The economics of Money, Banking and Financial Markets Part 10 pptx

Therefore, Fisher’s quantity theory of money suggests that the demand for money is purely a function of income, and interest rates have no effect on the demand for money.3Fisher came to

P a r t V I

Monetary Theory

PREVIEW In earlier chapters, we spent a lot of time and effort learning what the money supply

is, how it is determined, and what role the Federal Reserve System plays in it Now

we are ready to explore the role of the money supply in determining the price leveland total production of goods and services (aggregate output) in the economy The

study of the effect of money on the economy is called monetary theory, and we

examine this branch of economics in the chapters of Part VI

When economists mention supply, the word demand is sure to follow, and the

dis-cussion of money is no exception The supply of money is an essential building block

in understanding how monetary policy affects the economy, because it suggests thefactors that influence the quantity of money in the economy Not surprisingly, anotheressential part of monetary theory is the demand for money

This chapter describes how the theories of the demand for money have evolved

We begin with the classical theories refined at the start of the twentieth century byeconomists such as Irving Fisher, Alfred Marshall, and A C Pigou; then we move on

to the Keynesian theories of the demand for money We end with Milton Friedman’smodern quantity theory

A central question in monetary theory is whether or to what extent the quantity

of money demanded is affected by changes in interest rates Because this issue is cial to how we view money’s effects on aggregate economic activity, we focus on therole of interest rates in the demand for money.1

cru-Quantity Theory of Money

Developed by the classical economists in the nineteenth and early twentieth centuries,the quantity theory of money is a theory of how the nominal value of aggregateincome is determined Because it also tells us how much money is held for a givenamount of aggregate income, it is also a theory of the demand for money The mostimportant feature of this theory is that it suggests that interest rates have no effect onthe demand for money

The clearest exposition of the classical quantity theory approach is found in the work of

the American economist Irving Fisher, in his influential book The Purchasing Power of Money, published in 1911 Fisher wanted to examine the link between the total quantity

of money M (the money supply) and the total amount of spending on final goods and services produced in the economy P  Y, where P is the price level and Y is aggregate output (income) (Total spending P  Y is also thought of as aggregate nominal income for the economy or as nominal GDP.) The concept that provides the link between M and

P  Y is called the velocity of money (often reduced to velocity), the rate of turnover of

money; that is, the average number of times per year that a dollar is spent in buying the

total amount of goods and services produced in the economy Velocity V is defined more precisely as total spending P  Y divided by the quantity of money M:

(1)

If, for example, nominal GDP (P  Y ) in a year is $5 trillion and the quantity of

money is $1 trillion, velocity is 5, meaning that the average dollar bill is spent fivetimes in purchasing final goods and services in the economy

By multiplying both sides of this definition by M, we obtain the equation of

exchange, which relates nominal income to the quantity of money and velocity:

The equation of exchange thus states that the quantity of money multiplied by thenumber of times that this money is spent in a given year must be equal to nominalincome (the total nominal amount spent on goods and services in that year).2

As it stands, Equation 2 is nothing more than an identity—a relationship that is true

by definition It does not tell us, for instance, that when the money supply M changes, nominal income (P  Y ) changes in the same direction; a rise in M, for example, could

be offset by a fall in V that leaves M  V (and therefore P  Y ) unchanged To convert the equation of exchange (an identity) into a theory of how nominal income is deter-

mined requires an understanding of the factors that determine velocity

Irving Fisher reasoned that velocity is determined by the institutions in an omy that affect the way individuals conduct transactions If people use charge accountsand credit cards to conduct their transactions and consequently use money less oftenwhen making purchases, less money is required to conduct the transactions generated

econ-by nominal income (M↓ relative to P  Y ) , and velocity (P  Y )/M will increase.

