The full text on this page is automatically extracted from the file linked above and may contain errors and inconsistencies.
A Series of Occasional Papers in Draft Form Prepared by Members
of the Research Department for Review and Comment.
75-2
Reserve Requirements—
Are They Lagged in the
Wrong Direction?
Robert D. Laurent
Federal Reserve Bank of Chicago
■is S-S'SS
<t
1)5 5 5 5 5
•!(<< <<<{
55
•><<< < < < *
i 55 5 5 5 -u< < < < a
l)$55 5$ •!(<<<<<t
; ) >>>
!/ >>>
t' >
• ^
t <• <
(< i
-
-
- '
< <<
< :J 5 J
c J r _l
5
^
« < < < <<<: > > > > <> t f
((<<<<<<! 5 5 5 55 ;
( « < < < « 55 5 5 5 ;
«<< <<<(i SS> > ;
555S ^ 5 < < ! ^ > > >>! !
5
Research Paper No. 7 5 - 2
RESERVE REQUIREMENTS—
ARE THEY LAGGED IN THE WRONG DIRECTION?
By
Robert D. Laurent
Department of Research
Federal Reserve Bank of Chicago
This paper is being circulated for purposes of discussion and comment. The
contents should be regarded as preliminary and not for citation or quotation
without permission of the author. The views expressed are those of the author
and do not necessarily reflect those of the Federal Reserve Bank of Chicago or
the Federal Reserve System.
In September 1968, the Federal Reserve System Instituted a number of
changes dealing with the computation of reserve requirements and the treat
ment of reserve deficiencies.
The most important of these changes was a
shift to lagged reserve requirements, i.e.— setting a banks weekly average
required reserves on the basis of its average deposits at the close of
business in the settlement period two weeks earlier, rather than on the basis
of deposits in the current week (coincident reserve requirements)."*’ This
paper analyzes the effects of the shift to lagged reserves and finds them
generally deleterious.
Lagged reserves increase the costs of the individual
bank's reserve management, and by increasing uncertainty, decrease the
precision of monetary policy and increase the costs to the banking system of
policy shifts.
Conceptually, the basic problem with the lagged reserves
scheme is that it seems designed to facilitate the provision of a level of
reserves consistent with a given level of deposits, whereas monetary policy
utilizes the reverse process.
The analysis suggests that the lag in reserve
requirements might well be reversed— reserves being set first, with banks
setting required reserves two weeks later.
A reverse lag system is developed
which would allow monetary authorities to accurately move the banking system
to a desired level of required reserves.
The views expressed are those of the author alone and do not represent
the views of the Federal Reserve Bank of Chicago or the Federal Reserve System.
The author has benefited from the comments of John Hill, Jack Kalchbrenner,
George Kaufman, Nick Lash and William Poole. The paper has also been signi
ficantly improved as the result of a presentation at the Money and Banking
Workshop of the University of Chicago. The author is especially indebted to
Milton Friedman for a number of organizational suggestions and to Carl Vander Wilt
for his many valuable insights.
Mother changes were: 1) to establish the same one week reserve settlement
periods for country banks as for reserve city banks, 2) to count average vault
cash held at the close of business two weeks earlier in satisfaction of reserve
requirements and 3) to provide that an excess or deficiency in reserves may be
carried forward only into the next settlement week in an amount not to exceed
2 percent of average required reserves. For analyses of the effects of one or
more of the 1968 changes see Burger (1971), Coats (1972) (1973) (1974),
Gilbert (1973), Laufenberg (1975) and Poole and Lieberman (1972). It should
be noted that a theoretical analysis of the combined 1968 changes or an
empirical analysis of any single change would be extremely complicated.
2
The first section of the paper examines the effects of the change to
lagged reserves on the individual bank.
impact on the banking system as a whole.
The second section examines the
Section three examines the impact
of lagged reserves on the conduct of monetary policy.
In section four, the
analysis of the first three sections forms the basis for suggested changes in
the reserve computation scheme.
I.
Effects on the Individual Bank
Because Individual banks know with certainty their required reserves
entering the settlement week, it may appear that the adoption of lagged
reserves would aid individual bank reserve management.
nation of lagged reserves indicates the opposite.
However, closer exami
In reserve management,
banks are concerned about the variability of the difference between actual and
required reserves (i.e., excess reserves) rather than the variability of the
level of required reserves alone.
Fundamentally, unanticipated fluctuations
in reserves result from unanticipated fluctuations in deposits.
2
Lagged re
serves do not help the individual bank handle unexpected deposit flows.
In
fact, by not allowing required reserves to move with deposits, lagged reserves
increase the volatility of excess reserves and make the bank's reserve manage
ment problems more difficult.
Under coincident reserves the adjustment pres
sure of unanticipated deposit flows falls because required reserves move to
offset some of the change in reserves.
Under lagged reserves there is no off
set because required reserves do not change.
Given the same deposit volatility,
and assuming that transactions costs rise with the size of transactions, it will
cost a bank more to manage its reserve position under lagged reserves and the
There are a number of ways in which bank reserves may change without
deposits changing. However, the major ways in which this occurs (e.g., changes
in bank asset holdings, transfers of federal funds, changes in borrowings from
the Federal Reserve, raising of capital or paying of dividends) are readily
predictable and controllable by banks. The unpredictable elements in this
category would appear to be relatively minor, consisting of loan prepayments and
the drawing down of loan commitments#
3
banks holdings of excess reserves will rise.
II.
3
Effects on the Banking System
Relative to coincident reserves, lagged reserves alter the relative
importance of those factors determining the level of deposits and bank credit
which the banking system creates with a fixed level of unborrowed reserves.
Specifically, lagged reserves enhance the role of the banking systems future
interest rate expectations at the expense of the influence of the level of
unborrowed reserves in determining the banking systems equilibrium.
The reaction of deposits and interest rates to a fall in banks expected
future interest rates under coincident and lagged reserves, given a fixed
level of unborrowed reserves, are quite different.
Under both systems, banks
attempt to expand their holdings of assets (loans and investments) since lower
expected future interest rates imply greater capital gains for asset holders.^
With coincident reserves, the increase in bank assets increases deposits and
required reserves in the current week.
Since unborrowed reserves are fixed,
the Federal funds rate will rise by an amount necessary to contrain deposits
to a level at which required reserves do not exceed the level of reserves
(assuming no reserve deficiencies).
Deposits will increase and other interest
rates fall only to the extent that excess reserves fall and borrowed reserves*
4
For a more complete exposition of this point see Gilbert (1973). The Gilbert
analysis differs from and produces more ambiguous results than those in the text
because it analyzes a system in which both reserve requirements and vault cash
are lagged.
