Download Chapter 4: Money Market Equilibrium I. Determining the Money

Chapter 4: Money Market Equilibrium
I. Determining the Money Supply
Most people have a good sense of what we call money. This is because we all use money to
make purchases and to hold some of our wealth in that form. Most of us know that money is
currency and bank deposits. However, a deeper reflection shows that money is actually quite
abstract and becomes more so as we try to define it precisely and control it for policy purposes.
Some students think that money and income are the same things. This is not true, despite the fact
that we are used to asking “How much money do you make each year”, when what we really
mean is “What is your income per year”. Some students also confuse the terms “tax revenue”
and “money supply”. They are in fact very different ideas. One reason why students confuse
these terms is that they no doubt have heard (correctly) that government can sometimes finance
part of its operations by printing money. Governments can tax, borrow, and print money. But,
printing new money and collecting taxes are entirely different things. A rise in tax revenue does
not necessarily imply an increase in the money supply. Rather, it means that the government has
taken in a greater amount of tax revenue and thus has a greater command over the fixed level of
money in society. Likewise, if the government prints more money, the money supply increases.
But, the government has greater resources to use even though it has not explicitly raised taxes on
others or reduced the resources of the public.1
It will be useful to look first at the balance sheets of the commercial banking system and the
Federal Reserve, America’s central bank. These two balance sheets are shown below. These are
highly simplified t-accounts for both the commercial banking system and the Federal Reserve.
The actual balance sheets would be extremely complicated with many entries. We create instead
highly abstract versions of the balance sheets and by doing so better understand the working of
the essential elements determining the money supply in an economy.
1
We must be careful here since when the government creates money it in effect imposes what is known as an
inflation tax on people. When money is created by the government, its control over resources has increased at the
expense of the public. Not because a sales tax or income tax has taken place, but because the printing of money
reduces the purchasing power of the other dollars in existence and this is like a tax on those dollars. The real income
or revenue the government receives from creating new money is called seniorage. It is a very surreptitious tax on the
real value of the money balances people already have. One good aspect of this tax is that it is very broad based,
since everyone has money balances. There is really no escape, except to convert your cash into real assets or foreign
currency. The typical way in which the government increases the money supply is to trade non-interest bearing
government debt (money) for interest bearing government debt (Treasury bonds). Money becomes less valuable in
society (since there is now more of it) and bonds become more valuable (since there are less of them).
We begin by looking at the left hand side balance sheet showing the financial situation for the
banking system as a whole. Banks take in deposits and borrowings as their source of funds (they
also can issue stock and can borrow money). These funds can then be invested in three categories
of assets -- reserves (very low interest), securities (low interest government bonds), or loans
(relatively higher interest debt instruments). The distribution of funds among these three earning
asset categories is the subject of bank investment management. The bank will consider getting
the highest rate of return on the funds for an acceptable level of risk. Reserves are very low risk
assets, while loans are relatively high risk assets. Finding the proper mixture is a constant – one
might say daily – problem for the management of banks.
The definition of reserves is technically vault cash that commercial banks have plus all deposits
the commercial banks keep with the central bank – the Fed. The Fed will pay a small amount of
interest on the reserves that the central bank holds for them. The current rate of interest paid on
the reserves is 0.25 % per annum. 2
Commercial bank holding of securities is limited mainly to local and state government bonds,
non-Federal mortgage backed securities (30%) and Federal government and agency securities
implicit Federal government guarantees, including mortgage backed securities backed by (70%).
In January of 2013, for all commercial banks in the US (including US located foreign banks) the
first of these two categories amounted to $869 billion, while the second category was roughly
$1868 billion. Altogether securities held by commercial banks were equal to $2737 billion. 3 The
2
The rate is determined exclusively by the Fed and is paid on both required reserves and excess reserves. See the
following references http://www.federalreserve.gov/monetarypolicy/reqresbalances.htm for the most recent figures
available. Currently there is no distinction between the rate paid on required and excess reserves. The interest paid
on required reserves is meant to compensate banks for the reserves they are forced to keep with the Fed, while the
interest paid on excess reserves if meant to help the Fed conduct monetary policy. The Fed began paying interest on
reserves October 6, 2008. Thus, paying interest is a relatively new phenomenon for the Fed.
