks and the MBHC and OBHC subsamples.
40
LI T E R A T U R E
CITED
Atk ins on, Scott E., and R o b e r t Halvorsen.
"P a ra m e t ri c E ff ici en cy
Tests, Economies of Scale, and Input D e m a n d in U.S. Electric
Power Generat ion ."
International E c o n o m i c R e v i e w
25
(October 1984), 647-62.
____________________ . "A Test of Re la t i ve and A b s o l u t e
Ef f i c i e n c y in R e g u l a t e d Utilities".
The Review
E c o n o m i c s a n d S t a t i s t i c s 62
(F ebruary 1980), 185 - 96
Bell,
Fr e d r i c k W. , and Neil
Banking:
Its
A
Relation
Boston:
Quantitative
to B a n k
B.
Analysis
Regulation.
Federal R es e r v e
Murphy.
of
Bank
Costs
Behavior
Price
of
in C o m m e r c i a l
and
R e s e a r c h Re p or t No. 41,
Ba nk of Boston, 1968.
Benston, George J.
"Econo mi es of Scale and M a r g i n a l
Ba nk i ng Operati ons " .T h e N a t i o n a l B a n k i n g R e v i e w 2
(June 1965), 507-49.
Costs
in
____________________ . "Econo mi es of Scale of F i n a n ci a l
In s tit ut ion s. "
Journal of M o n e y , Credit, a n d B a n k i n g 4
(May 1972), 312-41.
Benston, George J., G e r a l d A. H a n w e c k and Da v id B. Humphrey.
"Scale Economics in Banking:
A R e s t r u c t u r i n g and
Re a ss e ss m e n t . "
J o u r n a l o f M o n e y , C r e d i t 5 a n d B a n k i n g 14
(November 1982, Part 1), 435-56.
Berger, A l l e n N., G e ra l d A. Hanweck, and D av id B. Humphrey.
"C o mp et iti ve V i a b i l i t y in Banking: Scale, Scope, and Product
Mix Economies."
J o u r n a l o f M o n e t a r y E c o n o m i c s 20
(December 1987), 501-520.
Bre snahan, Timothy.
"M ea su r i ng the Sp illovers From Te ch nic al
Advances: M a in f ra me Comp ut ers in Fi na ncial Servi ce s."
American Economic Review
76 (September 1986), 742-55.
Ch r ist en sen , Laurits R., and W i l l i a m H. Greene.
"Economies
Scale in U.S. El ect ri c Power Genera ti on. "
Journal of
P ol i t ic a l E c o n o m y 84 (August 1976, Part 1), 655-76.
of
Diewert, W. E.
" Ap pli ca tio ns of Du ality Theory" in M. In tr il iga to r
and D. Kendricks, editors.
F r o n t i e r s in Q u a n t i t a t i v e
E c o n o m i c s , vo lume
2.
Amsterdam:
North Holland, 1974.
Evanoff, Douglas D.
"Bank D e pos it Rate D e r e g u l a t i o n
Servi ce Levels." J o u r n a l o f C o n s u m e r A f f a i r s 23
(F o rt h co mi n g 1989).
and Customer
____________________ . "Branch B a nk i n g and Service A c c e s s i b i l i t y "
J o u r n a l o f M o n e y , C r e d i t , a n d B a n k i n g 2 0 (May 1988) ,
191-202.
41
Gilligan,
J oi n t
Journal
Thomas, and M i ch a e l Smirlock.
"An E m p ir i c a l
P rod uc tio n and Scale Economies in C o m m e r c i a l
o f B a n k i n g a n d F i n a n c e 8 (March 1984),
67-76.
Study of
Banking.”
Gilligan, Thomas, M i ch a el Smirlock, and W i l l i a m Ma rshall.
and Scope Economies in the M u l t i p r o d u c t B a n k i n g Firm."
J o u r n a l o f M o n e t a r y E c o n o m i c s 13
(May 1984), 393-40 5.
Green bau m, Stuart
the F ina nc ial
Credit* a n d
I., and Charles F. Haywood.
Services I n d u s t r y . ” J o u r n a l
B a n k i n g 3 (May 1971),
571-89.
"S ecular
of
"Scale
Change
in
Money*
He g ges ta d, A rn ol d A., and J o h n J. Mingo.
"On the U s e fu l n e ss
F u n c t i o n a l Cost A na l y s i s D a t a . ” J o u r n a l o f B a n k R e s e a r c h
8 (Winter 1978), 251-56.
Hotel lin g, H.
"Edgewo rth 's T a x a t i o n Parad ox and the Nat ur e
D e m a n d and Supply F u n c t i o n s . ” J o u r n a l o f P o l i t i c a l
E c o n o m y 40
(October 1932), 577-616.
of
of
Hunter, W i l l i a m C., and St ep he n G. Timme.
" T ec hn ica l Change,
O r g a n i z a t i o n Form, and the Structure of Ba nk Produ ct ion ."
J o u r n a l o f M o n e y * C r e d i t * a n d B a n k i n g 18
(May 19 86) ,
152-66.
Isr ail evi ch , Philip, and K. J. Kowalewski.
"The Ef fect of
R e g u l a t i o n on Ohio E le ct ri c U t ili ti es. "
Economic
R e v i e w , Federal R e se r ve
Bank of Cl e ve l a n d
(Quarter 1,
1987), 10-19.
