Retail Sweep Programs and Bank Reserves, 1994-1999
Anderson, Richard G., Rasche, Robert H., Federal Reserve Bank of St. Louis Review
In January 1994, the Federal Reserve Board permitted a commercial bank to begin using a new type of computer software that dynamically reclassifies balances in its customer accounts from transaction deposits to a type of personal-saving deposit, the money market deposit account (MMDA).  This reclassification reduces the bank's statutory required reserves while leaving unchanged its customers' perceived holdings of transaction deposits.
The use of deposit-sweeping software spread slowly between January 1994 and April 1995, but rapidly thereafter. Estimates of the amounts of transaction deposits reclassified as MMDAs at all U.S. depository institutions, prepared by the Board of Governors' staff, are shown in Figure 1.  By late 1999, the amount was approximately $372 billion. In contrast, the aggregate amount of transaction deposits (demand plus other checkable deposits) in the published M1 monetary aggregate, as of December 1999, was $599.2 billion.
In this analysis, we interpret the effects of deposit-sweeping software on bank balance sheets to be economically equivalent to a reduction in statutory reserve-requirement ratios. We seek to measure the amount by which such deposit-sweeping activity has reduced bank reserves (vault cash and deposits at Federal Reserve Banks). Currently, transaction deposits are subject to a 10 percent statutory reserve-requirement ratio on amounts over the low-reserve tranche ($44.3 million during 2000, $42.8 million during 2001), whereas personal-saving accounts, including MMDAs, are subject to a zero ratio. 
To be useful in policy analysis and empirical studies, aggregate quantity data on bank reserves must be adjusted for the effects of changes in statutory reserve requirements on the quantity of reserves held by banks.  In the past, such adjustments were straightforward because changes in statutory reserve requirements applied simultaneously and uniformly to groups of depository institutions within only a small number of broad classes. The effective date for changes in statutory requirements varied slightly among depositories that report data to the Federal Reserve weekly (larger banks), those that report quarterly (smaller banks), and those that report annually (very small banks). Within each group, however, the effective date was the same for all institutions. During the 1980s, the only changes in statutory requirements were due to the phase-in and indexation provisions of the Monetary Control Act. During the 1990s, the reserve-requirement ratio applicable to nonpersonal savings and time deposits was redu ced from 3 percent to zero (December 1990) and the highest marginal ratio applicable to transaction deposits was reduced from 12 percent to 10 percent (April 1992). 
The economic effect of deposit-sweeping software is unlike these previous changes. The essence of deposit-sweeping software is that it permits banks to change the share of their transaction deposits that are subject to a non-zero statutory reserve-requirement ratio (see the insert "How Deposit-sweeping Software Reduces Required Reserves"). Each bank is free to decide when and how to implement the software, subject to constraints discussed below. In this way, in part, banks' effective reserve requirements are "home brewed." As a result, the economic effects of deposit-sweeping software must be analyzed and measured bank-by-bank.
Our analysis suggests that required and total reserves in December 1999, measured by the reserve adjustment magnitude (RAM) developed in this article, were lower by $34.1 billion and $25.8 billion, respectively, as a result of deposit-sweeping activity. In addition, many depository institutions have reduced their required reserves to such an extent that the lower requirement places no constraint on the bank because it is less than the amount of reserves (vault cash and deposits at the Federal Reserve) that the bank requires for its ordinary day-to-day business. For these banks, the economic burden of statutory reserve requirements has been reduced to zero.
DEPOSIT-SWEEPING SOFTWARE, REQUIRED RESERVES, AND RAM
The effectiveness of deposit-sweeping software hinges on the use of the MMDA. This deposit instrument was created in 1982 by a provision in the Garn-St. Germain Act. At that time, many banks perceived extreme competitive pressures from money market mutual funds. The MMDA allowed them to offer a type of deposit that was fully competitive with money market mutual fund shares. The MMDA was not subject to Regulation Q interest rate controls, and, so long as no more than six withdrawals were made by check or pre-authorized transfer during a month, it was not subject to the statutory reserve requirements applicable to transactions deposits. (If a bank permitted more than six such withdrawals, the MMDA was reservable as a transaction deposit.) The Monetary Control Act specified three categories of deposits subject to reserve requirements: net transaction deposits, savings deposits (personal and nonpersonal), and time deposits (with a minimum maturity of seven days). The act set the reserve-requirement ratio for per sonal-saving deposits to zero, and the Board of Governors set the ratio for nonpersonal-saving deposits to zero in December 1990. Because MMDAs are not time deposits and the Garn-St. Germain Act prohibited the Federal Reserve from imposing transaction-deposit reserve requirements, they are classified as savings deposits for reserve-requirement purposes. 
