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Working Paper 73-l

SIMULATIONS OF MARGINAL RESERVE REQUIREMENTS
ON LARGE DENOMINATIO/JCERTIFICATES
OF DEPOSIT IN THE FRB MODEL

Philip itI.
Davidson

Federal Reserve Bank of Richmond
May 10, 1973

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

.

SUMMARY

As a substitutefor Regulation Q ceilings, Regulation D may be used to
control the volume of bank credit stemming from the issuance of large denomination,
negotiable certificates of deposit. The effects of the use of Regulation D, through
the vehicle of marginal reserve requirements, would be to increase the quantity of
required reserves and to raise the effective cost to the bank of acquiring funds
via CD's beyond some base level.

The effectiveness of marginal reserve requirements

would primarily depend on the interest elasticity of demand for bank loans. That
is, the higher effective cost of CD's would force the bank to raise its.commercial
loan rate, which to some degree would tend to reduce the demand for commercial loans.
The behavior of these financial variables may be examined by conducting some simulations of the FRB model.
Three simulations were conducted. The first was a simple matching of
history, including Regulation Q ceilings on CD's.

The second simulation removed

these ceilings, allowing the quantity of CD's to expand in response to prevailing
economic and financial conditions. The third simulation imposed marginal reserve
requirements on the banking system. Marginal reserve requirements on CD's were
introduced by raising the average required reserve ratio against CD's and by
raising the value of the CD interest rate in the commercial loan rate equation.
The results of these simulations were largely as expected.

CD volume

increased substantially with the removal of Regulation Q ceilings, but then
decreased slightly with the imposition of marginal reseme

requirements. In the

second simulation, the commercial loan rate fell somewhat, which, coupled with
the increase in CD's, expanded the quantity of commercial loans outstanding.
Commercial loan volume fell sharply in the third simulation as was expected
because of the higher required reserves and higher cost of CD funds that forced
banks to raise the interest rate charged on commercial loans. The decrease in

ii

commercial loans between the first and third simulations closely followed the
decrease in total deposits between these two simulations. The larger volume of
CD's outstanding, plus the higher level of required reserves, and the decline
in commercial loans resulted in an overall decrease in both demand deposits and
other time deposits.
In general, the results of these simulations suggest that marginal
reserve requirements would have been more effective in controlling bank credit
than Regulation Q ceilings were.
factors, however,

These results must be qualified by several

The FRB model, in its current version, does not explicitly

identify alternative sources of credit to borrowers.

Also, the behavior of

some of the variables examined was affected undesirably by certain structural
aspects of the model.

Finally, the marginal reserve requirements were implemented

in a necessarily arbitrary manner

that may have biased the results. On balance,

however, the results of these simulations appear to provide a basic understanding
of the role that marginal reserve requirem'entson CD%
system.

might serve in our banking

SIMULATIONS OF MARGINAL RESERVE REQUIREMENTS
ON LARGE DENOMINATION CERTIFICATRS OF DEPOSIT IN THE FRB MODEL*

. Introduction
Recently, a suggestion has been made that the Federal Reserve utilize
Regulation D (reserve requirements) rather than Regulation Q (deposit interest
rate ceilings) to control the volume of bank credit stemming from the issuance
of large denomination, negotiable certificates of deposit (CD's). Using the
authority granted under Regulation D to establish reserve requirements, the Fed
could develop a set of marginal reserve requirements to be applied against outstanding CD's that are in excess of some predetermined base level. Marginal
reseme

requirements would have a two-part effect on a bank's loans and invest-

ments.

First, the quantity of required reserves that would be released because

of a shift from demand deposits into CD's would be reduced if there were a
marginal reserve requirement against CD's.
reserves to loan or invest.

Thus a bank would have fewer excess

Second, a marginal reseme

requirement would raise

the effective cost to the bank of selling additional CD's, which would cause
the banks to raise the interest rate on loans made with such funds. Presumably,,
the bank's willingness to incur this added cost would depend upon the interest
elasticity of demand for commercial loans experienced by the bank.

