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Working Paper 74-5

COMMERCI,AL BANKING PERFORMANCE AND STRUCTURE:
A FACTOR ANALYSIS APPROACH

William Jackson

The views expressed here are solely those of
the author and do not necessarily reflect the
views of the Federal Reserve Bank of Richmond.

INTRODUCTION'

-

The Hunt Commission's recorrunendationsand other proposed banking
law changes have made comer, t ial bank performance
matter of some public concern.

under regulation a

Such changes in bank regulation should

depend on empirical evidence,, rather than on emotional value judgments,
if they are to be soundly based.

Indeed,

many empirical studies have been made of the relations

between the structure of the banking industry, banking regulation, bank
conduct, and the ,performance'of the industry.
numerous forces affect bankihg activity.
include differences

They have found that

These influences general JY

in regulatory policies, bank structural condit ions

(deposit concentration , new bank entry), and managerial
(bank operating

and financial traits) of various kinds.

categories
Additional

influences on banking performance that have been identified include
locational variations

in the demand.for financial services and the

erratic swings of monetary

and business cycles in recent years.

The trouble is, however, that such studies have partly contradicted each other.*

This literature does not generate a concensus of the

1
This paper draws upon parts of William Jackson, "Commercial'
Bank Regulation, Structure, and Performance" (un ublished doctoral
dissertation, University of'North Carolina, 1974 P . The analysis below,
however, factors all banking variables considered and is thus more
extensive than the factor analysis in the cited dissertation.
Moreover,
it utilizes factor analysis 'as an explanatory rather than as a purely
A Conference of State Bank Supervisors Dissertastatistical technique.
tion Fellowship and National Defense Education Act funds partly supported
this research. Ray Gobble programmed the analysis at the Federal Reserve
Bank of Richmond.
What It Means and
*Alfred Broaddus, "The Banking Structure:
Federal
Reserve
Bank
of
Richmond,
Monthly
Review
Why It Matters,"
(November, 1971), pp. 7-10.; Jackson, Chapter IV.

-2most important influences on bank activity that can guide bankers, legislators, and regulators in forming decisions to improve the performance
of this industry.
Accordingly,

this study briefly presents Phillips' theoretical

model of the banking environment that integrates the concepts that
underlie many of the previous studies in this area.

It then empir-

ically isolates the clusters of related traits that occur in banking,
as a guide to future research concerning the banking industry.

Finally,

it tentatively explains some sources of observed banking performance as
suggested by its empirical analysis.

A MODEL OF FINANCIAL INTERACTIONS

The reasons for numerous conflicting results of banking studies
may lie not only in their methodological

differences, but also in the

nature of the banking industry and its environment.

That is, important

traits, such as bank entry and demand, or bank size and branching 1aws;which
are nominally different, seem to be highly correlated.
that empirically

3

It would appear

isolated determinants of banking performance may capture

the effects of other variables and thus be partial proxies for complex

II

3Franklin R. Edwards, "The Banking Competition Controversy .,
Studies in Banking Competition and the Banking Structure (Washingto;
Comptroller of the Currency, 1966), pp. 334-35. Donald P. Jacobs, The
Interaction Effects of Restrictions on Branching and Other Bank Regu lations," Journal of Finance, XX (May, 1965), 332-39.

-3-

underlying strands of comnon, highly related influences.
Indeed, there is a;theoretical

4

basis for believing that such

Almarin Phillips' model of the

banking trait interactions exist.
market process shows an environment

in which real-world firms operate.

5

Although this model is applicable to any type of corporate activity, it
lucidly shows the channels of banking activity, as slightly modified
below.
Banking performance has much more than a single cause, as
Figure 1 shows.

Starting-in the
/

left-hand side of this Figure, the

goals of the firm (various combinations

of profits, growth, and safety)

and the goals of inter-firm groups (such as the high prices and restricted
competition advocated by trade associations)
firms.

enter into the behavior of

These goals, together with public-interest

considerations,

and bureaucratic

determine various forms of Government regulation by

Federal agencies and State banking commissions, which in turn limit

4Robert 3. Saunders,, 'On the Interpretation of Models Explaining Cross Sectional Differences Among Commercial Banks," Journal of
Financial and Quantitative An!alysis, IV (March, 1969), 25-37.
For
example, '... a relationship between concentration and price may appear
in the statistics, when none in fact exists, due to a correlation between
concentration and other price-determining variables . ...”
Jack M.
Guttentag and Edward S. Herman, Banking Structure and Performance
(New York: New York University Institute of Finance, Bulletin Nos. 4143, 1967), p. 82.
5

Almarin Phillips, 1'Structural and Regu1ator.y Reform for Commercial Banking," Issues in Banking and Monetary Analysis, eds.
G. Pontecorvo et. al. (New York: Holt, 1967), pp. 7-30; Phillips,
Market Structure, Foanization
and Performance (Cambridge: Harvard
University Press, 1962); Phillips, "A Conceptual Optimal Banking
Structure for the United States:
Discussant," Proceedings of a Conference
on Bank Structure and Competition (Chfcago:
Federal Reserve Bank of
Chicago, 1969), pp. 35-40. Compare Broaddus, pp. 2-10; Guttentag and
Herman, pp. 66-67, 80.