4
Throughout the paper assets refers to instruments such as loans and investments
which are exchanged between banks and the public. The purpose is to differentiate
these changes which affect deposits in the system from those bank adjustments such
as changes in borrowings from the central bank and Federal funds transactions which
do not affect deposits.
4
increase as a result of the increase in the Federal funds rate."*
Coincident
reserves serve to tether required reserves to the level of reserves in the
system, thereby constraining changes in bank assets, deposits, and the resulting
movement in interest rates.
Conversely, the Federal funds rate will be
relatively unconstrained, rising to whatever level is necessary to induce
the banking system as a whole to forego a greater deposit expansion.
The level
of the Federal funds rate required to do this will largely be determined by the
banking systems new level of future interest rate expectations.
The sharper
the expected fall in future interest rates, the higher the current Federal funds
rate must rise to induce banks to forego a further expansion in their asset
holdings.
Under lagged reserves, the expansion in bank assets resulting from lower
expected future interest rates has quite different results.
The creation of
deposits resulting from the purchases of assets does not change required reserves
since these were set two weeks previously.
The Federal funds rate is not
affected since required reserves and the level of reserves have not changed.
The banking system will continue to purchase assets from the public, expand
deposits and lower interest rates until the rate of return on these assets has
fallen to a level which removes any expected future profits.
The deposit
expansion and the resulting fall in interest rates will be primarily determined
by the banking systems expectations for future interest rates.
The reaction of the banking system to changed interest rate expectations
under the two reserve computation schemes is symmetrical.
In the coincident
Theoretically, banks could expand asset holdings by attracting a currency
inflow. However, as a practical matter, the rates paid for reserves in the
federal funds market do not hit high enough levels to justify the public holding
currency as a supply of reserves for banks in periods of tightness even were
Regulation Q not preventing banks from paying these rates to the public. Thus,
in this discussion and elsewhere in the paper, the possibility of banks adjusting
their intra-week reserve positions through currency flows is ignored.
5
system it is primarily reserves which determine bank asset holdings, deposits
and interest rates while expectations primarily determine the Federal funds
rate.
Under lagged reserves, reserves primarily determine the Federal funds
rate while expectations primarily determine bank asset holdings, deposits and
interest rates.
Lagged reserves reduce the importance of reserves in determining
the behavior of the banking system while enhancing the role of future interest
rate expectations.
III.
Effects on Monetary Policy
The effects on monetary policy of the shift to lagged reserves may be
demonstrated by comparing the demand for reserves under coincident and lagged
reserves.
For expository purposes, it is assumed that the percentage of
deposits held in each reserve requirement category is held constant and that
unborrowed reserves are provided over the settlement week in a given fixed
way (e.g., equal levels of unborrowed reserves each day or unborrowed reserves
three percent higher than average on the first four days and four percent lower
on the last three).
These assumptions eliminate from the analysis complications
arising from both shifts between different deposit categories and simultaneous
changes in both the level and pattern of unborrowed reserves within the week.
Coincident Reserves
Under coincident reserves, the monetary authorities conduct policy by
manipulating the level of unborrowed reserves so as to produce desired changes
in deposits and interest rates.
An increase (decrease) in unborrowed reserves
lowers (raises) the Federal funds rate because the level of reserves has been
increased (decreased) relative to the level of required reserves.
The lower
(higher) Federal funds rate is the mechanism by which the increase (decrease)
in unborrowed reserves is transmitted into new equilibrium levels of borrowed
reserves, excess reserves and required reserves.
An Increase (decrease) in
6
unborrowed reserves and the resultant fall (rise) in the Federal funds
rate will cause borrowed reserves to fall (rise) while required reserves
and excess reserves rise (fall).
Borrowed reserves fall (rise) because
as a substitute source of reserves, the discount window will be utilized
less (more) as the price of reserves in the Federal funds market falls
(rises).
Required reserves increase (decrease) because the spread between
the rate of return on bank assets and the lower (higher) Federal funds
rate is a measure of the incentive for banks to buy assets and thereby
increase required reserves.
Excess reserves rise (fall) because the
return to a reduction in excess reserves as represented by the lower
(higher) rates on Federal funds and bank assets has fallen (risen).
The demand for various types of reserves and the implementation of
monetary policy under coincident reserves is represented in Figure 1.
6
A level of unborrowed reserves equal to OA would produce a Federal funds
rate of OE, a level of excess reserves equal to DC, a level of borrowed
reserves equal to DB, and a level of required reserves equal to EB.
At an Increased level of unborrowed reserves equal to OF, the equilibrium
Federal funds rate would be lower at OG, borrowed reserves would fall to
IH and excess reserves and required reserves would rise to 1J and GH
respectively.
Under coincident reserves, the role played by the Federal funds rate in
moving the banking system to the new equilibrium is quite important.
The
^Figure 1 represents a segment of the demand for reserves. The demand
for unborrowed reserves reflects the increasing volume of deposits which
would be created at lower Federal funds rates. Borrowed reserves decline
(becoming zero at a Federal funds rate above the discount rate) and
excess reserves increase as the Federal funds rate falls.
7
FIGURE 1
The Market for Reserves under Coincident Requirements
8
lower (higher) Federal funds rate, relative to returns on loans and investments,
induces banks to expand (contract) their holdings of such assets.
As the banks
expand (contract) their holdings of assets, the rate of return on these falls
(rises) while the resulting increase (decrease) in deposits increases (decreases)
required reserves and raises (lowers) the Federal funds rate.
The increase
(decrease) in deposits continues until the gap between the marginal rate of
return on assets and the Federal funds rate is back in equilibrium with both
rates at a lower (higher) level.
Under coincident reserves, a deviation of
deposits from the equilibrium level causes the Federal funds rate to move so as
to induce banks to change their holdings of assets and move deposits in the
system back to the equilibrium level.
Lagged Reserves
The conduct of monetary policy under lagged reserves is similar in some
ways to that under coincident reserves.
Once again the monetary authorities
conduct policy by varying the level of unborrowed reserves.
Again an increase
(decrease) in unborrowed reserves lowers (raises) the Federal funds rate.
Again a lower (higher) Federal funds rate moves the banking system to lower
(higher) levels of borrowed reserves and higher (lower) levels of excess reserves.
The fundamental difference under lagged reserves is that required reserves are
fixed at a level determined two weeks previously and are not affected by deposit
changes in the current week.
