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FUNDAMENTAL REAPPRAISAL OF THE DISCOUNT MECHANISM

AN EVALUATION OF SOME
DETERMINANTS OF
MEMBER BANK BORROWING
LESLIE M. ALPERSTEIN
Prepared for the Steering Committee for the Fundamental Reappraisal ofthe
Discount Mechanism Appointed by
the Board of Governors of the Federal Reserve System




The following paper is one of a series prepared by the research staffs of the Board of Governors
of the Federal Reserve System and of the Federal Reserve Banks and by academic economists
in connection with the Fundamental Reappraisal of the Discount Mechanism.
The analyses and conclusions set forth are those of the author and do not necessarily indicate
concurrence by other members of the research staffs, by the Board of Governors, or by the Federal
Reserve Banks.







FUNDAMENTAL REAPPRAISAL OF THE DISCOUNT MECHANISM

An Evaluation of Some
Determinants of
Member Bank Borrowing

by

Leslie M. Alperstein
Formerly an Economist, Board of Governors, Federal Reserve System

1969

FUNDAMENTAL REAPPRAISAL OF THE DISCOUNT MECHANISM
An Evaluation of Some Determinants of
Member Bank Borrowing
by Leslie M. Alperstein

The major focus of this paper is to identify the determinants
of member bank borrowing and to measure certain relationships which exist
among these determinants.

Regression analysis is used to contrast various

forms of borrowing from the Federal Reserve with borrowing from sources
other than the Federal Reserve.

This methodology was selected so that it

would be possible to assign measurable weights to the causal factors felt
to be most responsible for borrowing and then compare these factors as
they differ in their ability to explain variations in borrowing from the
Federal Reserve as distinct from other sources.
It is becoming increasingly clear that the distribution of
financial assets throughout the banking system can materially affect the
speed and efficiency with which a given monetary policy takes hold.

Banks

of various sizes may be expected to respond differently over the business
cycle to changes in financial variables such as liquidity and interest
rates.

To the extent that banks react to fluctuating credit conditions

by adjusting their liquidity positions, they can affect to a significant
degree the amount of borrowing and credit expansion that takes place.
Consequently, both bank size and liquidity are examined in this paper
and tested for their significance in explaining different types of
borrowing.




-2-

Insofar as the structural characteristics of banks which borrow
from the Federal Reserve influence the degree to which they borrow,
sensitivity to interest rates has traditionally been a popular determinant.
The literature has from time to time reflected discussions, both theoretical
and empirical, on the influences of interest-rate spreads on banks 1 sensi­
tivity to borrowing.

Interest rates are examined closely for their influence

upon borrowing per s e , as well as for their degree of interaction with other
determinants of borrowing.
A discussion dating back only a few years centers around the
effects on member bank borrowing of possible differences in the administra­
tion of the discount window among the various Federal Reserve districts.
In order to facilitate a closer look at this problem an attempt is made
to distinguish between supply and demand factors in determining borrowing
among several Federal Reserve districts.
The variables tested for their significance in explaining borrowing
from the Federal Reserve and borrowing from other sources were:

(a) a

liquidity ratio, designed to reflect the banks 1 ability to meet loan demands
and unexpected deposit withdrawals out of internally generated short-term
assets;

(b) an interest-rate differential between the discount rate and

3-

month Treasury bill rate, to reflect the impact of banks 1 response to
least-cost considerations;

(c) the size of bank, to indicate differences

in the likelihood that some banks--say, those associated with financial
centers--might be less reluctant than others to borrow from the Federal
Reserve; and (d) Federal Reserve district, to shed light on the problem of
alleged differences in the administration of the discount window.




-3-

To lessen the degree to which the statistical results would be
affected by problems associated with aggregated data, the initial part of
the study examined the borrowing behavior of individual banks.

Tests were

made on weekly reporting member banks for six Federal Reserve districts
during the period July 1959 to October 1961.
The tests were divided into two parts:
and time-series analyses.

cross-section analyses

The cross sections estimated the relationship

between the likelihood of a borrowing by a particular bank and factors
associated with its indebtedness.

Additional cross sections estimated the

relationship between the frequency of borrowing from the Federal Reserve
and the postulated determinants of borrowing.
The time-series regressions estimated the relationship between
borrowing and the independent variables--liquidity, size, and district-and then with the addition of the temporal variable, the interest-rate
differential.

I.

Summary of Findings and Conclusions
The results of the cross sections and the time-series regressions

suggest that the liquidity condition of a bank*s short-term asset portfolio
as well as the interest differential between the discount rate and the bill
rate contributed significantly toward explaining variations in borrowing
from the Federal Reserve.