At its start, deposit-sweeping software creates a "shadow" MMDA deposit for each customer account. These MMDAs are not visible to the customer, that is, the customer can make neither deposits to nor withdrawals from the MMDA. To depositors, it appears as if their transaction-account deposits are unaltered; to the Federal Reserve, it appears as if the bank's level of reservable transaction deposits has decreased sharply. Although computer software varies, the objective is the same: to minimize a bank's level of reservable transaction deposits, subject to several constraints. The general parameters of this optimization problem are as follows:
* The Federal Reserve calculates a bank's required reserves based on a 14-day average of the close-of-day level of its transaction deposits. 
* Each calendar month, an unlimited number of transfers may be made from a customer's transaction deposit account into the shadow MMDA. However, only six transfers may be made out of the shadow MMDA to the customer's transaction-deposit account.
* Checks presented to the bank for payment are only debited against the customer's transaction-deposit account, not against the MMDA. If the amount of funds in the transaction deposit is inadequate, a transfer must be made from the MMDA.
* On the sixth transfer, all funds remaining in the MMDA are moved to the transaction deposit. (A seventh transfer would cause the MMDA to be subject to the reserve requirements applicable to transaction deposits.)
Because no debits are made to customer transaction deposits between just before the close of business on Friday and just before the opening of business on Monday, some early software simply reclassified transaction deposits as shadow MMDAs prior to the close of business on Friday. This reduced a bank's weekly average level of required reserves by 3/7: its transaction deposit liabilities for Friday, Saturday, and Sunday, as reported to the Federal Reserve, were zero. About ten times each year, a Monday holiday allowed delaying the return of funds to transaction deposits out of the MMDA until the opening of business on Tuesday. Later software is more sophisticated and analyzes the receipt and payment patterns of customers.  Of course, regardless of the efficiency of the software, the bank faces two additional constraints that limit how much it can reduce its reserves. It must keep on hand sufficient vault cash so as to be able to redeem customer deposits into currency, and it must maintain sufficient deposi ts at Federal Reserve Banks to avoid both excessive daylight overdrafts and overdrawing its account at the end of the day.
To measure the effect of deposit-sweeping software on bank reserves, we need a benchmark, or alternative. RAM furnishes one such measure because it was designed to measure the changes in bank reserves caused by differences in statutory reserve requirements--specifically, the differences between those requirements in effect during the current period and those for a specific benchmark, or base, period.  The view that deposit-sweeping activity should be analyzed as a change in statutory reserve requirements, and hence included within the framework of RAM, is not universally held, however. The Board of Governors staff, for example, does not publish reserve aggregates adjusted for the effects of deposit-sweeping activity, apparently believing that the impact of such activity is not to be interpreted as economically equivalent to a change in statutory requirements. 
In its economic aspects, deposit-sweeping software programs of the 1990s differ distinctly from the collateralized overnight-loan sweep programs of the 1970s--to borrow a phrase, they are not "your father's Oldsmobile." The business-oriented sweep programs of the 1970s essentially were overnight collateralized loans to mutual funds and banks, initiated by depositors (see Kohn, 1994, Chap. 9; or Stigum, 1990, Chap. 13). These loans were made with the full participation of depositors, who received directly the lion's share of the investment return; the bank's net earnings arose from being a middleman. Although such sweeps reduced banks' required reserves, their primary purpose was to simulate a legally prohibited interest-bearing demand deposit. 
