The Demand for Excess Reserves.

Dow, James P., Jr.

James P. Dow, Jr. [*]

This paper provides an estimate of the demand for excess reserves in the United States. It finds that excess reserves are negatively related to the Federal funds rate and positively related to transactions deposits. It also finds that clearing needs significantly affect the demand for reserves with increases in excess reserves coming in response to lower required reserve balances and higher clearing volume. Some implications for monetary policy are discussed.

1. Introduction

The demand for excess reserves is at the center of a number of issues in monetary economics. While at one time it was featured primarily in the calculation of money multipliers, more recently it has figured in Federal Reserve policy through its connection to the targeting of the Federal funds rate. Each week, the open market desk is obligated to forecast the demand for reserves, including the demand for excess reserves, to determine the amount of reserves to supply through open market operations. This shift in the role of excess reserves is reflected worldwide; a number of countries have abandoned reserve requirements altogether, and the entire connection between monetary policy and the economy is through the demand for "excess" reserves. This paper looks at recent data on excess reserves in the United States to determine the sensitivity of demand to changes in interest rates and other variables affecting the willingness to hold reserves.

The standard approach to modeling the demand for excess reserves is to treat it as part of a bank's liquidity management decision. Banks want to hold reserves to avoid overdraft or reserve deficiency penalties on their account at the central bank when facing uncertain flows of funds. This general model of the precautionary demand for reserves was given by Poole (1968). Two basic propositions fall out of this approach. The first is that the quantity of excess reserves demanded should vary inversely with short-term interest rates, which are the opportunity cost of holding reserves, assuming that excess reserves pay no interest. The second proposition is that since excess reserves are providing a buffer against uncertainty about reserve balances, demand should increase with uncertainty. The textbook model of excess reserve demand assumes that this uncertainty increases proportionately with the level of transactions deposits. This paper finds support for both of these propositions. In recent years, excess reserv es have increased with the growth in transactions deposits and were negatively related to interest rates, decreasing roughly $120 million for each percentage-point increase in the Federal funds rate.

The role of excess reserves in monetary policy depends on the particular operational strategy adopted by the central bank. The approach in the United States shifted in 1982, when the Federal Reserve moved to a borrowed reserve target from a policy of targeting the growth of nonborrowed reserves in response to the high variability of the Federal funds rate over the preceding years. [1] While some emphasis was still given to the monetary and reserve aggregates after that time, the implementation of policy effectively followed an interest rate targeting rule, although announcements of the intended Federal funds rate did not begin until 1994. The declared operating strategy of the open market desk ("the desk" henceforth) was to supply the amount of reserves demanded by banks less the borrowing target, relying on the fact that the demand for borrowing from the discount window was a relatively stable function of the difference between the intended Federal funds rate and the discount rate. This policy effectively t argeted the overnight interest rate since the only way to get the targeted amount of borrowing was by maintaining the appropriate spread between the Federal funds rate and the discount rate. The demand for excess reserves was believed to be relatively inelastic, and little attention was given to its response to changes in the intended Federal funds rate (e.g., Sellon and Seibert 1982).

By the 1990s, the stable borrowing relationship had fallen apart (Clouse 1994), so interest rate targeting would have to rely on something else for interest elasticity in the Federal funds market. Because excess reserves pay no interest, banks are likely to economize on them when market interest rates increase, which might provide the necessary elasticity. Given a downward-sloping demand for reserves, setting the supply of reserves each day would fix that day's interest rate in the Federal funds market. Of course, required reserves may also be sensitive to changes in the interest rate; an increase in opportunity cost may cause a shift out of non-interest-bearing deposits, producing a corresponding decline in required reserves. However, this is likely to be a slow process and thus difficult to use as the basis for short-term interest rate targeting. It is the demand for excess reserves that provides the short-term interest rate elasticity relied on by the desk.

This downward-sloping demand for excess reserves is the conceptual basis of interest rate targeting in the absence of reserve requirements (e.g., Longworth 1989; Sellon and Weiner 1996). A number of countries have already moved to monetary systems without reserve requirements so that their demand for reserves is entirely a demand for "excess" reserves (Borio 1997). The United States is also moving in that direction, although not for any reason of policy. Commercial banks have implemented "retail sweep programs," which have dramatically reduced the level of deposits subject to reserve requirements (Edwards 1997). As the level of required reserve balances has fallen, the risk of overdrafts at banks' accounts at the Federal Reserve has increased. Because of this, the demand for excess reserves is starting to have less to do with reserve requirements and more to do with the desire to avoid overdrafts. The latter demand, known as a clearing demand or payments-related demand, is now one of the central features of the Federal funds market. Indeed, some banks are no longer bound by reserve requirements and hold deposits at the Federal Reserve only because of clearing needs (Edwards 1997). It is thought that the lower level of required reserve balances and the increased risk of overdrafts might result in increased volatility of the Federal funds rate (Clouse and Elmendorf 1997) and an increased demand for excess reserves. This paper finds some support for an inverse relationship between required reserve balances and excess reserves, although the effect is small. Part of the reason for the small response may be the additional margin for adjustment provided by required clearing balances, which is examined in section 4 of this paper.

