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An empirical examination of bank reserve management behavior
Journal
of Banking
and
Finance
14 (1990)
131-143.
North-Holland
AN EMPIRICAL EXAMINATION OF BANK RESERVE MANAGEMENT BEHAVIOR
Douglas D. EVANOFF* Federal Reserce Bank of Chicago, Chicago, IL 60690, USA Received June 1988, linal version
received
May 1989
Bank regulators modify reserve accounting schemes for various purposes including to improve monetary control, simplify reserve account management, and decrease the reserve burden. However, the effect of modifications may not be as intended. Utilizing a micro-perspective we model the reserve management process, empirically estimate the model, and evaluate hypotheses concerning changes in the reserve accounting scheme. We find some unintended effects from modilications to the accounting scheme, tenuous support for the use of carryover as a futures in reserves instrument, and little change in banks ability to manage reserve balances as they moved from a lagged to a ‘contemporaneous’ reserve accounting environment.
1. Introduction
Although the theory of bank reserve account management has reached a fairly mature stage of development through examination by Orr and Mellon (1961), Poole (1968), Cooper (1971), Hinderliter (1974), Barth and Bennett (1975), Harrison and Meyer (1975), Friedman and Roberts (1983) and Spindt and Tarhan (1984), related empirical verification has been lacking. Factors expected to influence reserve management behavior include interest rates (including penalties), carryover provisions, length of the maintenance period, length of the lag between the maintenance and computation period (i.e., the role of accounting regimes), and the variance of reservable deposits. However, because of data limitations, the expected relationships have not been subjected to rigorous empirical verification. Here we formally develop the expected relationship between desired levels of excess reserves and elements influencing reserve management behavior, and use previously unavailable data to empirically test the relationship. Related issues considered include the influence of the move to a ‘contemporaneous’ reserve accounting scheme, whether the use of carryover produces a *The author would like to thank Herb Baer, Bob Laurent and Larry Mote for constructive discussions and comments on an earlier draft. Fred Wells and Sam Yen provided excellent assistance in collecting the data. None of the aforementioned is responsible for error, nor do the views herein necessarily reflect their views or those of the Federal Reserve System. 0378%4266/90/53.50
0
1990, Elsevier Science Publishers
B.V. (North-Holland)
132
D.D. Eranoff,
Bank reserce management
behavior
hypothesized cyclical excess reserve balance pattern over time (Friedman and Roberts), whether carryover is utilized as a passive buffer to absorb actual and required reserve mismatches (Harrison and Meyer), or whether via interest rate projections banks are able to use carryover aggressively as a ‘futures in reserves’ instrument (Spindt and Tarhan). The outline of the paper follows. Section 2 discusses the determinants of desired levels of excess reserves and the expected relationships, and the optimal level of desired excess reserves is formally derived in section 3. The empirical results are presented in section 4 and the last section is a summary.
2. Factors influencing reserve balance management In deciding on the desired level of excess reserves the bank reserve account manager encounters a classic inventory adjustment problem. The institution attempts to minimize expected costs given balance and deposit flows, opportunity costs, and potential penalty costs. Excess reserves incur an opportunity cost, whereas deficiencies produce penalties imposed by the regulator - the Federal Reserve Bank (FRB). Thus, intuitively, the level of desired excess reserves depends on the costs of excesses and deficiencies, and the variance of deposits, i.e., DXR = DXR( i, p, m, aR)
(1)
where DXR is desired excess reserves, i is the opportunity rate, p is the explicit FRB penalty rate, m is an implicit FRB penalty consisting of nonpecuniary costs incurred when reserves are deficient, and aR is the variance of the distribution of reserve balances. With the exception of the opportunity rate, all variables are expected to affect DXR positively.’ An additional element affecting DXR is the carryover provision. Introduced in 1968, this provision allowed institutions to satisfy reserve requirements by holding plus-or-minus 2 percent of the required level of reserves as long as the deviation was offset in the following maintenance period. The Federal Reserve introduced carryover to simplify individual bank reserve
‘The analysis is for a lagged reserve accounting scheme. It would be similar for a pure contemporaneous reserve accounting environment where banks would be required to hold sulficient reserves on deposit during the same time period (e.g. weekly). However, required reserves (resulting from deposit variability) would not be known with certainty and DXR could be positively related to the variance of the distribution of deposits. However, this pure form of CRR accounting has not been in place during the period considered. The period from which required reserves are based has changed over the time span analyzed. During the 1970s it was a one week period beginning two weeks prior to the reserve maintenance period. During the early 1980s this lag was significantly shortened.
D.D. Evanofl; Bank reserve management behavior
133
management, and it was expected to be utilized in a ‘passive’ manner to offset stochastic deviations from zero excess reserves [Board of Governors (1968b)]. This would allow banks to put less emphasis on achieving a precise reserve balance and to allocate fewer resources to reserve management. Despite regulators’ desire to have carryover be utilized passively, profit incentives could encourage banks to use it aggressively. This would result in oscillatory movements between surpluses and deficiencies in an individual bank’s successive reserve positions. The oscillations occur because the cost of more than offsetting the deficiency or surplus carried forward is essentially zero, and projected changes in future interest rates may make it advantageous to fully utilize the carryover provision and thereby position the bank to borrow fed funds at a lower rate, or to lend additional funds at a higher rate. The proposition that the cost of carrying balances in excess of those required to offset balances carried forward is essentially zero results from the need to offset carryover in the succeeding maintenance period and the ability to again carry forward to the following period. Assuming a negative carryover (F) is brought into the current reserve maintenance period, an institution can meet its reserve requirement, and avoid penalties, by holding required reserve balances (RR) plus the deficiency carried forward. However, the institution can carry excesses over (RR +F) into the next maintenance period, placing it in a position to hold fewer current balances in that period. As shown by Friedman and Roberts (1983) if the institution decides to do this the cost of holding idle balances is not figured as the foregone interest, but rather the value lost from making the same investment one period later. Since the time horizon is only one or two weeks the cost (value lost) is miniscule. If rates are not expected to change, the cost assuming a one week maintenance period is [i’/( 1 +i)] . [excess reserves], where i is the weekly interest rate. Different accounting schemes could produce a slightly different time horizon but the basic contention remains, i.e., banks incur little cost in holding up to 2 percent of required reserves in excess of the amount of carryover brought into the current maintenance period. However, once the 2 percent is exceeded the opportunity cost again becomes the foregone interest obtainable on alternative investments. This produces a desired level of excess reserves which is greater than that which would occur without the carryover provision. If a reserve excess was brought into the current period the same incentive would exist to more than compensate for the excess. Balances could fall short of the required level by the amount of the excess carried from the previous maintenance period plus an additional 2 percent of required reserves. The bank benefits by being able to extend loans one week earlier than would be possible without the carryover provision. Although the benefit is small, the bank will tend to undertake some additional carryover to avoid holding too
