Download 4. What is `money`? 4.1. Money demand function In a standard

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4. What is ‘money’?
4.1. Money demand function
In a standard macroeconomic textbook, a nominal money demand
function is formalized as
M tD = Pt GDPYt GDP L ( it ) ,
(4-1)
where it is a nominal interest rate, more precisely short-run interest rate,
and L ( i ) is decreasing in i . Equation (4-1) implies that nominal money
demand is proportional to both the GDP deflator ( Pt GDP ) and real GDP ( Yt GDP ).
L ( i ) is sometimes called liquidity demand; it represents a part of money
demand which decreases with an opportunity cost of holding money i . That
is, as a nominal interest is higher, households and firms are more reluctant
to hold money with zero interest due to more losses of interest revenues.
Given equation (4-1), nominal money demand ( M tD ) is increasing in
price levels and real GDP, but decreasing in nominal interest rates. An
alternative representation is that real money demand (
M tD
) is increasing in
Pt GDP
real GDP, but decreasing in nominal interest rates. Another alternative is
that the ratio of nominal money to nominal GDP (
M tD
), which is called
Pt GDPYt GDP
Marshallian k, is decreasing in nominal interest rates.
As an equilibrium condition of money markets, such money demand
from households and firms should be equal to money supply by the central
bank ( M tS ) in a nominal term.
M tD = M tS
(4-2)
4.2. Money as a medium of exchange
What is ‘money’ in a money demand function (4-1)?
We here define ‘money’ as a financial instrument which serves as a
medium of exchange. We claim that currencies including bank notes and
coins, and demand deposits including checking and ordinary accounts belong
to such ‘money’. An easier part of the above Q. and A. is why a currency is
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Figure 4-1: Currency as a medium of exchange
Currency
Agent X
Goods
Agent Y
‘money’. As shown in Figure 4-1, you always exchange currencies for goods,
or goods for currencies. Thus, a currency indeed plays a role as a medium of
exchange.
A harder part is why a demand deposit is ‘money’. A demand deposit,
including both checking and ordinary accounts, is a financial instrument on
which only zero or low interest rates are allowed, but from which funds can
freely be withdrawn, and through which money can be remitted from your
account to an account of someone else by a wire transfer and a remittance
check.
How can such demand deposits serve as a medium of exchange? Let us
begin with a simple case. Suppose that Agent X purchases goods of one
hundred million yen from Agent Y. It is fairly cumbersome and dangerous to
physically carry ten thousand 10,000 yen notes. In this case, a currency does
not work as an efficient medium of exchange. However, if Agent X and Agent
Y open checking account in Private Bank A, then it is easy to settle a
Figure 4-2: One private bank as a medium of exchange
Private Bank A
Account X
Transfer
Demand
Currency
Deposit
Agent X
Account Y
Goods
Agent Y
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Figure 4-3: Two private banks under a central bank
as a medium of exchange
Central Bank
Reserve
Account X
Transfer
Private Bank A
Account Y
Private Bank B
Account X
Account Y
Demand
Deposit
Agent X
Reserve
Currency
Goods
Agent Y
payment from Agent X to Agent Y by just transferring funds between the two
checking accounts (see Figure 4-2). Here, demand deposits, checking
accounts in this case, indeed serve as medium of exchange for the one
hundred million transaction.
What happens if Agent Y opens a checking account not in Private Bank
A, but in Private Bank B? In this case, they still need to physically carry ten
thousand 10,000 yen notes from Private Bank A to Bank B. Here, Central
Bank comes to fix such a difficulty. Both private banks are legally required
to open a zero-interest reserve account and deposit funds there in Central
Bank. As shown in Figure 4-3, once funds are transferred between the two
reserve accounts in Central Bank, a payment from Agent X to Agent Y is
settled. Thus, with the support of the reserve system of Central Bank,
demand deposits can serve effectively as a medium of exchange.
As demonstrated above, both currencies and demand deposits can serve
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as a medium of exchange, and are qualified as ‘money’. In the macroeconomic
statistics, the total balance of currencies and demand deposits is called
Money Stock 1, or M1. Thus, M1 denotes the total volume of ‘money’
circulating in a macroeconomy.