Entry

-I

Private

Inter-

i
Indivlduol

Figure 1.
.

Flow Chart of "The Market Process"

I
Source: Adapted from Almarin Phillips, "Structural and Regulatory Reform
for Comxrcisl Bznking," Issues in Canking and Monetar Anal sis
eds. G. Pontecorvo -et al.,jew
York: Ilolt,1967~y~&i&
duccd by permission of /ilmarinPhillips.

1

--

1,

-.

the range of firm behavior.: Moreover, Government regulatory policies
clearly dampen both new bank entry and bank "exit" as independent
decision-making

entities by:merger.

(Allowing the exit of badly

managed banks through totalcessation

of operations when unprofitable

seems to be contrary to public policy.)
The central section of Figure 1 shows that the number, sizes,
and locations of firms are influenced by structural changes, which in
turn are a direct function of Government regulations such as branching
laws as well as of firm behavior.

The behavior of firms also directly

influences the sizes of existing companies through plant and equipment
investment, which is a direct growth mechanism.

In banking, however,

investment in "capital accounts" will necessarily augment the size of
the firm through the acquisition of financial assets as well as through
the purchase of plant and equipment, given regulatory supervision of the
capital structure of the bank by guideline ratios that generally relate
risk assets and deposit liabilities to bank equity.

A bank can thus

only acquire new deposits to purchase financial assets if it invests
its "own funds" over time.
As banks grow, they may come to dominate their smaller competitors, allowing them to restrict the effective supply of bank services
through a quasi-monopolistic

relationship.

Alternatively,

in absolute size, they may ienjoy real (data processing,
cial (portfolio-related)

as banks grow

labor) or finan-

economies of scale in their operations that

should allow them to lower ,the cost and, hence, increase the supply of
I
their intermediation services. Technology, a function largely of external
influences (business-machine

company research) in this industry, may

-6-

generate such economies of scale, although the progress of the minicomputer industry may allow smaller banks to increase their operational
efficiency to match that of larger banks.
These diverse determinants of banking supply functions thus
combine to form the well-known branching-numbers-size
banking.

conundrum in

That is, the achievement of maximum operating efficiency in

the financial services rendered by banks may require the formation by
merger of gigantic branch systems of a size capable of absorbing the
deposits of an entire state.6

In

the lower right-hand section of Figure 1, the ultimate

market demand for financial services is largely external to a bank,
being based upon real-sector and monetary-sector

variations such as pop-

ulation growth, business activity, and economy-wide financial trends.
(Some forms of imperfect competition may allow a firm to alter the
slope or position of the demand curve it chooses to operate along,
however.)

The intersection of supply and demand vectors determines

various dimensions of banking performance, which are directly observable
in the market place.

Markedly imperfect competition, some forms of

regulation such as high reserve requirements, and contractionary
exogenous forces should reduce observed performance; while aggressive

6

A bank with $800 million in deposits appears to be more
operationally efficient than any smaller combination of firms, according
to six studies compared b.y "Bank Costs and Output--A Commentary on the
Evidence," Midwest' Banking in the Sixties, ed..Dorothy Nichols (Chicago:
Federal Reserve Bank of Chicaqo, 1970), P. 190. If so, then Alaska, New
Hampshire, Vermont, and the Virgin Isi&&
should have-been monopoly-bank
areas, while eleven other states should have been banking duopolies, if
reflecting later technological advances, based on 12/31/68
not monopolies
deposit levels. U. S. Department of Commerce, Statistical Abstract of the
United States (Washington: Government Printing Office, 1969), p. 445.

,

-7-

firm behavior, some other forms of regulation designed to increase
competition, and expansionary external forces should stimulate observed
performance.

In turn, bankers, customers, and regulators will change

their decisions over time corresponding to their desires to improve
industry performance to increase their own utility functions.

The

dashed lines in Figure 1 show that such feedback effects occur over
time, altering the conduct of all participants

in this market process.

(Customer reactions will appear as changes in external influences on
demand; new entrants will be attracted by high potential profits in an
area, etc.) In competitive

industries the feedback from performance

to structure is assumed to very strong.