D.D. ErunoJJ
134
Bank
reserrr
management
beharior
many idle balances2 Thus, again, there is a tendency to oscillate from positive to negative excess reserve balances. The bank may also change its level of desired balances if projected future rates differ from current levels. Intuitively, if rates are expected to rise in the next maintenance period the bank will be enticed to carry forward larger excesses (smaller deficiencies) to enable it either to lend more or to borrow less in the Fed funds market at the higher rate. Similarly, projected declines in the rate will encourage banks to carry forward a smaller excess (larger deficiency). The magnitude of this behavior however is constrained by the carryover limit. With the ability to carry reserve deficiencies (excesses) forward, the expectation that future rates will rise (fall) enhances the oscillations between positive and negative carryover positions. 3. Determining
the desired level of reserve balances
Given the above discussion, the optimal level of desired excess reserve balances can be formally derived. With uncertain deposit flows, the reserve manager chooses a level of desired excess reserves to minimize expected costs over the possible range of reserve deviations from target. Deviations from zero excess reserves result in either an opportunity cost or penalty cost which, as discussed above, is affected by the carryover position and interest rate projections. Assuming zero transaction costs to adjust reserve positions and a symmetric distribution of reserve gains or losses about the desired level, we can derive the expected costs of deviations from plan and minimize these to obtain the desired level of reserves. Let x be the targeted level of reserves, E the actual level held, RR, F, i, p, and m be as defined above, ? the projected opportunity rate in the next maintenance period, and 2b the range of the distribution of deviations from the targeted level of reserve balances which, for simplicity, is assumed to be rectangular. If a reserve deficiency is carried forward the expected cost of deviations is: E(C)=
j: L x-b
m-(p-i)E+(p-i)F]dE
2b
+F’orRR
&(i--
&)E+(i-
&)F]dE
x+b
O.OZRR+iE-i(F+O.O2RR)
i-I +F+kIRR
k[(
1 +i)
1
dE
(2)
‘Although it has differed at certain times, 2 percent has generally been the allowable level of carryover. For a more formal description of the behavior discussed here see Friedman and Roberts (1983).
D.D. Emnoff,
Bank reserce management
behacior
135
interest rates
excess reserves
F
Fig. 1. Desired
F+.OP(RR)
excess reserve determination.
where the tirst term depicts the cost of holding balances less than that required to offset the negative carryover, the second term the cost of holding balances ranging from an amount equal to the negative carryover to 2 percent (the allowable limit) above it, and the third term the cost of holding reserve balances above that required to offset the negative carryover from the previous period plus 2 percent of current required reserves. These three ranges3 are graphically depicted in fig. 1. Minimizing E(C) generates
m+4~-2i)+&O.OW+F
where
(3)
X=
P 2%
s
and
ax >(I a<()
a(T-
‘di
’
and
3~1 c?F
.
If an excess is carried forward into the current maintenance given the same assumptions, the optimal level of DXR becomes ‘The notation
used is similar
to that of Friedman
and Roberts
(1983).
period, and
136
D.D. Euano~,
Bank reserve management
behavior
;(O.O2RR)
m+b(p-2i)+
(l+i)
X= P
+ (F - 0.02RR).
(4)
An additional element which could influence reserve management behavior is the reserve accounting rules. These are dictated by Regulation D of the Federal Reserve Act and have been changed periodically to alter the reserve burden. The modifications affect reserve management to the extent that they impact the variables discussed above. Distinct time periods emerging as a result of changes to Regulation D include the following:4 (1) Prior to September, 1968 - contemporaneous reserve requirements (CRR), (2) September 12, 1968 to February, 1984 - lagged reserve requirements (LRA), and (3) February 198~current - a new contemporaneous reserve requirement scheme (‘CRR’). Under the LRA system the average daily level of reserves held in the current one week period were based on reservable deposit balances held two weeks earlier. Thus, the level of required reserves was known with certainty while legal reserves, because of their stochastic nature, had to be projected based on past experience. The carryover provision was introduced at the beginning of this period to allow reserve deficiencies or excesses to be offset in the succeeding maintenance period. The carryover was not allowed to exceed 2 percent of required reserves and could not be carried for more than one reserve period. The changes introduced with LRA were expected to reduce uncertainty’ and to ‘moderate pressures for reserve adjustments’. This would occur because the variance in reserves would be decreased since banks would know precisely what their required balances were prior to the maintenance period and, thus, would need only to be concerned with managing reserve balances. Previously, under CRR, uncertainty with respect to required reserves also existed. Although simplifying the reserve management process by reducing uncertainty was a major objective of moving to a LRA scheme, the effect may have been exactly the opposite. Under LRA, unexpected changes in deposits resulted in the need to offset the change to meet reserve requirements. Under the pre-1968 CRR regime, unexpected deposit changes produced changes in both legal and required reserves. The resulting adjustment &Many of the specilic characteristics of each of the regimes are not discussed here. For a more detailed discussion of the accounting schemes and an outline of the changes see Board of Governors of the Federal Reserve (1962, 1968b, 1983) and Evanoff (1989). ‘See Board of Governors (1968a) in which the Federal Reserve requests comment on the proposed amendment to Regulation D.
D.D. Ecanoff,
Bank reserce management
behacior
137
which the bank was required to make would be less than that under LRA because of the simultaneous cushioning change in required reserves [Gilbert (1973)]. This impact will be considered in our empirical analysis. The ‘CRR’ scheme introduced a longer computation and maintenance period (2 weeks) and a shorter lag (2 days) between the two periods. To aid banks in the transition period the carryover provision was temporarily increased to 3 percent of required reserves, was subsequently lowered to 2) percent in August 1984, and returned to 2 percent in December 1984. The net effect of these changes should be to lower the daily average variance of reserves because of the two week maintenance period, but increase uncertainty with respect to the level of required reserves because of the two day lag. The larger carryover, if used passively, would make it easier to achieve required reserve levels. However, it may encourage institutions to utilize the provision aggressively to generate a cyclical behavior of reserve excesses followed by more than offsetting reserve deficiencies. To the extent that the increased carryover provision and the decreased variability more than offset the decreased certainty concerning required reserve levels, banks would find the cyclical behavior of reserve management even more appealing. Additionally, banks previously not practicing this ‘line tuning’ of reserves may suddenly find it beneficial and begin utilizing it.6 The phasing down of the size of allowable carryover (from 3 percent to 2$ percent to 2 percent) should dampen the size of the reserve balance oscillations. The preceding discussion reviews and introduces a number of hypotheses, most of which can be empirically tested. The hypothesized relationships can be tested as can related questions including: (1) Does cyclical reserve management behavior occur when a carryover provision is in effect? (2) Do projected interest rates influence this behavior suggesting banks may use carryover as a futures in reserves instrument? (3) What was the impact of introducing ‘CRR’ in 1984? and (4) What was the impact of temporarily having a larger carryover provision?