As a result, lagged reserves eliminate intra-reserve
settlement week changes in required reserves as a means of the system absorbing
increases or offsetting decreases in unborrowed reserves.
This means that a
given change in unborrowed reserves will produce a greater change in the Federal
funds rate under lagged reserves because required reserves cannot change to
cushion the impact of the change in unborrowed reserves.
9
The demand for various types of reserves and the implementation of
monetary policy under a lagged reserve scheme is represented in Figure
The fixed level of required reserves set two weeks previous is represented
by the vertical line at magnitude OK.
A level of unborrowed reserves
equal to OA would produce a federal funds rate of OE, a level of excess
reserves equal to DC, and a level of borrowed reserves equal to DB.
At
an increased level of unborrowed reserves equal to OF, the equilibrium
Federal funds rate would be lower at OG, borrowed reserves would fall to
IH and excess reserves would rise to IJ.
A comparison of Figures 1 and 2
illustrates the greater sensitivity of the Federal funds rate to changes
in unborrowed reserves under lagged reserves.
Just as under coincident reserves, an increase (decrease) in unborrowed
reserves and the resulting fall (rise) in the Federal funds rate under
lagged reserves induces banks to buy (sell) assets, thereby increasing
(decreasing) deposits and lowering (raising) interest rates.
Under lagged
reserves, however, the feedback from changes in the level of deposits in the
banking system to the Federal funds rate has been eliminated.
Thus, the
Federal funds rate does not serve to guide deposits to a level at which
required reserves are in equilibrium with the level of reserves in the system.
Banks observe two apparently disparate phenomena in the aftermath of a change
in unborrowed reserves.
The lower (higher) Federal funds rate signals banks
to expand (contract) their holdings of bank assets.
However, the resulting
increase (decrease) in deposits which banks observe does not make them any
more willing to tolerate the Increased (decreased) level of unborrowed
reserves.
Without the feedback from changes in deposits to the Federal funds
Both figures 1 and 2 use the same relationships between the Federal funds
rate and excess reserves and the Federal funds rate and borrowed reserves.
10
FIGURE 2
The Market for Reserves under Lagged Requirements
11
rate, banks persist in responding to the initial change in unborrowed reserves.
Thus, under lagged reserves, a given change in unborrowed reserves will cause
a sharper change in the Federal funds rate, deposits and the interest rate on
bank assets.
Determination of Deposit Levels
Under lagged reserves, the extent of the deposit expansion and interest
rate decline arising from an increase in unborrowed reserves depends on a number of
factors.
The fall in the Federal funds rate induces banks to repay borrowings.
If the increase in unborrowed reserves is less than the level of borrowings
in the system then the Federal funds rate will not fall below the discount rate.
If the added reserves are greater than the initial level of borrowings in the
system then the Federal funds rate will fall toward zero as the end of the
settlement week approaches.
In either case, as the Federal funds rate falls,
banks will continue to purchase assets and expand deposits as long as they can
O
Increase their expected profits relative to selling Federal funds.
The
increasing level of deposits relative to reserves will not deter banks from
continuing their purchases of assets, though they are aware that above some
level of deposits, either assets must be transferred into reserves two weeks
in the future or reserves must be purchased or borrowed.
Assets maturing
this settlement week will be purchased as long as they yield a higher return
(after transaction costs) than Federal funds sales.
Assets maturing in the
next two settlement weeks will be purchased until the return on these assets
equals the expected return on Federal funds sales over the period to maturity.
Assets maturing more than two weeks in the future involve the risk of capital
loss when they must be sold and they will be bought until the expected return
g
An individual bank may take part in the adjustment without having excess
reserves. As the Federal funds rate falls relative to bank asset rates, a bank
without excess reserves may expand deposits in the system by purchasing assets
and covering the reserve loss with Federal funds.
12
on these assets (including capital gains or losses) falls below the expected
return on Federal funds sales over the same period.
Monetary policy influ
ences the size of the expansion through the effect of the lower current
Federal funds rate on banks expectations of future Federal funds rates.
Finally, deposit expansion is constrained by the physical limitation on the
value of assets that can be purchased within the settlement period.
Since
a bank must retain sufficient reserves to satisfy reserve requirements in the
current week, it must have either excess reserves on hand or purchase reserves
through the Federal funds market when acquiring assets.
The time required for
the purchase of assets and the shift of reserves from one bank to another,
given the level of excess reserves, imposes a limit on the deposit expansion.
Under lagged reserves, a contractionary policy is constrained with regard
to the level of total reserves that can be supplied.
Since required reserves
were set two weeks previous and cannot be changed, a level of total reserves
at least equal to required reserves must be provided.
A contractionary policy
may still be implemented by providing a low level of unborrowed reserves.
In this way the monetary authorities cause banks to bid up the Federal funds
rate until a sufficient amount of reserves are borrowed, in the aggregate, to
meet requirements.
The Federal funds rate will rise until the costs of
borrowing are attractive enough (relative to buying Federal funds) to induce
some banks to borrow the requisite quantity of reserves.
Thus, in periods of
tight policy any changes in unborrowed reserves will be nearly completely offset
by changes in borrowed reserves.
The extent of bank asset sales, the fall
in deposits and the interest rate increases which result from the contractionary
policy again depend on the influence of the higher Federal funds rate on banks'
expectations for future Federal funds rates.
The declining level of deposits
relative to reserves will not deter banks from continuing their liquidation of
assets, though if deposits drop below a level consistent with reserves, banks
13
will realize that reserves could be transferred into assets two weeks hence.
Banks will sell assets maturing within the settlement week if the return on
these assets is below the rate on Federal funds (taking account of transaction
costs).
Assets maturing in the next two settlement weeks will be sold as
long as the expected return on these assets is less than the expected rate on
Federal funds over the period to maturity.
Assets maturing more than two
weeks in the future will be sold as long as the return on these assets over
the next two weeks is expected to be lower than the return on Federal funds
(including any expected capital gains or losses from reinvesting the funds
into assets two weeks in the future).
This analysis of monetary policy reveals a symmetry between coincident
and lagged reserves similar to that described in examining the effects of
these schemes on the banking system as a whole, given a fixed level of
unborrowed reserves.
Under coincident reserves, the Federal funds rate moves
to whatever level is ne essary to induce the banking system to set required
reserves (and therefore deposits, bank assets and interest rates) at a level
determined by, and consistent with, the new level of unborrowed reserves in the
system.
The level of the Federal funds rate required to achieve equilibrium
is determined by the present and expected future interest rates on bank assets.
