Presentation on theme: "The Determinants of the Money Supply"— Presentation transcript:
1The Determinants of the Money Supply The money multiplier, reserve and currency ratios, and borrowed reserves
2M1 and the Monetary BaseRecall our definition of M1 as currency in circulation plus checkable depositsRecall our definition of MB as currency in circulation plus reservesThe Fed has greater control over MB than it does over M1Checkable deposits are influenced by a number of factors that the Fed does not have direct control over.We link MB and M1 together through the money multiplierM1 = m*MBFor every $1 increase in the MB, the money supply (M1) increases by m*$1m is almost always greater than 1.
3The Currency RatioHow much currency does the public hold relative to their checkable deposits?We assume that the desired level of currency (C) is a constant fraction of checkable depositsThe currency ratio is a constant (in equilibrium) defined as:c = C/DC can change, but only in constant proportion to D
4Reserve RatiosWhat fraction of checkable deposits do banks hold in reserve?Banks are required by the Fed to hold a minimum fraction in reserve defined as the reserve requirement ratio (rr)Banks may choose to hold excess reserves (i.e. a fraction of deposits held in reserve above and beyond the minimum required by the fed).Let RR be the required reserves held by banksRR = rr*D, where rr is a parameter set by the FedLet ER be the excess reserves held by banksER = e*D, where e is assumed to be a constant proportion set by banksTotal reserves (R) = RR + ER = rr*D + e*D = (rr+e)*DNote that we have been assuming so far that ER=0 (i.e. the reserve requirement is binding).
5Deriving the Money Multiplier We define MB as currency (C) plus reserves (R)Using our definitions:MB = C + RMB = c*D + rr*D + e*DMB = (rr + e + c)*DThe monetary base is equal to the fraction of deposits allocated to required reserves, excess reserves, and currency in circulation
6Deriving the Money Multiplier MB = (rr + e + c)*DRearranging gives:Recall M1 = C + D = (c*D) + D = (1+c)*DPlugging in our definition of D:Since M1 = m*MB:
7The Money Multiplier The money multiplier is defined as: m = (1+c)/(rr+e+c)If no currency is held and banks hold no excess reserves, then the money multiplier is simply the inverse reserve ratioA 10% rr will produce a multiplier of 10A 20% rr will produce a multiplier of 5In reality, people do hold currency and banks do hold excess reserves.As a result, the banking system is limited in the amount of money it creates through fractional reserve banking (i.e. multiple deposit creation)Money held as currency or in reserve is not being loaned out.
8Example 1Suppose the desired currency ratio is 40%, the reserve requirement is 10% and the excess reserve ratio is 0.5%The money multiplier ism = (1+0.4)/( ) = 2.77A one dollar increase in the monetary base will lead to a $2.77 increase in the money supplyNote that if c = e = 0, then the money multiplier would have been 10.Accounting for currency and excess reserves is clearly important.
9Example 2Let c = 0.25, e = 0.001, and rr = Compute the money multiplierm = (1+0.25)/( ) = 3.56The Fed decides to increase rr to 20%. What happens to the money multiplier (and the money supply as a result?)m = 1.25/0.456 = 2.74A smaller multiplier means that banks create less money through lending and therefore the money supply will fall.
10Example 3What happens to the money multiplier when the desired currency ratio rises?Let c = 0.2, rr = 0.25, and e = 0.05m = (1+0.2)/( ) = 1.2/0.5 = 2.4Now suppose c rises to 0.3, while all other variables remain constantm = (1+0.3)/( ) = 1.3/0.6 = 2.17Increasing the fraction of deposits held as currency causes the money supply to fallMoney is being taken out of the banking system where it could have been used to make loans.
11Factors that Determine the Money Multiplier Changes in the required reserve ratio rThe money multiplier and the money supply are negatively related to rChanges in the currency ratio cThe money multiplier and the money supply are negatively related to cChanges in the excess reserves ratio eThe money multiplier and the money supply are negatively related to the excess reserves ratio e
12Changes in the Currency Ratio We have assumed that the constant currency ratio is an independent parameter for simplicity.A more complete analysis would examine the factors that cause c to change.Changes in income/wealthLarger proportions of currency are held by people with low income/wealthAs income/wealth rises, the ratio of currency to deposits fallsChanges in expected returnsAs the interest rate on deposits rises, c fallsAs the cost of acquiring currency falls, c risesFears of bank insolvency (i.e. bank panics) cause c to rise sharplyIncreases in illegal activity cause c to rise
13The Currency Ratio Over Time Series of bank panicsATM’s lower the cost of acquiring currencyBig tax increasesIncreased illegal drug trade
14Changes in the Excess Reserve Ratio What are the costs and benefits to banks of holding excess reserves?Market Interest Rates (-)Every dollar held as an excess reserve has an opportunity cost equal to the interest rate it could have earned as a bank loanAs market interest rates rise, this opportunity costs increases and banks hold fewer excess reservese is negatively related to market interest ratesExpected Deposit Outflows (+)The main benefit of holding excess reserves is that they insulate the bank (somewhat) from sudden deposit outflowsWith excess reserves, banks do not have to call in loans, sell off other assets, or borrow from the Fed to cover deposits being withdrawnIf banks think that deposit outflows will increase, they would be wise to increase their excess reserve ratioe is positively related to expected deposit outflows.
16The Decline of the Reserve Ratio as a Policy Tool The preceding analysis suggests that the Fed can increase/decrease the money supply by lowering/raising the reserve ratio.While the Fed used this policy tool in the past, it has become ineffective in the past decade or so.The Fed allows banks to classify some of their membership deposits at the Fed as required reservesBanks have found that they need to keep extra currency in ATM’s over weekends and holidays. This currency is classified as vault cash and counts toward required reservesWith these two developments, banks actually hold more reserves than the minimum required by the FedIf rr is not binding, then any change in rr will have little to no effect. (only works if you significantly increase rr!)
17Borrowed ReservesOpen market operations are controlled by the Fed, but the Fed does not directly control the amount of borrowing by banks from the FedWe split the monetary base into two components, the non-borrowed monetary base (MBn) and borrowed reserves by banks (BR)MBn= MB – BR MB = MBn + BRM1 = m*MB = m*(MBn + BR)The money supply increases with both the non-borrowed base and with borrowed reservesAn increase in BR frees up more bank deposits for loansBR tends to be very small since the Fed keeps the discount rate above the market interest rate.
20Explains long run movements Explains short run fluctuations
21The Bank Panics of the Great Depression The model we have developed here can be used to explain the sharp reduction in the money supply during the Great DepressionPrior to FDIC, there was no publicly provided insurance for bank depositsWith the Great Depression, many bank loans failedPeople worried (rightfully) that their bank did not have enough in reserves to cover all depositsThey rushed to their bank to withdraw their money while their was still something left in reserveThis sparked a series of bank panics where even financially stable banks were affectedThese bank panics directly led to a reduction in the money supply, even though the Fed would have actually preferred an increase in M1 at this timeFears of bank insolvency caused c to riseIncreases in expected deposit outflows caused e to riseThe multiplier declined sharply
22Currency and Excess Reserve Ratios During the Great Depression