The policy of targeting the interest rate on a day-to-day basis requires high-frequency estimates of the demand for excess reserves in order to guide the actions of the desk. Each week the staff at the Board of Governors of the Federal Reserve and the New York Federal Reserve Bank make forecasts of this demand. The estimate will depend on persistent factors, such as the level of transactions deposits or interest rates, but also on short-run factors that affect clearing demand. This paper reports the desk's response to several of these factors.

Estimating the demand for excess reserves is complicated by the fact that what is observed is not the demand but the quantity of excess reserves supplied, which is determined primarily by the actions of the desk. This is simplified somewhat by the current operational policy of the desk, which is to supply the level of reserves demanded at the targeted Federal funds rate. Since the supply function is trying to mimic any changes in demand, we can use estimates of supply to infer changes in demand. The ability to get accurate estimates this way depends on how well the desk does in matching shifts in demand. Overall, the effective Federal funds rate is close to the intended rate, suggesting that the desk does well in meeting its target, making this an effective way to estimate excess reserve demand. However, the information from interest rate deviations can also be used to improve the desk's performance, particularly in reacting to changes in clearing needs. In the future, there will probably be an increasing ne ed to use interest rate information of the kind presented in this paper to guide policy.

2. The Demand and Supply of Excess Reserves

Banks hold balances at the Federal Reserve for two purposes: to meet reserve requirements and to facilitate transactions that require the transfer of Federal funds. For purposes of meeting reserve requirements, the level of reserves are calculated as the average amount held over a 14-day "maintenance period" (Meulendyke 1998). Excess reserves refer to balances held at the Federal Reserve above the required amount and are used to buffer against unexpected fluctuations in reserve balances or required reserves since there are substantial penalties to not meeting reserve requirements. [2] The demand for excess reserves is primarily a "14-day" or maintenance period concept since reserves held on one day are perfect substitutes for reserves held on other days of the period in terms of meeting reserve requirements. However, banks with accounts at the Federal Reserve are also required to have nonnegative levels of balances each day, or else pay an overdraft penalty. Because of this, additional balances held on one d ay do not provide protection against overdrafts on future days, making balances imperfect substitutes across days.

The basic model of a precautionary demand for excess reserves, where banks hold extra reserves as a precaution against fluctuations in reserves or reserve requirements, was developed in Poole (1968). This approach has been used recently in the discussion of the demand for clearing balances in the context of both Canadian (Longworth 1989) and U.S. (Furfine 1998) monetary policy. Most of the recent literature has tended to concentrate on patterns in the Federal funds rate over the days of the week and maintenance period (Spindt and Hoffmeister 1988; Griffiths and Winters 1995; Hamilton 1996; Clouse and Dow 1999) rather than directly measuring the connection between the Federal funds rate and the level of reserves.

Because excess reserves have historically not played an important role in monetary policy, they have received only sporadic empirical attention. Evanoff (1990) examined nominal excess reserve demand for 13 large banks in the 7th Federal Reserve district (Chicago) for the period 1975-1985. The paper uses the one-month Treasury bill rate as the opportunity cost of holding reserves and the discount rate and the spread between the Federal funds rate and the discount rate as measures of the explicit and implicit cost of reserve deficiencies. Increases in the Treasury bill rate were found to reduce excess reserve demand by about $150 million, while increases in either of the penalty costs decreased demand by slightly less. While not directly about excess reserve demand, Hamilton (1997) provides another estimate of the sensitivity of demand to changes in the interest rate. He examines the interest rate response to unexpected changes in the supply of reserves during the period 1989-1991. He finds that a one-percenta ge-point increase in the Federal funds rate was associated with an $300 million decline in nonborrowed reserves.

Excess reserves are plotted in Figure 1. The most striking change in the behavior of excess reserves during this time is the spike in 1991. The cut in reserve requirements that year left banks uncertain about the level of reserves they would like to hold and the desk uncertain about how much reserves to supply. This uncertainty resulted in unexpected volatility of the Federal funds rate, and the desk responded by providing an unusually large amount of reserves. As banks and the desk adapted to the new reserve requirements, excess reserves settled down quickly and remained in the neighborhood of $1000 million afterward. There was another cut in reserve requirements at the start of 1992, but by this time both the banks and the Federal Reserve had a better understanding of how to handle the change, and there was a much smaller disruption to the Federal funds market.

To get a basic idea of how excess reserve demand can be inferred from excess reserve behavior, I will abstract for a moment from the current institutional structure and imagine the demand for excess reserves in a one-day maintenance period. Let demand (Ed) be given by

[E.sup.d] = [a.sub.0] + [a.sub.1]I + [a.sub.2]D + [a.sub.3]RRB + [a.sub.4]Z + [a.sub.5]X, (1)

where Z is a demand factor observed by the desk and X represents an unobserved factor. The term I is the opportunity cost of holding excess reserves, which will be assumed to be the overnight interest rate since excess reserves in the United States pay no explicit return. The term D is the level of transactions deposits, which is presumed to have a positive effect on excess reserve demand, and RRB is the level of required reserve balances that is thought to have a negative effect. In practice, the demand is likely to depend on the average or expected level of deposits since banks probably do not reevaluate their response to these factors on a week-to-week basis.

