Chapter 4: Money Market Equilibrium - Kleykamp in … 4: Money Market Equilibrium I. Determining the Money Supply Most people have a good sense of what we call money. This is because

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

1 1C

M C D DC TRH C TR

D D

which can be rewritten as

1( )M H H

where C

D is the currency-deposit ratio as determined by the public, and where

TR

D is the

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

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) small-

denomination 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 non-

money 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

eP R

P P

where eP

P

the expected change in the price of the non-money asset and where R the

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.

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

( )d

o o

Mh Y f r

P

where Y real output or real GDP and where r nominal interest rate. The two constant

parameters oh and of 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

( )s

d

o o

M Mh Y f 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

determine the demand for money. That is, sM is determined by one set of people and ( )dM

P is

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 sM by P generates the stock of real money

balance in the economy and equating this to ( )dM

P produces equilibrium. How do we know that

these two will move to equality? How do we know that sM

P and ( )dM

P will not be different?

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

given level of the money supply, sM , 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

( )d

o o

Mh Y f 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.

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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.