Jo rge nso n, Dale W.
"E co n o me t r i c Methods for M o d e l i n g Pr oducer
Behavior.”
in Z. Gr ili c h es and M. D. I n t r i l i g a t o r ( e d s . ) ,
H a n d b o o k o f E c o n o m e t r i c s , Volume
III.
E l se vi er Science
Publishers, 1986.
Joskow, Paul L.
"I nf la t io n and E n v i r o nm e n t al Concern:
Structural
Change in the Process of Public U t il i t y Price R e gu l at io n."
J o u r n a l o f L a w a n d E c o n o m i c s 17
(October 1974), 291-327.
Kolari,
and
Lau,
James,
and A sg h a r Zardkoohi.
. L e x i n g t o n Mass.:
Performance
Bank
D.C.
Costs* Structure*
Heath,
1987.
L aw r en c e J., and Pan A. Yotopoulos.
"A Test For R e lat ive
E f f i c i e n c y and A p p l i c a t i o n to Indian A g r i c u l t u r e . "
American Economic Review
61 (March 1971), 94-109.
Lawre nce ,
Colin,
Innovation*
and Ro be r t
Regulation*
Cambridge,
Mass.:
and
the
Shay,
editors.
Monetary
Economy
Ballinger,
Technological
.
1986.
Lovell, C. A. Knox, and R ob i n Sickles.
"T esting E f f ic i e n cy
H y p o t h e s e s in Join t Production:
A P a r a me t r i c Ap pr ach."
R e v i e w o f E c o n o m i c s a n d S t a t i s t i c s 6 5 (February 1983) ,
51-58.
42
McN ulty,
James
Proceedings
of
Competition.
E.
a
"Economies
Conference
on
of Scale:
Bank
Federal R e s e r v e
Structure
D i s c u s si o n . "
and
Bank of Chicago
(May 1983)
456-61.
Nelson, Ra nd y A., and M a r k E. Wohar.
"Regulation, Scale
and P ro d u c t i v i t y in S t e a m - E l e c t r i e G e ne r a t io n . "
International E c o n o m i c R e v i e w
24 (February 1983), 57-79.
Economies,
Pavel, Christine, and Paula Binkley.
"Costs and C o m p e t i t i o n
Bank Credit Cards."
E c o n o m i c Perspectives.
Fed er al
Re se r ve Bank of Chica go (March 1987), 3-13.
Sea l ey C. W. Jr., and James T. Lindley.
"Inputs, Outputs,
T h eo r y of P r o d u c t i o n and Cost at D e p o s i t o r y Fi n a n ci a l
Institutions.
J o u r n a l o f F i n a n c e 32
(September 1977),
1251-66.
Shaffer, Sherrill.
of F irm Sizes."
467-76.
"Competition,
____________ .
E co nom ie s in M u l t i p r o d u c t
R e s e a r c h 36
(1984), 51-58.
Bulletin
of
"Scale
Economic
Applied
Ec onomies of Scale,
17 (June 1985),
in
and a
and Diversity
Economics
Firms."
____________ and Ed mond David.
"Economies of S u pe r s c a l e and
In te r st a te Ex pansion."
U n p u b l i s h e d m a nu sc ri pt , Federal Reserve
Bank of New York, (October 1986).
Shephard, R. W.
Princeton:
Solomon,
The
Theory
Cost
and
Production Functions.
P ri n c e t o n U n i v e r s i t y
Elinor H.
Public
of
Policy
Electronic
Issues.
Funds
Boston:
Press,
Transfers
and
1970.
Payments:
K l u w e r - N i j h o f f , 1987.
Tod a Yasushi. " S u b s t i t u t a b i l i t y and Price D i s t o r t i o n in the Demand
for Factors of Production:
An Empi ri cal Es t im a t i on . "
Applied Economics 9
(Septe mb er 1977), 203-17.
_____________ .
"E st im a ti on of a Cost F u nc ti on W h e n the Cost is
Not Minimum:
The Case of Soviet M a n u f a c t u r i n g Industries,
1958-1971. " T h e R e v i e w o f E c o n o m i c s a n d S t a t i s t i c s 5 8
(August 1976), 259-268.
Appendix
1.
Testi ng
the A p p r o p r i a t e n e s s
U s i n g A l te r n a t i v e
of the R e s t r i c t e d Model
Ou tput M e a s ur e s
k
Out p ut Me as ur e
t
hlr
a
Total Assets
.554
6.93
36.08
.02(10)-7
Total
Loans
.520
7.02
35.98
.02(10)-7
Total
Loans
.569
6.46
31.36
.02(10)-6
Securi tie s
.581
6.05
27.59
.02(10)-5
the
t-ratio
and Deposits
Total
L o a n s ,D e p o s i t s , and
In v es t me nt
Note:
t denotes
as ymp t o t i c
h y p ot h es is
of k equal
h o o d ratio
test
of
are
to unity;
statistic;
in the Ch i- sq u a re
a sym pt oti c
s ta nd ar d
for
is
t e st i n g
the
and a is the
test.
errors.
the null
likeli
s i g n i f ic a n c e
Parenthetical
entries
level
@FedFRASER