Excess reserves are defined as the total amount of reserves held (TR) less the reserve requirement (RR): [3]

E = TR - RR. (2)

Reserves consist of vault cash applied to meet reserve requirements (AVC) and deposits at the Federal Reserve, which are either supplied by open market operations (OMO) or borrowed from the discount window. In this model, open market operations are equivalent to nonborrowed reserve balances. In the past, borrowed reserves were often thought to be related to the spread between the Federal funds rate and the discount rate. However, this relationship has effectively disappeared, although borrowing is strongly related to deviations of the effective Federal funds rate from the intended rate (Clouse 1994; Dow 2000). Letting borrowed reserves be a linear function of this spread, the level of total reserves is given by

TR = OMO + [b.sub.1] + [b.sub.2](I - [I.sup.T] + AVC. (3)

Reserves can also be divided by how they are used. After banks have applied their vault cash to meet reserve requirements, the remainder of their requirement, the required reserve balances (RRB), are met by holding deposits at the Federal Reserve. Any deposits above that are excess reserves, so, following Equation 2,

TR = E + RRB + AVC. (4)

The desk is assumed to target a level of excess reserves such that the Federal funds rate will equal the intended rate ([I.sup.T]) based on the desk's expectation of required reserves and other factors affecting reserve demand,

[E.sup.T] = [[a.sup.*].sub.0] + [[a.sup.*].sub.1][I.sup.T] + [[a.sup.*].sub.2][D.sup.*] + [[a.sup.*].sub.3][RRB.sup.*] + [[a.sup.*].sub.4]Z, (5)

where * indicates the desk's estimate. The amount of reserves the desk supplies through open market operations equals the desk's estimated level of required reserve balances plus their target for excess adjusted by their estimate of borrowed reserves ([b.sub.1]):

OMO = [RRB.sup.*] + [E.sup.T] - [[b.sup.*].sub.1] + U. (6)

While not strictly part of open market operations, a shock term U is added here to reflect unexpected changes in the supply of reserve balances due to factors such as float and changes in treasury balances (see Edwards 1997 for a description of these factors). Combining Equations 3, 5, and 6 into Equation 4 produces the excess reserves equation,

E = [[a.sup.*].sub.0] + ([b.sub.1] - [[b.sup.*].sub.1]) + [[a.sup.*].sub.1][I.sup.T] + [[a.sup.*].sub.2][D.sup.*] + [[a.sup.*].sub.3][RRB.sup.*] + ([RRB.sup.*] - RRB) + [b.sub.2](I - [I.sup.t]) + [[a.sup.*].sub.4]Z + U. (7)

Comparing Equation 7 with Equation 1 illustrates a number of points about excess reserve demand estimation. The first is that we are trying to recover demand coefficients by looking at the reaction function of the desk. Since the desk is trying to shift the supply function to mimic the demand function, we can use changes in the supply function to infer the behavior of demand as long as the desk is successful in hitting its target. The second point is that while the coefficient on the intended rate ([[a.sup.*].sub.1]) will not be affected by the borrowing function, the other coefficients will to the extent that changes in the demand for funds are not matched by shifts in supply but instead result in a deviation of the effective Federal funds rate from the intended rate and so result in an increase in borrowing.

This interpretation of Equation 7 is modified somewhat by the 14-day length of the maintenance period. The desk can react to errors in its estimate of the quantity of reserves demanded if it observes deviations of the Federal funds rate from target early enough in the maintenance period. This possibility of feedback affects excess reserve demand estimation much like the borrowing function; it produces an increase in the supply of reserves if the effective Federal funds rate is above the targeted rate. The ability of the desk to respond will depend on the length of the maintenance period. If there were no risk of overdrafts, then an increase in reserves on one day could just be matched with a decrease on future days. However, the risk of overdrafts might limit the desk's ability to cut reserves substantially in the future, particularly if there are few days remaining in the maintenance period, so that a one-day increase in clearing demand may translate to a increase in demand on a period-average basis.