Again, the

bank's ability to make loans would most likely be impaired.
Given the well-specified markets appearing in the FRB model for
commercial loans, CD's, and other deposits, a series of simulations of the model
designed to test the impact of marginal reserve requirements on bank credit
appears feasible. The remaining sections of this paper will explain the details
of the simulations and the results obtained therefrom.

SThe author acknowledges considerable help from Joe Crews in the specification of
simulations on the FRB model and from Cathy Gaffney in the operation of the model.

2.

Structure of the'loan and Deposit Marketsin

the FRB Model

Although the financial sector of the FRB model is not in general well
specified, the markets for bank loans and deposits are constructed in sufficient
detail for our purposes,

The commercial loan market is represented by the follow-

ing two equations:
lagged value of
corporate discount
loans
rate , commercial loan rate,
commercial loan rate = f(deposits, bond rate,
dummy for introduction
of negotiable CD's , CD interest rate)

demand for commercial loans - f(inventory investment, inventory valuation adjustment,
expenditures on producers' durables, Treasury bill
rate - commercial loan rate, corporate bond rate commercial loan rate, lagged value of commercial loans).
In the rate equation, the CD interest rate used is the secondary market rate, and
it only comes into use when it exceeds the Regulation Q ceiling on CD rates payable
by banks.
The market for CD's contains the following equations:
demand for CD's - f(CD interest rate, Treasury bill rate, commercial paper rate)
loans
supply of CD's = f(CD interest rate, Treasury bill rate, deposits).
In the operation of the model, the CD demand equation is solved for the CD interest
rate.

The coefficients for these two equations were estimated only during periods

when Regulation Q ceilings on CD rates were not binding.
The equatioxmfor demand deposits and time deposits are specified as
follows:
time
lagged value of discount
demand for
Treasury
rate )
demand deposits = f(bill rate, deposit rate, demand deposits,
time
household
disposable
demand for
time deposits - f(persona1 income - consumption, net worth, deposit rate,
savings and loan mutual savings Treasury
disposable
share rate
, account rate , bill rate, personal income).

3.

In the operation of the model, ,the demand deposit equation is solved for the
Treasury bill rate.

Further, the behavior of each of these deposit variables

is at least partially constrained by the reserve structure of the model, which
may be seen in the following identities:
unborrowed monetary base - unborrowed reserves + currency outside banks
. free reserves - excess reserves - borrowe4 resemes
7
+
unborrowed reserves - free reseves = demand deposits (required reserve tatioj
time deposits (required reserve ratio).
L.
In order to permit demand deposits to respond to shifts of other deposits and
changes in required reserves, the model was simulated using the monetary base
as the exogenous instrument variable.1

Tbe transmission process using the

monetary base as the instrument variable is as follows:

monetary
base -

unborrowed /
reserves

free reserve
5s

Treasury bill rate . . .
demand /
*deposits\Commercial
loan rate,
time deposit rate . m .

Under this regime the unborrowed monetary base is held constant and unborrowed
reserves may fluctuate only to the extent that the allocation of currency between
the banks and the public changes. Thus, because the supply of unborrowed reserves
is not unlimited, an increase in CD's, for example, would most likely lead to a
decrease in demand deposits, other time deposits, or both.

Changes in the Structure of the Model
A system of marginal reserve requirements may be introduced into the
model by making adjustments in two equations. First, required reserves must be
altered to reflect the higher reserve ratio against CD's that are issued in excess
of some base level. This change may be effected in the reserve equation containing

1All other simulations of the model at this bank have used the money supply (Ml) as
the exogenous instrument variable. That regime severely constrains the behavior
of demand deposits, which would not have produced meaningful results for the
simulations we have planned.
.

4'.

the required reserve ratios by ,splitting the reserve ratio for time deposits into
two components, one for CD's and another for other time deposits.

B

Thus, given a

specific marginal reserve requirement for CD's, as they increase beyond some base
level, the average reserve requirement against CD's will rise.
The second adjustment in the model will be made in the commercial loan
interest rate equation.