Imperfect competition will make

this feedback subject to behavioral and regulatory intervention, as
shown in the left-hand side'of Figure 1.
Clearly, various causes of banking performance work with,
through, or in opposition to each other over time in this model.
model shows that bank behavior

This

(competition), structure, and regulation

are separate concepts that interact with external influences to form
bank performance.
and performance

In theory, any relationship between, say, technology

is a one-totone association.

Yet, in practice the

observed correlation may not be of the predicted direction or magnitude.
This effect may occur when strong influences, such as Government regulation, swamp the effects of some of the other influences illustrated
Figure 1.

in

(How did technology--a direct determinant of supply in Phillips'

original model --limit bank passbook deposit savings interest rates to
4.50% in the 1970-71 period?)

-8-

BANKING DATA

One standard way of approximating

these types of interactive

effects is to compute simple correlation coefficients for
representing the influences illustrated in Figure 1.

variables

Fortunately,

numerical proxies for most of these influences can be created in forms
that allow the relative comparison of banks in various locations over
time.

In

order to explore inductively this approach to banking per-

formance, fifty-three variables are computed for a sample of 1,644
banks in 44 states.

These variables are selected to represent impor-

tant theoretical or institutional banking traits,

based

in part upon

the influences found important by previous researchers.
The data consist of averaged yearly ratios at essentially the
bank level or the appropriate external-environment
cover the sample period of 1969 through 1971.7
these variables.
managerial

(state) level and

Table 1, below, lists

They are divided into regulatory (R), structural (S),

(M), demand (D), and performance

(P) categories for ease of

exposition.
Their correlation matrix, containing 1,378 items of information, is not shown because of space limitations.

Over 67% of its

correlation coefficients are significant at the 0.01 level, while
another 10% of its correlation coefficients are significant at the

7

Unpublished data were provided by the Board of Governors of
the Federal Reserve System and by the Federal Deposit Insurance Corporation. See Jackson, Chapter V. The period studied was one in which bank
accounting methods were roughly comparable to those of industrial fimrs.
Moreover, the distortions of wage and price controls did not significantly
affect banking during this period.

-9-

Table 1.

Banking Variable List

REGULATORY TRAITS (O-l dummy variables)

Rl

:

R2 :

STRUCTURAL VARIABLES

(by state)

national bank

s,

:

yearly entry rate, relative to firm numbers

state member bank

s*

:

yearly merger rate , relative to firm numbers

s3

I

5-banking organization deposit concentration
ratio, 1969

*-~-insured nonmember banks
R3 *

--

R4 :

unlimited branching state

R5 :

limited branching state

R6 :

unit only state

R7 :

unlimited multibank holding company state'

RB :

limited multibank holding company state

Rg :

multibank holding companies prohibited state

1
Changes in bank holding company regulation
have made R,, RQ, and R, less important than they
were during'thi? period?

s4 :

S3's long-term change, 1961-69

s5

:

mean bank size, 1969 deposits

s6

:

coefficient of variation of bank deposits,
1969 (Sg/its standard deviation; bank size
variation)

s7

:

Herfindahl index, 1969 deposits (the sum
of all banks' squared market shares; an
oligopoly proxy)

S8 :

Gini coefficient, 1969 deposits (inequality
of size)

sg

mutual savings bank and savings and loan
association time and savings deposit market
shares, 1970 (nonbank competition)

:

-~-----

- 10 -

Table l--continued
MANAGERIAL VARIABLES (bank figures)

Ml :

branchinj dummy variable, 0 or 1 branches
operated

M2 :

branching dummy variable, 2 to 5 branches
operated

M3 :

branching dummy variable, 6 or more branches
operated

M4 :

multibank holding company affiliation dummy
variable

M5 :

time and savings deposits/total deposits

M6 :

"investments"/assets

M7

:

M8 :

cash/assets (liquidity)
agricultural loans/loans

*Data deficiencies prevented the treatment of
bank branching as a cardinal variable.

Mg :
Mlo:
M11:
M12:
M13:
M14:

commercial and industrial loans/loans
consumer and individual loans/loans
trust revenue/total revenue
equity/assets

(leverage measured inversely)

labor expense/revenue
occupancy expense/revenue

M15:

dividends/net income (a proxy for the goal
of the firm acting through "investment")

96:

bank asset size (economies of scale)

- 11 -

Table l--continued
DEMAND VARIABLES

(by state or year)

PERFORMANCE VARIABLES

Dl :

percentage of labor force in agriculture

Dp :

percentage of labor force in manufacturing

D3.:- percentage~of laborforce
and real estate

-in finance.,

insurance, -.