4. Data and empirical results A linear model describing the reserve preceding section can be presented as:
behavior
as discussed
DXR=a,fa,(F)+a,(i)+a,(P’)+r,(~‘)+r,(di)+r,(a,)+u,
in the
(5)
where 6However, the 3 percent provision was known to be temporary and some institutions may have simply adjusted to the new regime and not extended resources to develop expertise in a system which, after repeal, would not generate the same benelits. If this occurs the projected increased use of the cyclical excess reserve balance procedure may not materialize.
138
D.D. Evanoff,
Bank reserce management
behavior
F =carryover from the previous period, i = opportunity cost of holding excess reserves, P’=explicit penalty rate on reserve deficiencies, Pi = implicit penalty rate, Ai=projected change in rates between the current and succeeding maintenance period, F-i, cR= variance of reserves, u =an error term, and a’s= the parameters to be estimated. Given the theory, projected signs are as follows:’ cc,<0
r3,a,,cc,,a,>0
and
2,=-l.
To test the hypotheses discussed above, data were collected for 13 midwest commercial banks located in the Seventh Federal Reserve District - all with assets exceeding $400 million. The data span the period 1975-1985, thus, incorporating information from both the period of lagged reserve accounting and the period of ‘contemporaneous’ reserve accounting. Data were not available for the earlier pre-LRA period.’ Variables used in the empirical analysis were chosen to represent the factors previously discussed and to avoid potential collinearity problems. This is a particular concern with interest rates. An implicit and explicit penalty rate were utilized since the Federal Reserve does not impose a true explicit ‘penalty’. However, non-pecuniary costs are also imposed and the total penalty is thought to be accounted for by the two rates. The following variables and proxy variables were utilized in the analysis: F =reserves carried forward, i =one month T-bill rate in the secondary market, P’= the Chicago Federal Reserve Bank discount rate plus 2 percent, Pi= the difference between the weekly average Fed funds rate and
the discount rate, Ai = the difference between the current Fed funds rate and one projected for the following maintenance period,
‘The expected sign on z, is negative because of the way F is detined - e.g., banks are negating carryover deficits or excesses. The variance of reserve balances is included to differentiate between banks. The discussion in section 2 was for an individual bank and assumed a symmetric distribution. Differences between banks and asymmetries obviously exist. ‘Friedman and Roberts attempted to empirically verify the oscillatory behavior. However, use of aggregate data did not allow them to view individual tirm behavior. There were certain maintenance periods during the 1975-1985 span for which reserve information was not available for all the institutions considered. Most of these were during 1979. These adjustments left a sample of 5,577 observations.
D.D. Evanojj; Bank reserve management behavior
139
oR= the relative variation of reserve balances measured as the coefftcient of variation.’ Since pooled cross-section and time series data were used, eq. (5) was estimated using a generalized least squares method which assumes a firstorder autoregressive model where the error terms are both serially and contemporaneously correlated [Parks (1967)]. The preferred choice of a forecasted rate, to generate Ai, was not obvious. No direct means of obtaining a forecast equal to that of bank managers is possible, therefore, a number of alternatives were considered. The reported results assumed the bank managers accurately forecasted the future rate. Alternative techniques to derive forecasts generally resulted in similar findings to the extent that they accurately forecasted future rates. Less accurate forecasts generated slightly inferior results.” The results from estimation of eq. (5) are presented in table 1. All of the coefftcients have the expected sign and most are significant at the 5 percent level. The significance level of the coefficient for the variable depicting the difference between projected and future opportunity rates fell just outside this range. The coefhcient on carryover is as projected, suggesting that banks do indeed manage their reserve accounts relatively accurately and utilize the carryover provision in an aggressive manner. That is, they manage their accounts to obtain benefits from this provision instead of using it as a cushion for unexpected reserve account variability. Tests indicate the coefficient is not significantly different from - 1.0 suggesting a complete offset of excesses or deficiencies carried into the period. The other variables then impact balances as hypothesized. The impact of moving to a ‘contemporaneous’ reserve accounting scheme ‘Goldfeld and Kane (1966) utilized the t-bill rate as an opportunity rate in their analysis of discount window borrowings. T-bill forecasts were also derived as an alternative measure for Ai, however, the results from utilizing this alternative measure were not appreciably different. The coefficient of variation was also calculated using alternative time lags (as well as a CV for each different. The bank over the entire period) and the results, again, were not appreciably derivation of the implicit penalty rate assumes the regulator chastises the reserve delicient institution verbally and with paper work to the extent that the total penalty from being deficient is not preferred to borrowing funds in the open market. In reality, the degree of this implicit penalty probably varies according to the institution’s frequency of deficiency. Thus, this ‘average’ measure may not accurately reflect the penalty for all institutions. “‘To test the robustness of the results with respect to alternative measures of Ai, numerous one step out-of-sample forecast models were developed. A stepwise autoregressive method was utilized as were various ARIMA models. However, it is not obvious that the processes embedded in these models resembles those used by reserve account managers. In general. results found substituting Ai values from these forecasts produced a slightly less significant coefficient for the implicit penalty rate (our least precise measure since we are assuming it to be the same for each institution) and a positive but insignificant coefficient for Ai. The impact of the remaining variables was unchanged. Results found using an ARIMA (1,l.O) to generate Ai are presented in tables A.1 and A.2. It appears that to the extent that managers accurately forecast future rates, results in tables I and 2 are more applicable.