Of the two factors, liquidity had the greater

impact on borrowing in all of the periods studied; but in those periods
when the discount rate was less than the bill rate, the importance of




-4-

liquidity as an explanatory factor diminished somewhat in favor of the
interest-differential factor.
The behavior of the liquidity and interest-differential variables
supports the least-cost hypothesis--that banks, in general, are sensitive
to interest-rate differentials to the extent that they will borrow from
the least expensive source even when that source is the Federal Reserve.
In the period when the bill rate exceeded the discount rate, the explanatory
power of the bank liquidity variable in explaining the likelihood of in­
debtedness to the Federal Reserve was not quite half that made as when the
discount rate exceeded the bill rate.

This suggests that banks are less

reluctant to borrow from the Federal Reserve when it is the least expensive
alternative source of funds.
Banks borrowed more often when it was profitable to do so.

The

frequency of borrowing from the Federal Reserve was negatively associated
with liquidity, corroborating the results of the conditional probability
estimates.

Banks were more likely to borrow, and borrowed more often,

from the Federal Reserve with relatively higher levels of liquidity when
the bill rate exceeded the discount rate.

The cross sections demonstrated

that in the period when the bill rate exceeded the discount rate (rb > rd)
banks were less willing to use Treasury bills as a secondary source of
reserves and shifted instead to the Federal Reserve.
The time-series regressions supported the inferences made from
the cross sections.

When the interest-rate differential was explicitly

included in the regressions, banks were found to be sensitive to variations




-5-

in the interest-rate spread as well as to variations in liquidity levels.
Inasmuch as aggregate data can sometimes mask the effects of microrelations,
it is not immediately clear whether the variations in relative amounts of
borrowing were being caused by the same number of banks borrowing greater
amounts, the same number of banks borrowing the same amounts but more often,
or fewer banks borrowing greater amounts.

To distinguish between these

effects, an estimate was made of the proportion of banks in each Reserve
District that were borrowing over time.

The results indicated that the

number of banks per district as well as the relative

amounts of borrowing

from the Federal Reserve increased when the discount rate was the leastcost alternative.
On the basis of the regression results, it was concluded that for
the period studied the incentive of banks to borrow stemmed from the
liquidity condition of their short-term assets as well as, and to a lesser
extent, the "profitability" of borrowing.

It cannot be concluded from the

results that banks borrow from the Federal Reserve to reinvest in short­
term Government securities.

It was demonstrated that Treasury bills were

liquidated in periods when the bill rate exceeded the discount rate.

The

results would have been the reverse if banks had been engaged in "profiteer• A !
mg. I
Among the other determinants, size of bank was shown to have a
significant, though uncertain, effect on borrowing from the Federal Reserve.
Although considerable differences were found to exist among banks of varying
sizes with respect to their likelihood, as well as to their frequency, of




-6-

borrowing, no discernable pattern emerged among size groups.

Borrowing from

other sources, however, was found to be an increasing function of size, a
result which was not unexpected.
There was variation among Federal Reserve districts in relative
amounts of borrowing from the Federal Reserve, in the proportion of banks
borrowing, and in the frequency of borrowing per bank.

These results

suggest the existence of other causal factors not explicitly considered,
such as those with characteristics of demand or supply.
If nonuniformities in the administration of the discount function
were, in fact, responsible for the disparate patterns of borrowing among
districts, these patterns would be expected to differ substantially from
those markets in which nonprice rationing was nonexistent.

Banks are not

precluded from borrowing elsewhere--for example, Federal funds markets-on grounds other than price constraints or smallness of transaction.
Therefore, the patterns of ex post borrowing among districts between that
market and the discount window would differ to the extent that funds were
more accessible at some discount windows by virtue of easier lending
policies.

Although the six districts differed substantially with respect

to borrowing from the Federal Reserve after liquidity and cost were taken
into account, there was a similarity in the borrowing for each district by
type of borrowing.

The cross-section findings showed that roughly the

same patterns of borrowing existed among Federal Reserve districts for
borrowing from the Federal Reserve and borrowing from other soures.

The

time-series analysis indicated that the patterns of borrowing were precisely




-7-

the same after taking into account the liquidity condition of the district
as a whole and the interest-rate differential.
This does not prove that supply factors are of no importance in
the determination of differences in borrowing among districts--rather that
for the period of time covered and the districts involved, differences in
demand explained to some degree the importance of the Federal Reserve
district as a determinant of borrowing.

II.

Design of the Study
A.

Data
The sample consisted of nearly all weekly reporting member banks

in six Federal Reserve districts:
Dallas, and San Francisco.
vjere available.