Conversely, if it is more convenient for purchases to be paid for with cash or checks(both of which are money), more money is used to conduct the transactions generated

by the same level of nominal income, and velocity will fall Fisher took the view that

where P average price per transaction

T number of transactions conducted in a year

V T  PT/M  transactions velocity of money Because the nominal value of transactions T is difficult to measure, the quantity theory has been formulated

in terms of aggregate output Y as follows: T is assumed to be proportional to Y so that T  vY, where v is a constant of proportionality Substituting vY for T in Fisher’s equation of exchange yields MV T  vPY, which can

be written as Equation 2 in the text, in which V  V /v.

http://cepa.newschool.edu/het

/profiles/fisher.htm

A brief biography and summary

of the writings of Irving Fisher.

the institutional and technological features of the economy would affect velocity onlyslowly over time, so velocity would normally be reasonably constant in the short run.

Fisher’s view that velocity is fairly constant in the short run transforms the equation

of exchange into the quantity theory of money, which states that nominal income is

determined solely by movements in the quantity of money: When the quantity of

money M doubles, M  V doubles and so must P  Y, the value of nominal income.

To see how this works, let’s assume that velocity is 5, nominal income (GDP) is tially $5 trillion, and the money supply is $1 trillion If the money supply doubles to

ini-$2 trillion, the quantity theory of money tells us that nominal income will double to

$10 trillion ( 5  $2 trillion)

Because the classical economists (including Fisher) thought that wages and prices

were completely flexible, they believed that the level of aggregate output Y produced

in the economy during normal times would remain at the full-employment level, so

Y in the equation of exchange could also be treated as reasonably constant in the short run The quantity theory of money then implies that if M doubles, P must also dou- ble in the short run, because V and Y are constant In our example, if aggregate out-

put is $5 trillion, the velocity of 5 and a money supply of $1 trillion indicate that theprice level equals 1 because 1 times $5 trillion equals the nominal income of $5 tril-lion When the money supply doubles to $2 trillion, the price level must also double

to 2 because 2 times $5 trillion equals the nominal income of $10 trillion

For the classical economists, the quantity theory of money provided an

explana-tion of movements in the price level: Movements in the price level result solely from changes in the quantity of money.

Because the quantity theory of money tells us how much money is held for a givenamount of aggregate income, it is in fact a theory of the demand for money We can

see this by dividing both sides of the equation of exchange by V, thus rewriting it as:

where nominal income P  Y is written as PY When the money market is in librium, the quantity of money M that people hold equals the quantity of money demanded M d , so we can replace M in the equation by M d Using k to represent the quantity 1/V (a constant, because V is a constant), we can rewrite the equation as:

Equation 3 tells us that because k is a constant, the level of transactions generated by a fixed level of nominal income PY determines the quantity of money M d that peopledemand Therefore, Fisher’s quantity theory of money suggests that the demand for money

is purely a function of income, and interest rates have no effect on the demand for money.3Fisher came to this conclusion because he believed that people hold money only toconduct transactions and have no freedom of action in terms of the amount they want

to hold The demand for money is determined (1) by the level of transactions generated

econ-of exchange and as a store econ-of wealth.

by the level of nominal income PY and (2) by the institutions in the economy that affect the way people conduct transactions and thus determine velocity and hence k.

Is Velocity a Constant?

The classical economists’ conclusion that nominal income is determined by movements

in the money supply rested on their belief that velocity PY/M could be treated as

reason-ably constant.4Is it reasonable to assume that velocity is constant? To answer this, let’slook at Figure 1, which shows the year-to-year changes in velocity from 1915 to 2002(nominal income is represented by nominal GDP and the money supply by M1 and M2).What we see in Figure 1 is that even in the short run, velocity fluctuates too much

to be viewed as a constant Prior to 1950, velocity exhibited large swings up anddown This may reflect the substantial instability of the economy in this period, whichincluded two world wars and the Great Depression (Velocity actually falls, or at leastits rate of growth declines, in years when recessions are taking place.) After 1950,velocity appears to have more moderate fluctuations, yet there are large differences in

4

Actually, the classical conclusion still holds if velocity grows at some uniform rate over time that reflects changes

in transaction technology Hence the concept of a constant velocity should more accurately be thought of here as

a lack of upward and downward fluctuations in velocity.