The funds rate can be determined by setting Equation 1 equal to Equation 7:

I = (1/[a.sub.1] - [b.sub.2])[([[a.sup.*].sub.1] - [b.sub.2][I.sup.T] + ([[a.sup.*].sub.0] - [a.sub.0]) + ([b.sub.1] - [[b.sup.*].sub.1]) + ([RRB.sup.*] - RRB) + [[a.sup.*].sub.2][D.sup.*] - [a.sub.2]D + [[a.sup.*].sub.3][RRB.sup.*] - [a.sub.3]RRB + ([[a.sup.*].sub.4] - [a.sub.4])Z - [a.sub.5]X + U]. (8)

If the desk accurately estimates the effect of persistent shifts in demand, those due to interest rates, deposits, and the average level of required reserve balances, Equation 8 reduces to

I - [I.sup.T] = (1/[a.sub.1] - [b.sub.2])[[RRB.sup.*] - RRB + ([[a.sup.*].sub.4] - [a.sub.4])Z - [a.sub.5]X + U]. (9)

The average deviation of the Federal funds rate from the intended rate provides a measure of how good the desk's estimates of the demand coefficients are. The maintenance period average deviation of the effective Federal funds rate from its target for the period 1992:6-1997:12 was 2.1 basis points (0.021%), suggesting that [[a.sup.*].sub.0], [[a.sup.*].sub.1], [[a.sup.*].sub.2], [[b.sup.*].sub.1] are near the true values. Another approach to measuring [a.sub.1], instead of directly estimating Equation 7, would be to use Equation 9 and regress the deviation of the Federal funds rate from its target against a shock identified as a component of U. This is effectively what was done by Hamilton (1997), who examined the effect of shocks to the Treasury's balances on the daily change in the Federal funds rate.

3. Estimating the Demand for Excess Reserves

To determine the demand for excess reserves, I estimate Equation 7 using maintenance period data for June 1992 to December 1997, a period that is relatively free of disruptions to the Federal funds market and that avoids some of the problems of trying to control for the structural shift introduced by the 1991 and 1992 cuts in reserve requirements.

The series for the intended Federal funds rate was constructed from data reported in Rudebusch (1995). The deposits series was constructed as the sum of demand deposits and other checkable deposits adjusted for the effect of sweep programs. Retail sweep programs, which began in 1994, transfer funds out of checking accounts to nonreservable savings accounts to avoid reserve requirements (Edwards 1997). These transfers do not affect the net flows in and out of an individual's accounts and so should not directly affect the demand for excess reserves. Because of this, the reported level of transactions deposits underestimates the actual level of transactions deposits. To correct for this, the value of the swept deposits must be added back into the reported deposits series. The Federal Reserve makes available data on the dollar value of new sweep programs implemented each month. However, it reports only the amount of funds initially swept and not the current reduction in deposits due to sweeps. To get a sweep-adj usted series, one wants to add the data on initial sweeps back to the series for transactions deposits while making some adjustment for the general growth in transactions deposits over that time. To do this, two separate series were constructed: reported deposits (assumed to be nonswept) and swept deposits (assumed unreported). It is assumed that both types of deposits have the same underlying growth rates and that the data series on initial sweeps represents transfers from the first category to the second. The growth rate of the reported series is determined assuming that the swept deposits are removed at the start of the month. The current value of swept deposits equals its previous value, plus new sweeps, adjusted for the overall growth of deposits. The series on swept deposits was then added back into nonswept deposits to get the final deposits series.

An additional variable must be added to the regression to take into account the ability of banks to substitute reserves across maintenance periods due to carryover provisions. If a bank has excess reserves this period, it can apply some of them (up to 4% of its current reserve requirement) toward its reserve requirement next period. Equivalently, if it is short reserves this period, an amount equal to no more than 4% of its reserve requirement can be made up next period with no penalty. Reported data on excess reserves (from the Federal Reserve release F.R.3) is calculated before assessing the effect of carryover. Banks that actively manage their reserve positions are believed to take advantage of the carryover provision by alternating their reserve holdings so that if they have positive carry-in (reserves carried over from the previous maintenance period), they would run lower or negative excess reserves this period and then target positive excess reserves the following period (Friedman and Roberts 1983 and Spindt and Tarhan 1984 contain more detailed discussions of the effect of carryover). To control for this, carry-in will be added as an explanatory variable to the excess demand equations. The coefficient on this term should be between -1 and 0, depending on how aggressive banks are in managing their reserve positions.

Required reserve balances need to be decomposed into expected and unexpected components in order to separate the effect of errors in open market operations from increased overdraft risk due to lower balances. To do this, required reserve balances were regressed against four own lags and seasonal dummies. There is a pronounced seasonal effect on required reserve balances in part because of the increase in vault cash associated with increased transactions around Christmas and New Year's Day. This effect is strongest in late January and early February because of the lag in applying vault cash to reserves. Monthly dummy variables for the months from January to June along with August were found to be significant and included in the regression. The residual from the regression was taken to be the unexpected component, and the predicted value was used as the desk's estimate. Since the estimate of required reserve balances made by the desk is going to be much better than that produced by this simple autoregressive quation, the unexpected component will include variation that was actually expected by the desk and the market. While the unexpected component of reserve balances should have a coefficient of -1 (from Equation 7), the fact that part of it was expected will bias the coefficient towards [[a.sup.*].sub.3], the coefficient on expected balances.