Boston, Richmond, St. Louis, Minneapolis,

These were the districts for which adequate data

Banks for which complete records were not available for

one reason or another were dropped from the sample*

The Bank of America

was dropped because it was believed that this bank was not of the same
nature as the other banks in the sample and, because of its size, might
bias the results.
Each bank was checked for changes in structure.
merged during the period July 1959 to October 1961

Banks which

were deleted.

When

the sample of banks was finally completed, the raw data from the weekly
balance sheets were averaged for 2-week periods giving 35 biweekly
observations for each of the 143 banks.




-8-

Information on interest rates was obtained from the Federal
Reserve Bulletin

and from Section 12 of the Supplement to Banking and

Monetary Statistics, 1966.

Special calculations required for weekly

averages of daily figures on 3-month Treasury bill rates were made
available by the Government Finance Section of the Board1s Division of
Research and Statistics.

B.

Description of the Explanatory Variables
The variables used to explain the various forms in which

borrowing is presented include the following:
a)
where LQ = the ratio of:

LQ - measure of a bankfs liquidity
(Loans to domestic commercial banks + Loans to

brokers and dealers for purchasing or carrying other securities + Treasury
bills + Currency and coin + Balances in banks in the United States - Borrow­
ing from the Federal Reserve - Lagged borrowing from others) to (Demand
deposits adjusted + Time deposits - Required reserves).
The approach taken in this study is to regard the maintenance
of good banker-customer relationships as the deciding factor in assessing
the short-run "needs 11 or liquidity of the bank.

Accordingly, bankers will

alter their optimum asset portfolio in order to accommodate customers who
they feel have long-run profit potentials outweighing current considerations.




-9-

b)

P - measure of the cost of borrowing from the Federal Reserve
in contrast to borrowing from other sources,

where P = (rd - rb), rd = the discount rate, and rb = Treasury bill rate.
When (rd - rb) is negative, there is a negative cost associated with
borrowing from the Federal Reserve.
c)
where

- measure of the bank's demand deposit size

= under $25 million;

$100 million;

= $25 million - $50 million;

= $100 million - $300 million;

= $50 million -

= over $300 million.

In the regressions, the L^'s are represented by dummy variables.
d)

C - dummy variable indicating the bank's reserve classification.
Reserve city banks were assigned a value of 1 for variable
C, country banks were given a value of 0.

e)

- dummy variables representing the six Federal Reserve
districts

where D-^ = Boston;
Du

= Richmond; Dg = St. Louis;

= Minneapolis;

= Dallas; D -^ = San Francisco.
2

III.

Results
A.

Cross-section Analysis
Ordinary least-square regressions were used to ascertain if, and

to what extent, a relationship existed between a bank's borrowing from the
Federal Reserve and such characteristics as size of bank, Federal Reserve
district, and the liquidity position of the asset portfolio.

The conditional

probability estimates predicted the likelihood of nonzero borrowing.

In

addition, they served to indicate the nature of the relationship between




-10-

the independent variables and the likelihood of borrowing, that is, would
banks in one particular district be more likely to borrow than those in
another?
1.

Likelihood of Indebtedness

Four cross sections were taken:

two for dates when the Treasury

bill rate was greater than the discount rate--August 19, 1959, and December
23, 1959--and two for dates when the bill rate was less than the discount
rate, July 22, 1959, and March 16, 1960.

Estimates were made for the

likelihood of borrowing from the Federal Reserve (B^) and from other
sources (Bq ).

The final equations for the conditional probability estimates

1/
were:
—
July 22, 1959
=

B

.549 - .35 3 ( D ) * - .203(D) + .039(D)
(.439)
(.141)
(.140)
(.160)

+

(1)

.256(L2)* + .108(Lo) + . 194(L,) + .015(Lc) - .001(LQ)*
(.107)
(.121)
(.116)
(.161)
(.000)

*

-

.115(D)
(.137)

-

.224(D1?)
(.141)

R 2 = .203, F = 3.352**

August 19, 1959
(2)

Bf =

+

.195 - .110(0^
(.370)
(.1L‘
0

-

.088(Dg) + .208(D9) + .017(DU ) - .084(D12)
(.118)
(.136)
(.116)
(.121)

.224(L2)* + .126(L3) + .153(L4 ) - .074(L5) - .001(LQ)*
(.090)
(.100)
(.093)
(.145)
(.000)

R 2 = .152, F = 2.360*

1/ In all of the equations




* indicates significant at .05 level of confidence and
** indicates significant at . 0 1 level of confidence.