Because the marginal reserve requirement against CD's

will raise the cost of this source of funds to the bank, some upward adjustment
in the rate charged for commercial loans \'I11be likely. The higher loan rate,
which appears in the demand for loans equation, should tend to.slow the rate of
growth of loans made by commercial banks,

Three Simulations of the FRB Model
The role marginal reserve requirements might play in controlling the
volume of bank credit may be tested with three simulations of the FRB model.
Initially, a control solution must be determined as a reference point for evaluating the results of the other simulations. This first simulation will be a simp:Le
historical match for the period l9691.- ld721V.2 The purpose of this simulation
is to observe the actual behavior of the variables in which we are interested
when they were influenced by Regulation Q ceilings on CD rates.
.
The second simulation will differ from the first only in that Regulation Q
ceilings on CD rates will be completely removed. The purpose of this change will
be to observe the behavior of CD's, CD rates, commercial loans, and deposits under
a system of relative interest rate freedom. It is expected that the volume of
CD's will increase sharply during those periods when the ability of a bank to issue
CD's was sharply curtailed by the presence of market interest rates in excess of

2Technically, a historical match is a rather complex process involving a set of
adjustment factors determined by the difference between the results produced
from the initial step in solving.the model and the actual historical values
of the variables.

5.
ceiling rate levels. An increased quantity of CD's should put upward pressure on
CD rates, provide more funds for:commercial loans, and decrease demand deposits
and other time deposits. The decrease in deposits is attributable to the limited
supply of reserves.
The third simulation will introduce marginal reserve requirements on
CD's as described in the preceding section. Marginal reserve requirements should
have the effect of reducing the quantity of CD's below the quantity appearing when
there were no CD rate ceilings, but not nearly as low as the quantity appearing
with rate ceilings. Both the higher level of required reserves and the higher
cost to the bank of issuing CD's when marginal reserve requirements are in effect'
should put downward pressure on the quantity of CD's outstanding. Marginal reserve
requirements should not be nearly as stifling as CD rate ceilings, however.
The reduced quantity of CD's and the effects of higher required.reserves
and higher CD costs should raise the commercial loan rate and lower the volume
of commercial loans outstanding as compared to a system of unlimited CD rate
ceilings. A priori, it is difficult to specify the effects of marginal reserve
requirements as compared to Regulation Q ceilings. Essentially, the Federal
Reserve would be substituting a price rationing mechanism (marginal reserve requirements) for a quantity rationing mechanism (Regulation Q rate ceilings). Under
the latter system the quantity of CD's was tightly controlled, forcing banks to
develop alternative sources of funds such as Eurodollars and commercial paper.
Moreover, borrowers rationed by banks found alternative sources of credit in the
open market and from other financial inter'nediaries
such as commercial finance
companies.
If marginal reserve requirements were to be implemented, however, banks
could still obtain funds in the CD market, although they would be costlier, which
would put upward pressure on loan rates. The crucial question regarding the

6.

effectiveness of marginal

reserve requirements in controlling bank credit hinges

on.the interest elasticity of demand for bank loans.

The more elastic the relation-

ship, the more effective marginal reserve requirements would be in reducing loan
demand and bank credit.

Reducing bank credit is only a necessary, not a suffici.ent

condition, however, for controlling the rate of growth of total credit.

Borrowers

who consider bank loan rates unattractively high may well turn to alternative
sources of credit, as they have in the past under a system of Regulation Q ceilings.
Until the interest rate elasticity of commercial loans can be specified, the effectiveness of marginal reserve requirements on CD's will be difficult to ascertain. The
results of the third simulation should shed some light on this question. The problem
of borrowers seeking alternative sources of credit outside the banking system must
remain unresolved at this juncture, however, because the markets for such credit
are unspecified in the FRB model.

Chances in the Structure of the FRB Model
Marginal reseme

requirements will be introduced into.the model by

specifying a separate required reserve ratio for CD's in the reserve equation
set forth above.

All CD's issued in excess of some base level will be subject

to a higher reserve requirement in addition to the basic reserve requirement
specified in Regulation D.