The retail-oriented deposit-sweeping activity of the 1990s differs. First, except for competitive market pressures, it seems unlikely that banks have directly passed along the earnings from deposit-sweeping activity to transaction-account customers.  In part, this may be due to few retail depositors understanding the process, despite many banks notifying customers via monthly statement inserts (containing phrases such as "...your deposit may be reclassified for purposes of compliance with Federal Reserve Regulation D..."). Banks' answers to question 12 of the Federal Reserve's May 1998 Senior Financial Officer Survey are illustrative. On that question, banks responded that even if they were permitted to pay interest on demand deposits and if the Fed paid interest on deposits at Federal Reserve Banks, they most likely would tier rates paid on demand deposits and that the highest rate "would still be considerably below the level of market interest rates." Second, the sweeps of the 1970s required banks to m aintain a significant amount of high-quality liquid collateral for use in repurchase agreements with large business customers. The retail sweeps of the 1990s allow a bank to deploy into higher-earning assets, as it sees fit, the funds released by reduced required reserves. In the boxed insert "How Deposit-Sweeping Software Reduces Required Reserves," for example, the bank's earning assets increase with no increase in total deposits or funding costs.
Linkages among retail deposit-sweep programs, the Depression-era prohibition of the payment of (explicit) interest on demand deposits, and the payment by the Fed of interest on deposits at Federal Reserve Banks have been discussed by Federal Reserve Governor Lawrence Meyer in recent Congressional testimony.  An important issue is whether banks would reduce or eliminate the use of deposit-sweeping software if the Federal Reserve paid interest on reserve balances. Because the economic effects of deposit-sweeping software are similar to reductions in statutory reserve requirements, in our opinion such an outcome is unlikely. First, as noted above, it seems unlikely that banks have passed much of the benefit from 1990s-style deposit-sweeping activity on to their transaction-deposit customers. Second, because newly released funds may be invested as the bank sees fit, including in consumer and business loans, it seems unlikely that deposits at Federal Reserve Banks, earning interest at the federal funds rate, would be an attractive investment. In question 10 of the May 1998 Senior Financial Officer Survey, banks were asked whether they would dismantle sweep programs if the Federal Reserve paid interest on deposits. In their summary of the survey, Board staff noted that "several" banks said that they would, or might, dismantle sweep programs. More than half of the respondents, however, said that interest paid at the federal funds rate would be unattractive, relative to the higher returns available on alternative investments. The staff summary also notes, on page 8, that "the results on this question seem qualitatively different from the responses to a similar question on the May 1996 Senior Financial Officer Survey. On that survey, two thirds of the respondents indicated that they would dismantle their retail sweep programs either immediately or over time if interest were paid on Fed account balances held to meet reserve requirements." In our opinion, retail deposit-sweeping software is here to stay for the same ec onomic reasons that cause banks to prefer decreases, rather than increases, in statutory reserve requirements.
Reserve-Requirement Ratios and Economically Bound Banks
To measure the effect of deposit-sweeping software on the amount of reserves held by banks, we need to separate banks wherein the quantity of reserves demanded is sensitive to changes in reserve-requirement ratios from those in which it is not.  When reserve requirements are "low," a depository institution's demand for reserves may be largely, or even entirely, determined by its business needs (converting customer deposits into currency, originating interbank wire transfers, settling interbank check collection debits) rather than by statutory requirements. In the United States, the level of reserves held in the absence of statutory reserve requirements might be very small indeed because banks are permitted daylight overdrafts on their deposit accounts at the Federal Reserve Banks (Emmons, 1997: Furfine, 2000). When statutory reserve requirements are "high," the amount of reserves held will be approximately equal to its required reserves. (This statement assumes that all base money held by depository inst itutions can be used to satisfy reserve requirements. In the United States, member banks could not apply vault cash to satisfy reserve requirements between 1917 and 1959.) Hence, measuring RAM requires a model of banks' demand for reserves that includes an explicit role for statutory requirements.