It is generally thought that there are certain days when the flow of funds through banks' accounts at the Federal Reserve tends to be large and volatile, which will increase the clearing demand for reserves (Edwards 1997). The desk may recognize this and provide additional reserves on those days. While the need for additional reserves may last only one day, the extra reserves supplied by the desk are often not completely worked off during the rest of the period since that would require balances to be so low that banks would risk overdrafts. To try to capture the effect of some of these shocks, dummy variables will be included for maintenance periods containing federal holidays and days when two- and five-year government bonds are settled. Since the ability to run off the funds depends on how many days remain in the maintenance period, the dummy variables were split according to whether the day was in the first or the second week of the maintenance period. Only the dummy variables for the second week were sig nificant, and so only they were left in the final regressions. Dummy variables were also introduced for February and year-ends, when there has historically been concerns about Federal funds rate volatility.

Because of noticeable serial correlation, the regressions were run in AR(1) form. Lagged values of excess reserves and the intended rate were included in trial regressions but not found to be significant. All quantity variables in the regressions are deflated by the consumer price index (CPI) scaled to the maintenance period frequency. For convenience, variables are reported in end-of-1997 dollars.

The results of the excess reserves regressions are reported in Table 1. Column 1 contains the baseline estimate. The coefficient on the intended rate is significant and implies an increase in excess reserves of roughly $120 million for a one-percentage-point decline in the Federal funds rate. The coefficient on carry-in is also significant and effectively equal to -1. Banks seem to be very efficient in managing their reserves; an increase in carry-in results in an equal reduction in excess reserves. The coefficient on sweep-adjusted deposits is also significant. An increase in deposits of $1 billion (producing an increase in required reserves of $100 million) corresponds to an additional $3 million of excess reserves. Overall, the behavior of excess reserves during this period seems consistent with the standard precautionary model of the demand for excess reserves.

The importance of clearing demand should show up in two places. It is hypothesized that the decline in required reserve balances will result in an increase in the demand for excess reserves. This is borne out in the regression, with a decrease in expected required reserve balances of $100 million producing an additional $1 million in excess reserves. Splitting the change in required reserve balances into expected and unexpected components was necessary to isolate the effect of lower average balances but was not so successful in capturing the response to errors in open market operations. As discussed previously, the coefficient on unexpected changes in required reserve balances should be between - 1 and the value of the coefficient on the change in expected required reserve balances (estimated to be -0.01), depending on how much of the change was actually expected by the desk. Since the coefficient is -0.063, most of what I am treating as an unexpected change was in reality expected by the desk. Several of th e dummy variables used as proxies for days of unusually high clearing demand are significant, suggesting that the desk does respond to these times. The supply of excess reserves increases in maintenance periods with holidays, at year-end, and in February. However, there seems to be only a slight response on days with the settlement of two- and five-year notes, and it is not statistically significant.

The interpretation of the clearing demand terms depends on how well the desk does in matching its changes in the supply of reserves to shifts in demand. One measure of this is the deviation of the Federal funds rate from target. Table 2 reports the results of regressions of this deviation against the clearing demand dummy variables that were included in the excess reserves regression along with significant months. There was a tendency for the Federal funds rate to be firm on maintenance periods with holidays or on days of the settlement of two- and five-year notes, although the effect is fairly small. Year-ends, on the other hand, produce negative average deviations of 11 basis points, which argues that the desk is aggressive in providing reserves to the market around this time of year, probably reflecting concern about the occasional spikes in the Federal funds rate on the very last day of the year. Combining the information in Tables 1 and 2 indicates that the desk responds to holidays but not enough, does not respond to days with the settlement of notes but should, and perhaps overresponds at year-end.

The additional reserves needed to be added to keep the Federal funds rate on target could be calculated as ([a.sub.1] - [b.sub.2]) multiplied by the average deviation of the Federal funds rate on that maintenance period. Of course, this is the maintenance-period-average value of reserves; the actual amount added on the particular day would be 14 times that (or 14/3 if it were a Friday), and while estimates of [a.sub.1] can be obtained from Table 1, the size of the feedback or borrowing response is less clear.

The interpretation of the coefficients on the demand shocks also depends on how the desk and the discount window respond to interest rate movements during the maintenance period. Column 2 of Table 1 reports the results when the spread between the effective rate and the intended rate is added to the regression. Since the unobserved shock to reserve supply (U) will be highly (negatively) correlated with this deviation, the coefficients of the regression potentially may be biased, particularly the coefficient on the interest rate deviation. This coefficient reflects both the feedback from interest rates to the supply of excess reserves and the effect of unobserved shocks and so cannot be interpreted as the response of excess reserve demand (or supply) in response to interest rate changes. As shown in column 2, the effect of unobserved shocks dominates, so that the coefficient is negative. The inclusion of the interest deviation term makes very little difference to the rest of the regression, suggesting that the estimates of column 1 are little affected by feedback in response to interest rate changes. Column 3 reports the same regression with excess reserves replaced by free reserves, which are defined as excess reserves less borrowed reserves. Using free reserves removes one source of feedback to the Federal funds market. This has a substantial effect on only two coefficients. It makes the coefficient on the interest rate deviation more negative, as would be expected, since it is removing a source of positive response to changes in interest rates. This difference is, in principle, equal to (-)[b.sub.2], making it an estimate of the responsiveness of borrowing to interest rate deviations. Using free reserves as the dependent variable also substantially reduces the coefficient on the year-end dummy variable, suggesting that banks get much of their additional excess reserves at this time of year through the discount window. The free reserve specification also results in significantly larger standard errors on the coe fficients for the intended rate, the forecast of required reserve balances and deposits, causing the latter term to lose statistical significance. The exclusion of borrowed reserves seems to add noise to the regression rather than improving the fit.