-11-

December 23, 1959
(3)

Bf =

+

.313 - .105(0,) - .031 (Do) - .001(Dq ) - .066(DU ) - .129(D12)
(.402)
(.128)
(.129)
(.144)
(.125)
(.130)

.073(L2) + .030(L3) + .147(L4 ) - .154(L5 ) - .OOl(LQ)*
(.097)
(.111)
(.400)
(.149)
(.000)

R 2 = .079, F = 1.126

March 16, 1960
(4)

Bf =

+

.624 - .236(D-.) - . 154(Dg) - .058(Dq ) - .038(DU ) - .184(D12)
(.465)
(.149)
(.150)
(.170)
(.147)
(.154)

.052(L2) + .087(L3) - .065(L4 ) + .122(L5) - .002(LQ)*
(.110)
(.130)
(.117)
(.206)
(.000)

R 2 = .113, F = 1.674

July 22, 1959
(5)

B

=

.399 - .054(D ) - .099(D.) + .180(D„) - .024(DU ) - .235(D12)
(.422)
(.135)
(.135)
(.155)
(.132)
(.137)

+

.226(L2)* + .251(L3)* + .493(L4 )** + .533(L5)* - .002(LQ)*
(.102)
(.116)
(.112)
(.155)
(.000)

R 2 = .317, F = 6.121**

August 19, 1959
(6)

Bq =

+

.388 + .033(0,).022(D) + .207(D) + .024(D ) (.392)
(.126)
(.125)
(.143) y
(.123) 11

.273(L )* + .279(L )* + . 5 9 5 ( L ) * * + . 6 0 9 ( L ) * (.095) 2
(.106) 3
(.099) 4
(.154) 5

R2 . .404, F = 8.934**




.175(D
(.128)

.002(LQ)*
(.000)

)

-12-

December 23, 1959
(7)

B = .144 - .022 (D,) + . 122(Df ) + .236(D9) + .020(0,,) + .077(D12)
t
°
(.384)
(.123)
(.123)
(.137)
(.120)
(.126)

+

.374(L2)** + .189(Lo) + . 680(L,)** + .491(L-)*.001(LQ)*
(.093)
(.103)
(.094)
(.153)
(.000)

R 2 = .407, F = 9.071**

March 16, 1960
(8)

B

=

.365 - .106(D ) - .017(D„) + .004(Dq) - .008(Dn ) - .098(D12)
(.379)
(.121)
(. 121)
(.138)
( 121)
.
(. 123)

+

.260(L2)** + .409(L3)** + .572(L,)** + .706(L5 ) * * (.091)
(.104)
(.095)
(.157)

.002(LQ)*
(.000)

R 2 = .442, F = 10.484**
Of the eight regressions, six revealed the presence of debt as being
significantly related to the three characteristics:
liquidity.

size, district, and

On each date the reason for borrowing from other sources was more

fully explained than borrowing from the Federal Reserve.

This was to be

expected, however, as certain unobservable variables would affect borrowing
from the Federal Reserve in a different way than borrowing from other sources.
For instance, an ostensibly important factor, the profit spread, has not been
considered explicitly.

The differences in availability of funds from the

discount window and other sources would also affect the ability of the in­
dependent variables to explain borrowing.

It is inferred, therefore, that

2
the relatively lower R 1s for borrowing from the Federal Reserve are explained
at least in part by factors that constrain borrowing from the Federal Reserve




-13-

but not borrowing from other sources, that is, reluctance to borrow and
availability of supply.
For the two equations that showed a significant relationship
between borrowing from the Federal Reserve and the factors determining
the likelihood of borrowing, each of the factors was tested to determine
its net contribution to the total explained variation in indebtedness.
The partial relationships for borrowing from the Federal Reserve and
borrowing from other sources are given in Table 1.

These partial

relationships indicate the amount of explanation contributed by the
addition of the factor considered.
All three factors--liquidity, district, and size--were found to
contribute to the explanation of borrowing.

Worth noting are the differences

in impact of the independent factors on borrowing from the Federal Reserve
in contrast to those on borrowing from other sources.
In terms of the size of the partial coefficient of determination,
the Federal Reserve district made the largest contribution to the explained
variation in borrowing from the Federal Reserve.

In contrast, the district

played a much smaller role in borrowing from other sources, while size ex­
plained most of the variations in such borrowing.

On August 19, 1959, when

the bill rate was greater than the discount rate, indicating that banks
could borrow more cheaply at the discount window, the partial correlation
coefficient for the liquidity variable dropped more than 50 per cent of the
value which it attained when the bill rate was less than the discount rate.