Let us denote a depository institution's reserve demand function as [TR.sup.D](D,rr), where D denotes the institution's deposit liabilities and rr the statutory reserve-requirement ratio. Further, omitting all tiering of reserve requirements, let us denote its required reserves as RR(D,rr) = rr x D. Then, when rr is relatively large,
[partial][TR.sup.D](D,rr)/[partial]rr [congruent] [partial]RR(D,rr)/[partial]rr = D [greater than] 0
such that statutory reserve requirements are, at the margin, the binding constraint that determines the amount of reserves held.  When rr is relatively small, we assume that
[partial][TR.sup.D](D,rr)/[partial]rr = 0,
such that the bank's business needs, rather than statutory requirements, are the binding constraint. In Anderson and Rasche (1996b), we introduced the term economically nonbound to describe banks where
[partial][TR.sup.D](D,rr)/[partial]rr = 0
and economically bound to describe banks where
[partial][TR.sup.D](D,rr)/[partial]rr [greater than] 0.
To measure RAM, we must know (or infer) the sign of the derivative
at all dates and for all banks in our sample. To be specific, for an individual bank, let RR([D.sub.t],[rr.sub.0]) and RR([D.sub.t][rr.sub.t]) and denote the period t levels of required reserves when the statutory requirements of a base period, 0, and of period t, respectively, are in effect. For all cases, assume that sufficient data on reservable liabilities during period t exist so as to permit calculation of the quantity RR([D.sub.t],[rr.sub.0]). Then, consider four cases:
Case 1: If [rr.sub.0] = [rr.sub.t], that is, reserve requirements have not changed, RAM = 0.
Case 2: If
[partial][TR.sup.D](D,rr)/[partial]rr[\.sub.D=[D.sub.0] rr=[rr.sub.0]] = 0 and [partial][TR.sup.D](D,rr)/[partial]rr[\.sub.D=[D.sub.t] rr=[rr.sub.t]] = 0,
that is, if the business needs of the bank were the binding constraint in both the base period 0 and period t, then RAM = 0.
Case 3: If both
[partial][TR.sup.D](D,rr)/[partial]rr[\.sub.D=[D.sub.0] rr=[rr.sub.0]] [greater than] 0 and [partial][TR.sup.D](D,rr)/[partial]rr[\.sub.D=[D.sub.t] rr=[rr.sub.t]] [greater than] 0,
that is, if the statutory requirements were a binding constraint on the bank in both the base period 0 and period t, then the RAM adjustment for period t (conditional on the choice of period 0 as the base period) is
[RAM.sub.t] = RR([D.sub.t], [rr.sub.0]) - RR([D.sub.t],[rr.sub.t]).
Case 4: If
[partial][TR.sup.D](D,rr)/[partial]rr[\.sub.D=[D.sub.0] rr=[rr.sub.0]] [greater than] 0 but [partial][TR.sup.D](D,rr)/[partial]rr[\.sub.D=[D.sub.t]rr=[rr.sub.t]] = 0,
that is, if the statutory requirements were binding in the base period but not in period t, then to measure RAM we must find the smallest reserve-requirement ratio, say [rr.sup.*], for which
[partial][TR.sup.D](D,rr)/[partial]rr[\.sub.D=[D.sub.t] rr=[[rr.sup.*].sub.t]] [greater than] 0.
Then, [RAM.sub.t] = RR([D.sub.t], [rr.sub.0]) - RR([D.sub.t], [rr.sup.*]).
The above analysis is applicable to cases where the only change in statutory reserve requirements between two periods is the reserve-requirement ratio, rr, and data exist to calculate the counterfactual level of required reserves, RR([D.sub.t],[rr.sub.0]). For analysis of other cases, see Anderson and Rasche (1999).
An empirical criterion for measuring RAM in Case 4, for dates beginning November 1980, was developed by Anderson and Rasche (1996b) based on statistical analysis of a large panel dataset. That analysis suggested that a bank was economically bound during a reserve maintenance period if the bank was legally bound and had more than $135 million in net transaction deposits.