140
D.D. Evanoff, Bank reserve management Table Estimates
of the
1
level of desired pooled data.’
excess
Coetlicient estimate
Variable
-428.91 - 1.03 - 155.05 117.09 139.37 85.34 19.94
Intercept F i P’ P’ Ai QR
behavior
reserves
-
Absolute value
r
(1.1) (20.8)b (2.7)b (2.l)b (2.3)b (1.8)c (2.3)b
R2=0.031 ‘n = 5577. bSignilicant ‘Significant
at the 5 percent level. at the 10 percent level. Table 2
Estimates
of the
Variable Intercept F P’ P’ Ai &F.
level of desired excess impacted by ‘CCR’.’ Coefficient estimate - 406.82 - 1.03 - 153.45 114.49 140.51 86.07 19.87 - 163.26
reserves
Absolute value
as
r
(1.0) (20.8)b (2.7)b (2.l)b (2.3)b (1.8)’ (2.3)b (0.6)
R2 = 0.031 ‘n = 5577. ‘Signilicant ‘Significant
at the 5 percent level. at the 10 percent level.
can also be analyzed. If the effects discussed earlier create sufficient uncertainty, banks can be expected to increase the levels of DXR to help avoid unexpected reserve deficiencies. Alternatively, if reserve management is actually less difficult under ‘CRR’ we would expect DXR to actually decrease. This was tested by adding a binary variable to eq. (5) to account for periods after February 1984 and reestimating the model. The estimates are presented in table 2. The introduction of the binary variable only marginally affects the results and although it enters with a negative sign, the t statistic suggests the influence is not significantly different from zero. Apparently no increased uncertainty was introduced by ‘CRR’ or it is being captured by changes in the reserve balance coefficient of variation. It may be that reserve managers
D.D. Ecuno&
Bank reserve management
behacior
141
are actually in a preferred position under ‘CRR’ in spite of the fact that they argued so aggressively against it. Attempts to quantify the impact of phasing down carryover between February 1984 and December 1984 proved fruitless. In no case did the inclusion of a binary to account for the beginning of a carryover phase-down period enter significantly or significantly alter the magnitude of the remaining coefficients. Apparently, the sample banks simply continued to fully utilize their allowable carryover, and phased down as the allowable limits were lowered.
5. Summary
and conclusions
The purpose of this study was to empirically examine individual bank reserve account management behavior. Formal relationships were derived and adjustments to these relationships resulting from regulatory changes in reserve accounting rules were discussed. However, the issue involves more than simply analyzing whether banks adhere to accounting rules. Regulatory changes introduced by the Federal Reserve to allow banks to extend fewer resources to reserve account management may have had the exact opposite effect. An environment was created in which banks would alter reserve balances even if deposit levels remained constant. Additional fine tuning may also be employed to utilize the carryover provision as a futures in reserves instrument. However, the extent to which this occurs depends directly on the ability of banks to forecast rates. The theorized relationships were empirically tested by analyzing previously unavailable data for a number of institutions located in the Seventh Federal Reserve District. The results indicate that penalty and opportunity cost rates do influence the level of reserves in the manner expected. Additionally, the carryover provision is shown to be fully and aggressively utilized by the institutions over the 1975-1985 period. The coefficient on the level of carryover was not statistically different from - 1.0 suggesting an oscillatory pattern of reserves between deficiencies and excesses in successive maintenance periods. There is also limited evidence that the institutions analyzed do alter their reserve levels based on projected interest rates; i.e., carryover is used as a futures in reserves instrument. However, problems in obtaining true rate projections make this finding tenuous. Moving from a lagged reserve accounting scheme to one more contemporaneous was not found to influence the ability of banks to accurately manage balances. The temporary ability of banks to have larger carryover positions resulted in the full use of the additional allowance. Banks apparently were quite capable of responding to the revised reserve accounting procedures. Thus, some expected relationships were empirically verified as were some unintended effects as a result of altering the reserve accounting scheme.
D.D. Eranoff, Bank reserc‘e management behavior
142
Table Estimates
of the
l.A (via ARI,MA:
1. 1.0)
level of desired pooled data.’
excess
Coeflicient estimate
Variable
- 498.49 - 1.03 - 137.76 116.51 93.65 17.94 19.11
Intercept F i P’ P Ai OR
reserves
-
Absolute value
t
(1.4)
(20.7)b (2.3)b (2.l)b (1.6) (0.1) (2.4)b
R’=0.031 ‘n = 5577. ‘Significant
at the 5 percent
level.
Table 2.A (via ARIMA: Estimates
of the
Variable Intercept F i P’ P’ Ai OR CRR
1.1.0)
level of desired excess impacted by ‘CRR’.” Coefficient estimate - 472.40 - 1.03 - 135.87 114.24 93.92 19.96 18.80 - 175.20
reserves
Absolute value
as
I
(1.3) (20.7)b (2.2)b (2.O)b (1.6) (0.1) (2.5)b (0.1)
R2 =0.031 an = 5577. “Signilicant
at the 5 percent
level.
References Barth, James R. and James T. Bennett, 1975, Optimal reserve management reconsidered, Southern Economic Journal 41, April, 678-682. Board of Governors of the Federal Reserve System, 1962, Law department - Resources of member banks, Federal Reserve Bulletin 48, Aug., 975-978. Board of Governors of the Federal Reserve System, 1968a, Reserves of member banks, Federal Reserve press release dated January 29. Board of Governors of the Federal Reserve System, 1968b, Law department - Computation of reserve requirements, Federal Reserve Bulletin 54, May, 437-438. Board of Governors of the Federal Reserve System, 1983, Contemporaneous reserve requirement handbook (Washington, DC). Cooper, J. Phillip, 1971, Stochastic reserve loss and expansion of bank credit: Note, American Economic Review 61, Sept., 741-745. EvanoN, Douglas D., 1989, Reserve account management behavior: Impact of the reserve accounting scheme and carry forward provision, Staff Memoranda Series, Federal Reserve Bank of Chicago (WP-89-12) June. Friedman, Richard M. and William Roberts, 1983, The carry-forward provision and management of bank reserves, Journal of Finance 38, June, 845-855.
D.D. Ecanoff, Bank reserce management brhacior
143
Gilbert, R. Alton, 1973, The etTects of lagged reserve requirements on the reserve adjustment pressure on banks, Financial Analysts Journal 29, Sept’Oct., 3443. Goldfeld, Stephen M. and Edward Kane, 1966, The determinants of member bank borrowing: An econometric study, Journal of Finance 21, 499-514. Harrison, William B. and Paul A. Meyer, 1975, Banks buffer accounts, uncertainty, and institutional variables, Southern Economic Journal 42, July, 107-I 19. Hinderliter, Roger H., 1974, Market access, uncertainty, and reserve-position adjustments of large commercial banks in the 1960s. Journal of Finance 39, March. 41-56. Orr, Daniel and W.G. Mellon, 1961, Stochastic reserve losses and expansion of bank credit, American Economic Review 51, Sept., 614623. Parks, Richard W., 1967, Efficient estimation of a system of regression equations when disturbances are both serially and contemporaneously correlated, Journal of the American Statistical Association 62, June, 500-509. Poole, William, 1968, Commercial bank reserve management in a stochastic model: Implications for monetary policy, Journal of Finance 23, Dec., 769-791. Spindt, Paul A. and Vefa Tarhan. 1984, Bank reserve adjustment process and the use of reserve carryover as a reserve management tool, Journal of Banking and Finance 8, 5-20.
of Banking
and
Finance
14 (1990)
131-143.