Under lagged reserves there is no mechanism moving the banking system to a
level of deposits consistent with the level of unborrowed reserves in the system.
Rather, the level of unborrowed reserves determines the Federal funds rate and
the influence of the current Federal funds rate on the banking systems expectatations of future Federal funds rates determines the change in deposits, bank
assets and interest rates.
The shift to lagged reserves has enhanced the role
of future Federal funds rate expectations in monetary policy while diminishing
the role of unborrowed reserves.
14
Precision and Costs of Monetary Policy
There is reason to believe that the adoption of lagged reserves has
adversely affected the precision with which monetary policy is conducted.
While the adoption of lagged reserves does not affect the impact on deposits
or interest rates of the initial purchase or sale of securities by the
monetary authorities, it does affect the precision of monetary policy, by
changing the predictability of the banking systems response to the initial
change in unborrowed reserves.
The preceding analysis indicates that the
shift to lagged reserves has enhanced the role of expected future Federal
funds rates in determining the effects of monetary policy, at the expense of
the role played by unborrowed reserves.
Were the economic relationships
known perfectly, the monetary authorities could conduct policy with absolute
o
accuracy under either system.
However, given the apparently more difficult
task involved in estimating a monetary mechanism in which unobservable
expectations play an important role, the shift to lagged reserves would
appear to have reduced the precision of monetary policy.
Under lagged
reserves the monetary policy effect of a change in unborrowed reserves and
the Federal funds rate depends critically on the effect on banks expectations
of future Federal funds rates.
If the movement in the Federal funds rate
is thought temporary then the changes in deposits and interest rates will be
minor.
Alternatively, if the banks believe the movement in the Federal funds
9
The analysis of monetary policy under lagged reserves indicates that if
the authorities wished to change the equilibrium level of unborrowed reserves
in the system, they would initially make a smaller change in unborrowed
reserves. This smaller change would be precisely that change which would cause
the banking system to set a level of deposits consistent with the desired
long-run level of unborrowed reserves. In two weeks the monetary authorities
would change unborrowed reserves by an amount sufficient to bring the total
change in unborrowed reserves to the desired amount.
15
rate is a precursor of future movements then the changes in deposits and
10
interest rates could be very large.
An additional consideration in evaluating lagged reserves is the effect
of a shift in monetary policy on banking system costs of adjustment.
Ideally,
the banking system minimizes the costs of a change in policy by immediately
changing its asset holdings so as to move the gap between the return on bank
asset holdings and the cost of reserves (Federal funds rate) back to an
equilibrium level.
This is the process which occurs under coincident reserves
when, following the initial change in reserves, changes in bank asset holdings
move both the return on bank assets and the cost of reserves toward the new
equilibrium.
Under lagged reserves however, changes in bank asset holdings
cannot change required reserves and so do not affect the price of reserves
(Federal funds rate).
Thus, saddled with a level of required reserves set two
weeks previously, banks cannot cushion the effects of a change in monetary policy
on the cost of reserves, no matter what their response in setting deposits.
The drawbacks of the present lagged reserve scheme seem clear.
Under lagged
reserves, banks set a particular policy by their expansion or contraction of
deposits based on expectations of the future cost of reserves.
Two weeks later,
the monetary authorities enter the picture by, in essence, supporting or resisting
the banks behavior.
The monetary authorities can only change this behavior by
imposing costs on the banks at a time when the ability of the banks to reduce
these costs is sharply constrained, even were they to move deposits immediately
to the level desired by the monetary authorities.
As used here, the adjustment
costs to banks of monetary policy are the returns foregone by the holding of
excess reserves under an expansionary monetary policy and the difference between
In connection with this last point it is interesting to note the recent
emphasis given by the open market desk to an apparent increase in banks
securities speculation and its impact on monetary policy (Federal Reserve Bank
of New York 1972, pp. 90-91)
16
the marginal cost of reserves (Federal funds rate) and the return on the
marginal dollar of deposit creation when banks are forced to borrow under a
contractionary policy.^
These costs rise, the more monetary authorities
wish to cause banks to deviate from their past behavior.
The discussion
presented here argues that the same monetary policy (i.e. open market operations)
would involve higher bank adjustment costs with lagged reserves than coincident
reserves.
If the monetary authorities are reluctant to let the Federal funds rate
move by large amounts, or to impose costs on the banking system, then monetary
policy under lagged reserves will tend to conform more closely to the policy
set by the banks, thereby altering the behavior of the system only slowly.
12
In this case the cost of the lagged reserves scheme would fall less heavily on
member banks but rather result in a less optimal monetary policy.
Summary
The preceding analysis indicates that lagged reserves raise the costs
of reserve management to the individual bank.
Lagged reserves increase the
volatility of both interest rates and the level of deposits in the adjustment
process to a given change in unborrowed reserves.
Lagged reserves make the
task of predicting the results of a change in unborrowed reserves on either
deposits or interest rates more difficult.
Lagged reserves raise the costs to
the banking system of the conduct of a given change in monetary policy.
^ I t might seem that excess reserves are a cost only in the sense of an
opportunity cost. However, if banks compete for deposits and do not identify
those deposits which are added to excess reserves (e.g., those made late on a
Wednesday afternoon) then there appear to be explicit costs to an addition to
excess reserves.
12
For a less critical view of lagged reserves which makes somewhat the same
point, see (Holmes 1973, pp. 73-75).
17
Against these effects, lagged reserves have made It easier, assuming the level
of unborrowed reserves can be set with precision, for the monetary authorities
to set the Federal funds rate.
13
This is because under lagged reserves the
monetary authorities know the demand for reserves in the current week since
it is based on the level of deposits two weeks previous.
However, this
potential increased control over the Federal funds rate does not appear to
be a great gain.
The same factor which makes the Federal funds rate potentially
easier to control— the breaking of the connection between changes in deposits
and the Federal funds rate— makes it more difficult to predict the effect on
the level of deposits or other interest rates of a given Federal funds rate.
In short, the losses entailed in the shift to lagged reserves seem to far out
weigh the gains.
IV.
Proposed Reverse Lag System
The problems with lagged reserves arise because the system reverses the
fundamental mechanism of monetary policy.
Every beginning student of monetary
policy learns that the monetary authorities change reserves and banks react
with a multiple expansion or contraction in deposits which moves required
reserves to a level consistent with the new level of reserves.
monetary authorities act and banks react.
That is,
However, under the present lagged
reserves system the banks act, the monetary authorities react, and banks
respond to this reaction by the monetary authorities.