Because the design, implementation, and operation of sweep software is idiosyncratic, our analysis focuses on a longitudinal panel of 1231 depository institutions between January 1991 and December 1999. A depository institution is included in the panel if, during at least one reserve-maintenance period, it was either economically or legally bound.  Our panel is a subset of a larger dataset containing more than 7500 depository institutions, which, in turn, is an updated version of the dataset used in Anderson and Rasche (1996b). For some banks, data begin after January 1991 because the bank opened for business at that point, was created by the merger of existing banks, or only then began reporting data to the Federal Reserve. For others, the data stop before December 1999 because the bank failed, merged with another bank, or was dropped from the reporting panel. For each such bank, we use the Federal Reserve's bank structure database to trace predecessors and successors. When a bank with deposit-sweeping activity is acquired by another bank, we add the amount of activity at the acquired bank to the amount at the acquiring bank. In all cases, we focus special attention on those institutions where deposit-sweeping software has reduced the level of transaction deposits to such an extent that the level of the depository's required reserves is less than the amount of reserves (vault cash and deposits at the Federal Reserve) that the bank requires for its ordinary day-to-day business.
We begin by re-examining RAM from January 1991 through December 1993. Our previous measure of RAM was based on the statistical models of Anderson and Rasche (1996b). Those results suggested that economically bound banks (the only ones included in that measure of RAM) were characterized by two features: (i) a level of required reserves that exceeded their vault cash and (ii) having more than $135 million in net transaction deposits. This framework allowed us to classify banks into broad groups without tedious examination of time-series data for individual banks.
In this analysis, we revise our measure for 1991-93 for two reasons. First, because deposit-sweeping software allows banks to home-brew reserve requirements, our analysis for 1994-99 must necessarily be based on the examination of data for individual banks. It is important to assess whether this change in procedure--from using aggregated data for groups of banks to using individual-bank data--has any effect on measured RAM. The 1991-93 period provides an experimental control for this change in procedure. Second, we seek to reduce the number of occurrences when a bank, as well as its deposits, moves from being included in RAM to being excluded. It seems unlikely that a bank's responsiveness to possible changes in a statutory reserve-requirement ratio fluctuates very much from period to period. Absent changes in statutory reserve requirements (or a merger), we assume that a typical bank switches infrequently between economically nonbound and bound.
The most reliable indicator of a bank's economically bound or nonbound status is its response to a change in statutory reserve requirements. An economically bound bank will reduce its holdings of reserves, following a reduction in reserve requirements, by approximately the same amount as the decrease in its required reserves. An economically nonbound bank will not, although it might reduce its holdings by a smaller amount. Between January 1991 and December 1993, there were only two ways that the statutory reserve-requirement ratio for a bank could change:
* In April 1992, the Federal Reserve reduced the statutory reserve-requirement ratio on transaction deposits above the low-reserve tranche from 12 percent to 10 percent. If a bank reduced its deposits at Federal Reserve Banks (relative to transaction deposits) following the April 1992 reduction in reserve requirements and did not begin or increase the size of a clearing-balance contract, we classified the bank as economically bound from January 1991 to December 1993. If the bank began or increased the amount of a clearing balance contract, we classified the bank as economically nonbound from the date of that increase through the end of December 1993. An increase in the bank's clearing balance contract at the time of the reduction indicated that payments activity, not statutory reserve requirements, had been determining the level of reserves held by the bank.
* The second change affected only banks that acquired another bank. Federal Reserve regulations permit an acquiring bank to "amortize" over eight quarters the reserve exemption amount and low-reserve tranche of the acquired bank.  For an acquirer with transaction deposits greater than the low-reserve tranche, the amortization reduces the acquirer's required reserves. If an acquirer did not reduce its holdings of reserves so as to match the reduced required reserves, we classified the bank as nonbound beginning in that maintenance period.
Finally, we also classified a bank as economically nonbound in a reserve-maintenance period if it is legally nonbound (that is, if its eligible vault cash exceeds its required reserves). Because some banks alternate between legally bound and nonbound, we modify this presumption by judgmentally smoothing changes in status.
Figure 2 compares two measures of RAM for 1991-93. One is based on our 1996 method, and the other on the method outlined above. The two measures, for all practical purposes, are the same.