-14Table 1
Partial Relationships of Conditional Probability Estimates of
Borrowing from the Federal Reserve and from Other Sources 1/
Variables in
regress ion

Added variable

Partial coefficient of determination
Federal Reserve
Other sources

July 22, 1959
D.
l

L.
l

L.
l

D.
l

Di

.065
(2.32)*

.214
(9. 04)**

.010
(2 .66)**

.092
(2. 69)**

LQ

.083
(12.29)**

. 163
(26.38)**

L.
1

LQ

.082
(12.18)**

(16.55)**

D ± ,LQ

Li

.052
(1.82)

.146
(5.60)**

L i5LQ

Di

.080
(2.28)*

.071
(2 .00)*

D.,L.
l’ l

LQ

.070
(9.93)**

.089
(12.94)**

D.
l

Li

.061
(2.16)*

.272
(12.40)**

Li

Di

.079
(2.28)*

.095
(2.79)**

D.
l

LQ

.029
(4.06)**

. 186
(31.02)**

L

LQ

.041
(1.57)

. 168
(27.70)**

Li

.062
(2.19)*

.232
(9.96)**

Di

.068
(1.93)*

.066
(1 .86)

LQ

.030
(6.08)**

.014
(21.70)**

.011

August 19, 1959

i
D i»LQ

L.,LQ

Di.Li

1/ F-ratios are in parentheses.
* indicates significant at 0.05 level of confidence.
** indicates significant at 0.01 level of confidence.




-15-

Lending support to the least-cost hypothesis is the finding that
less importance is attributed to liquidity considerations when borrowing
from the Federal Reserve is "profitable.1
1
Borrowing from other sources was influenced very little by liquidity
when the bill rate was greater than the discount rate.

This indicates that

banks are sensitive to changes in interest-rate differentials.

During this

period, the bill rate was also greater than the rate on Federal funds, and
so it is likely that banks tended to absorb Treasury bills during this time
by meeting liquidity considerations through the Federal funds market.
hypothesis is supported by the behavior of the size variable.

This

During the

period when the bill rate was relatively low, the partial coefficient for
size was 0.146 and significant at the 1 per cent level.

When the bill rate

was high in relation to other rates, the larger banks were less reluctant
to borrow, as indicated by the increase in the partial correlation coefficient

21

to 0.232, significant at the 1 per cent level.—

2.

Comparisons by Reserve Districts between Borrowing from
the Federal Reserve and from Others

The most interesting finding with respect to the determinants of
borrowing was the behavior of the variables for Federal Reserve districts.
It has been argued that there are differences in borrowing among districts
and that these differences reflect nonuniformities in the administration of
the discount window.

If the different borrowing patterns that emerge among

2/ The assertion that borrowing from other sources is functionally related
to size is explained more fully later.




-16-

districts could be attributed to nonuniform administration of the discount
window, the patterns of borrowing from the Federal Reserve would differ
among districts from borrowing from other sources.

On the other hand, if

differences in demand were responsible for the borrowing patterns which
emerge, as distinct from differences in supply, the patterns of borrowing
among districts would be similar for both borrowings.
In Table 2, the districts have been ranked in order of the likeli­
hood of borrowing by their banks from the Federal Reserve and from other
sources.

The order was obtained from the regressions and derived from the

coefficient attached to the district variables.

A negative district coef­

ficient in the regressions places the district below
base district in the regression) in Table 2.

(Richmond was the

Banks located in the district

with the largest negative value on a given date show the least probability
of borrowing.

Banks in the district with the largest positive value show

the greatest probability of being in debt.
The comparative likelihoods of borrowing from the Federal Reserve
(B^) and of borrowing from other sources (BQ) are roughly similar.
For July 22, 1959, only

differed in its ranking among the six

districts borrowing from the Federal Reserve and borrowing from other
sources.
1959, D

D

On August 19, 1959,
and D

LZ.

and

changed their order of rank.

changed its rank between Bf and B .




changed position while on December 23,
On March 15, 1960, only D

y

-17-

Table 2
Federal Reserve Districts Ranked by Likelihood of Banks
Borrowing from the Federal Reserve and from Other Sources
Jul. 22, 1959
Order

B

B

Aug. 19, 1959
B

B

Dec. 23, 1959
B

B
o

Mar. 16, 1960
B

B

f

o

f

o

D1

D12

D1

D12

D12

D1

D1

D1

D12

°8

D8

D8

D1

°5

°12

D12

3

D8

D1

°12

D5

D1 1

D1 1

°8

°8

4

D1 1

D1 1

D5

D1 1

D8

°12

d9

D1 1

°5

D5

D1 1

D1

D9

°8

D1 1

D5

°9

°9

°9

°9

D5

°9

°5

D9

1
2

5

6

f

o

f

NOTE,--Order is from least likely to most likely to borrow.
Had the patterns of borrowing among districts differed by type of
borrowing, one might conclude that some discount windows are more accessible
than others.

However, since the patterns are roughly the same between

borrowing from the Federal Reserve and from other sources, it remains only
to explain differences in the demand borrowing among districts.

There are,

no doubt, a number of conceivable explanations, one of which is the
possibility that the liquidity variable does not accurately reflect the
demands for credit in the various districts.
A comparison of size of bank was made for borrowing from the
Federal Reserve and borrowing from other sources.