4.3. What is demanded and what is supplied
As equation (4-2) implies, money demand from households and firms is
equal to money supply by the central bank. It is quite natural to regard M1
as the total demand for money from households and firms. But, it is rather
difficult to consider M1 as the total supply of money by the central bank,
because the central bank cannot directly control the volume of demand
deposits in private banks. All the central bank can control directly is the
volume of currencies and reserve deposits, both of which are issued as
Figure 4-4: Bank deposits, currency, and
reserves at a central bank
Central Bank
Assets
Government
bonds
Private Banks
Liabilitie
Assets
Reserves
(R)
Reserves
(R)
Currency
(C)
Government
bonds
Monetary
Base
Liabilitie
Demand
Deposits
(DD)
Households/Firm s
Assets
Demand
Deposits
(DD)
Corporate
bonds
Loans
Currency
(C)
Alternative
investme nt
opportunities
Money
Demand
(M1)
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liabilities by the central bank.
How can we create a bridge between what is determined in private
banks and what is controlled by the central bank? Let us do it step by step
using Figure 4-4.
Households and firms decide to allocate funds between money and
alternative investment opportunities. They decide so by balancing between
the conveniences of holding money as a medium of exchange and its
opportunity costs as a consequence of zero or low interest on money. In the
second step, they determine the allocation between demand deposits and
currencies.
The funds allocated to demand deposits go to private banks, while
those to currencies reach the central bank by way of private banks. But, you
may not be comfortable with the latter half of the statement. If you regard a
bank note as a certificate of deposit issued by the central bank, which carries
no interest coupon without any specific date of maturity, then you may see
the whole picture. Your bank withdraws a part of its reserve deposits in the
form of bank notes at a branch of the central bank, and puts bank notes in
ATMs. Then, you can get bank notes from one of ATMs. Conversely, you bring
bank notes to your bank, which in turn brings and puts them as reserve
deposits at a branch of the central bank. Thus, one of important jobs for your
bank is to frequently transfer funds between its reserve account, one form of
the central bank’s deposits, and bank notes, the other form.
On the other hand, private banks invest the funds collected through
demand deposits on government bonds, corporate bonds, commercial loans,
residential loans, and so on. In addition, private banks are legally required
to deposit funds at zero-interest reserve accounts in the central bank. The
required volume of reserve deposits is in proportion to the volume of demand
deposits. As mentioned above, the reserve system installed by the central
bank helps demand deposits of private banks to work as an effective medium
of exchange. Thus, the above legal requirement for private banks can be
interpreted as the enforcement mechanism to maintain the reserve system
in a national economy. Given positive interest rates, private banks pay a
charge for use of the reserve system by being forced to deposit at zero
interest rates. Obviously, the funds required for reserve deposits go to the
central bank.
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In this way, the central bank issues currencies (bank notes) to
households and firms by way of private banks, and collect funds through
reserve deposits from private banks. The flip side of this is that the central
bank collects funds from private banks by requiring reserve deposits, and
from households and firms by issuing currencies. The central bank invests
the collected funds mainly on government bonds including long-term ones.
The total balance of currencies and reserve deposits is called the monetary
base, often denoted by MB. The monetary base can be controlled at least to
some extent by the central bank. Thus, it is considered as money supply.
How can we establish the linkage between M1 as money demand ( M tD )
from households and firms, and the monetary base MB as money supply by
the central bank? To begin with money demand, M tD may be divided
between cM tD as currencies ( Ct ) and
(1 − c ) M tD
as demand deposits ( Dt ),
where 0 < c < 1 . The total of reserve deposits ( Rt ) is proportion to the total
Rt θ (1 − c ) M tD .
volume of demand deposits at the ratio θ . Hence, =
The monetary base, consisting of currencies and reserve deposits, is
now written as follows.
MBt = cM tD + θ (1 − c ) M tD
=c + θ (1 − c )  M tD
(4-3)
By equation (4-3), we now establish the linkage between the monetary base
and money demand. Substituting equation (4-1) to equation (4-3), an
equilibrium condition of money markets is derived as follows.
MBt =c + θ (1 − c )  Pt GDPYt GDP L ( it )
As a final word on equation (4-3), we should be cautious about a
statement that the monetary base MBt creates nominal money demand M tD
by
1
1
MBt . A reason for this is that c of
may not be
c + θ (1 − c )
c + θ (1 − c )
constant, but may be influenced by a nominal interest rate it . An increase in
it may induce a shift from currencies with zero interest rates to demand
deposits with low, but still positive interest rates. Note that a nominal
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interest rate it is also responsible for liquidity demand L ( it ) in a money
demand function (4-1). Thus,
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MBt and M tD are simultaneously
c + θ (1 − c )
rivate determined, and there is not a one-way causality from MBt to M tD ,
but a two-way causality between the two.