Column 4 contains the results of a regression with variables in logs rather than levels. Discussions of excess reserves are usually in levels, in contrast to similar money demand regressions, most likely because the desk makes its need-to-add calculations in levels. Log specifications present a particular difficulty in excess reserve regressions since excess reserve data for individual banks, and carry-in both for individual banks and in the aggregate, can become negative. Since only aggregate data are being used in the regressions here, only carry-in is a difficulty. Since the coefficient on carry-in in the previous equations was very close to -1, carry-in was added directly to excess reserves before estimating the log equation. As can be seen, the log specification is qualitatively quite similar to the levels specification, with the demand curve for excess reserves being quite inelastic.

Overall, the regressions of Table 1 support a model of the precautionary demand for excess reserves with demand coming from both reserve requirements and clearing needs. The effect of changes in the interest rate is particularly interesting given the current policy of interest rate targeting. Two papers that provide alternate estimates of the effect of changes in the intended rate both imply larger responses than found here. Evanoff (1990) estimates a response of around $150 million for large banks in the Chicago Federal Reserve district. While he does not extrapolate from this number to estimate the total response of all banks across districts, it is clear that the implied total response would be several times larger. However, besides examining a later time period, this paper differs from Evanoff in several ways. Most important, by splitting the interest rate effect into intended and unintended components, this paper is better able to separate the effect of demand and supply shocks and persistent and tempor ary changes. Also, this paper incorporates the effects of changes in transactions deposits and required reserve balances.

Hamilton (1997) finds that a change in reserves of $300 million is associated with a one-percentage-point change in the Federal funds rate. Hamilton's method calculates the response of the Federal funds rate on the final day of the maintenance period to an unexpected change in nonborrowed reserves. Using the last day is key since there are no later days in the maintenance period for banks to adjust their reserve positions, so that the appropriately scaled response to a change in reserves on the last day of the maintenance period is analogous to the effect of a persistent change in the supply of reserves. Hamilton uses unexpected changes in the Treasury's balance at the Federal Reserve as a measure of the unexpected change in reserves. There are several reasons why his method may find a more elastic demand curve. Carryover allows banks to substitute reserves across maintenance periods, making the shock on the last day not a true permanent shock. Also, banks probably do not have a good idea of the effect of a T reasury shock and the size of their reserve balances until later in the day (indeed much of the volatility in the Federal funds rate comes at the end of the day). The true reaction of the Federal funds rate to a supply shock is much larger than what would be estimated when using the effective rate, which is an average rate over the entire day. Turned around, using the effective rate would make it look like banks were more sensitive to changes in interest rates.

How one interprets the interest response depends on the source of interest elasticity in the Federal funds market. Hamilton assumed that when there is a reduction in nonborrowed reserves, the reserves are made up by borrowing at the discount window. If so, his method is providing an estimate of the interest sensitivity of the borrowing function. This paper has attempted to distinguish between the long-run response to persistent changes in interest rates, given by [a.sub.1], and the shorter-run response, which will mix together adjustments to the level of nonborrowed excess reserves and borrowing from the discount window. By using daily data, Hamilton probably provides a better estimate of the effect of temporary changes in interest rates on reserves, but this paper may provide better estimates of the longer-run response. Given the greater opportunities for short-run substitution (the carryover provision and borrowing), it is not surprising that the longer-run response is less elastic.

4. The Demand for Required Clearing Balances

While most discussions of excess reserve demand focus exclusively on excess reserves, there are actually two types of reserves that banks can voluntarily choose to hold. In addition to excess reserves, banks can contract with the Federal Reserve to hold a specified amount of reserve balances above their reserve requirement, which are called "required clearing balances." These balances earn credits that can be applied to charges for services the bank receives from the Federal Reserve. There is a relatively small penalty for not meeting the clearing balance requirement, making these contracts a good way to provide a buffer against shocks to the bank's overall reserve position. While required clearing balances earn income, it can be used only to pay for Federal Reserve services, which places a limit on the clearing balance requirement banks wish to have. If the Federal funds rate increases, it will cause this limit to be lower since the maximum return can be earned with fewer balances. Even though required clear ing balances should not be very sensitive to changes in interest rates since they earn interest, banks at their limit will tend to vary their clearing balance requirement inversely with interest rates.