North-Holland
AN EMPIRICAL EXAMINATION OF BANK RESERVE MANAGEMENT BEHAVIOR
Douglas D. EVANOFF* Federal Reserce Bank of Chicago, Chicago, IL 60690, USA Received June 1988, linal version
received
May 1989
Bank regulators modify reserve accounting schemes for various purposes including to improve monetary control, simplify reserve account management, and decrease the reserve burden. However, the effect of modifications may not be as intended. Utilizing a micro-perspective we model the reserve management process, empirically estimate the model, and evaluate hypotheses concerning changes in the reserve accounting scheme. We find some unintended effects from modilications to the accounting scheme, tenuous support for the use of carryover as a futures in reserves instrument, and little change in banks ability to manage reserve balances as they moved from a lagged to a ‘contemporaneous’ reserve accounting environment.
1. Introduction
Although the theory of bank reserve account management has reached a fairly mature stage of development through examination by Orr and Mellon (1961), Poole (1968), Cooper (1971), Hinderliter (1974), Barth and Bennett (1975), Harrison and Meyer (1975), Friedman and Roberts (1983) and Spindt and Tarhan (1984), related empirical verification has been lacking. Factors expected to influence reserve management behavior include interest rates (including penalties), carryover provisions, length of the maintenance period, length of the lag between the maintenance and computation period (i.e., the role of accounting regimes), and the variance of reservable deposits. However, because of data limitations, the expected relationships have not been subjected to rigorous empirical verification. Here we formally develop the expected relationship between desired levels of excess reserves and elements influencing reserve management behavior, and use previously unavailable data to empirically test the relationship. Related issues considered include the influence of the move to a ‘contemporaneous’ reserve accounting scheme, whether the use of carryover produces a *The author would like to thank Herb Baer, Bob Laurent and Larry Mote for constructive discussions and comments on an earlier draft. Fred Wells and Sam Yen provided excellent assistance in collecting the data. None of the aforementioned is responsible for error, nor do the views herein necessarily reflect their views or those of the Federal Reserve System. 0378%4266/90/53.50
0
1990, Elsevier Science Publishers
B.V. (North-Holland)
132
D.D. Eranoff,
Bank reserce management
behavior
hypothesized cyclical excess reserve balance pattern over time (Friedman and Roberts), whether carryover is utilized as a passive buffer to absorb actual and required reserve mismatches (Harrison and Meyer), or whether via interest rate projections banks are able to use carryover aggressively as a ‘futures in reserves’ instrument (Spindt and Tarhan). The outline of the paper follows. Section 2 discusses the determinants of desired levels of excess reserves and the expected relationships, and the optimal level of desired excess reserves is formally derived in section 3. The empirical results are presented in section 4 and the last section is a summary.
2. Factors influencing reserve balance management In deciding on the desired level of excess reserves the bank reserve account manager encounters a classic inventory adjustment problem. The institution attempts to minimize expected costs given balance and deposit flows, opportunity costs, and potential penalty costs. Excess reserves incur an opportunity cost, whereas deficiencies produce penalties imposed by the regulator - the Federal Reserve Bank (FRB). Thus, intuitively, the level of desired excess reserves depends on the costs of excesses and deficiencies, and the variance of deposits, i.e., DXR = DXR( i, p, m, aR)
(1)
where DXR is desired excess reserves, i is the opportunity rate, p is the explicit FRB penalty rate, m is an implicit FRB penalty consisting of nonpecuniary costs incurred when reserves are deficient, and aR is the variance of the distribution of reserve balances. With the exception of the opportunity rate, all variables are expected to affect DXR positively.’ An additional element affecting DXR is the carryover provision. Introduced in 1968, this provision allowed institutions to satisfy reserve requirements by holding plus-or-minus 2 percent of the required level of reserves as long as the deviation was offset in the following maintenance period. The Federal Reserve introduced carryover to simplify individual bank reserve
‘The analysis is for a lagged reserve accounting scheme. It would be similar for a pure contemporaneous reserve accounting environment where banks would be required to hold sulficient reserves on deposit during the same time period (e.g. weekly). However, required reserves (resulting from deposit variability) would not be known with certainty and DXR could be positively related to the variance of the distribution of deposits. However, this pure form of CRR accounting has not been in place during the period considered. The period from which required reserves are based has changed over the time span analyzed. During the 1970s it was a one week period beginning two weeks prior to the reserve maintenance period. During the early 1980s this lag was significantly shortened.
D.D. Evanofl; Bank reserve management behavior
133
management, and it was expected to be utilized in a ‘passive’ manner to offset stochastic deviations from zero excess reserves [Board of Governors (1968b)]. This would allow banks to put less emphasis on achieving a precise reserve balance and to allocate fewer resources to reserve management. Despite regulators’ desire to have carryover be utilized passively, profit incentives could encourage banks to use it aggressively. This would result in oscillatory movements between surpluses and deficiencies in an individual bank’s successive reserve positions. The oscillations occur because the cost of more than offsetting the deficiency or surplus carried forward is essentially zero, and projected changes in future interest rates may make it advantageous to fully utilize the carryover provision and thereby position the bank to borrow fed funds at a lower rate, or to lend additional funds at a higher rate. The proposition that the cost of carrying balances in excess of those required to offset balances carried forward is essentially zero results from the need to offset carryover in the succeeding maintenance period and the ability to again carry forward to the following period. Assuming a negative carryover (F) is brought into the current reserve maintenance period, an institution can meet its reserve requirement, and avoid penalties, by holding required reserve balances (RR) plus the deficiency carried forward. However, the institution can carry excesses over (RR +F) into the next maintenance period, placing it in a position to hold fewer current balances in that period. As shown by Friedman and Roberts (1983) if the institution decides to do this the cost of holding idle balances is not figured as the foregone interest, but rather the value lost from making the same investment one period later. Since the time horizon is only one or two weeks the cost (value lost) is miniscule. If rates are not expected to change, the cost assuming a one week maintenance period is [i’/( 1 +i)] . [excess reserves], where i is the weekly interest rate. Different accounting schemes could produce a slightly different time horizon but the basic contention remains, i.e., banks incur little cost in holding up to 2 percent of required reserves in excess of the amount of carryover brought into the current maintenance period. However, once the 2 percent is exceeded the opportunity cost again becomes the foregone interest obtainable on alternative investments. This produces a desired level of excess reserves which is greater than that which would occur without the carryover provision. If a reserve excess was brought into the current period the same incentive would exist to more than compensate for the excess. Balances could fall short of the required level by the amount of the excess carried from the previous maintenance period plus an additional 2 percent of required reserves. The bank benefits by being able to extend loans one week earlier than would be possible without the carryover provision. Although the benefit is small, the bank will tend to undertake some additional carryover to avoid holding too