3
These figures can be found in the Fed’s H.8 release entitled Assets and Liabilities of Commercial Banks in the
United States (Weekly) – H.8. See http://www.federalreserve.gov/releases/h8/current/#fn6
category “loans” in the balance sheet is a very complicated item that includes such things as
commercial and industrial loans, real estate loans, consumer loans, and a general category called
“other loans and leases”. The basic division between these four types of loan categories in
January of 2013 was commercial loans (21%), real estate loans (49%), consumer loans (15%)
and all other loans (15%). The total amount of loans outstanding in January 2013 was $7241
billion.
With $2737 billion in securities and $7241 billion in loans, the final big item in the consolidated
banks’ balance sheet is cash (including reserves) which is equal to about $1714 billion. We
should also note that there are some other assets we have not mentioned that includes the value
of buildings and other capital and is equal to $1144 billion, as well as three other small assets
listed below. Thus adding these big items and additional items up we get total assets equal to
$13,123 billion = $1714 billion + $2737 billion + $7241 billion + $1144 billion + (allowance for
loan lease loss + interbank loans + trading assets), where this last term in parentheses is equal to
$287 billion. Note that the cash asset item includes reserves which we can verify from Fed
statistics in January 2013 was $1614 billion with $95 billion in required reserves and $1519
billion in excess reserves. Thus, there is an additional $100 billion in cash which is not classified
as reserves. This is not really a bad approximation for our balance sheet of the entire commercial
banking sector of the US for January 2013.
What can we say about the level of liabilities of the US commercial banking system? Again, we
have a problem of grouping very detailed and complicated entries into large, general categories.
One fact that we must remember is that total assets are equal to total liabilities plus a residual
which includes total equity.4 Total liabilities of the entire banking sector can be grouped into
three rough categories – namely, deposits, borrowings, and other liabilities. For the entire
commercial banking sector, in January 2013, deposits were equal to $9253 billion, while
borrowings were equal to $1581 billion. Other liabilities were about $828 billion. Adding these
three together and subtracting from total assets, we find the residual was equal to $1461 billion.
We next turn to the Federal Reserve’s balance sheet.
The Fed’s balance sheet has undergone enormous change in the last five years because of the
chaos of the housing debacle, the subsequent financial crisis, and the attendant economic
recession. Once again we note that in order to make any progress in our understanding of the
economy there are numerous items in the actual balance sheet of the Fed that must be collected
together rationally under a few categories. On the asset side we have Treasury securities, other
securities, and other assets. For the last week of February of 2013, Treasury securities were
4
The Fed analysts who construct H.8 caution against thinking of the residual as a precise measure of owners equity
although the textbook definition of equity is the difference between assets and liabilities. One major difference is
that we are adding together many firms rather than considering one firm. In any event, we will follow their
admonishment and assume that the term is a complicated combination of things which only partially reflect the
equity position of banks. For this reason, we call the difference between assets and liabilities the residual.
$1745 billion, other securities (mainly mortgage backed securities) were $1099 billion, and other
assets were $295 billion. Altogether total assets for the Fed amounted to $3139 billion. To give
you some idea of the tremendous growth in Fed assets in recent years, the comparable figure for
total asset of the Fed in December 2007 was $926 billion, or roughly a 240% increase in assets in
little over 5 years. Such a thing would have been unthinkable in the past.5 The idea that Fed
assets could grow at such a high rate over a short period would have implied monetary chaos to
most any economist. It is indeed amazing that the Fed has been able to maintain monetary
stability during this time; such a daring rescue of the economy has nevertheless placed the US in
a difficult bind as we shall see.
Liabilities at the Fed can be broadly categorized into three groups – currency, reserves, and other
liabilities. Currency as of February 27, 2013 totaled $1169 billion, while reserves totaled $1684
billion. Other liabilities were equal to $286 billion. These three items taken together totaled
$3139 billion, exactly the same as assets.
