If a bank borrow money from a central bank but keeps it as a reserve instead of lending it to someone else, is it counted in the monetary base (MB) or money supply measure M1, using US definitions ? Maybe that case just doesn't happen.
EDIT: A related question: if every debt is paid back (including money lent by central banks), does MB remain constant (which could not be the case according to the answer to the previous question) ?
Yes, it is in both but we have to be careful not to double count:
The Fed’s definition of M1 is the sum of (1) currency outside bank vaults, (2) traveler's checks of nonbank issuers, (3) customers’demand deposits at commercial banks (with minor deductions), and (4) other checkable deposits, like negotiable order of withdrawal (NOW) and automatic transfer service (ATS) accounts. Basically, this is currency held by the public plus demand deposit balances outside the Fed. M2 consists of M1 plus (1) savings deposits (including money market deposit accounts), (2) small-denomination time deposits (less than $100,000), and (3) balances in retail money market mutual funds. Individual retirement account (IRA) and Keogh account balances are excluded from M2. Excess reserves, required reserves, clearing balances held at the Federal Reserve banks, and the like, are components of the Fed’s monetary base but would constitute double-counting of the same factors if included in M1 and other monetary aggregates. Such accounts are readily spendable media of exchange (transaction accounts), but counterparts of these accounts already are included in M1, for example, as components of customers’ demand deposits at commercial banks. The quantities of liquidity to fear for inflationary consequences are either monetary base or M1/M2, but not both simultaneously.
The Problem of Excess Reserves, Then and Now (Todd (2013))
What is the monetary base?
In economics, the monetary base (also base money, money base, high-powered money, reserve money, outside money, central bank money or, in the UK, narrow money) in a country is defined as the portion of the commercial banks' reserves that are maintained in accounts with their central bank plus the total currency circulating in the public (which includes the currency, also known as vault cash, that is physically held in the banks' vault).
The monetary base should not be confused with the money supply which consists of the total currency circulating in the public plus the non-bank deposits with commercial banks.
This is how it works:
Creating Money through the Discount Window. When a bank needs new reserves to support loans and investments it has already made or anticipates making, it ordinarily borrows from other banks at the Federal Funds rate. But during times of stress, which are reflected by a shortage of liquidity in many banks, the whole banking system needs new reserves — hence the Fed's discount window. When a bank borrows funds overnight from the Fed's discount window (at an interest rate the Fed sets, called the discount rate), the bank's reserve account at the Fed is credited with the amount borrowed (and the Fed adds to its assets the additional amount owed to it by the borrowing bank). Since the borrowing bank gets new reserves and no other bank lost reserves, net new reserves have been created for the banking system as a whole. If the amount is also \$10 million, the banking system as a whole has a new capacity to expand loans and deposits by as much as \$100 million. Thus, the Fed's open market purchases and discount window loans have the same ultimate impact on the money supply, at least until the discount window loans are repaid.
How the Fed Creates Money (McTeer and Villarreal (2008))