D4 :

unemployment rate

D5 :

population density

D6 :

urban population percentage

D7 :

per capita income

D8 :

population growth rates, 1960-70

Dg :

gross state product growth rates, 1960-70

P, :

operating revenue less demand deposit service
charges/assets (a proxy for output relative
to bank assets in flow terms)

P2 :

net income/equity

P3 :

loan interest minus loan loss provisions/loans

P4 :

time and savings deposit interest/time and
savings deposits

P5 :

Y3 minus YJ, price spread (the "price of bank
intermediation services")3

i$j

D10:
D69:
D70:
D71:

households per banking office
1969 time dummy variable
1970 time dummy variable
1971 time dummy variable

(bank figures)

:

(profitability)

~.

~-~

loans/total deposits (a stock-type output
prow)

'This linear combination of variables can be
analyzed since the factor analysis model (unlike.
the usual regression model) contains no intercept
term. It may approximate the overall "monopoly
power" of a bank, to a better extent than Lerner's
index. Ti bar SCI~~OVS~JP,
"Economic Theory and the
NBER, Business ConMeasurement of Concentration,"
centration and Price Policy, (Princeton: Princeton
University Press, 1955), p. 105.

~~----

- 12 -

0.10 level.

Numerous interactions between nominally independent traits

thus seem to exist in the environment of this industry.8

FACTOR ANALYSIS TECHNIQUE

Clearly, the underlying relationships among these correlated
variables should be isolated.

Multivariate

summarize such interrelationships.

analysis may be used to

(The process of completely speci-

fying Figure 1 would involve the estimation of an excessive number of
differential equations in a way resembling the construction of a
general equilibrium system.')
variable interrelationships

One approach to reducing these banking

to manageable proportions is factor

analysis.
This technique seeks to isolate common dimensionality
the clustering together of interrelated variables.

through

It is both an

exploratory analysis that seeks to "map" domains of common influence
and a method of data reduction.

Factor analysis will outline the

8
The variable correlations range in value from -0.73 to 0.82.
A value of 21.0 would show a perfect fit, in which such variables would
be identical. The variables thus embody multicollinearity ("many-onthe-same-line") that frustrates multiple-mode regression techniques
generally used in banking analyses.
"... when multicollinearity occurs,
each variable in the collinear set may be sharing in the explanatory
role of any and all variablesin the set. Consequently, it is very
misleading to interpret the partial regression coefficient as the distinct effect of a separate, individual variable." James L. Murphy,
Introductory Econometrics (Homewood, Ill.: Irwin, 1973), p. 369.
9

Phillips, "Conceptual," pp. 35-40.

I

- 13 -

I
common patterns that underl!e any large data set.

10

Factor analysis is designed to reduce any correlation matrix,
by a least squares fit, to a space containing the minimum dimensions
that are necessary to explain the data's basic variability.

As shown

by Table 2, below, for any set of n variables V, through V,, this
procedure will estimate m statistically

independent "factors," Fl

through Fm, in a series of linear equations.

In

Table 2, the a's

are the factor loadings that connect the derived factors F with the
known variables V.
coefficients

These factor loadings are multivariate

correlation

that measure the extent of association between the factors

and the variables.

The m factors represent the basic "dimensions"

(where m should be less than n) that explain the variation
observed variables.

Characteristics

in the

that are highly related will

cluster onto a factor, while unrelated ones (being orthogonal
other in factor space) wills appear on different factors.

to each

In the last

column of Table 2, corranunalityis the proportion of total variance
in a characteristic
together.

that is explained by all of the factors taken

Communality, the sum of squared factor loadings across

rows, is thus the analogue of R2 in regression analysis.

(The Appendix

may further clarify the essence of this analytical technique for those

10

R. J. Rummel, Applied Factor Analysis (Evanston: Northwestern
University Press, 1970.) Examples of its application in financial
analysis include Saunders ; iLeonal1 C. Andersen and Jules M. Levine, "A
Test of Money Market Conditions as a Means of Short-run Monetary flanagemerit," National B;;,"lnz Rev,iew, IV (Sept., 1966), 45-48; and.William L.
f Regulation, Population Characteristics, and
Sartoris, "Th Ef
Competition 0: the Market for Personal Cash Loans "'Journal of Financial
and Quantitative Analysis, iv11 (Sept., 1972), 194&53.

- 14 -

Table 2.

Factors

IA
aJ
F
n
CTJ
*r
L
2

Fl

Factor Analysis Equation System
F2

. . .

Fm

Comnunality

v,

=

allFl. + a12F2 + . . . + almFm

Eta1 I2

v2

=

a2,Fl + a22F2 + . . . + a2mFm

cb212

v3

=

a3lFl + a32F2 + . . . + a3mFm

zb312

.