We can now put these figures together and present the current state of the commercial banking
system and the Federal Reserve as follows:
5
To give you some idea of how exaggerated things have become at the Fed due to the financial crisis, the growth
rate of Fed assets from Dec. 2002 – Dec. 2007, also a five year period, was about 24% -- ten times less than the
period Dec. 2007- Feb. 2013. To compare Fed balance sheets over many weeks, months, and years see
http://www.federalreserve.gov/releases/h41/ . This stupendous growth of Fed assets (and liabilities) has provoked
intense debate over if and how these Fed positions could be safely “wound down”. Chairman Bernanke remains
confident that the level of assets and liabilities can be orderly wound down, if the situation presents itself.
Note that the “Cash” item on the balance sheet of commercial banks is very closely related to the
“Reserves” variable that is on the liabilities side of the Fed’s balance sheet. Indeed they are
nearly equal. In most books on macroeconomics and money, these two items are simply assumed
to be equal. They are extremely important to the conduct of monetary policy, so it will be
profitable for students to pay attention to these items and how they can change relative to the
other items in the balance sheets. The very concept of balance in the balance sheet is crucial. It
says that if one item changes then some other collection of items on the balance sheet must
change as well. They must balance. The student should be able to grasp the important fact that by
purchasing or selling securities to the commercial banks, the Fed can alter the level of reserves
and cash in the banking system.
Reserves are very special to the determination of the money supply. Reserves are defined as
vault cash (i.e. currency in commercial banks) plus commercial banks’ deposits at the Fed. This
is the formal definition of reserves, but we can take total reserves and divide them in a different
way. This is done as follows
TR  RR  ER
where TR  total reserves, RR  required reserves, and ER  excess reserves. Required
reserves are the reserves that equal the legal percentage of deposits that absolutely must be kept
at the Fed. Thus, if the required reserve ratio is 10% of deposits and deposits are $9000 billion,
commercial banks must keep at least $900 billion in deposits at the Fed. If the required reserve
ratio rises to 15%, then required reserves must rise to $1350 billion. Whatever the amount of
total reserves that exceed required reserves are called excess reserves. These reserves are also
kept on deposit at the Fed. All reserves, regardless of being required or excess are kept at the Fed
(unless the reserves are vault cash). Hence, if total reserves are $1600 billion and required
reserves are $900 billion, then excess reserves are equal to $700 billion. The student should
remember that the equation above is not a definition of reserves. It is a division of reserves into
two separate components.
What do the actual reserves data look like at the Fed?
On the next page we have included a table showing total reserves, required reserves, and excess
reserves as monthly averages. For February 2013, the Fed has provided a preliminary estimate of
total reserves of the commercial banking sector equal to about $1731 billion. Compare this with
our earlier balance sheet figure of $1684 billion. The two figures are not exactly equal because of
many factors such as the period over which the average is being taken and errors in estimates
made by the member banks in reporting. This difference underscores the danger of placing too
much confidence in the precision of monetary statistics, which are by the way among the very
best data we have in economics. In the table below, borrowed reserves are equal to total reserves
minus total borrowings from the Fed. The NSA stands for not seasonally adjusted. The last term
in the table that we have yet to discuss is the monetary base.
The monetary base is defined as currency outstanding plus commercial bank reserves. The
foundational variable for the money supply is the monetary base. It is sometimes called high
powered money because each dollar gives rise to a multiple expansion in the money supply.
For the period February 2013 the monetary base was estimated to be $2843 billion. Reserves
were estimated to be $1731 billion. This means that currency was equal to $1112 billion. This is
not far off the amount contained in the balance sheet of the Fed, which was estimated at $1169
billion. The figure below shows just how exaggerated the movement in the monetary base has
become. Under ordinary circumstances, such an enormous change in the monetary base would
generate an enormous increase in the money supply. It has not, so far. We will explain why in a
moment.
Finally, we can conclude this section by putting all the parts together and explaining how that the
money supply is determined.