Required clearing balances and required reserve balances are plotted in Figure 2. The Federal Reserve reports the clearing balance requirement, which is plotted here, rather than balances held to meet the requirement. Required clearing balances moved sharply upward in response to the cut in reserve requirements and the drop in required reserve balances in 1991 and again alter the second cut in reserve requirements in 1992. The dip in required clearing balances in 1994-1995 was associated with the increase in short-term rates during that period.

While there should be a connection between excess reserves and required clearing balances since they are alternate ways of providing a cushion against fluctuations in reserves, how they are connected may depend significantly on the individual bank. Some banks do not maintain clearing balance requirements and so are not affected by them. Other banks hold the maximum allowable clearing balance. If there is an increase in interest rates, they will reduce their clearing balance requirement and may choose to compensate for this by holding additional excess reserves. In this case, the direct effect of an increase in interest rates is to reduce the amount of excess reserves held, but indirectly it may cause an increase in the demand for excess reserves through a required clearing balance channel. This mix of effects would reduce estimates of the sensitivity of excess reserves to changes in interest rates. Banks that hold required clearing balances but that are not at their limit may still choose to hold excess rese rves since there is some cost to not meeting the clearing balance requirement, but they would not be as sensitive to changes in the limit on earned credits.

The use of aggregate data on required clearing balances presents several problems, most significantly heterogeneous behavior across banks. However, aggregate data might provide some indication of how required clearing balances and excess reserves interact and so how to pursue this topic in the future. Table 3 reports the results of regressions set up to do this. Required clearing balances differ from excess reserves because the requirement is set in advance. Because of this, they are less likely to respond to temporary changes in clearing demand, and so those terms were dropped from the regression. While tests of excess reserves easily reject a random walk specification, things are much less clear for required clearing balances. Dicky-Fuller tests could not reject a unit root, and autoregressive estimates of required clearing balances find the autoregressive coefficient at or above 0.9. Columns 1 and 2 of Table 3 report the results of a regression of required clearing balances against the intended rate and o ther factors in level and difference specifications. Both specifications imply that required clearing balances are negatively related to interest rates, as would follow from binding limits on the amount of required clearing balances that banks want to hold. The effect of required reserve balances is small and not even statistically significant in the difference specification, even though Figure 2 showed that required clearing balances increased in response to the decline in required reserve balances in 1991 and 1992.

To see whether required clearing balances would matter for excess reserve demand, they were added to the excess reserve regression (reported in column 3), and excess and required clearing balances were added together to form a new dependent variable: "voluntarily held balances" (column 4). Regressions were run in levels to match the preferred specification for excess reserves. Required clearing balances have only a small negative effect on excess reserves, but their inclusion serves to increase the size of the coefficient on the intended rate, which is consistent with the direct and indirect interest rate effects canceling in the excess reserves equation. The effects on the other coefficients are small since required clearing balances do not vary much with short-term changes in clearing demand. When required clearing balances are added to excess reserves (column 4), the interest rate effect is much larger, exceeding the sum of the two effects measured separately. Accurate estimates of the influence of requir ed clearing balances will likely require bank-level data, but the results of these regressions suggest that this could be an area of interest.

5. Conclusion

This paper has examined the behavior of excess reserves in the 1990s. This period provides a clean sample of bank behavior and may be a useful guide for Federal Reserve policy in the future. The estimated equations are broadly consistent with the hypothesized behavior of excess reserve demand. Additional transactions deposits increase the demand for excess reserves, while higher interest rates reduce the quantity demanded. Clearing needs also seem to be important. The decline in required reserve balances have resulted in a small increase in excess reserves. In addition, the desk seems to respond to times associated with higher clearing activity, although evidence from the interest rate regression suggests that there may be some opportunity for fine-tuning their operations.

Aggregate data for excess reserves has some advantages: It is convenient, publicly available, and the basis for Federal Reserve projections; however, other sources of data may also be useful in examining specific questions about excess reserves. Examining the reserve holdings of individual banks may be particularly helpful. Indeed, Fisher et al. (1998) report that there was an increase in excess reserve demand in the last half of 1997 that seemed to be due to a few banks that had limited use of carryover provisions when their required reserve balances fell near zero. These kinds of issues are likely to become increasingly important as the focus of monetary policy in the future shifts to clearing needs and away from reserve requirements. Developing an understanding of excess reserve demand is the first step in the analysis of the operations of monetary policy in this new world.

(*.) Department of Economics, California State University, Northridge CA, 91330-8374, USA; E-mail james. dow@csun.edu.

This paper owes much to extensive conversations with Jim Clouse, Doug Elmendorf, Chris Hanes, Gerard Sinzdak, Bill Whitesell, and especially Sherry Edwards.

Received October 1999; accepted March 2000.

(1.) See Meulendyke (1998) and Thornton (1988) for a discussion of this period.

(2.) Excess reserves do not include vault cash held above the level needed to meet reserve requirements, nor do they include required clearing balances, which are deposits held at the Federal Reserve by contract and earn credits that can be used to pay for services from the Federal Reserve.

(3.) Abstracting from balances held to meet clearing requirements.

