The monetary base is the only magnitude that the Fed directly controls. It consists of currency held by the general public (including both Federal Reserve notes and Treasury coin) and the total aggregate reserves of banks and other depositories (whether held in the form of vault cash or deposits at one of the regional Federal Reserve banks).
Some would translate this control over the base into direct Fed control over total reserves, but that is not strictly correct. Even though the Fed initially increases (or decreases) the base by increasing (or decreasing) reserves, the general public and the banks determine how much of the base is ultimately held instead in the form of currency in circulation. Thus, it would seem desirable to have the Fed report the base and its two components accurately. Yet the Fed's reported measures of total reserves exclude significant amounts of bank vault cash. Even with changes in the Fed's monthly releases implemented in July 2013, the problem has not been rectified. Moreover, there also remains a minor omission from the total base that while not yet serious could become so in the future. More important, once the Fed began paying interest on reserves in 2008, it dramatically altered the monetary relevance of its base and reserve measures.
Misreporting Total Reserves
Several different measures of total reserves exist. Both the St. Louis Fed and the Board of Governors have reported total reserves adjusted for changes in reserve requirements. Although the St. Louis Fed continues to do so, the Board of Governors discontinued its adjusted series in July 2013. But these series, especially when seasonally adjusted as well, are not the raw numbers. While allegedly (but dubiously) useful for conducting monetary policy, adjustments for changes in reserve requirements grossly distort the historical record.
Only the Board of Governors in its weekly H.3 Release reports total reserves unadjusted for reserve requirements. But this series excludes any excess reserves held in the form of vault cash, and before July 2013 all required clearing balances and Fed float, and therefore under reports the total. For some idea of how massive the resulting misrepresentation can be, consider December 2007. The Board of Governors reports total reserves (monthly, not seasonally, adjusted, and not adjusted for changes in reserve requirements) of $42.7 billion. If you add in vault cash not covering reserve requirements, that number jumps to $60.3 billion. And when you bring in required clearing balances and float, the number rises to $72.6 billion, 70 percent greater than the Board's estimate. If the distortion were consistent across time, the Board's reserve totals would still tell us something. But the distortion is not close to consistent across time, in part because banks used increasing amounts of vault cash in their ATMs.
Consequently, to arrive at an accurate series for total reserves, one has to take the Board of Governors Monetary Base (not seasonally adjusted and not adjusted for changes in reserve requirements) and subtract the currency in circulation component of M1 (not seasonally adjusted). Or alternatively, one could make the same subtraction of M1 currency from what the St. Louis Fed calls the Source Base (monthly and not seasonally adjusted), which is virtually identical to the Board's measure of the base. And just to add to the potential confusion, one must not use the so-called "currency in circulation" reported in the Board's H.3 and H.4.1 Releases. That measure includes not only currency in the hands of the public but also the vault cash of banks and other depositories. Subtracting it from the monetary base would yield the same misleading measure of total reserves as that of the Board. Only the currency component of M1, reported in the Fed's weekly H.6 Release, confines itself to currency held by the public.
In July of 2013 the Board made a few changes. It introduced a new measure of the monetary base in the H.3 Release at the same time that it eliminated the small clearing balances banks were required to hold and revised Regulation D to simplify the administration of reserve requirements. Although the Board has calculated this new, modified version of the monetary base going back to January 1959, its differences with the old version are so minor as to be hardly noticeable. The elimination of the requirement that banks hold clearing balances, however, offers a third way of calculating total reserves from mid-2013 forward. One can simply add "Surplus Vault Cash" to "Total Reserves" in Table 2 of the H.3 Release. Yet this remains probably the least accurate of the three ways because it excludes the small amount of vault cash held by depositories whose total checking accounts fall below the level subject to reserve requirements.
It goes without saying that none of three ways of correctly determining total reserves is directly available on the St. Louis Fed's interactive FRED website. Curiously, the St Louis Fed considers the Board's "narrow" definition of total reserves less than satisfactory for "modeling the role of depository institutions in the economy."[9 ] As far as I can tell, it uses the broader definition that includes all vault cash, rather than the Board's narrow definition, as the basis for its series of total reserves adjusted for reserve requirements. Yet it has nowhere reported its preferred unadjusted broad measure. Figure 1 illustrates how significant were the differences in these various measures of total reserves between 1979 and 2008.