Money, as we have stated above, is defined as currency plus commercial bank deposits. One way
we can write this is
M CD
The definition of high powered money is
H  C  TR
Now, let’s divide M by H to get
C  1
M CD
 1
D



H C  TR C  TR
 
D
D
which can be rewritten as
M (
1 
)H   H
 
C
TR
is the currency-deposit ratio as determined by the public, and where  
is the
D
D
reserves-deposit ratio as determined by the commercial banking sector as a whole. The
coefficient  is known as the money multiplier. There will be a money multiplier for each type
where  
of money supply defined (i.e. each type of definition of deposits that are considered). Change the
definition of D and we will have a completely new multiplier.
The Fed has two basic measures of money M1 and M2 on which it routinely collects data.6 M2 is
actually an extension of M1 (i.e. M2 = M1 + other types of near-money assets). We say that M2 is
broad money while M1 is narrow money. Many economists believe that M2 is the appropriate
measure of money for purposes of monetary policy. It apparently has a relatively more stable
relation to nominal GDP and prices than does M1. The money supply, whether M1 or M2, is
almost always increasing. Only in very special circumstances will the money supply contract.
This is because the economy is almost always in the midst of growth. More spending and
transactions requires more money to accomplish this spending and transactions. During the Great
depression of the 1930’s the money stock fell precipitously – from 1929 -1933 M1 fell by 25%
while M2 fell by 33%. Over the period 1959-2012, M2 has averaged around 7% growth per year,
rising occasionally to nearly 15% during the early 1950s and falling somewhat below zero during
the early 1930s. M2 growth slowed a little to 6.5% during the period 1997-2012.
6
According to the Federal Reserve, M1 consists of (1) currency outside the U.S. Treasury, Federal Reserve Banks,
and the vaults of depository institutions; (2) traveler's checks of nonbank issuers; (3) demand deposits at commercial
banks (excluding those amounts held by depository institutions, the U.S. government, and foreign banks and official
institutions) less cash items in the process of collection and Federal Reserve float; and (4) other checkable deposits
(OCDs), consisting of negotiable order of withdrawal (NOW) and automatic transfer service (ATS) accounts at
depository institutions, credit union share draft accounts, and demand deposits at thrift institutions. Seasonally
adjusted M1 is constructed by summing currency, traveler's checks, demand deposits, and OCDs, each seasonally
adjusted separately.
By contrast M2 consists of M1 plus (1) savings deposits (including money market deposit accounts); (2) smalldenomination time deposits (time deposits in amounts of less than $100,000), less individual retirement account
(IRA) and Keogh balances at depository institutions; and (3) balances in retail money market mutual funds, less IRA
and Keogh balances at money market mutual funds. Seasonally adjusted M2 is constructed by summing savings
deposits, small-denomination time deposits, and retail money funds, each seasonally adjusted separately, and adding
this result to seasonally adjusted M1.
II. The Demand for Real Money Balances
In the previous section we considered the supply of money; we now briefly look at the demand
for money and then put the two together to get monetary equilibrium.
Many students may feel that the demand for money is a rather silly concept. After all, don’t we
all want an infinite amount of money? How can we make sense of this? The answer is that we
may want an infinite amount of money, but we are not able to demand it because our demand is
ultimately limited by the size of our personal wealth. If the total value of our wealth is $100,000
then the maximum amount of money we could possibly hold is $100,000. This is what we would
have if we converted all our assets to money and held no other physical assets – no houses, stock,
bonds, gold, or anything. In fact, we can imagine holding no money and having all our assets in
other things. Or, we could hold all our wealth in money form. Those are two extremes. The
demand for money is simply the desired percentage of our wealth that we wish to hold in the
form of money. Many people no doubt, if asked, would say they would hold 10%-20% of their
assets in money, with the rest in interest or dividend earning assets like bonds or stocks,
respectively. If people felt worried about the future state of the economy, this demand for money
might rise to 30% or even 40%. Their pessimism and fear would drive them to sell stock and
bonds and convert their assets to a more liquid form, like money. At other times, with strong
confidence in the economy, these people might reduce their desired holding to only 5% of their
total assets.7
Confidence can at times be an important determinant of the demand for money. However, most
of the time we are not worried so much about whether the economy is going to turn suddenly bad
or suddenly good. Instead, we are concerned with having enough money in our pockets and bank
account to guarantee that we can pay our bills and buy a few things on the weekend. Naturally,
this means that our level of income (which determines our spending) is the over-riding factor
determining the level of our money demand. Our income determines spending and spending
determines our money demand. Simple, right? Not quite. We use money as a medium of
exchange and anything can be exchanged...not just goods and services.