The order of comparison

is shown in Table 3 where the banks by size are listed from least likely to
most likely to be in debt.




-18-

Table 3
Bank Size by Likelihood of Borrowing from the
Federal Reserve and from Other Sources
Jul. 22. 1959
Order

1
2
3
4
5

B

B
o

f

Aug. 19, 1959
B
o

f

Dec. 23, 1959
B£
f

Mar. 16, 1960

B
o

B

f

o

L1

Li

L5

L1

L5

L1

L4

L1

L_
5

L_
2

L,
1

L2
0

1

3

1

L~
2

L3

L3

L3

2

L2

L

4

L,
4

L,
4

L,
4

L0
2

L_
5

L0
3

L,
4

L2

L5

L2

L5

L4

L4

L5

L5

l

3

l

3

l

2

l

NOTE.--Order is from least likely to most likely to borrow.
There is a strong functional relationship between size of bank and
borrowing from other sources.

For each date except December 23, 1959, the

likelihood of a bank*s indebtedness was an increasing function of size.
results are not unexpected.

These

As credit tightens, smaller banks draw down

balances with their larger correspondent banks--shifting the burden of
liquidity to them.

The larger, more aggressive banks usually carry smaller

relative quantities of excess reserves, and therefore would be expected to
borrow more.
In contrast to borrowing from other sources, borrowing from the
Federal Reserve showed considerably less association with size of bank.

On

August 19, 1959, and December 23, 1959, the largest banks were less likely
to borrow than the smallest banks, as seen in Table 3.
not inconsistent.




These results are

Borrowing from the Federal Reserve, unlike borrowing from

-19-

other sources, is neither anticipated nor orderly.

It is more spontaneous

and consequently, it would be expected to show a less orderly pattern.

3.

Frequency of Borrowing at the Discount Window

Cross section regressions were used to estimate the relationship
between the frequency of borrowing from the Federal Reserve and the determin­
ants that had been used to estimate the likelihood of indebtedness, with the
addition of a reserve classification variable (C).
The period from July 8, 1959, to November 2, 1960, was divided into
three subperiods.

The subperiods were chosen to emphasize patterns of

borrowing when the relationship between the bill rate and discount rate
differed.

In particular, all individual bank data were aggregated--pro-

viding totals for the first subperiod when the discount rate was above the
bill rate.

A second aggregation covered the subperiod when the bill rate

was greater than the discount rate; the third aggregation covered the entire
period.
District, size, class, and liquidity variables were used to explain
variations in the frequency of borrowing by bank in each of the designated
subperiods.

The frequency of borrowing from the Federal Reserve (F^) re­

presented the number of weeks that a given bank was indebted during the
subperiod considered.

A weekly average was made of the data within each

subperiod.
For the entire period, July 8, 1959, to November 2, 1960, frequency
of borrowing from the Federal Reserve was estimated by:




-20-

(9)

Ff =

14.575 - 1.398(D^) - 1. 767(Dg) + 5.194(D9) - 2.337(DU )
(8.882)
(2.950)
(2.872)
(3.288)
(2.817)

-

6.611(D12) * (2.950)

4.151(C)* + 5.399(L2)*
(1.805)
(2.144)

+

+

4.050(L3) * +
(2.498)

2.073(L4)
(2.398)

2.362(L ) - .030(LQ)*
(3.741)
(.012)

R 2 = .209, F = 3. 144**
In order to examine the effects of holding short-term Treasury
bills, the variable T was substituted for LQ in equation 10.
(10) Ff =

-

-

9.768 .221(D ) - 1.640(Dg) + 7.104(Dg)* - 2.890(DU )
(8.874)
(2.984)
(3.209)
(2.784)
(2.894)
5.138(D,2)* - 4.110(C)* + 5.488(L2)* + 5.157(L3) * +
(2.893)
(1.801)
(2.145)
(2.506)

5.440(L,)*
(2.384)

10.371(L5)* - .055(T)*
(4.351)
(.022)

R 2 = .210, F = 3.169*
From August 19, 1959 to March 2, 1960, when the bill rate was above
the discount rate, the estimating equation was able to explain to a lesser
extent the variation in F^.
(11) F f =

In particular:

5.649 +
.444(DX) +
.904(Dg) + 3.059(Dg) * +
(5.009)
(1. 671)
(1. 616)
(1.834)

.352(DU )
(1.583)

-

2.157 (D -2 ) - 1.440(C) + 2.852(L2) * + 2.326(L3) * +
i
(1.636)
(1.015)
(1.223)
(1.364)

+

1.498(L5) - .016(LQ)*
(2.149)
(.006)