Deposit-sweeping activity by banks substantially complicates measuring RAM for 1994-99. To cope, we follow a three-step procedure. First, we identify the dates (reserve-maintenance periods) affected by new or expanded deposit-sweeping activity and estimate the amounts of transaction deposits relabeled as MMDA. Second, we classify each bank, for each reserve-maintenance period between January 1994 and December 1999, as economically bound or nonbound. This procedure is similar to our revised measure for RAM during 1991-93 and relies heavily on the observed response of the bank to changes in reserve-requirement ratios and the effects of implementing its deposit-sweeping software. Finally, we calculate RAM based on the framework of Cases 1, 2, 3, and 4 introduced above.
Sweep Dates and Amounts
Our first task is to identify the dates on which banks either began or changed their deposit-sweeping activity Although the date of the first such deposit-sweep program is known (January 1994), banks are not required to notify the Federal Reserve when a program is implemented, expanded, or discontinued; nor are they required to report the amount of deposits affected.  To identify those dates when deposit-sweeping activity either began or was expanded, we visually analyzed time-series data for each bank. The variables examined were changes in the levels of transaction and savings deposits, changes in the size of a clearing-balance contract, and the ratios of vault cash and deposits at Federal Reserve Banks to transaction deposits.  For a typical bank, the data signature of deposit-sweeping activity consists of two simultaneous changes:
* The level of transaction deposits decreases and the level of savings deposits increases, during the same reserve-maintenance period and by approximately the same dollar amount, while the bank's level of total deposits is approximately unchanged. It is important to condition the analysis on the level of total deposits because, in some cases, mergers of banks with different mixtures of deposits otherwise create false signals.
* The ratio of vault cash to reported transaction deposits (that is, transaction deposits not reclassified as MMDAs) increases sharply. This most likely occurs because the amount of vault cash held by a bank depends on its customers' perceived amount of transaction deposits, not the amount of reservable transaction deposits reported by the bank to the Federal Reserve.
For each so-identified maintenance period, our estimate of the amount of deposits affected is the smaller of the increase in savings deposits and (the absolute value of) the decrease in transaction deposits. For some identified periods, however, transaction deposits increased, savings deposits decreased, and the ratio of vault cash to transaction deposits fell. We interpret these changes to indicate that deposit sweeping was discontinued or reduced in amount. The amount of the change in deposit-sweeping activity is calculated as the negative of the above calculations, but is capped at the maximum amount that we estimate the bank previously had been sweeping.
Overall, we observed deposit-sweeping activity at 680 of the 1231 banks in our panel dataset.  Due to mergers, acquisitions, and liquidations, as of December 1999 our panel includes only 649 active banks. Of these, we estimate that 463 banks were operating deposit-sweeping software, affecting $255.9 billion of transaction deposits. Figure 3A shows estimates of the amount of deposit-sweeping activity at our panel of banks during 1994-99. For comparison, the figure also shows the Board of Governors staff's estimate of the amount of deposit-sweeping activity at all depository institutions. As of December 1999, the Board staff estimate is $371.8 billion. Figure 3B shows the ratio of the two estimates. Prior to mid-1995, the aggregate amount measured in our panel of banks is approximately 85 to 90 percent that of the Board staff's; since mid-1997, our measure has been approximately 65 to 70 percent of their total. The difference between the amounts may be due to one or more of three factors:
1. Deposit-Sweeping Programs at Smaller Banks. Our panel includes only 1231 banks, those which are relevant to measuring RAM; the Board staff's estimate seeks to include all banks. For our purpose--measuring the reduction in total and required reserves due to deposit-sweeping activity--the difference is unlikely to be important. Our previous analysis (Anderson and Rasche, 1996b) suggests that the smaller banks omitted from our panel are unlikely to change their holdings of reserves in response to a change in statutory reserve-requirement ratios.
2. Overlooked Deposit-Sweeping Programs. Repeated re-examinations of our data suggest that we have overlooked few, if any, banks within our sample that are operating deposit-sweeping programs. We have searched not only for the implementation of deposit-sweeping software but also for subsequent changes in the level of sweep activity.