If the monetary
authorities are hesitant to impose costs on the banking system then policy
will be sluggish in changing bank actions.
uncertainty is generated.
13
In addition, a great deal of
Banks must determine what a particular current
It is not clear that the monetary authorities control over unborrowed
reserves is sufficiently precise to insure that the shift to lagged reserves
has, in fact, improved their control over the Federal funds rate.
18
policy portends for future policy.
Monetary authorities must determine
what current policy will generate expectations on the part of banks con
sistent with the desired changes in the level of deposits or interest rates.
It would seem more appropriate to have the monetary authorities act and banks
react.
this.
Reversing the lag between required reserves and reserves would accomplish
Reserves would be set In the current week with required reserves
determined by the banks two weeks hence.
This would allow the banking
system to make changes in the level of deposits more easily since banks would know
ahead of time the adjustment required.
Fundamental Changes
Two changes in the present reserve computation scheme would create a
system in which the monetary authorities initiate policy and the banking
system reacts to the known level of reserves set by the authorities.
This
new system would appear to be superior to either the old coincident system
or the present lagged cistern.
1)
The changes are:
Reserve settlement in a given week would use required
reserves based on deposits in the given week and the level
of reserves held two weeks previous.
2)
A banks net clearings (i.e., the value of checks deposited
minus the value of checks drawn against the bank at the
Federal Reserve so far in the settlement week) would
create an equal amount of interbank deposits.
A bank with
positive net clearings so far in the week will be considered
to have an equal amount of interbank deposits "due from" other
banks as of the end of the day, while a bank with negative
net clearings in the week has an equal amount of Interbank
deposits "due to" other banks.
19
Reserves at the Federal Reserve would be determined at days end, just
as at present.
A banks reserves each day would be equal to the banks
reserves at the beginning of the week plus the banks net clearings so far
in the week.
Weekly average reserves would be the average of the dally
reserves.
Reversing the lag creates a reserve computation system consistent with
the broad scheme of monetary policy.
Banks enter the settlement period
with a fixed level of reserves, necessitating adjustment through changes in
required reserves.
The process of the individual bank moving to equilibrium
mirrors that of the banking system as a whole, which does not move into
equilibrium through changes in reserves, but through changes in required
reserves.
14
As shown below, treating a banks net clearings as interbank deposits,
sharply reduces the influence of factors outside the banks control which
affect its required reserves.
Since interbank deposits "due from" other banks
are subtracted and interbank deposits "due to" other banks are added to
deposits in computing required reserves, flows of demand deposits between
banks leave the banks with unchanged required reserves.
Under the reverse lag, banks may move into equilibrium very easily.
A bank with reserves two weeks ago that could support $100 more than its
level of deposits entering the current reserve settlement week, knows that
the purchase of $100 in assets at the beginning of the week will move it into
equilibrium for the week.
The bank pays for the assets with a check for $100.
If the check is deposited at the bank itself then deposits rise by $100 and
the bank is in equilibrium.
If the check is deposited at another bank, the
other bank has an increase in demand deposits of $100 offset by an increase of
^Ignoring again the possibility of adjustment occurring through changes
in the publics currency holdings.
20
$100 in "due from" interbank deposits when the check is cleared.
The adjusting
bank has an increase of $100 in deposits "due to" other banks when the check
is cleared and thus achieves equilibrium.
Deposits in the system increase
$100, the adjusting bank is in equilibrium and no other bank experiences a
change in required reserves.
A bank with deposits $100 higher than its level
of reserves two weeks previous could support, would sell $100 in assets and
move into equilibrium by either reducing its deposits or adding to its deposits
"due from" other banks in the check clearing process.
The adjusting bank's reserves in the current week are affected primarily
by the banks net clearings at the Federal Reserve to which the check issued
(received) by the bank expanding (contracting) its asset holdings contributes
a loss (gain) of $100 in reserves.
This reserve shift only affects the
reserve computation period two weeks in the future.
Markets facilitating Adjustment
In practice, bank adjustments would not be as extreme as the process
outlined above.
Adjustment would be facilitated by two separate markets.
The first is the Federal funds market just as exists presently.
Imagine
Bank A and Bank B are both in equilibrium (having deposits just equal to the
amount which could be supported by their reserves two weeks previous) and
assume that a $100 check written on Bank B is deposited at Bank A.
After
the check is cleared, Bank A has a $100 Increase in demand deposits offset
by a $100 increase in deposits "due from" other banks, while Bank B has a
$100 decrease in demand deposits offset by an Increase of $100 in deposits
"due to" other banks.
While the banks remain in equilibrium this week, it is
clear that both must adjust two weeks in the future.
Assuming reserve require
ments are 20 percent, Bank A's current level of deposits is $400 below, and
Bank B's $400 above the level of deposits which they could have two weeks in
the future.
While they could adjust as described above (i.e., Bank A buying
21
$400 in assets and Bank B selling $400 In assets at the beginning of the
settlement period two weeks hence), this could lead to large reserve flows
two weeks in the future.
It is possible that some of the adjustment will
occur through a sale of Federal funds from Bank A to Bank B in the current
week.
The sale of $80 in Federal funds would obviate the need for any
asset adjustments two weeks in the future.
A second market facilitating adjustment, which would likely develop,
would be one for future interbank deposits.
An interbank deposit for some
week in the future is a demand deposit "due from" another bank for that week
and thus would be an offset to deposits requiring reserves in that future
reserve settlement week.
These future interbank deposits would not involve
the transfer of reserves and so would involve only banks without the
participation of the Federal Reserve.
Assume the banking system is in equilibrium, under the reverse lag,
when the Federal Reserve purchases $100 in securities.
This increases
deposits in the system by $100, offset by a $100 increase in the banking
systems net clearings at the Federal Reserve.^
For the banking system
as a whole, there are $80 more in reserves than the current level of
deposits would require.
Banks holding these $80 know that in two weeks they
can purchase $80 in assets, creating $80 in deposits and not be reserve
deficient.
This is exactly the reaction of banks in the same situation
under a coincident reserve system.
But under the reverse lag these banks
also know that these reserves they currently hold could support yet an
additional $320 in deposits two weeks hence.
This ability to support future
deposits may be sold in an interbank deposits market.
The rate on these
future "due from" interbank deposits will fall until some banks find the rate
attractive relative to the expected return
on assets they might acquire and
The assumption here is that the monetary authorities purchase the securi
ties from a non-bank dealer. Transactions with bank dealers will be discussed
later.
22
hold during the settlement period two weeks hence.