References

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 Excess Reserves Equations
 Excess Reserves Free Reserves
 (Levels) (Levels)
Constant -281.1 -186.4 212.4
 (701.6) (690.2) (1467.0)
Intended rate -119.9 [**] -124.3 [**] -133.5 [*]
 (25.5) (25.2) (51.5)
Carry-in -0.97 [**] -1.00 [**]' -1.16 [**]
 (0.11) (0.11) (0.12)
Deposits 0.0027 [**] 0.0026 [**] 0.0020
 (0.0008) (0.0008) (0.0016)
Required balances -0.010 [*] -0.010 [*] -0.009
 forecast (0.004) (0.004) (0.008)
Error in required -0.063 [**] -0.063 [**] -0.068 [**]
 balances forecast (0.017) (0.016) (0.019)
Holiday 242.3 [**] 256.1 [**] 206.1 [**]
 (42.4) (43.4) (47.2)
Treasury settlement 49.7 60.1 40.9
 (37.4) (38.2) (41.2)
Year-end 212.9 [*] 170.4 76.2
 (91.3) (96.5) (108.1)
February 174.9 [*] 160.2 [*] 179.4 [*]
 (68.6) (69.0) (87.1)
Interest deviation -401.2 -678.4 [*]
 (289.6) (330.5)
Rho 0.27 [*] 0.26 [*] 0.58 [**]
 (0.12) (0.12) (0.08)
[R.sup.2] 0.55 0.56 0.50
Durbin E Watson 2.04 2.03 2.19
 Excess
 Reserves
 (Logs)
Constant -16.59 [*]
 (7.16)
Intended rate -0.33 [**]
 (0.07)
Carry-in
Deposits 1.85 [**]
 (0.51)
Required balances -0.11 [*]
 forecast (0.05)
Error in required
 balances forecast
Holiday 0.17 [**]
 (0.04)
Treasury settlement 0.09 [**]
 (0.03)
Year-end 0.03
 (0.07)
February 0.11 [*]
 (0.05)
Interest deviation
Rho 0.23 [**]
 (0.09)
[R.sup.2] 0.47
Durbin E Watson 1.99
The dependent variable is excess reserves or free reserves in
millions. Maintenance period data from 1992:6:24 to 1997:
12:31. 21. Standard errors in parentheses.
(*.)Significant at 5% level.
(**.)Significant at 1% level.
 Federal Funds Rate Deviation
Constant 0.007
 (0.006)
Holiday 0.041 [**]
 (0.015)
Treasury 0.037 [**]
 settlement (0.012)
Year-end -0.114 [**]
 (0.027)
Error in 0.00006
 required (0.00004)
 balances
 forecast
February -0.044 [**]
 (0.012)
September 0.029 [*]
 (0.017)
December 0.021
 (0.019)
Interest 0.286 [**]
 deviation (0.089)
 (first lag)
Interest -0.201 [*]
 deviation (0.080)
 (second lag)
[R.sup.2] 0.29
Durbin E Watson 1.98

The dependent variable is the spread between themaintenance period average effective Federal funds rate and theintended rate in percentage points. Maintenance period data from1992:6:10 to 1997:12:31. Standard errors in parentheses.

(*.)Significant at 5% level.

(**.)Significant at 1% level.

 Effect of Required Clearing Balances
 Required Clearing Excess
 Balances Excess Reserves +
Dependent Reserves RQCB
Variable Levels Differences (Levels) (Levels)
Constant 1300.4 [**] 7.9 48.4 1912.3
 (289.6) (8.9) (699.4) (1362.7)
Intended -100.0 [**] -239.8 [**] -223.9 [**] -865.8 [**]
 rate (34.9) (90.2) (80.7) (91.6)
Carry-in -0.93 [**] -1.35 [**]
 (0.11) (0.17)
Required -0.014 [**] -0.001 -0.02 [*] -0.09 [**]
 balances (0.004) (0.006) (0.01) (0.01)
 forecast
Error in -0.07 [**] -0.08 [**]
 required (0.02) (0.02)
 balances
 forecast
Deposits 0.00003 0.0003 0.004 [**] 0.012 [**]
 (0.00054) (0.003) (0.001) (0.002)
Holiday 246.6 [**] 252.0 [**]
 (42.9) (48.4)
Treasury 51.7 85.1 [*]
 settlement (37.9) (42.9)
February 150.1 [*] 51.7
 (69.7) (92.8)
Year-end 213.4 [*] 207.2
 (91.9) (108.7)
Required -0.11
 clearing (0.08)
 balances
Dependent 0.91 [**] 0.16
 variable (0.04) (0.08)
 (first lag)
Rho 0.08 0.23 0.53 [**]
 (0.09) (0.12) (0.08)
[R.sup.2] 0.99 0.05 0.56 0.95
Durbin E Watson 2.01 1.87 2.02 2.12

Maintenance period data from 1992:6:24 to 1997:12:3l. Standard errors in parentheses.

(*.) Significant at 5% level.

(**.) Significant at 1% level.