3. Inaccurate Estimates of the Amount of Reclassified Deposits. Our estimated amounts are the smaller of the absolute values of the change in transaction and savings deposits, subject to caveats explained above. As a further check, we visually examined two ratios for each bank: vault cash (VC) divided by reported (reservable) transaction deposits (NT), VC/NT, and vault cash divided by the sum of net transaction deposits plus the estimated amounts of deposits reclassified as MMDA (SWP), VC/(NT + SWP). These data suggest that our estimates of the amounts being reclassified are quite accurate. The ratio VC/NT almost always increases sharply when deposit-sweeping activity begins or expands. On these same dates, the ratio VC/(NT + SWP) shows no such jumps.
Figure 4 displays total transaction deposits at the banks in our panel. The smaller series is the amount of transaction deposits reported by our panel of banks to the Federal Reserve, NT, and hence subject to statutory reserve requirements. The larger series is the sum of NT plus SWP. The difference, of course, is deposit-sweeping activity.
We emphasize that our purpose in this analysis is not to estimate either the total number of banks using deposit-sweep software or the total amount of deposits involved. Rather, we wish to identify how deposit-sweeping activity at economically bound banks has reduced the quantity of reserves held during each reserve maintenance period during 1994-99. The concept and calculation of RAM focuses on deposits, not on banks. It is the derived demand for reserves, arising from the level of deposits and the characteristics of the banks, that is of primary interest to us. Our next step, therefore, is to classify, for each biweekly reserve-maintenance period, a bank (and its deposits) as either economically nonbound or economically bound. To do so, we visually analyzed time-series data, for individual banks, on a period-by-period basis from 1994-99. Similar to 1991-93, we believe that banks should not (and do not) alternate often between bound and nonbound status.
The most important indicator of the bank's bound and nonbound status is the change in its holdings of reserves, relative to the change in its required reserves.
* If a bank acquired another bank, did it make use of the reduction in required reserves as provided for by Federal Reserve regulations? If not, then the acquiring bank is revealed to be economically nonbound during those periods. In most cases, such a bank is classified as economically nonbound in all subsequent periods.
* If a bank implemented a sweep program, did its ratio of reserves to reported transaction deposits (after subtracting required reserves against the low-reserve tranche from the numerator and the deposit-amount of the lowreserve tranche from the denominator) increase above 10 percent? If so, the bank is revealed to be economically nonbound because it holds more reserves than is necessary to satisfy statutory reserve requirements. In most cases, such a bank is classified as economically nonbound for all subsequent periods.
* If a bank implemented a sweep program, did it increase its required clearing-balance contract? If so, the bank is revealed to be economically nonbound because it voluntarily increased its reserves above the amount necessary to satisfy legal requirements. In most cases, the bank is classified as economically nonbound for all subsequent periods unless it reduces or eliminates its clearing balance contract.
* If a bank implemented a sweep program, did its required reserves decrease below its vault cash (that is, did the bank become legally nonbound)? If so, the bank is revealed to be economically nonbound because the amount of vault cash necessary for its ordinary business exceeds its required reserves. The bank is classified as economically nonbound for all periods in which it is legally nonbound.
In general, if a bank is reclassified to economically nonbound from economically bound, it remains nonbound through to the end of the sample. We observed, however, that a few banks subsequently sharply reduced their excess reserves and began responding to changes in reserve requirements. Although the reasons for such changes in behavior are unknown to us, we reclassified these banks as economically bound beginning at the date of the change.
Banks that neither implemented a deposit-sweep program nor acquired another bank during 1994-99 experienced no change in their statutory required-reserve ratio. Hence, we use different criteria to classify these as economically bound or nonbound. For most banks, their status as of December 1993 is extended forward through December 1999. A bank's status might be changed if it significantly changes its level of excess reserves, enters into a clearing-balance contract, or experiences a major change in its level or mixture of deposits. In our sample, there are 551 such banks; 88 of these had their classification changed between January 1994 and December 1999.
Figure 5 shows the numbers of banks in our panel classified as economically bound and nonbound and the amounts of their reservable transaction deposits. Changes in the numbers of banks should not be over-interpreted because of the large number of bank mergers and acquisitions since 1995. Regardless, the figure shows clearly that a major shift has occurred since deposit-sweeping computer software began to spread rapidly through the U.S. banking industry. In late 1994, for example, deposits in our panel's economically bound banks totaled approximately $500 billion, whereas deposits in economically nonbound banks were less than $100 billion. By late 1999, reported transaction deposits (subject to statutory reserve requirements) in economically bound banks totaled less than $100 billion, and reported transaction deposits in economically nonbound banks were approximately $250 billion.