The quantity of CD's detennizdngthe marginal reserve

requirement will be the difference in each quarter between the quantity of CD's
appearing in the second simulation (no CD rate ceilings) and the first simulation
(history match with CD rate ceilings). A marginal reserve requirement of 25 percent
will be used.

This ratio was chosen using two guidelines. First, we felt that

the average reserve

ratio for CD's should about equal the reserve ratio for demand

deposits at large banks (17 percent) during that period when the largest quantity
of CD's appeared in the second simulation, Second, we felt that the effective cost
to the bank of issuing additional CD's should fall within a range of about 10 percent

to 13 percent. .This range appeared to be commensurate with the costs of alternative

funds obtained by banks during those periods when they were subject to binding Regulation Q ceilings on CD rates.
Admittedly, these guidelines are rather arbitrary, but probably no more so
than any others we might have used.

Given the preliminary status of marginal

reserve requirements, it was difficult to specify any one method of implementing
them that appeared to be absolutely "correct."
The 25 percent marginal reserve requirement produced the following
average reserve requirements on CD's and effective interest rate cost to the bank:
Average
Reserve Requirement
1969

I
II
III
IV
1970
I
II

Effective
Interest Cost

11%
11%
15%
17%
14%
14%

9.72%
10.53%
11.36%
11.76%
11.16%
10.74%

The commercial loan rate was adjusted to reflect the above cost increases
to the bank of issuing CD's subject to a marginal reserve

requirement. These six

quarters constitute the longest consecutive period during,which Regulation Q ceilings on CD's were binding. We have assumed that marginal reserve

requirements

would have been implemented during such periods.

Simulation Results
The results for the three simulations are set forth In'Table I.

For the

most part, each of the variables behaved as we expected. The most noteworthy
exception was the behavior of the commercial loan variable in the third simulation,
which included marginal reserve requirements on'CD's. The decreases in commercial
loans in the third simulation were much larger than we anticipated.
Scanning the numbers in Table I, we observe that the volume of CD's
increased sharply with the removal of inteiest rate ceilings, but then decreased

TABLE I
SIMULATION RESULTS

Year, by quarters

1969
I

CD VOLUME
Control
No interest rate ceilings
Marginal Reserve Requirements

II

III

IV

1970
I

II

18.847a
27.246
26.765

16.656
28.731
26.857

13.313
27.856
26.409

12.165
28.808
26.076

14.296
27.164
24.030

16.793
30.766
27.624

CD INTEREST RATE
Control
No interest rate ceilings
Marginal Reserve Requirements

6.52Sb
7.286
8.861

6.878
7.765
8.764

7.536
8.517
10.920

7.720
8.817
9.804

7.685
8.367
7.465

7.307
8.058
7.893
L

COMMERCIAL LOAN VOLUME
Control
No interest rate ceilings
Marginal Reserve Requirements

99.506a
100.700
96.403

103.555
105.191
98.825

106.777
108.849
100.578

108.467
110.385
101.386

110.575
112.235
102.712

COMMERCIAL LOAN RATE
Control
-No interest rate ceilings
Marginal Reserve Requirements

7.257b
6.773
9.279

7.657
7.009
10.507

8.400
7.484
11.564

8.298
7.191
11.549

8.314
7.324
11.692

113.034
114.699
102.870-.

8.059
7.239
11.592

I

DEMAND DEPOSITS IN Ml
Control
No interest rate ceilings
,Marginal Reserve Requirements

156.296a
155.265
149.442

157.407
156.090
148.847

157.285
155.759
144.477

158.182
156.364
144.991

160.053
158.397
149.575

161.663
159.729
149.289

TIME DEPOSITS (OTHER THAN LARGE CD’S)
Control
No interes.t
rate ceilings
Marginal Reserve Requirements

143.149a
143.139
138.388

142.929
142.443
136.355

140.836
139.967
130.995

139.903
138.642
129.021

141.905
140.605
131.954

144.503
143.084
134.440

abillions of dollars
bpetcent

slightly with the imposition of marginal reserve requirements, This decrease was
not large enough to lower CD volume to anywhere near its Regulation Q levels.