.

.

.

.

.

.

.

v,

=

a,,Fl + an2F2 + . . . + a

nmFm

Han)2

,

- 15 -

I
who are unfami liar w ith it,,since the mathematics

of factor analysis

is too complex to be concisely discussed.)

EMPIRICAL ANALYSIS

The empirical factor analysis of banking influences shown by
Table 3 thus attempts to isolate the common causality present in highly
correlated banking data.

11 ~
lThis analysis captures over 64% of the

total variance in the data set.

It shows that thirteen independent

dimensions exist among the fifty-three bank-related variables analyzed.
The first thirteen columns of Table 3 are the factor loadings (exceeding
0.30 in absolute value) that connect the variables with the factors.
The communality column shows that this analysis generally explains most
of the variation in this data set.

In particular, the communality for

most of these traits exceedjs the R2 values generally obtained by microbanking cross-sectional

studies.

CLUSTERING
OF BANKING
TRAITS
The analysis is b:est visualized by reading down the factor
loading columns.

The signs of the loadings are meaningful

only along

'lTechnically, factors are extracted from the correlation
matrix with unities in the main diagonal using the eigenvalue-one
criterion, iterated through eight cycles of communality estimation.
The factors are rotated through sixteen cycles to a varimax solution.
Computer program BMD08M is ,utilized. m
Biomedical Computer Programs,
ed. W. J. Dixon (Berkeley: University of California Press, 1973),
pp. 225-68. This technique is better suited than is Saunders' principal
Principal components
components for the isolatiqn of common variance.
forces most variables onto,one or two "general" factors, with important
sources of data variation being relegated to weaker, "bipolar" factors.

- 16 -

Table 3.

Factor Analysis of Banking Data,
rounded to two decimal places

Variable

Factor
Fl

F2

F3

F4

F5

Rl

0.84
-0.76
-0.33

R6
R7

0.31

R8

-0.58

0.79

-0.33

R9
s1

-0.45

52

0.58

53

0.80

-0.32

s4
55

-0.54

0.37

s6
0.86

S7
'8

-0.42

S9

-0.67

1'1

0.48
-0.39
-0.31

0.68
-0.45

0.39

;

-17-

'Table 3--continued

I

Variable
Fl

Factor
F2

F3

M5

-0166

M6

-0.42

F5
0.49

0.71

M7
M8

F4

0.49

0.36

-0.34

0.74

M9
ho

0.63

'411

-0.51

Ml2

-0.52

'93
Ml4
0.31

Ml5

0.63

Ml6
Dl

0.36

0.77

-0.63

D2
D3

-0.75
IO.33

D4
D5
D6
D7
D8

-0.67
-0.87
-0.80
-0.57

D9
DlO

-0.67

-0.41

- 18 -

Table 3--continued

Variable

Factor
Fl

F2

F3

D69
D70
D71
pl
p2
p3
0.40

p4
P5
'6

,

F4

F5

-19-

Table 3--continued

Variable
F6

/
'F7

Factor
F8
-0.75

Rl
R2

0.80

R3
R4
R5
R6
R7
R8
R9
Sl
S2
53
54
55
s6
57
s8
S9
Ml
M2
M3
M4

0144

F9

FlO

- 20 -

Table 3--continued

Variable

Factor
F6

F7

F8

M5
M6
-0.38

M7
M8
M9
M10

-0.51

Ml1
Ml2
Ml3
Ml4

-0.40
-0.38

Ml 5
I416
Ol
D2
D3
O4

-0.45

D5
D6
D7
D8
D9
DlO

0.52
0.87

F9

FlO

- 21 -

(Table 3--continued

Factor

Variable
F6

F7

F8

F9

FlO

-0.83

D69

D70

-0.83

0.48

0.86

0.46

-0.55

0.32

-0.79

0.32
0.46

-0.83

- 22 -

Table 3--continued

Variable
Fll

Factor
F12

Comunality
Fl3
0.63
0.11
0.71
0.77
0.71
0.78
0.82

0.78
0.33

0.66
0.82

-0.83

0.43
0.57
0.79
0.35
0.61
0.79

0.68
0.85

-0.70

0.95
0.73
0.66
0.27
0.32

0.34

0.24

- 23 -

Table 3--continued

Factor

Variable
Fll

Fl2

Comnunality
813
0.83

-0.68

0.72
0.79
0.63
0.61
0.45
0.49
0.33
0.60
0.39
0.19
0.53
0.83
0.59
0.79
0.57
0.76
0.87
0.85
0.75
0.82
0.77

,

- 24 -

Table 3--continued

Variable

Factor
Fll

F12

Communality
F13
0.71

D69
D70

0.92

D7l

0.97
0.44

0.76
0.16
0.79
0.57
0.74

0.88

0.90

I

- 25 -

one factor or as related tom a variable loading on two or three common
factors.