The above analysis allows us to classify each bank in our dataset, during each reserve-maintenance period, as being in Case 1, 2, 3, or 4. For those banks in Cases I and 2, RAM = 0. For those in Case 3, calculation of RAM is straightforward, as shown above. For banks in Case 4, it remains to estimate [rr.sup.*].
We remind the reader that [rr.sup.*] does not equal the marginal reserve-requirement ratio against transaction deposits but, rather, is the smallest (counterfactual) reserve-requirement ratio for which
[partial][TR.sup.D](D,rr)/[partial]rr[\.sub.D=[D.sub.t] rr=[[rr.sup.*].sub.t]] [greater than] 0,
[partial][TR.sup.D](D,rr)/[partial]rr[\.sub.D=[D.sub.0] rr=[rr.sub.0]] [greater than] 0, [partial][TR.sup.D](D,rr)/[partial]rr[\.sub.D=[D.sub.t] rr=[rr.sub.t]] = 0,
[rr.sub.0] [greater than] [rr.sub.t], and [rr.sub.0] and [rr.sub.t] are, respectively, the base period and period t reserve-requirement ratios. In this case, [RAM.sub.t] = RR([D.sub.t], [rr.sub.0]) -RR([D.sub.t], [rr.sup.*]). An estimate of [rr.sup.*] is calculated only once, for the maintenance period before the sweep activity that allows the bank to become economically nonbound. This mimics in spirit the pre-1994 Federal Reserve statutory regime in which reserve-requirement ratios changed by specific amounts at specific dates and then remained fixed at the new values until the next change. RAM is calculated for all subsequent periods in the dataset as if the calculated value for [rr.sup.*] were the applicable statutory ratio.
In what follows, we treat [rr.sub.t] and [rr.sup.*] as ratios of reserves (vault cash, VC, plus deposits at Federal Reserve Banks, RB) divided by the sum (NT + SWP).  Complications regarding tiering (the reserve-exemption amount and low-reserve tranche) are omitted because all aspects of the statutory reserve requirement system, including tiering, are irrelevant to Case 4 banks. To estimate [rr.sup.*], recall that the amount of reserves held by an economically nonbound Case 4 bank is determined by its day-to-day business needs, not by statutory reserve requirements. Hence, the amount is less than the product of [rr.sup.*] times the sum
(NT + SWP):
VC + RB [less than] ([rr.sup.*])x(NT + SWP).
Note that the opposite is true for an economically bound Case 3 bank where, at the margin, the amount of reserves is determined by the statutory reserve-requirement ratio [rr.sub.t]: 
VC + RB [greater than or equal to] ([rr.sub.t])x(NT + SWP).
These two relationships are not sufficient, however, to provide an estimator for [rr.sup.*]. To do so, we impose one additional condition: We assume that the amount of a bank's vault cash is determined by its day-to-day retail business needs and is not affected by statutory reserve requirements or deposit-sweeping activity. Conditional on this assumption, we examine separately the ratios VC/(NT + SWP) and RB/(NT + SWP). From these ratios, we infer upper and lower boundaries for [rr.sup.*] and, thereafter, a value for [rr.sup.*] itself.
We begin by comparing the reserves held by banks before and after they implemented deposit-sweeping software. Selection of the appropriate "before" and "after" reserve-maintenance periods requires some judgement. Our data suggest that at many banks deposit-sweeping activity was phased-in during a number of reserve-maintenance periods. Also, we observed some banks increasing their sweep activity at later dates, often a year or more after the initial implementation.  For each deposit-sweeping bank, we visually searched the data to select the first ("before") reserve-maintenance and last ("after") reserve-maintenance periods affected by changes in the intensity of deposit-sweeping activity--that is, the period before sweep activity began and the period during which the bank's transaction and savings deposits later settled down to <