D.D. ErunoJJ
134
Bank
reserrr
management
beharior
many idle balances2 Thus, again, there is a tendency to oscillate from positive to negative excess reserve balances. The bank may also change its level of desired balances if projected future rates differ from current levels. Intuitively, if rates are expected to rise in the next maintenance period the bank will be enticed to carry forward larger excesses (smaller deficiencies) to enable it either to lend more or to borrow less in the Fed funds market at the higher rate. Similarly, projected declines in the rate will encourage banks to carry forward a smaller excess (larger deficiency). The magnitude of this behavior however is constrained by the carryover limit. With the ability to carry reserve deficiencies (excesses) forward, the expectation that future rates will rise (fall) enhances the oscillations between positive and negative carryover positions. 3. Determining
the desired level of reserve balances
Given the above discussion, the optimal level of desired excess reserve balances can be formally derived. With uncertain deposit flows, the reserve manager chooses a level of desired excess reserves to minimize expected costs over the possible range of reserve deviations from target. Deviations from zero excess reserves result in either an opportunity cost or penalty cost which, as discussed above, is affected by the carryover position and interest rate projections. Assuming zero transaction costs to adjust reserve positions and a symmetric distribution of reserve gains or losses about the desired level, we can derive the expected costs of deviations from plan and minimize these to obtain the desired level of reserves. Let x be the targeted level of reserves, E the actual level held, RR, F, i, p, and m be as defined above, ? the projected opportunity rate in the next maintenance period, and 2b the range of the distribution of deviations from the targeted level of reserve balances which, for simplicity, is assumed to be rectangular. If a reserve deficiency is carried forward the expected cost of deviations is: E(C)=
j: L x-b
m-(p-i)E+(p-i)F]dE
2b
+F’orRR
&(i--
&)E+(i-
&)F]dE
x+b
O.OZRR+iE-i(F+O.O2RR)
i-I +F+kIRR
k[(
1 +i)
1
dE
(2)
‘Although it has differed at certain times, 2 percent has generally been the allowable level of carryover. For a more formal description of the behavior discussed here see Friedman and Roberts (1983).
D.D. Emnoff,
Bank reserce management
behacior
135
interest rates
excess reserves
F
Fig. 1. Desired
F+.OP(RR)
excess reserve determination.
where the tirst term depicts the cost of holding balances less than that required to offset the negative carryover, the second term the cost of holding balances ranging from an amount equal to the negative carryover to 2 percent (the allowable limit) above it, and the third term the cost of holding reserve balances above that required to offset the negative carryover from the previous period plus 2 percent of current required reserves. These three ranges3 are graphically depicted in fig. 1. Minimizing E(C) generates
m+4~-2i)+&O.OW+F
where
(3)
X=
P 2%
s
and
ax >(I a<()
a(T-
‘di
’
and
3~1 c?F
.
If an excess is carried forward into the current maintenance given the same assumptions, the optimal level of DXR becomes ‘The notation
used is similar
to that of Friedman
and Roberts
(1983).
period, and
136
D.D. Euano~,
Bank reserve management
behavior
;(O.O2RR)
m+b(p-2i)+
(l+i)
X= P
+ (F - 0.02RR).
(4)
An additional element which could influence reserve management behavior is the reserve accounting rules. These are dictated by Regulation D of the Federal Reserve Act and have been changed periodically to alter the reserve burden. The modifications affect reserve management to the extent that they impact the variables discussed above. Distinct time periods emerging as a result of changes to Regulation D include the following:4 (1) Prior to September, 1968 - contemporaneous reserve requirements (CRR), (2) September 12, 1968 to February, 1984 - lagged reserve requirements (LRA), and (3) February 198~current - a new contemporaneous reserve requirement scheme (‘CRR’). Under the LRA system the average daily level of reserves held in the current one week period were based on reservable deposit balances held two weeks earlier. Thus, the level of required reserves was known with certainty while legal reserves, because of their stochastic nature, had to be projected based on past experience. The carryover provision was introduced at the beginning of this period to allow reserve deficiencies or excesses to be offset in the succeeding maintenance period. The carryover was not allowed to exceed 2 percent of required reserves and could not be carried for more than one reserve period. The changes introduced with LRA were expected to reduce uncertainty’ and to ‘moderate pressures for reserve adjustments’. This would occur because the variance in reserves would be decreased since banks would know precisely what their required balances were prior to the maintenance period and, thus, would need only to be concerned with managing reserve balances. Previously, under CRR, uncertainty with respect to required reserves also existed. Although simplifying the reserve management process by reducing uncertainty was a major objective of moving to a LRA scheme, the effect may have been exactly the opposite. Under LRA, unexpected changes in deposits resulted in the need to offset the change to meet reserve requirements. Under the pre-1968 CRR regime, unexpected deposit changes produced changes in both legal and required reserves. The resulting adjustment &Many of the specilic characteristics of each of the regimes are not discussed here. For a more detailed discussion of the accounting schemes and an outline of the changes see Board of Governors of the Federal Reserve (1962, 1968b, 1983) and Evanoff (1989). ‘See Board of Governors (1968a) in which the Federal Reserve requests comment on the proposed amendment to Regulation D.
D.D. Ecanoff,
Bank reserce management
behacior
137
which the bank was required to make would be less than that under LRA because of the simultaneous cushioning change in required reserves [Gilbert (1973)]. This impact will be considered in our empirical analysis. The ‘CRR’ scheme introduced a longer computation and maintenance period (2 weeks) and a shorter lag (2 days) between the two periods. To aid banks in the transition period the carryover provision was temporarily increased to 3 percent of required reserves, was subsequently lowered to 2) percent in August 1984, and returned to 2 percent in December 1984. The net effect of these changes should be to lower the daily average variance of reserves because of the two week maintenance period, but increase uncertainty with respect to the level of required reserves because of the two day lag. The larger carryover, if used passively, would make it easier to achieve required reserve levels. However, it may encourage institutions to utilize the provision aggressively to generate a cyclical behavior of reserve excesses followed by more than offsetting reserve deficiencies. To the extent that the increased carryover provision and the decreased variability more than offset the decreased certainty concerning required reserve levels, banks would find the cyclical behavior of reserve management even more appealing. Additionally, banks previously not practicing this ‘line tuning’ of reserves may suddenly find it beneficial and begin utilizing it.6 The phasing down of the size of allowable carryover (from 3 percent to 2$ percent to 2 percent) should dampen the size of the reserve balance oscillations. The preceding discussion reviews and introduces a number of hypotheses, most of which can be empirically tested. The hypothesized relationships can be tested as can related questions including: (1) Does cyclical reserve management behavior occur when a carryover provision is in effect? (2) Do projected interest rates influence this behavior suggesting banks may use carryover as a futures in reserves instrument? (3) What was the impact of introducing ‘CRR’ in 1984? and (4) What was the impact of temporarily having a larger carryover provision?