F I G U R E 1 Change in the Velocity of M1 and M2 from Year to Year, 1915–2002

Shaded areas indicate recessions Velocities are calculated using nominal GNP before 1959 and nominal GDP thereafter.

Sources: Economic Report of the President; Banking and Monetary Statistics; www.federalreserve.gov/releases/h6/.

1920 1915

A summary of how various

factors affect the velocity of

money

the growth rate of velocity from year to year The percentage change in M1 velocity(GDP/M1) from 1981 to 1982, for example, was 2.5%, whereas from 1980 to 1981velocity grew at a rate of 4.2% This difference of 6.7% means that nominal GDP was6.7% lower than it would have been if velocity had kept growing at the same rate as

in 1980–1981.5 The drop is enough to account for the severe recession that tookplace in 1981–1982 After 1982, M1 velocity appears to have become even morevolatile, a fact that has puzzled researchers when they examine the empirical evidence

on the demand for money (discussed later in this chapter) M2 velocity remainedmore stable than M1 velocity after 1982, with the result that the Federal Reservedropped its M1 targets in 1987 and began to focus more on M2 targets However,instability of M2 velocity in the early 1990s resulted in the Fed’s announcement inJuly 1993 that it no longer felt that any of the monetary aggregates, including M2, was

a reliable guide for monetary policy

Until the Great Depression, economists did not recognize that velocity declinessharply during severe economic contractions Why did the classical economists notrecognize this fact when it is easy to see in the pre-Depression period in Figure 1?Unfortunately, accurate data on GDP and the money supply did not exist beforeWorld War II (Only after the war did the government start to collect these data.)Economists had no way of knowing that their view of velocity as a constant wasdemonstrably false The decline in velocity during the Great Depression years was sogreat, however, that even the crude data available to economists at that time suggestedthat velocity was not constant This explains why, after the Great Depression, econo-mists began to search for other factors influencing the demand for money that mighthelp explain the large fluctuations in velocity

Let us now examine the theories of money demand that arose from this search for

a better explanation of the behavior of velocity

Keynes’s Liquidity Preference Theory

In his famous 1936 book The General Theory of Employment, Interest, and Money, John

Maynard Keynes abandoned the classical view that velocity was a constant and developed

a theory of money demand that emphasized the importance of interest rates His theory

of the demand for money, which he called the liquidity preference theory, asked the

question: Why do individuals hold money? He postulated that there are three motivesbehind the demand for money: the transactions motive, the precautionary motive, andthe speculative motive

In the classical approach, individuals are assumed to hold money because it is a medium

of exchange that can be used to carry out everyday transactions Following the classicaltradition, Keynes emphasized that this component of the demand for money is deter-mined primarily by the level of people’s transactions Because he believed that thesetransactions were proportional to income, like the classical economists, he took thetransactions component of the demand for money to be proportional to income

Transactions

Motive

5

We reach a similar conclusion if we use M2 velocity The percentage change in M2 velocity (GDP/M2) from 1981

to 1982 was 5.0%, whereas from 1980 to 1981 it was 2.3% This difference of 7.3% means that nominal GDP was 7.3% lower than it would have been if M2 velocity had kept growing at the same rate as in 1980–1981.

Keynes went beyond the classical analysis by recognizing that in addition to holdingmoney to carry out current transactions, people hold money as a cushion against anunexpected need Suppose that you’ve been thinking about buying a fancy stereo; youwalk by a store that is having a 50%-off sale on the one you want If you are holdingmoney as a precaution for just such an occurrence, you can purchase the stereo rightaway; if you are not holding precautionary money balances, you cannot take advan-tage of the sale Precautionary money balances also come in handy if you are hit with

an unexpected bill, say for car repair or hospitalization

Keynes believed that the amount of precautionary money balances people want

to hold is determined primarily by the level of transactions that they expect to make

in the future and that these transactions are proportional to income Therefore, hepostulated, the demand for precautionary money balances is proportional to income