Misreporting the Monetary Base
Less serious are some peculiarities in the Fed's reporting of the total monetary base, but they have the potential of becoming more misleading in the future. They arise because banks and other depositories are not the only institutions that can deposit reserves at the Federal Reserve Banks. The Board's weekly H.4.1 Release divides these additional deposits into two categories: "foreign official" and "other." Foreign official deposits are balances of foreign central banks and monetary authorities, foreign governments, and other foreign official institutions. The deposits labelled "other" include balances of international and multilateral organizations such as the International Monetary Fund, the United Nations, and the World Bank, along with such government-owned agencies or government-sponsored enterprises as Fannie Mae, Freddie Mac, and the Federal Homes Loan Banks. Neither of these two categories of deposits at the Fed has ever been included within measures of the monetary base.
The case for excluding foreign official deposits seems straightforward. Being held by institutions abroad, these deposits are not part of the domestic monetary base. But this does create an odd asymmetry; large amounts of U.S. currency are also held abroad, presently at least half of that in circulation, by most estimates. Currency in circulation, in turn, is a large component of the reported monetary base: about 90 percent prior to the financial crisis and today, after quantitative easing and the huge increase in banks reserves, still about 30 percent. It would be nice to have two consistent estimates of the monetary base, one including all currency and all reserves, whether held domestically or abroad, and the other including only domestically held currency and reserves. But estimates of currency held abroad are quite unreliable. Fortunately, the total amount official foreign deposits have been and remain small.
None of these mitigating factors, however, holds as strongly for the category of deposits listed on the Fed balance sheet as "other." To begin with, Fannie, Freddie, and other government-sponsored enterprises are domestic institutions. We could debate exactly where their Fed deposits belong in the monetary base. Because these institutions do not create money, one could argue that their deposits at the Fed are really only an alternative form of currency and should be counted as such in the base. On the other hand, Fed deposits allow these institutions to participate in the Federal funds market. Indeed, because these institutions do not currently earn interest on these deposits, they have become the major players keeping the Federal funds rate below the interest rate on reserves. Few banks are going to loan out their reserves at less than what the Fed is paying them. As a result, the introduction of interest on reserves in October 2008 and the resulting accumulation of reserves by banks not only caused a collapse of Federal funds lending from over $200 billion to nearly a third of that, but the Federal Home Loan Banks became the dominant lenders in this market. This would suggest that their deposits should be counted in the base as total reserves.
Wherever in the base these "other" deposits should be categorized, they were as insignificant as "official foreign" deposits prior to the financial crisis. Yet since then they have risen as high as $107 billion in December 2011. (See Figure 2.) Although that amount, if counted in the base at that time, would have increased the total base by only 4.1 percent, the same $107 billion would have increased the pre-quantitative base by more than 10 percent. There is no guarantee that a Fed exit strategy that decreases the monetary base will pari passu decrease these non-interest earning deposits. In fact, it is likely that access of government-sponsored enterprises to Fed deposits will expand in the future.
Indeed, a change introduced by the Board of Governors on February 18, 2014, portents such an expansion of non-bank deposits at the Fed. The Dodd-Frank Act permits the Fed to provide financial services to what are styled Financial Market Utilities (FMU's), and the new Financial Stability Oversight Committee has so far designated eight such FMU's. They are the Clearing House Payments Company, CLS Bank International, Chicago Mercantile Exchange, the Depository Trust Company, Fixed Income Clearing Corporation, ICE Clear Credit, National Securities Clearing Corporation, and the Options Clearing Corporation. All FMU's now lodge deposits at the Fed and may eventually earn interest on them. Some of these entities previously had Fed deposits, but before February 2014, their deposits, along with those of banks, were counted in the monetary base. Now all FMU deposits are in the "other" category and have been dropped out of the the base. In other words, this represent still another omission that could in the future more seriously distort reported measures of both total reserves and the monetary base.
Monetary Relevance of the Base and Reserves
Up to this point, I have focused on statistical inconsistencies in the Fed's reported measures of both the monetary base and total reserves. But once the Fed began paying interest on reserves, it created a theoretical problem with the reported versions of these measures. Monetary economists distinguish between outside money and inside money. Checking accounts and other deposits at banks qualify as inside money because they have both an asset and liability side; they are an asset of the depositor and a liability of the bank. Redeemable for Federal Reserve notes, they therefore entail financial intermediation in which the depositor can be thought to lend cash to the bank, which then relends part or all of it. Federal Reserve notes, on the other hand, are outside money. While nominally a liability on the Fed's balance sheet, this paper fiat money is not a genuine liability and not redeemable for anything other than an equal amount of more of the same. Federal Reserve notes therefore are an asset only; like gold coins in a commodity money system. Prior to the financial crisis, the monetary base consisted entirely of outside money.