These loadings , ais correlation coefficients, measure relationI

ships On a minus One to plus one scale (the -0.30

I

to 0.30 range, h*hich

explains less than 10% of the variance in common between a factor and a
variable, is not worth reporting).
characterizes

For convenience, Table 4,

below,

the results of this analysis.

The first two factors show statewide trends.

Fl, clustering

structural forces with demand, shows the association between limited
holding company states, newt entry, large average bank size, deposit
inequality (3~)~ nonbank CO&petition,
density, urbanization,

financial activity, population

per capita income, population growth, and house-

holds per banking office, in opposition to unlimited multibank holding
company States , agriculturaj

loans , and agricultural employment.

It

I
seemingly reflects some regFona1 traits, illustrating one vector of
higher-order

./
(fourteen-variable)

correlation present among this indus-

try's possible sources of performance.

F2, "state-concentration,"

clusters unlimited branching laws, mergers, the concentration

ratio,

large average bank size, Herfindahl concentration, deposit inequality,
I
and the unemployment rate in a negative relationship with unit-only
I
This factor illustrates the tendency for banks to branch,
legislation.
merge, and concentrate where permitted that some economists would describe
I
as the search for real

or ~financial economies of scale and other econoI
mists would describe as monopolization.
I
The third factor,' "large-bank" influences, associates branch
system banks, cash holdings~, commercial and industrial loans, trust
I
activity, the payout ratio, bank asset size, and time and savings deposit

- 26 -

Characterization

Table 4.

Variables

Factor
Fl

R8, Sl, S5, S8, Sg,

of Factors for Banking Data*

Included

D3, D5, D6, D7, D8, D10

Characterization
State
Structure-Demand

R7, M8, D,

F2

State
Concentration

R4, SE, S3, S59 S7, S8' D4
R6

F3

F4

F5

M3,

)I79

Mg, Ml,, M15,

Ml, M5,

M6

R5,

S2,

M23 D2,

R6,

Ml, M8s D,‘

R8’

sg, M8' Ml29 Ml3

Ml63

P4

Large Banks

Limited Branches
Versus Units

D5

Financial
Ratios

M5

F6

Ml03 Ml33

F7

S4, D8, Dg

M,4s

P,, P3,

P5

Price and Cost

Economic Growth

D4

*Variables are listed with the dominant-signed pattern on the first
line and the opposing-sign pattern on the second line.

- 27 -

iTable 4--continued
Characterization

Factor
F8

5'

M7

Bank Legal Status
and Liquidity

I

R3

F9

Time
071
D70

FlO

D70' 071' pl' P35 P4

Banking Time Trends

D69

Fll

Multibank
Holding Companies

R7' M4
R9

F12

M6

F13

Bank Output
Proxies

'1' '6

R8' '6
'8

,

State Deposit
Size Variation

- 28 interest rates in a negative direction from unit-type banks, time
and savings deposit liabilities, and bank portfolio securities.

F3

thus shows an association between bank product mix and size that
makes casual observations

in banking analysis highly dangerous.

is the limited branches versus units factor.

F4

It shows that limited

branching states, bank mergers, moderately branching banks, manufacturing activity, and population density are generally clustered
oppositely from unit states, unit-type banks, and agricultural
activity,

limited branching and not large branching

Interestingly,

banks seem to be the direct opposite of unit banks on this factor.
F5 assembles limited holding company states, nonbank competition, agricultural loans, low leverage, and labor expense in a largely
financial pattern that is negatively related to the time and savings
deposit ratio.

F6 is an interesting price-cost relationship.

It

relates consumer and individual loans, labor expense, occupancy expense,
adjusted revenue/assets,

risk-adjusted

price-cost spread ratios to each other.

loan interest, and the financial
This important factor is dis-

cussed in depth in the next section.
The seventh factor, reflecting statewide economic patterns,
associates an increase in banking concentration positively with population growth and economic growth but negatively with the unemployment
rate, reflecting the consolidation of bank resources that may be
necessary to accommodate
status and liquidity,

rapid economic growth.

F8 captures bank legal

showing that national banks have higher cash

ratios than expected while state nonmember banks have generally low
pure liquidity ratios, reflecting their low levels of required cash
reserves.

~

- 29 -

F9 is a rather definitional time pattern.
shows strong banking time trends.

It

FlO, however,

associates adjusted revenue/assets,

risk-adjusted loan interesti, and deposit interest rates paid with the
1970 and 1971 years in opposition to the 1969 year, as discussed below.
The eleventh pattern clearly outlines a multibank
company dimension.