If Keynes had ended his theory with the transactions and precautionary motives,income would be the only important determinant of the demand for money, and hewould not have added much to the classical approach However, Keynes took the

view that money is a store of wealth and called this reason for holding money the ulative motive Since he believed that wealth is tied closely to income, the speculative

spec-component of money demand would be related to income However, Keynes lookedmore carefully at the factors that influence the decisions regarding how much money

to hold as a store of wealth, especially interest rates

Keynes divided the assets that can be used to store wealth into two categories:money and bonds He then asked the following question: Why would individualsdecide to hold their wealth in the form of money rather than bonds?

Thinking back to the discussion of the theory of asset demand (Chapter 5), youwould want to hold money if its expected return was greater than the expected returnfrom holding bonds Keynes assumed that the expected return on money was zerobecause in his time, unlike today, most checkable deposits did not earn interest Forbonds, there are two components of the expected return: the interest payment and the

expected rate of capital gains.

You learned in Chapter 4 that when interest rates rise, the price of a bond falls Ifyou expect interest rates to rise, you expect the price of the bond to fall and thereforesuffer a negative capital gain—that is, a capital loss If you expect the rise in interestrates to be substantial enough, the capital loss might outweigh the interest payment,

and your expected return on the bond would be negative In this case, you would want

to store your wealth as money because its expected return is higher; its zero returnexceeds the negative return on the bond

Keynes assumed that individuals believe that interest rates gravitate to some mal value (an assumption less plausible in today’s world) If interest rates are below thisnormal value, individuals expect the interest rate on bonds to rise in the future and soexpect to suffer capital losses on them As a result, individuals will be more likely tohold their wealth as money rather than bonds, and the demand for money will be high.What would you expect to happen to the demand for money when interest ratesare above the normal value? In general, people will expect interest rates to fall, bondprices to rise, and capital gains to be realized At higher interest rates, they are morelikely to expect the return from holding a bond to be positive, thus exceeding theexpected return from holding money They will be more likely to hold bonds thanmoney, and the demand for money will be quite low From Keynes’s reasoning, we can

nor-conclude that as interest rates rise, the demand for money falls, and therefore money demand is negatively related to the level of interest rates.

Speculative

Motive

Precautionary

Motive

In putting the three motives for holding money balances together into a demand formoney equation, Keynes was careful to distinguish between nominal quantities andreal quantities Money is valued in terms of what it can buy If, for example, all prices

in the economy double (the price level doubles), the same nominal quantity of moneywill be able to buy only half as many goods Keynes thus reasoned that people want

to hold a certain amount of real money balances (the quantity of money in real

terms)—an amount that his three motives indicated would be related to real income

Y and to interest rates i Keynes wrote down the following demand for money tion, known as the liquidity preference function, which says that the demand for real money balances M d /P is a function of (related to) i and Y:6

equa-(4)

The minus sign below i in the liquidity preference function means that the demand for real money balances is negatively related to the interest rate i, and the plus sign below Y means that the demand for real money balances and real income Y are posi-

tively related This money demand function is the same one that was used in ouranalysis of money demand discussed in Chapter 5 Keynes’s conclusion that thedemand for money is related not only to income but also to interest rates is a majordeparture from Fisher’s view of money demand, in which interest rates can have noeffect on the demand for money

By deriving the liquidity preference function for velocity PY/M, we can see that

Keynes’s theory of the demand for money implies that velocity is not constant, butinstead fluctuates with movements in interest rates The liquidity preference equationcan be rewritten as:

Multiplying both sides of this equation by Y and recognizing that M dcan be replaced

by M because they must be equal in money market equilibrium, we solve for velocity:

An interesting feature of Equation 5 is that it explains some of the velocity ments in Figure 1, in which we noted that when recessions occur, velocity falls or itsrate of growth declines What fact regarding the cyclical behavior of interest rates (dis-cussed in Chapter 5) might help us explain this phenomenon? You might recall that