A bank entering a week for
which It holds previously purchased "due from" interbank deposits can purchase
and hold during the week, additional assets equal to the value of the inter
bank deposits.
The clearing of the check used to purchase the assets results
in an equal amount of "due to" interbank deposits which will be offset by the
previously purchased "due from" Interbank deposits.
The "due to" interbank
deposits resulting from the asset purchase Involve an equal loss of reserves
for use two weeks in the future which is not offset by the previous purchase of
future interbank deposits since there is no reserve transfer associated with
the purchase of future interbank deposits.
Conversely, if the Federal Reserve sold assets, some banks would find
themselves with less reserves than their current level of deposits would
require two weeks hence.
These potentially deficient banks would bid up the
future interbank deposit rate until future 'interbank deposits are created by
other banks willing to sell assets or the deficient banks themselves decide
to sell assets in the future settlement week.
Advantages of the Reverse Lag
The basic attraction of the reverse lag is that it allows banks to
know precisely what action is necessary to get into equilibrium before
entering any settlement week.
Markets will then allow the banking system to
make an efficient adjustment.
A net negative level of clearings for the
banking system in the current week signals that deposits must contract two
weeks in the future.
The interbank deposit rate for two weeks in the
future moves up to a level at which an appropriate value of
interbank deposits two weeks in the future will be sold.
Banks selling
future interbank deposits in the current week will be those banks with the
lowest expected marginal return on assets two weeks in the future.
This is
an efficient way for the banking system to contract the level of deposits
two weeks in the future.
23
Reserve computation schemes may be compared by examining the individual
bank adjustment to equilibrium in light of what is required for the banking
system as a whole.
Since the banking system cannot change the level of
reserves, it must adjust to disturbances (e.g., currency flows, monetary
policy actions) through changes in deposits.
The extent to which individual
banks adjust through reserves or deposits depends on the reserve computation
scheme.
A problem with the present lagged reserves, is that the individual
bank adjusts entirely through reserves.
out of equilibrium by the same amount.
In adjusting, banks put other banks
The banking system as a whole cannot
get into equilibrium (i.e., change excess reserves) regardless of what happens
to deposits.
Under coincident reserves, individual banks adjust primarily
through reserves but some adjustment occurs through deposits since deposit
flows affect required reserves in the reserve settlement week.
Under coincident
reserves each adjusting bank puts other banks out of equilibrium but by a
progressively smaller amount until equilibrium is achieved.
Under the proposed
reverse lag where complete adjustment occurs through deposits, adjustments
required for individual banks are the same as those required for the entire
banking system and no other banks are put out of equilibrium in the process of
adjustment.
This makes the banking systems adjustment under the reverse lag
quicker and less disequilibrating than either the coincident or the present
lagged reserve scheme.
Setting Required Reserves
Adoption of the two changes proposed above would greatly improve the
monetary authorities' control over the quantity of deposits while simultane
ously reducing the banking systems costs of adjustment to changes in the
level of reserves.
More importantly, the proposals suggest the possibility
that a system could be devised in which a bank's level of excess reserves,
within the settlement week, would not be affected by factors outside its control.
24
Banks could then eliminate excess reserves by adjusting asset holdings so as
to set their required reserves exactly equal to their level of reserves two
weeks previous.
Counting net clearings as Interbank deposits already
removes intra-week changes in required reserves arising from demand deposit
flows.
Four additional changes would create a system in which banks would
set a level of required reserves equal to their level of reserves two weeks
previous without fear of reserve deficiences.
The four changes are:
3)
Count a fraction of current vault cash equal to the reserve require
ment against demand deposits as reserves in the current week.
4)
Compute required reserves against non-demand deposits as at present
except that net changes in the level of these deposits from the
end of the previous week will be considered for reserve requirement
purposes to release or require reserves as though they were
demand deposits.
5)
Eliminate the reserve carry-over allowing a bank to carry over
an excess or deficiency of up to two percent of required
reserves for one week.
6)
Assess deficiences a severe penalty such as ten percent above
a market rate such as the three month treasury bill rate.
Counting current vault cash as reserves against current deposits completes
the reversal of the present lagged reserves.
Under the present lagged re
serves system, vault cast*, from two weeks previous counts in satisfaction of
required reserves.
Counting a percentage (equal to the reserve requirement
against demand deposits) of current vault cash as reserves available against
deposits this week serves two purposes.
It prevents changes in excess reserves
as a result of shifts by the public between currency and demand deposits.
also provides an incentive for banks to quickly transmit vault cash changes
to the Federal Reserve where the monetary authorities may offset the impact
It
25
on the future level of deposits.
Setting reserve requirements equal to those against demand deposits for
the weekly net change in non-demand deposits removes any effect on excess
reserves, in the current week, of changes in non-demand deposits.
Thus,
the effects of a change in time deposits would be offset by the effects of
the simultaneous change in demand deposits, vault cash, or check clearings
at the Federal Reserve.
For example, a shift from demand deposits to time
deposits will not change a banks required reserves in the initial week.
In the following week the reserve requirements against the increased time
deposits will be equal to the level set by regulation and the bank will
know at the beginning of the week the increased quantity of assets it may
purchase (and therefore deposits it may create) due to the shift from demand
deposits to time deposits in the previous week.
16
Elimination of the present carry-over of excesses and deficiencies by banks
is necessary if banks are to move to a level of required reserves equal to
the level of reserves provided two weeks previous.
If banks are allowed to
run excesses or deficiencies to be compensated for in future weeks, required
reserves in any week could deviate from the level of reserves two weeks
earlier.
A significant penalty on deficiencies would prevent banks from
intentionally being deficient.
Banks could easily avoid being deficient
since no actions other than changes in the banks holdings of assets could
affect required reserves in the current week.
^ Though the present graduated reserve system would not prevent the banking
system from setting required reserves equal to the level of reserves two weeks
previous, it would seem desirable to eliminate graduated reserves from the reverse
lag system. Unless it can be shown that the setting of reserve requirements
dependent on a banks total deposits gives a more useful aggregate for monetary
policy, graduated reserves would appear to be an unnecessary complication. The
reader is referred to Kaufman (1972, pp. 20ff) for a description of the problems
entailed in a proliferation of reserve categories.
26
Constraints under the Reverse lag
Some constraints would be imposed on monetary policy by adoption of
the changes listed above.
Under the reverse lag, monetary authorities
would lose some control over interest rates in the markets for reserves.