4. Data and empirical results A linear model describing the reserve preceding section can be presented as:
behavior
as discussed
DXR=a,fa,(F)+a,(i)+a,(P’)+r,(~‘)+r,(di)+r,(a,)+u,
in the
(5)
where 6However, the 3 percent provision was known to be temporary and some institutions may have simply adjusted to the new regime and not extended resources to develop expertise in a system which, after repeal, would not generate the same benelits. If this occurs the projected increased use of the cyclical excess reserve balance procedure may not materialize.
138
D.D. Evanoff,
Bank reserce management
behavior
F =carryover from the previous period, i = opportunity cost of holding excess reserves, P’=explicit penalty rate on reserve deficiencies, Pi = implicit penalty rate, Ai=projected change in rates between the current and succeeding maintenance period, F-i, cR= variance of reserves, u =an error term, and a’s= the parameters to be estimated. Given the theory, projected signs are as follows:’ cc,<0
r3,a,,cc,,a,>0
and
2,=-l.
To test the hypotheses discussed above, data were collected for 13 midwest commercial banks located in the Seventh Federal Reserve District - all with assets exceeding $400 million. The data span the period 1975-1985, thus, incorporating information from both the period of lagged reserve accounting and the period of ‘contemporaneous’ reserve accounting. Data were not available for the earlier pre-LRA period.’ Variables used in the empirical analysis were chosen to represent the factors previously discussed and to avoid potential collinearity problems. This is a particular concern with interest rates. An implicit and explicit penalty rate were utilized since the Federal Reserve does not impose a true explicit ‘penalty’. However, non-pecuniary costs are also imposed and the total penalty is thought to be accounted for by the two rates. The following variables and proxy variables were utilized in the analysis: F =reserves carried forward, i =one month T-bill rate in the secondary market, P’= the Chicago Federal Reserve Bank discount rate plus 2 percent, Pi= the difference between the weekly average Fed funds rate and
the discount rate, Ai = the difference between the current Fed funds rate and one projected for the following maintenance period,
‘The expected sign on z, is negative because of the way F is detined - e.g., banks are negating carryover deficits or excesses. The variance of reserve balances is included to differentiate between banks. The discussion in section 2 was for an individual bank and assumed a symmetric distribution. Differences between banks and asymmetries obviously exist. ‘Friedman and Roberts attempted to empirically verify the oscillatory behavior. However, use of aggregate data did not allow them to view individual tirm behavior. There were certain maintenance periods during the 1975-1985 span for which reserve information was not available for all the institutions considered. Most of these were during 1979. These adjustments left a sample of 5,577 observations.
D.D. Evanojj; Bank reserve management behavior
139
oR= the relative variation of reserve balances measured as the coefftcient of variation.’ Since pooled cross-section and time series data were used, eq. (5) was estimated using a generalized least squares method which assumes a firstorder autoregressive model where the error terms are both serially and contemporaneously correlated [Parks (1967)]. The preferred choice of a forecasted rate, to generate Ai, was not obvious. No direct means of obtaining a forecast equal to that of bank managers is possible, therefore, a number of alternatives were considered. The reported results assumed the bank managers accurately forecasted the future rate. Alternative techniques to derive forecasts generally resulted in similar findings to the extent that they accurately forecasted future rates. Less accurate forecasts generated slightly inferior results.” The results from estimation of eq. (5) are presented in table 1. All of the coefftcients have the expected sign and most are significant at the 5 percent level. The significance level of the coefficient for the variable depicting the difference between projected and future opportunity rates fell just outside this range. The coefhcient on carryover is as projected, suggesting that banks do indeed manage their reserve accounts relatively accurately and utilize the carryover provision in an aggressive manner. That is, they manage their accounts to obtain benefits from this provision instead of using it as a cushion for unexpected reserve account variability. Tests indicate the coefficient is not significantly different from - 1.0 suggesting a complete offset of excesses or deficiencies carried into the period. The other variables then impact balances as hypothesized. The impact of moving to a ‘contemporaneous’ reserve accounting scheme ‘Goldfeld and Kane (1966) utilized the t-bill rate as an opportunity rate in their analysis of discount window borrowings. T-bill forecasts were also derived as an alternative measure for Ai, however, the results from utilizing this alternative measure were not appreciably different. The coefficient of variation was also calculated using alternative time lags (as well as a CV for each different. The bank over the entire period) and the results, again, were not appreciably derivation of the implicit penalty rate assumes the regulator chastises the reserve delicient institution verbally and with paper work to the extent that the total penalty from being deficient is not preferred to borrowing funds in the open market. In reality, the degree of this implicit penalty probably varies according to the institution’s frequency of deficiency. Thus, this ‘average’ measure may not accurately reflect the penalty for all institutions. “‘To test the robustness of the results with respect to alternative measures of Ai, numerous one step out-of-sample forecast models were developed. A stepwise autoregressive method was utilized as were various ARIMA models. However, it is not obvious that the processes embedded in these models resembles those used by reserve account managers. In general. results found substituting Ai values from these forecasts produced a slightly less significant coefficient for the implicit penalty rate (our least precise measure since we are assuming it to be the same for each institution) and a positive but insignificant coefficient for Ai. The impact of the remaining variables was unchanged. Results found using an ARIMA (1,l.O) to generate Ai are presented in tables A.1 and A.2. It appears that to the extent that managers accurately forecast future rates, results in tables I and 2 are more applicable.