As

might be expected, the increase in CD volume in the second simulation put upward
pressure on CD rates. That is, banks had to raise the rate offered on CD's to
induce the market to absorb the higher quantity of CD's,

In the third simulation,

CD rates again increased, which was not in line with'our expectations. Because
CD volume had decreased and because of the increased cost of CD's to banks, we
expected CD rates

to decline. A detailed examination of the model helped to

explain this anomalous result. Noticing that demand deposits decreased sharply
in the third simulation, which.was at least partially expected because of the
increase in required reserves and decline in commercial loans, we checked the
role of demand deposits in the model and discovered that they influence the
Treasury bill rate, which appears in the CD rate equation.

Thus, the decrease

in demand deposits put,upward pressure on the bill rate, which tended to raise
the CD rate.
The quantity of

commercial loans increased in the second simulation and

then fell off dramatically in the third simulation. We expected a larger increase
in the second simulation, but the effect on loans of the increase in CD's was
partially offset by the rise in the CD rate. Also, we might perhaps conclude
that loan demand was largely satisfied during these periods with funds that the
banks obtained via alternative-sources. The decrease in loans in the third simulation appears to stem for the most part from the increase in the loan rate, whkh,
of course, was caused by the higher effective cost to banks of issuing CD's,
Apparently, the demand for bank loans is rather interest elastic, at least more
so than most observers seem to think.
Demand deposits and time deposits moved in the general directions that
were expected in each of the simulations, although somewhat more sharply than was

9.
expected. The total deposits of the banking system, including CD's, decreased
between the first and third simulations by an amount that was roughly equal to
the decrease in commercial loans, as can be seen InTable

II.

This result was

encouraging because it suggested the presence of some sort of balance sheet
constraint that helped to provide simulation results that were internally consistent.

Evaluation of the Results
In general, we might conclude that a system of marginal reserve requirements is more effective in controlling bank credit, especially loans, than is a
system of Regulation Q ceilings. Several qualifications to this generalization
are in order, however.

Foremost is the narrow focus of these simulations.

Because

the financial sector of the FRB model is not specified in detail beyond the markets
examined here, it is difficult to draw conclusions regarding these results. That
is, because the model does not specify what is happening outside the banking sector
in these simulations, the sharp decrease in loans in the third simulation reveals
only part of the overall effects of the marginal reserve requirements. For example,
what alternative sources of funds might banks employ if issuing CD's becomes too
costly, or what alternative sources of credit might borrowers turn to if bank
borrowing becomes too costly? The current version of the FRB model is not capable of
answering these questions.
Another qualification is that we are not fully comfortable with the
elasticity of the interest rate-loan demand relationship. At this juncture we
are unable to identify a completely satisfactory explanation of the sharp decrease
in loans. One problem may lie in the adjustment of the loan rate.

Since CD's

are a marginal source of funds, it would probably be more appropriate to adjust
only the interest rate on loans made with such funds.
area might incorporate this suggestion.

Further research in this

.

TABLE II

DIFFERENCES BETWEEN FIRST JUD THIRD SIMULATIONS

Change in
Total Deposits*
1969

I
II
III
IV

1970

I
II

-

2.510
3.339
7.259
8.201

- 8.747
- 9.114

*billions of dollars

Change in
Commercial Loans*
-

3.103
4.730
6.199
7.081

- 7.863
- 10.164

10.

The magnitude of the feedback effects of the decrease in demand deposits
on the Treasury bill rate and ultimately on the CD rate are disturbing. Naturally,
during periods of tight credit conditions an increase in market interest rates
would be expected. But the increase in the bill rate in the third simulation is
much too large. Again, further research efforts might.fi-nda way to produce a
milder increase in the bill rate.
On balance, these simulations provide us with some empirical insight
into the effects that marginal reserve requirements might have on commercial banks.
Although we are not fully confident of the precision of some of the results, they
do suggest a direction and order of magnitude that are believable.

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