In a sense, the thrust of the changes advocated up to this point has been
to construct an institutional framework in which the interest rates on
reserves (i.e., the Federal funds rate and the interbank deposit rate)
would go wherever they must to insure the banking system establishes a
level of required reserves equal to the level of reserves two weeks pre
vious.
This does not mean these rates would be more volatile.
If the
rate on bank assets were stable, so would be the rate on Federal funds and
inter-bank deposits since these rates will gravitate toward the bank asset
rate.
Monetary policy could change these rates only by running operations large
enough to change bank asset rates.
In addition, under the present system,
control over the Federal funds rate is not as great an advantage as might
appear at first.
As mentioned previously, this still leaves the monetary
authorities with the major problem of estimating the response of deposits
and other market rates to a given Federal funds rate and the solution to
this problem has become more difficult.
Under the reverse lag, response to policy actions would be slower.
Unlike the present lagged reserves or coincident reserves where there can
be an immediate response to monetary policy, policy cannot have an impact
for two weeks under the reverse lag since equilibrium for the banking
system in the current week is determined by the level of reserves two weeks
previous.
This does not appear to be a serious constraint since two weeks
would appear too short a time to produce irreversible influences on the
ultimate goals of policy (e.g., prices, unemployment and output).
It is
also possible to reduce the lag to one week, though it would then be
preferable to have the settlement week begin on Monday to facilitate
inter-week adj us tments.
27
It should also be noted that the required reserves which the banking
system would set under the reverse lag differs somewhat from required
reserves as defined currently.
Since changes In non-demand deposits within
the week are treated as If they had reserve requirements equal to those
against demand deposits, the level and distribution of deposits set under
the reverse lag will differ from one whose regulatory required reserves are
equal to the level of reserves two weeks previous.
The fundamental cause
of this discrepancy is the existence of two differing relationships between
different types of deposits.
The public can exchange different types of
deposits, dollar for dollar, while the reserve requirements against
different types of deposits may not be equal.
In such a situation, the
reserve computation system cannot avoid the existence of some imprecision.
If a banks reserve requirements against various types of deposits are
always equal to the level set by regulation, banks would be impelled to
move, within the week, to offset shifts by the public between different
types of deposits.
Though this would produce movement by the banking system
toward a deposit aggregate whose regulatory required reserves equalled the
level of reserves two weeks previous, imprecision still enters since banks
would hold excess reserves to guard against changes in required reserves
due to shifts by the public between different types of deposits.
The
choice made in the reverse lag system is to remove from banks the effects
of deposit shifts on required reserves by equating the marginal reserve
requirements on all types of deposits.
This approach accepts the
discrepancy of having the regulatory required reserves of bank deposits in
the current week differ from the level of reserves two weeks previous by
a factor dependent on the magnitude of the net shifts between demand and
28
non-demand deposits in the current week."^
Since shifts in non-demand deposits are treated as if they require or
release reserves like demand deposits only in the week during which the
shift occurs, required reserves will change as a result of the deposit
shifts in the following week.
Banks, knowing this, will change their asset
holdings in the following week so as to move required reserves to a level
consistent with the shift between deposit types and the reserve requirements
set by regulation.
For example, in the week following a shift from time
deposits to demand deposits, banks will sell assets and deposits will fall
because the increased reserve requirements due to the increase in demand
deposits will no longer be offset by the decrease in reserve requirements
due to the decline in time deposits.
Under a reverse lag then, as under
other reserve computation schemes, there should be careful consideration
of which aggregate monetary policy is intended to influence.
As presently
set, reserve requirements appear designed to influence a monetary aggregate
in which a dollar of demand deposits is given a weight approximately five
times that of a dollar of time deposits.
narrow money—
If it were desired to influence
(currency plus demand deposits), the dropping of reserve
requirements against time deposits would be appropriate.
It it were desired
to influence broad money— M£ (Ml plus time deposits), equal requirements
would be appropriate.
For a system designed to control M2 (i.e. equal
reserve requirements on demand and time deposits) under the reverse lag,
■^Another reason for differences between actual deposits and a level of
deposits whose regulatory required reserves equal reserves two weeks previous
is open market operations in the current week. An open market transaction affects
deposits if conducted with a non-bank dealer. This would not appear to be a great
problem under a reverse lag. A quick solution would be to accept the change in
deposits involved in open market operations with non-bank dealers and omit checks
directly exchanged between the Federal Reserve and dealer member banks from those
banks net clearings and interbank deposits. A more thorough solution would involve
an analysis of the virtues of conducting open market operations with member banks
and/or non member-bank dealers, which is beyond the scope of this paper.
ISgqual requirements for all types of deposits would also be appropriate for a
policy focused on interest rates.
29
the actual level of M2 would be one whose level of required reserves was
equal to the reserves of two weeks previous, eliminating the discrepancy
described above.
Setting Reserves
The six changes proposed above would still not allow the monetary authorities
to set the level of required reserves exactly because of the effects of
Federal Reserve float, currency flows and Treasury deposits at the Federal
Reserve on the level of reserves.
Four additional changes however, would
enable the monetary authorities, under the reverse lag, to precisely set
the level of reserves and therefore required reserves two weeks later:
7)
Eliminate the discount window.
8)
Eliminate Federal Reserve float by ceasing to provide funds
to banks for checks being cleared before the checks have
been debited from other banks.
9)
Eliminate Treasury deposits at the Federal Reserve.
10)
Add a banks net shipment of currency to the Federal
Reserve in the previous two weeks to actual vault cash
holdings in computing daily vault cash used in
satisfaction of reserve requirements.
Under the reverse lag there would appear to be no reason for a
discount window.
Banks would know before the settlement week begins what
they must do to achieve equilibrium and factors outside their control could
not cause disequilibrium.
Bank solvency problems could be handled in an
ad-hoc manner.
The practice whereby the Federal Reserve sometimes credits a bank pre
senting a check for collection before it debits the bank on which the check is
drawn adds a fluctuating quantity of reserves to the system week by week.
Ending this practice under the reverse lag would eliminate Federal Reserve float.
Reserves would be credited to one bank only at the same time as they are
debited from another.
30
Treasury deposits at the Federal Reserve make it more difficult to
accurately set reserves because variations in the value of Treasury checks
cleared affect the provision of reserves to the banking system.
Under the
reverse lag the Treasury would not hold deposits at the Federal Reserve.
Aside from the benefits for monetary control, elimination of Federal Reserve
19
Treasury deposits would appear to have benefits for the Treasury. 7
Services
now provided for the Treasury by the Federal Reserve would be provided by
commercial banks.