140
D.D. Evanoff, Bank reserve management Table Estimates
of the
1
level of desired pooled data.’
excess
Coetlicient estimate
Variable
-428.91 - 1.03 - 155.05 117.09 139.37 85.34 19.94
Intercept F i P’ P’ Ai QR
behavior
reserves
-
Absolute value
r
(1.1) (20.8)b (2.7)b (2.l)b (2.3)b (1.8)c (2.3)b
R2=0.031 ‘n = 5577. bSignilicant ‘Significant
at the 5 percent level. at the 10 percent level. Table 2
Estimates
of the
Variable Intercept F P’ P’ Ai &F.
level of desired excess impacted by ‘CCR’.’ Coefficient estimate - 406.82 - 1.03 - 153.45 114.49 140.51 86.07 19.87 - 163.26
reserves
Absolute value
as
r
(1.0) (20.8)b (2.7)b (2.l)b (2.3)b (1.8)’ (2.3)b (0.6)
R2 = 0.031 ‘n = 5577. ‘Signilicant ‘Significant
at the 5 percent level. at the 10 percent level.
can also be analyzed. If the effects discussed earlier create sufficient uncertainty, banks can be expected to increase the levels of DXR to help avoid unexpected reserve deficiencies. Alternatively, if reserve management is actually less difficult under ‘CRR’ we would expect DXR to actually decrease. This was tested by adding a binary variable to eq. (5) to account for periods after February 1984 and reestimating the model. The estimates are presented in table 2. The introduction of the binary variable only marginally affects the results and although it enters with a negative sign, the t statistic suggests the influence is not significantly different from zero. Apparently no increased uncertainty was introduced by ‘CRR’ or it is being captured by changes in the reserve balance coefficient of variation. It may be that reserve managers
D.D. Ecuno&
Bank reserve management
behacior
141
are actually in a preferred position under ‘CRR’ in spite of the fact that they argued so aggressively against it. Attempts to quantify the impact of phasing down carryover between February 1984 and December 1984 proved fruitless. In no case did the inclusion of a binary to account for the beginning of a carryover phase-down period enter significantly or significantly alter the magnitude of the remaining coefficients. Apparently, the sample banks simply continued to fully utilize their allowable carryover, and phased down as the allowable limits were lowered.
5. Summary
and conclusions
The purpose of this study was to empirically examine individual bank reserve account management behavior. Formal relationships were derived and adjustments to these relationships resulting from regulatory changes in reserve accounting rules were discussed. However, the issue involves more than simply analyzing whether banks adhere to accounting rules. Regulatory changes introduced by the Federal Reserve to allow banks to extend fewer resources to reserve account management may have had the exact opposite effect. An environment was created in which banks would alter reserve balances even if deposit levels remained constant. Additional fine tuning may also be employed to utilize the carryover provision as a futures in reserves instrument. However, the extent to which this occurs depends directly on the ability of banks to forecast rates. The theorized relationships were empirically tested by analyzing previously unavailable data for a number of institutions located in the Seventh Federal Reserve District. The results indicate that penalty and opportunity cost rates do influence the level of reserves in the manner expected. Additionally, the carryover provision is shown to be fully and aggressively utilized by the institutions over the 1975-1985 period. The coefficient on the level of carryover was not statistically different from - 1.0 suggesting an oscillatory pattern of reserves between deficiencies and excesses in successive maintenance periods. There is also limited evidence that the institutions analyzed do alter their reserve levels based on projected interest rates; i.e., carryover is used as a futures in reserves instrument. However, problems in obtaining true rate projections make this finding tenuous. Moving from a lagged reserve accounting scheme to one more contemporaneous was not found to influence the ability of banks to accurately manage balances. The temporary ability of banks to have larger carryover positions resulted in the full use of the additional allowance. Banks apparently were quite capable of responding to the revised reserve accounting procedures. Thus, some expected relationships were empirically verified as were some unintended effects as a result of altering the reserve accounting scheme.
D.D. Eranoff, Bank reserc‘e management behavior
142
Table Estimates
of the
l.A (via ARI,MA:
1. 1.0)
level of desired pooled data.’
excess
Coeflicient estimate
Variable
- 498.49 - 1.03 - 137.76 116.51 93.65 17.94 19.11
Intercept F i P’ P Ai OR
reserves
-
Absolute value
t
(1.4)
(20.7)b (2.3)b (2.l)b (1.6) (0.1) (2.4)b
R’=0.031 ‘n = 5577. ‘Significant
at the 5 percent
level.
Table 2.A (via ARIMA: Estimates
of the
Variable Intercept F i P’ P’ Ai OR CRR
1.1.0)
level of desired excess impacted by ‘CRR’.” Coefficient estimate - 472.40 - 1.03 - 135.87 114.24 93.92 19.96 18.80 - 175.20
reserves
Absolute value
as
I
(1.3) (20.7)b (2.2)b (2.O)b (1.6) (0.1) (2.5)b (0.1)
R2 =0.031 an = 5577. “Signilicant
at the 5 percent
level.
References Barth, James R. and James T. Bennett, 1975, Optimal reserve management reconsidered, Southern Economic Journal 41, April, 678-682. Board of Governors of the Federal Reserve System, 1962, Law department - Resources of member banks, Federal Reserve Bulletin 48, Aug., 975-978. Board of Governors of the Federal Reserve System, 1968a, Reserves of member banks, Federal Reserve press release dated January 29. Board of Governors of the Federal Reserve System, 1968b, Law department - Computation of reserve requirements, Federal Reserve Bulletin 54, May, 437-438. Board of Governors of the Federal Reserve System, 1983, Contemporaneous reserve requirement handbook (Washington, DC). Cooper, J. Phillip, 1971, Stochastic reserve loss and expansion of bank credit: Note, American Economic Review 61, Sept., 741-745. EvanoN, Douglas D., 1989, Reserve account management behavior: Impact of the reserve accounting scheme and carry forward provision, Staff Memoranda Series, Federal Reserve Bank of Chicago (WP-89-12) June. Friedman, Richard M. and William Roberts, 1983, The carry-forward provision and management of bank reserves, Journal of Finance 38, June, 845-855.
D.D. Ecanoff, Bank reserce management brhacior
143
Gilbert, R. Alton, 1973, The etTects of lagged reserve requirements on the reserve adjustment pressure on banks, Financial Analysts Journal 29, Sept’Oct., 3443. Goldfeld, Stephen M. and Edward Kane, 1966, The determinants of member bank borrowing: An econometric study, Journal of Finance 21, 499-514. Harrison, William B. and Paul A. Meyer, 1975, Banks buffer accounts, uncertainty, and institutional variables, Southern Economic Journal 42, July, 107-I 19. Hinderliter, Roger H., 1974, Market access, uncertainty, and reserve-position adjustments of large commercial banks in the 1960s. Journal of Finance 39, March. 41-56. Orr, Daniel and W.G. Mellon, 1961, Stochastic reserve losses and expansion of bank credit, American Economic Review 51, Sept., 614623. Parks, Richard W., 1967, Efficient estimation of a system of regression equations when disturbances are both serially and contemporaneously correlated, Journal of the American Statistical Association 62, June, 500-509. Poole, William, 1968, Commercial bank reserve management in a stochastic model: Implications for monetary policy, Journal of Finance 23, Dec., 769-791. Spindt, Paul A. and Vefa Tarhan. 1984, Bank reserve adjustment process and the use of reserve carryover as a reserve management tool, Journal of Banking and Finance 8, 5-20.