Another factor is the level of interest rates, or more correctly the nominal rate of return on nonmoney assets.8 The rate of return on non-money assets, like corporate stock, is given by
7
While it is true that total assets or perhaps net wealth provides an upper bound on the amount of cash one can hold,
it is not an important factor in the demand for money since most wealth is extremely illiquid and remains so for
good reason. We need our assets to live day to day. From publications by the Fed on the US Flow of Funds we can
estimate the total assets and net worth of US households in 2012 as equal to about $79.5 trillion and $66 trillion,
respectively. Money, defined as currency plus checkable deposits (M1), was merely $814 billion. That is less than
2% of total assets. What is important for the demand for money is the value of transactions, both from the sale of
newly produced goods and services (income) and the sale of existing assets (both real and financial).
8
The student should be warned that we are considering only the rates of return on non-money assets. Therefore, we
exclude consideration of the interest paid on bank deposits. The rate of interest paid on bank deposits is a rate of
P e R

P
P
P e
 the expected change in the price of the non-money asset and where R  the
P
income on the asset. Given current expectations and income as fixed, the only way that this rate
of return can increase is for P , the price of the non-monetary asset, to fall. This may sound
strange to you at first, but the current price must fall in order for the rate of return to increase.
Similarly, if the price of the asset falls, then the rate of return for the asset must rise, given all
other things constant. The equation for the return shown above illustrates this clearly since P is
in the denominator of both terms. For example, a simple way to see this is to assume you invest
100 dollars now to get 110 dollars one year later. This can be written as 110/100 = 1.10 or a 10%
annual return, ignoring other factors. To make this return increase to 20%, the price must fall
from 100 to 91.67. Thus, 110/91.67 = 1.20 which is a 20% return.
where
Now imagine that you feel the rate of return on an asset is unusually low and will be rising in the
future. This means that you think the price of that asset will be falling, using the same logic as
the above paragraph. Naturally, if you think that the price will be falling you will be wanting to
put your assets into cash in order to be ready to buy a low priced, high yielding asset in the future.
You will want your assets in “ready cash” or highly liquid form. This is an important reason for
people to hold money. They are speculating that asset returns will rise and asset prices will fall
and that they will be able to buy such assets at a low price in the future. In simpler terms, if you
think the stock market is going to go down, you should put your assets into cash and wait for the
stocks to fall. You can then buy the stocks at a low price and ride them up making a bundle of
cash. You will then enjoy a big return. The conclusion from this is that when rates of return on
assets fall to extremely low levels, people will expect that this will not last and that returns will
soon rise and asset prices will be dropping in the future. They will want to hold money and wait
for the fall. Low interest rates, or rates of return, mean high demands for money. We therefore
say that interest rates are negatively related to the demand for money.
Putting the two main factors – real income and nominal interest rate – together we can write the
demand for real money balances as
(
M d
)  hoY  f o r
P
where Y  real output or real GDP and where r  nominal interest rate. The two constant
parameters ho and f o measure the strength of the effects that the two variables have on the real
money demand. Note that we write the demand for money as a demand for real money balances.
return on money assets, not non-monetary assets. Such a rate of return will be positively related to the demand for
money since it is interest paid on money – making it attractive to hold money.