F12 is the bank output proxy factor.

both the adjusted revenue/assets

holding

It

shows that

and loan/deposit ratios are negatively

related to the bank portfolio securities ratio.

(The historical function

of a bank is, clearly, to lend and not to hold cash or to purchase debt
securities at relatively 1oW interest rates except for use as internal
reserves.)

The last factor, state deposit size variation, shows that

limited holding company legjslation and deposit size variability are
oppositely related to bank size inequality.

CONCLUSIONS
: PERFORMANCE
V/$RIABLE
RELATIONSHIPS
The communality column of Table 3 shows that this analysis has
explained a large percentage of most of the banking variables of this
study.

For example, about 90% of the variance of the loan/deposit

ratio (P6) is explained by the factor

analySiS.

The factor analysis captures all but two variables:
membership

and profitability.

It

would thus appear that bank profitability

is not strongly related to any of the variables considered.12

12Table

state bank

Tentatively,

3 shows patterns of association, which are not necessarily causal in nature. However, traits highly conducive to any of the
performance variables will load.on the same factor with that variable.
Irma Adleman and Cynthia T. 'Moriss, "A Factor Analysis of the Interrelationships Between Social and Political Variables and Per Capita Gross
National Product ,I’ Quarterly’Journal
of Economics, LXXXIX(November,

1965), 555-78.

- 30 -

internal bank returns would appear to depend on intangible managerial
quality to a larger extent than the other performance traits would.
In particular, state bank membership per se (exclusive of reserve
effects such as excessive cash requirements) would not appear to depress
bank profitability,

according to this analysis.

The performance variables P,, P3, and P4 are evidently directly
demand-determined
formance variables

on FlO.

The proximate supply determinants of the per-

(except for profitability) appear on factors such as

F3, F6, and Fl2, which largely contain portfolio and operating characteristics that are apparently internal to a bank.

These supply traits

may be indirectly related to other forces, however, such as bank regulation, as theoretically implied by Figure 1 and as empirically implied
by the overlapping of some factors through the common factor loadings
of variables such as M6 and P,.

13

This adjusted revenue/assets

ratio, P,, first loads on F6,

being related to price elements such as higher-yielding

consumer loans

and, as expected, the differential between adjusted loan interest rates
received and time and savings deposit interest rates paid.

It

is also

positively associated with both cost element ratios, since higher costs
imply higher average prices.

(Alternatively, costs may rise under im-

perfect competition to meet price.)

Risk-adjusted

is associated on F6 with the same elements.

loan interest, P3,

Moreover, the financial

13Either principal components or "oblique rotation" would show
even greater overlapping of variable loadings. Rumnel, pp. 338-45, 395-

432.

I

- 31 -

price-spread ratio, P6, is $ssociated with labor and physical-capital
costs as well as with price; elements on F6.
of the complementary

To the extent that the costs

inputs to time and savings deposits are at high

levels, such costs would be expected to keep output low and, hence, to
keep the average financial ;/price of intermediation

services" of a

with high labor and physicail-capital costs at a high level.

bank

P5 is also

associated on F6 with relatively uncontrolled loan rates to a far greater
i
extent than it is with deposit interest rates paid. This tendency
I
clearly reflects the depressing effects of Regulation Q on time and
savings deposit interest rates during this period.
The adjusted revenue/assets
seems to share some of the traditional

ratio also loads on F12.

It

bank output characteristics

thus
of

14
the loan/deposit ratio (P,),, with its associated low portfolio securities ratio.

I

The time and savings deposit interest rate, P4, appears in the
i
F3 pattern. This price is, to a considerable degree, associated with
!
large-bank influences such was branching systems and banks that extend
1
relatively large amounts ofi loans--particularly commercial loans.
I
Somewhat surprisingly, given the demand-depressing

recession

occurring during part of th~is period, the adjusted revenue/assets,

loan

interest, and deposit interest variables all exhibit a rising time trend
pattern from 1969 through 1~971. This result is independent of any other
i
measure of competition on 610.

Thus, the relatively tight-money environ-

ment of 1970 and 1971 clearly raised average bank rates received on both

14

Broaddus, p. 7.:

- 32 -

loans and total assets relative to those of 1969.15

The liberaliza-

tion of Regulation Q during 1970 also strongly appears in the loading
of P4 on this factor.

These effects are consistent with an external

increase in the nominal demand for banking services.
trends, as well as microeconomic

characteristics,

to influence banking performance very strongly.