R 2 = .153, F = 2.149*




1.335(L,)
(1.334)

-21-

(12) F f =

2.897 +
.753(D ) +
. 769(D ) + 3.954(D )* .147(D
(5.071)
(1.723) 1
(1.635)
(1.830)
(1.584)

-

1.492(D
(1.639)

)-

+

)

1.201(C) + 2.995(L2)* + 2. 735(L^)*+ 2.889(L,)*
(1.019)
(1.240)
(1.385)
(1.337)

4.984(L5)* - .019(T)*
(2.433)
(.009)

R 2 = .132, F = 1.805
In the subperiods when rd was greater than rb, the estimating
equations that using LQ and T were equations 13 and 14, respecitvely.
(13) F

=

10.257 - 1. 798(D ) - 2.382(D ) + 1.809(D ) - 2.270(D
(5.046)
(1.679)
(1.630)
(1.823)
(1.599)

)

-

4.909(D12)* - 2.843(C)* + 2.363(L2) * +
1.971(Lo)+
,220(L4 )
(1.680)
(1.022)
(1.219)
(1.420)
(1.362)

+

.734(L ) - .022(LQ)*
(2.129)
(.007)

R 2 = .241, F = 3.792**
(14) F

=

6.764 - 1.135(D ) - 2.365(D ) + 3.219(D ) - 2.741(D
(5.126)
(1. 709)
(1. 657)
(1.853)
(1.609)

-

3.744(D)*(1.671)

+

)

5.394(L5)* - .031(T)*
(2.483)
(.014)

2.795(C)* + 2.309(L„)*+ 2.618(L~) + 2.338(L,)
(1.041)
(1.240)
(1.444)
(1.374)

R 2 = 2.17, F = 3.306*
The cross-sectional regressions suggest that the frequency with
xrtiich a bank borrows from the Federal Reserve is related to its size, Reserve
district, portfolio of liquid assets, and perhaps its reserve classification,
A compact arrangement of the variable coefficients is presented in Table 4.




-

22

-

Table 4

R e la t io n s h ip Between Frequency o f Borrowing from the F ed era l
Reserve and D i s t r i c t , S i z e , Reserve C l a s s i f i c a t i o n , L i q u i d i t y ,
and Treasury B i l l s

Period

Equation Constant

D1

D8

°
9

D 11

°
12

L2

L3

L4

L5

C

LQ

( 9)

2.073
2.362 -4.151* -.030*
5.194 -2.337 -6.611* 5.399* 4.050
14.575 -1.398 -1.767
(8.882) (2.950) (2.873) (3.288) (2.817) (2.950) (2.144) (2.498) (2.398) (3.741) (1.805) (.012)

(10)

7.104* -2.890 -5.138* 5.488* 5.157* 5.441* -10.371* -4.119*
9.768 - .221 -1.641
(8.874) (2.984) (2.873) (3.209) (2.784) (2.894) (2.145) (2.506) (2.384) (4.351) (1.801)

(11)

1.498 -1.440 -.016*
1,335
2,852* 2.326
.352 -2.157
.940
3.059
.444
5.649
(5.009) (1.671) (1.616) (1.834) (1.583) (1.636) (1.223) (1.364) (1.334) (2.14^) (1.015) (.006)

(12)

2 .889* 4.984* -1.201
3.954* - .147 -1.492
2.995* 2.735
.769
.753
2.897
(1.723) (1.635) (1.830) (1.584) (1.639) (1.241) (1.385) (1.337) (2.434) (.019)
(5.071)

(13)

10.257* -1.798
(5.046) (1.679)
■
6.764 -1.135
(5.126) (1.709)

Entire
period

When
rb rd

When
rd
rb
(14)

Note:

.734 -2 .843** -.022**
.220
1.971
-2.382
1.809 -2.270 -4.909** 2.363
(1.599) (1.680) (1.220) (1.420) (1.362) (2.128) (1.023) (.007)
(1.630) (1.873)
5.394* -2.795*
2.338
2.618
3.218 -2.741 -3.744* 2.309
-2.365
(1.657) (1.853) (1.609) (1.672) (1.240) (1.444) (1.374) (2.483) (1.041)

Standard errors are in parentheses under variables.

F-ratios are in parentheses under R^.

* indicates significant at 0.05 level of confidence, and
** indicates significant at 0.01 level of confidence.




T

R2
.209**
(3.144)

-.055*
.210**
(.022) (3.169)
.153*
(2.149)
.132
-.019
(.010) (1.805)
.241**
(3.772)
-.031*
.217**
(.014) (3.306)

-23-

In all three subperiods there was a significant association between
liquidity and frequency of borrowing from the Federal Reserve,

When the bill

rate was greater than the discount rate (rb > rd), liquidity became less
important as a determinant of frequency.