Under the reverse lag, shifts between currency and deposits by the public
have no effect on banks in the first instance since the change in reserves
through the change in vault cash (i.e., the reserve requirements against
demand deposits times the change in vault cash) will exactly match the change
in required reserves due to deposit changes.
As long as the currency changes
on the part of the public are not reflected in currency shipments to or
from the Federal Reserve, there would be no need for the Federal Reserve to
offset the flows.
However, under the reverse lag computation scheme there is
an incentive for banks to economize on holdings of vault cash since reserves
at the Federal Reserve count in full while only a percentage of vault cash
counts as reserves.
Thus it could be expected that there would be substantial
shipments of currency between the banks and the Federal Reserve.
A shipment
of vault cash from a bank to the Federal Reserve under the reverse lag
scheme would reduce reserves available from vault cash immediately but would
not increase reserves available to meet required reserves at the Federal
Reserve for two weeks.
19
Reserves are lost for two weeks.
Conversely, a ship-
Current practice costs the Treasury the amount of money spent by the
Federal Reserve in servicing Treasury deposits while the Treasury receives
an implicit interest rate equal to the Treasury bill rate on its deposits at
the Federal Reserve. Placing these deposits at commercial banks would likely
lower net costs to the Treasury.
31
ment of currency from the Federal Reserve to the banks does not reduce
reserves available to meet required reserves at the Federal Reserve for two
weeks while increasing reserves available from vault cash immediately.
is a form of double counting for two weeks.
There
20
A solution is to adjust the definition of vault cash by adding net currency
shipments to the Federal Reserve in the previous two weeks to the actual vault
cash position.
Thus, a shipment of currency to the Federal Reserve would not
produce a gap in reserves nor a shipment from the Federal Reserve a double
counting.
While this avoids the immediate change in reserves as a result of a
change in vault cash, the monetary authorities still must offset the impact
of a currency shipment on reserves for use two weeks in the future.
A shipment of currency to (from) the Federal Reserve will, unless offset,
increase (decrease) reserves available for use two weeks in the future by
one minus the reserve requirement against demand deposits times the currency
shipment.
A shipment to (from) the central bank increases (decreases)
reserves available for use two weeks in the future at the Federal Reserve
by the full amount while the decline in vault cash reduces (increases)
reserves by the reserve requirement against demand deposits times the value
of the shipment.
To offset the influence of currency shipments on reserves
for future use, the monetary authorities would sell (buy) securities equal
to one minus the reserve requirement against demand deposits times the value
of currency shipped to (from) the central bank.
Two changes involved in adopting the reverse lag would impose additional
costs on member banks of the Federal Reserve system.
The elimination of
Federal Reserve float and the counting of only a percentage of vault cash
20
uFor an exposition of the reserve adjustment possibilities opened to banks
as a result of the counting of vault cash reserves from one time period and
reserves at the Federal Reserve from another see Coats (1973).
32
as reserves would reduce reserves available to member banks.
Due to the
Increased precision with which required reserves could be set under the
reverse lag, reserve requirements could be reduced far more than the
approximately twenty percent necessary to offset the reduction in reserves.
Besides resulting in a lowering of costs to member banks, a sharp cut in
reserve requirements would further improve the monetary authorities control
over monetary policy by making Federal Reserve membership more attractive.
Conclusion
Analysis indicates that the 1968 shift to lagged reserves has had
deleterious effects on the individual bank, the banking system and monetary
policy.
Lagged reserves increase the costs of reserve management for the
individual bank, while increasing the costs imposed on the banking system
by shifts in monetary policy.
Lagged reserves also reduce the precision with
which monetary policy may be conducted.
The analysis further suggests
that a reserve computation scheme in which required reserves are set two weeks
after reserves would be more in keeping with the fundamental scheme of
monetary policy.
The reverse lag system developed here would allow the monetary authori
ties to precisely set a level of reserves in the current week which the bank
ing system would match with required reserves two weeks hence.
Banks,
knowing precisely what change in asset holdings is required to set and keep
required reserves equal to their level of reserves two weeks previous, would
eliminate excess reserves.
Since banks would know their required adjustments
ahead of time, markets would develop enabling
the banking system to make the
necessary changes in required reserves efficiently.
The precision with which
required reserves could be set would allow reserve requirements to be cut
sharply, lowering the costs of membership in the Federal Reserve system and
further improving the precision of monetary policy.
The resulting banking
33
sector would be much simplified without a discount window or reserve carry
over.
Monetary authorities would no longer be required to take account of
Federal Reserve float, Treasury deposits or changes in public currency hold
ings to implement policy.
Only knowledge of net currency shipments between
banks and the Federal Reserve would be required.
34
References
Burger, Albert E., "Lagged Reserve Requirements:
Their Effects on Federal
Reserve Operations, Money Market Stability, Member Banks and the Money
Supply Process," unpublished paper, Federal Reserve Bank of
St. Louis, 1971.
Coats, Warren L. Jr., "The September 1968, Changes in 'Regulation D' and
their Implications for Money Supply Control," unpublished Ph.D. thesis,
University of Chicago, June 1972.
_______________________ "Regulation D and the Vault Cash Game."
of Finance, XXVIII, (June 1973):
Journal
pp. 601-607.
_______________________ "Lagging Deposits for Bank Reserve Requirements and
the Money Supply Mechanism," unpublished paper, University of Virginia,
1973.
Gilbert, R. Alton, "The Effects of Lagged Reserve Requirements on the
Reserve Adjustment Pressure on Banks," Financial Analysts Journal XXIX,
(September/October 1973), pp. 34-43 and "Appendix" pp. 88-89.
Holmes, Alan R., "Operational Constraints on the Stabilization of Money
Supply Growth, Controlling Money Aggregates, Federal Reserve Bank of
Boston, Conference Series, No. 1, 1969:
pp. 65-77.
Kaufman, George G., "Federal Reserve Inability to Control the Money Supply:
A Self-Fulfilling Prophecy."
(September/October 1972):
Financial Analysts Journal XXVIII, No. 5,
p. 20ff.
Laufenberg, Daniel, "Lagged Versus Contemporaneous Reserve Accounting and
Short-Run Fluctuations in Deposits," unpublished paper, Federal Reserve
Board, 1975.
Federal Reserve Bank of New York, "Open Market Operations and the Monetary
and Credit Aggregates— 1971," Monthly Review, April 1972: pp. 79-94.
Poole, William and Lieberman, Charles, "Improving Monetary Control,"
Brookings Paper on Economic Activity, No. 2 (1972):
pp. 293-342.
@FedFRASER