Short-term time

accordingly seem
Banking law based on

the experience of the Great Depression, over thirty years ago, may
thus be somewhat invalid in the 1970's.
Clearly, many interactive relationships are present in the
environment of the banking industry.

Researchers examining banking

performance should carefully note such clusters of characteristics
before attempting to strictly define banking causality.
numerous correlated variables

(loading on one or more common factors)

in regression may thus give rise to econometric
studies.

16

The use of

inconsistencies

in banking

More importantly, given these complex patterns, policy makers

should not be surprised if attempts to restrict banking competition lead
to unanticipated,

if not undesirable, effects on the nation's financial

structure, conduct, or performance.

15
Although some interest rates declined in 1971, the average
yields on bank earning assets remained greater in 1971 than they were
in 1969. FDIC, Bank Operating Statistics
(Washington: FDIC, 1969 and
1971, n.p.).
16
As examples, deposit inequality (S8) and agricultural loans
(M ) would be poor regressors, since they load on three factors. On the
ot Rer hand, the variable loadings on Fl support the variable deletions
made because of multicollinearity before regression by Eric Brucker,
"A Microeconomic Approach to Banking Competition," Journal of Finance
(December, 1970)' 1133-41.

I

- 33 -

APPENDIX: 1 FACTOR

ANALYSIS
ILLUSTRATED

The nature of the! banking-variable factor analysis may be
I
clarified by an identical analysis of simpler variables whose nature is
known in advance.

The reduction of multicollinearity

and isolation of

common variance by factor analysis may be illustrated by factoring
physical-object

data

to a conceptually greater extent than that re-

sulting from a discussion of the hyperellipsoidal

projections of vectors

in m-space that underlie factor analysis. 17
For this example,~ a length "L" and width "W" dimension

is

estimated for each of one hundred rectangles, each of which is denoted
by the subscript "i."

Variables are created, including a one-digit

random number e introduced as a "noise" element, by the formulas shown
in Table 5.18
Table 5. ~Rectangle Data Formulas

xJi T

Li

'2i y wj
x3i = 1OLi + e3i
17

For example, the reader unfamiliar with factor analysis is
unlikely to find his knowledge significantly increased by the statement
that it begins by finding "the orthonormal eigenvectors of the matrix
for which a similarity transformation is its eigenvalue matrix" (Rummel,
p. 99) to create the original factors that are subject to later, more
complex, transformations.
~
I
18The data are taken from William Cooley and Paul Lohnes,
Multivariate Procedures forithe Behavioral Sciences (New York: Wiley,
lg62), pp. 154-57. Copyright 1962 by John Wiley and Sons, Inc., and
used with its permission.
i

- 34 -

'4i
x5i
'6i

= lOWi + e4i
= 20Li + 1OWi + e5i
= 20Li + 20wi + e6i

x7i = 1OLi + 20Wi + e7i
'8i

= 40Li + 1OWi + egi

As would be expected, these interactive variables generate an
extremely multicollinear

correlation matrix, whose elements are shown in

Table 6.
Rectangle Data Correlation Matrix

Table 6.

Variables

Xl

Xl
1.000

x2
x3
x4
x5
'6
x7
x8

x2

x3

x4

x5

'6

x7

x8

.140
1.000

.987
.160
1.000

.168
.930
.185
1.000

.931
.491
.927
,489
1.000

.804
.693
.807
,671
.962
1.000

.597
.887
.608
.835
.848
.950
1.000

.980
.331
.972
.347
,984
.903
.743
1.000

Clearly, less than eight independent dimensions exist in these
data, since these correlation coefficients are almost all significant at
the 0.10 level of a two-tailed test.

A statistically

independent data

set, in contrast, would generate insignificant, low correlation coefficients near zero.

The two underlying independent dimensions in these

data are shown by Table 7, below.

- 35 -

Factor Analysis of Rectangle Data,
rounded to two decimal places

Table 7.

Variable

Factor 1, "L"

Xl
x2
x3
X4
x5
x6
x7
x8

1.00
0.08
0.98
0.11
0.91
0.77
0.55
0.97

Factor 2, "W"
0.06
1.00
0.08
0.93
0.42
0.63
0.84
0.26

Communality
1.00
1.00
0.98
(s.87
1.00
0.99
1.00
1.00

Clearly, factor 1 outlines length (variables X1, X3, X5, X6, X7, and X8),
while factor 2 captures width (variables X2, X4, X5, X6, and X7).

Varia-

bles X5, X6, and X7, being derived from both length and width elements,
load on both factors.

These factors can also be seen as plotted in

two-space by Figure-Z, below.

If some of the variables had negative

relationships, more than one quadrant of the figure tiould possess variable
points.

Figure 2.

Plot of Rectangle Factor Analysis