This changed when the Fed began paying interest on reserves. Through these interest payments, these reserves have become a genuine liability on the Fed's balance sheet. They are just like interest-earning Treasury securities. The Fed is now in effect borrowing money from banks in order to relend it on the asset side of its balance sheet. In short, the Fed is now involved in financial intermediation, doing the same thing as Fannie Mae, Freddie Mac, and the Federal Home Loan Banks. Interest-earning reserves therefore cease to be outside money and become another form of inside money. Or to put it another way, the Fed in essence is conducting fiscal policy just like the U.S. Treasury. When the Treasury borrows money, even with short-term Treasury bills, those securities are not considered part of the monetary base. There is no good reason why Fed borrowing should be any different.
The Fed's Term Deposit Facility(TDC), created on April 30, 2010, helps highlight this logic. The TDC is a mechanism through which banks can convert their reserve deposits at the Fed (which are like Fed-provided, interest-earning checking accounts for banks) into deposits of fixed maturity at higher interest rates set by auction (making them like Fed-provided certificates of deposit for banks). The Fed so far has only tested term deposits, which peaked at $404 billion in February 2014, with maturities ranging from 14 to 84 days. But for obvious reasons, this form of Fed borrowing is quite correctly excluded from Fed measures of both total reserves and the monetary base.
Not all bank reserves earn interest—only those reserves held as deposits at the Fed. A bank's vault cash earns nothing, but vault cash currently amounts to a little less than $70 billion, about the same as total reserves before the Fed began quantitative easing. Thus, at least $2.5 trillion of the post-crisis explosion of the monetary base constitutes interest-bearing inside money that in substance is government debt merely intermediated by the Fed. Confining the definition of the monetary base and total reserves to only non-interest bearing, Fed-created outside money would yield the results for the period from 2001 to mid-2015 depicted in Figure 3, 4, and 5. With this adjustment, the mere $500 billion increase in what we can call the "outside base" since September 2008 represents merely a slightly more rapid rate of increase than the rate of increase in the base the decade prior, and nearly all of that recent increase has been in the form of hand-held currency.
No wonder that the high inflation that so many expected from quantitative easing never materialized.
 Richard G. Anderson and Robert H. Rasche, with Jeffrey Loesel, "A Reconstruction of the Federal Reserve Bank of St. Louis Adjusted Monetary Base and Reserves," Federal Reserve Bank of St. Louis Review 85 (September/October 2003): 39-69. The Board of Governors adjusted series is labelled as TRARR on the St. Louis Fed "FRED" website.
 Required clearing balances arose out of the Fed's check-clearing operations, paid interest, and are explained in E. J. Stevens, "Required Clearing Balances," Federal Reserve Bank of Cleveland Economic Review 29 (1993, Quarter 4): 2–14. Float also results from the Fed's check clearing and is reported in the Fed's H.4.1 Release. It requires the smallest adjustment. Before extensive electronic clearings, the time it took for checks to clear almost always exceed the brief hold the Fed puts on checks submitted for clearing. So the float would be positive, and two banks would temporarily be counting the same reserves, giving a small boost to total reserves and the monetary base. Despite being quite small, however, float usually made a bigger contribution to reserves than Fed discount loans to depositories. For instance, on July 26, 1996, the float was a mere $769 million, or only 0.17 percent of Fed assets. But on the same date, total discounts were even less: $258 billion. Now with electronic clearings, the float is almost always negative. Checks clear faster than banks receive credit for them, trivially reducing total reserves and the base. On August 28, 2002, for example, the float was a negative $324 million, but still larger in absolute value than the $189 million in total discounts. With the huge increase in reserves resulting from quantitative easing, the affect of the float is so insignificant as to be hardly worth bothering about.
 The change was announced in the H.3 Release of June 6, 2013, and implemented in the H.3. Release of July 11, 2013. The new monetary-base series is labeled BOMGBASE at "FRED," and the revisions of Regulation D are detailed in the Federal Register.
 Among the "Technical Q&As" on the H.3 Release at the Board's website, it states that the "levels and growth rates of the two series are nearly identical," and provides a confirming graph. But I double-checked with an Excel spreadsheet of the two series just to make sure.
 St. Louis Adjusted Reserves are reported bi-weekly and monthly, and both seasonally adjusted and not seasonally adjusted. The monthly not seasonally adjusted series is labelled ADJRESNS at the FRED website. See also Richard G. Anderson and Robert H. Rasche, "A Revised Measure of the St. Louis Adjusted Monetary Base," Federal Reserve Bank of St. Louis Review (March/April 1996).