This is because the number of dollars doesn’t really tell us much unless we can compare those
dollars with prices. Or, alternatively you can ask yourself why that holding $10 in April of 1954
was different than holding $10 dollars now. Of course, prices were much lower in 1954. The
purchasing power of ten dollars in April of 1954 translates to holding $86.66 now (February of
2013). That is, thing in 2013 are about 8.5 times more expensive than in 1954. Don’t forget that
incomes are also about 8.5 times higher now. The point to remember is that when it comes to
money the most important thing is how much can be bought with that money and not just how
many dollars there are.
III. Equilibrium in the Money Market
Now that we have explained the money supply and money demand in an economy, we need to
put the two sides of the market together to get monetary equilibrium. 9 Equilibrium is a process
or a force in which certain variables in the economy adjust to produce a stable configuration for
the economy. In nearly every case, equilibrium must be met by some way or another. If prices, or
incomes, or interest rates are controlled and do not move, something else will invariably adjust to
bring about stability. When prices are controlled, it may be long and costly lines at the market or
when rents are controlled, it may be an acute shortage of places to live. The market will seldom
display runaway values for the variables we face. The economy naturally tends to some stable
configuration. Economists are interested in these stable configurations and whether there exists
more than one. Free markets make equilibrium a simple matter of equating supply and demand
and letting prices and quantities adjust to bring about a stable market configuration.
When we put supply and demand for money together we get the following
Ms
M
 ( )d  hoY  f o r
P
P
where we recognize that the government, public, and banking sector come together to determine
the nominal money supply and where the public (including business and banks) come together to
M
determine the demand for money. That is, M s is determined by one set of people and ( ) d is
P
9
Some students may wonder why that we have not discussed the foreign exchange rate. After all, when we speak
of money there is domestic and foreign money. Isn’t it reasonable to expect than an increase in the demand for
foreign money would reduce the demand for domestic money? And, wouldn’t a change in the exchange rate have
an impact on this demand for domestic money we have been discussing. This is perceptive but not quite right. The
demand for money in an economy can exist even when there is no foreign trade. Nevertheless, the foreign sector
can have an effect on the money markets and vice versa. This is related to what is known as the monetary
approach to the balance of payments. We will have to hold off on such considerations for now.
determined by another set of people. Dividing M s by P generates the stock of real money
M
balance in the economy and equating this to ( ) d produces equilibrium. How do we know that
P
M
Ms
and ( ) d will not be different?
P
P
We can never be sure. Our assumption of a stable market is a metaphysical thing since no one
could ever prove these two (if they truly exist) are equal. On the other hand, how do you know
that you love your wife? How can you prove that by talking to someone you can make them
understand you....always? Of course, you can’t, but there are good reasons to believe that you do
love your wife and that you can be understood. In each case, if you this was not true you would
be able to see noticeable effects. You could see it from the data. Likewise, if markets were often
in disequilibrium we would see it in the data. There would be runaway values for the
equilibrating variables. In the money market, the equilibrating variables are Y , P , and r. For any
these two will move to equality? How do we know that
given level of the money supply, M s , these three variables will move to bring both sides of the
money market into equality.
Are there other variables that affect real money demand – anything in addition to Y and r ? Of
course, there are a multitude of variables having different impacts on money demand. The most
important of these is probably a generic risk factor encompassing both the problem of confidence
in the banking sector and the risks present in the economic system. Letting this risk factor be
denoted by  , our demand for real money balances becomes
(
M d
)  hoY  f o r  
P
Thus, a rise in risk or a fall in confidence will be associated with an increase in  and a
corresponding increase in the real demand for money.
--------------------------------------------------------------------------------A Note on Banks’ and Other Financial Institutions’ Profitability
Using data from the BEA, we find that banks and other financial institutions have traditionally
made anywhere from 20% to 40% of the before-tax profits in the US corporate sector. However,
they only made 9% during 2008. On average since 1998 banks have made 28% of corporate
profits. The percentage of profits earned by banks and financial institutions tend to rise unusually
high during the first two or three years following a recession. Manufacturing on average
accounts for about 17% of corporate profits, but this is highly variable. Non-financial business
accounts for about 68% of all before-tax corporate profits in the US.