In contrast, when rb was greater

than rd, a smaller drop in the level of liquidity prompted an increase in
the frequency of borrowing.
The movements in Treasury bills showed much the same pattern as
liquidity.

Although movements in bills were inversely related to frequency

in every subperiod, banks were less willing to reduce holdings of bills when
their yield exceeded the cost of funds at the discount window.

This finding

supports the hypothesis that banks adjust reserves in accordance with the
least-cost alternative; banks with low levels of liquidity chose to borrow
more often at the Federal Reserve when it was the least expensive source of
funds.

When the discount rate exceeded the bill rate (rd > rb), the fre­

quency of borrowing was related to larger swings in bills, and banks dis­
played a greater willingness to liquidate bills rather than borrow from-the more costly--discount window.
The determinants of borrowing were less able to explain the
frequency of borrowing when the yield on Treasury bills exceeded the dis­
count rate.

Two reasons for this may be cited.

First, the exclusion of the

price variable reflects its importance when the bill rate is greater than
the discount rate.

Least-cost considerations demonstrate their impact

during this time at the expense of liquidity considerations.

It appears,

then, that banks are more inclined to borrow from the Federal Reserve when




-24-

it is least costly.

Consequently, the reduction in importance of liquidity,

which has been shown to be a significant factor in determining borrowing,
reduces the explanatory power of the equation when the bill rate is greater
than the discount rate.
The second reason is the control over borrowing at the discount
window.

As the bill rate rises relative to the discount rate, discount

officers must remain alert to the potential for banks to take advantage of
the interest-rate differential.

As administrative factors, and therefore,

unspecified supply factors increase in importance, the demand factors are
less able to explain the variations that occur in the frequency of borrow­
ing from the Federal Reserve.

B.

Time-Series Analysis
The inclusion of the price variable P = (rd - rb) substantiated a

large part of what was suggested by the cross-section analysis.

The results

of the test indicate that both liquidity and relative prices play significant
roles in the amounts of borrowing that banks, on balance, will wish to under­
take and that this relative amount differs among Federal Reserve districts.
The aim of the time series was to observe over time the effect of
liquidity, district, and cost on the patterns of borrowing.

In order to do

this, the cross-sectional variable for the Reserve district had to be pooled
with the temporal variable P.

The procedure was to aggregate all banks with­

in each district for each date; this provided six district observations for
each of the 35 dates, or a total of 210 observations.
represented by dummy variables.




The districts were

-28-

Equations 17 demonstrates that a strong relationship existed
between the proportion of banks in each district which borrowed from the
Federal Reserve and the explanatory variables.

The proportion of banks

that borrowed from the Federal Reserve varied inversely with the profit
spread and liquidity position.

This indicates that the increased amounts

of borrowing that took place when the bill rate exceeded the discount
rate resulted from an increase in the number of borrowing banks.

This

finding would seem to demonstrate that the effects of tight money are
passed from one bank to another--affeeting greater proportions as alternative
sources of liquidity dry up.
As in previous equations, there were differences in borrowing
among districts.

The proportion of banks borrowing from the Federal Reserve

is roughly the same as the relative amounts borrowed.

The rankings by

district for relative amounts and proportions are combined in Table

6.

Equation 18 focusing on the proportion of banks borrowing from
other sources, is more difficult to explain.
of the cost variable P is negative.

In the first place, the sign

This suggests that as the cost of

discounting becomes greater than the rate on borrowing from other sources,
the proportion of banks borrowing from other sources falls.
unlikely.

This seems

The variable P itself, however, was not statistically significant.
As with borrowing from the Federal Reserve, the proportion of

banks borrowing from other sources varied noticeably among districts.

How­

ever, in the former this variation was attributed to demand factors on the




-29-

Table

6

Rankings by Districts of the Relative Amounts of Borrowing
(11 /DD and B /DD ) and the Proportion of Banks Borrowing
f a
o
a
,
(Bff and BQf)

Order

Bf/DDa

1

12

2

Bff

Bof

12

1

9

1

1

12

8

3

5

5

9

1

4

8

8

8

11

5

9

9

11

12

11

5

5

6

11

V

DDa

NOTE.--Order is from least to most amount of borrowing.
basis that the same patterns of borrowing were prevalent for borrowing from
the Federal Reserve as well as borrowing from other sources.

The proportion

of banks borrowing from other sources varied among districts, but the rank­
ings were not similar to the rankings by district of borrowing from the
Federal Reserve.

This behavior on the part of district borrowing patterns

for the proportion of banks borrowing from other sources is not immediately
determinable.





Federal Reserve Bank of St. Louis, One Federal Reserve Bank Plaza, St. Louis, MO 63102