4.4. How to control reserve deposits by monetary operations
How does the central bank control the monetary base?
Let us begin with a supply of currencies, one component of the monetary
base. According to a standard macroeconomics textbook, the central bank
accommodates a supply of currencies to cash demand from households and
firms. That is, demand for currencies is determined by not the central bank,
but by the force of markets. There is little room for the central bank to
control currencies.
Let us move to a supply of reserve deposits, the other component of the
monetary base. Again according to a standard textbook, the central bank can
expand reserve deposits by buying operations, and contract them by selling
operations. Monetary operations by the central bank, buying and selling
operations, are conducted through transactions of government bonds with
private banks.
By buying operations, the central bank purchases government bonds
from private banks, and make payment on reserve accounts held by private
banks from which it buys government bonds. Consequently, in terms of the
balance sheet of the central bank, there are increases in government bonds
as assets, and in reserve deposits as liabilities.
By selling operations, on the other hand, the central bank sells
government bonds to private banks, and receives payment through reserve
deposits of buying private banks. As a result, there are decreases in
government bonds as assets, and in reserve deposits as liabilities.
Thus, the central bank may control reserve deposits by monetary
operations in a short run, say within one month, but it may not beyond one
month. As long as nominal short-run interest rates are positive, private
banks have no incentive to make zero-interest reserves in excess of required
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reserves. As mentioned above, required reserves are proportional to the
volume of demand deposits, which are determined by demand from
households and firms. Thus, the level of required reserves is eventually
dictated by a market need for demand deposits, and out of control of the
central bank.
However, there are two cases in which the central bank can actively
control reserve deposits. Firstly, when short-run interest rates are guided
toward zero by the central bank, private banks are indifferent between
making zero-interest reserve deposits and investing in financial markets at
zero interest rates. Hence, with active buying operations by the central bank,
private banks may be interested in making reserve deposits in excess of
required reserves.
Secondly, if the central bank allows positive interest rates on reserve
deposits, then private banks may be willing to respond to aggressive buying
operations by the central bank, and make reserve deposits in excess of
required reserves. In some occasions, central banks indeed pay interest rates
on excess reserves.
Then, is it possible for the central bank to expand reserve deposits when
not positive, but negative interest rates are allowed on excess reserves? In
principle, it is impossible to do so, because private banks have no incentive
to make negative-interest reserves in excess of required reserves. However,
when market participants expect that prices of long-term government bonds
will increase with declines in their yields, private banks may purchase
long-term bonds from the government at lower prices, and sell them to the
central bank at higher prices. Such possible capital gains from reselling may
convince private banks to respond to large-scale buying operations by the
central bank. To understand the above story precisely, you are reminded of
one important fact that bond pricing decreases with yields on bonds.
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4.5. An empirical exercise on Japanese money markets
Given the following historical episodes of the Japanese money markets,
interpret Tables 4-1 through 4-2, and Figures 4-5 through 4-9.
A series of historical episodes in the Japanese money markets
1. Overnight call rates (interest rates in interbank markets) had been
above 0.5% per year up to mid-1995.
2. The Bank of Japan (BOJ) guided overnight call rates to 0% for the
period from February 1999 to August 2000. This monetary policy is
called the zero interest rate policy, or the ZIRP.
3. In March 2001, the BOJ guided overnight call rates to zero, and
carried the excess reserves, the reserve deposits beyond required
reserves. The latter monetary policy, BOJ’s carrying excess reserves,
is called the quantitative easing or the QE.
4. The BOJ terminated the QE in March 2006, and the ZIRP in July
2006. After taking off the ZIRP, overnight call rates stayed at around
0.5% per year.
5. In response to the Lehman shock in September 2008, the BOJ guided
overnight call rates to blow 0.2% by December 2008, and to below
0.1% since January 2009. At the same time, the BOJ resumed to
carry the excess reserves.
6. The BOJ started to allow +0.1% on the excess reserves in October
2008; she still maintained 0% interest on the required reserves.
7. The BOJ started to aggressively purchase long-term government
bonds to accelerate the QE in April 2013.
8. The BOJ upgraded the QE by further expanding her purchases of
long-term government bonds in October 2014.
9. The BOJ decided to adopt the negative interest rate policy or the
NIRP in January 2016, and started to apply -0.1% interest rate to an
increment in the excess reserves from February 2016, although she
maintained +0.1% interest rate on the balance of the excess reserves
accumulated by private banks up to February 2016.
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