 The H.4.1. Release lists these deposits in the table labelled "Factors Affecting Reserve Balances of Depository Institutions" and again in the table labelled "Consolidated Statement of Condition of All Federal Reserve Banks."
 Ruth Judson, "Crisis and Calm: Demand for U.S. Currency at Home and Abroad from the Fall of the Berlin Wall to 2011," Board of Governors of the Federal Reserve System, International Finance Discussion Papers, IFDP 1058 (November 2012).
 Although the amount of these deposits rose from the neighborhood of $100 million prior to the financial crisis to as high as $11.2 billion afterwards, they have never exceeded 0.4 percent of the total monetary base. This series is labelled as WLFOL at FRED.
 Gara Afonso, Alex Entz, and Eric LeSueur, "Who's Lending in the Fed Funds Market?" Federal Reserve Bank of New York Liberty Street Economics (December 2, 2013).
 John G. Gurley and Edward S. Shaw, Money in a Theory of Finance (Washington: Brookings Institution, 1960), first coined the terms inside and outside money. Their distinction was between money that was issued through financial intermediation (inside), with an offsetting liability side, and money that was an asset only (outside), without an offsetting liability side. They were challenged by Boris P. Pesek and Thomas R. Saving, Money, Wealth, and Economic Theory (New York: Macmillan, 1967), who argued that the critical distinction was between interest-bearing and non-interest bearing money. But Pesek and Saving then leapt to the conclusion that much bank-created money over and above bank reserves counted as outside money. The subsequent tortuous debate was best sorted out by Friedman and Schwartz, Monetary Statistics of the United States: Estimates, Sources, Methods (New York: Columbia University Press, 1970), pp. 110-118, 128-130; who argued that the bank-created money that Pesek and Saving were implicitly counting as outside money was better thought of as reflecting the valuable charters of banks, often because of the monopoly privileges that banks then enjoyed.
 With the possible exception of the small amount of interest-earning required clearing balances mentioned in the first section and discontinued in July 2013.
 The Fiscal Theory of the Price Level implicitly denies that even currency in circulation is genuine outside money but, because it is payable of taxes, a form of inside money, as pointed out in Jeffrey Rogers Hummel, "Mises, the Regression Theorem, and Free Banking," Liberty Matters: An Online Discussion Forum (January 2014). Here is not the place to fully address this contention.
 This series is reported in the Board's H.4.1 Release and is labelled WLTDHDIA at FRED. Other forms of Fed borrowing that are also quite correctly not counted as reserves or in the monetary base are Treasury deposits (which during the financial crises were expanded with what was called the Supplementary Financing Account, discontinued in July 2011) and reverse repurchase agreements. For details about these as well as the Term Deposit Facility, see Jeffrey Rogers Hummel, "The Federal Reserve's Exit Strategy: Looming Inflation or Controllable Overhang," Mercatus Research, Mercatus Center at George Mason University, September 2014.
 A more sophisticated approach would treat interest-bearing reserves as partly both inside and outside money that should be weighted on the basis of the difference between the interest rate paid on reserves and some higher market rate. But then one would have to view the liquidity services of many other financial assets as making them partly outside money as well. Although this is an enormous, if not totally insurmountable, empirical problem, it is an approach that has been frequently suggested and is similar to what Divisia aggregates try to do with measures of the money stock weighted according to liquidity.
 The total outside base is calculated by taking the Board's base series (monthly, not seasonally adjusted) available at "FRED" as BOMGBASE and, beginning in September 2008, subtracting the Board's series on Total Reserves Maintained at Federal Reserve Banks (monthly, not seasonally adjusted), reported in the H.3 Release and available at "FRED" as RESBALNS. Currency is still the currency component of M1, reported in the H.6 Release and as CURRNS at "FRED." Outside reserves is the difference between the total outside base and currency.
 Since the crisis, the growth rate of the non-interest bearing base (outside money) has risen from less than 2 percent in mid-2008 to has high as 9 percent annually. The irrelevance of interest-bearing base money for genuine monetary policy has also been noted by John A. Tatom, "U.S. Monetary Policy in Disarray," Journal of Financial Stability. 12 (2014): 47-58. One minor difference between Tatom's analysis and mine is that his "adjusted monetary base" only subtracts excess reserves held as deposits at the Fed from the monetary base, whereas I subtract all interest-bearing reserves, whether excess or required.