The classical economists’ money demand equation can also be written in terms of real money balances by

divid-ing both sides of Equation 3 by the price level P to obtain:

M d

P  k  Y

interest rates are procyclical, rising in expansions and falling in recessions The uidity preference theory indicates that a rise in interest rates will cause velocity to risealso The procyclical movements of interest rates should induce procyclical move-ments in velocity, and that is exactly what we see in Figure 1.

liq-Keynes’s model of the speculative demand for money provides another reason whyvelocity might show substantial fluctuations What would happen to the demand formoney if the view of the normal level of interest rates changes? For example, what ifpeople expect the future normal interest rate to be higher than the current normal inter-est rate? Because interest rates are then expected to be higher in the future, more peo-ple will expect the prices of bonds to fall and will anticipate capital losses The expectedreturns from holding bonds will decline, and money will become more attractive rela-

tive to bonds As a result, the demand for money will increase This means that f (i, Y )

will increase and so velocity will fall Velocity will change as expectations about futurenormal levels of interest rates change, and unstable expectations about future move-ments in normal interest rates can lead to instability of velocity This is one more reasonwhy Keynes rejected the view that velocity could be treated as a constant

Study Guide Keynes’s explanation of how interest rates affect the demand for money will be easier

to understand if you think of yourself as an investor who is trying to decide whether

to invest in bonds or to hold money Ask yourself what you would do if you expectedthe normal interest rate to be lower in the future than it is currently Would you rather

be holding bonds or money?

To sum up, Keynes’s liquidity preference theory postulated three motives forholding money: the transactions motive, the precautionary motive, and the specula-tive motive Although Keynes took the transactions and precautionary components ofthe demand for money to be proportional to income, he reasoned that the speculativemotive would be negatively related to the level of interest rates

Keynes’s model of the demand for money has the important implication thatvelocity is not constant, but instead is positively related to interest rates, which fluc-tuate substantially His theory also rejected the constancy of velocity, because changes

in people’s expectations about the normal level of interest rates would cause shifts inthe demand for money that would cause velocity to shift as well Thus Keynes’s liq-uidity preference theory casts doubt on the classical quantity theory that nominalincome is determined primarily by movements in the quantity of money

Further Developments in the Keynesian Approach

After World War II, economists began to take the Keynesian approach to the demandfor money even further by developing more precise theories to explain the threeKeynesian motives for holding money Because interest rates were viewed as a crucialelement in monetary theory, a key focus of this research was to understand better therole of interest rates in the demand for money

William Baumol and James Tobin independently developed similar demand formoney models, which demonstrated that even money balances held for transactions

Transactions

Demand

purposes are sensitive to the level of interest rates.7In developing their models, theyconsidered a hypothetical individual who receives a payment once a period andspends it over the course of this period In their model, money, which earns zerointerest, is held only because it can be used to carry out transactions.

To refine this analysis, let’s say that Grant Smith receives $1,000 at the beginning

of the month and spends it on transactions that occur at a constant rate during thecourse of the month If Grant keeps the $1,000 in cash in order to carry out his trans-actions, his money balances follow the sawtooth pattern displayed in panel (a) ofFigure 2 At the beginning of the month he has $1,000, and by the end of the month

he has no cash left because he has spent it all Over the course of the month, his ings of money will on average be $500 (his holdings at the beginning of the month,

hold-$1,000, plus his holdings at the end of the month, $0, divided by 2)

At the beginning of the next month, Grant receives another $1,000 payment,which he holds as cash, and the same decline in money balances begins again Thisprocess repeats monthly, and his average money balance during the course of the year

is $500 Since his yearly nominal income is $12,000 and his holdings of money

aver-age $500, the velocity of money (V  PY/M ) is $12,000/$500  24.

Suppose that as a result of taking a money and banking course, Grant realizes that

he can improve his situation by not always holding cash In January, then, he decides

to hold part of his $1,000 in cash and puts part of it into an income-earning securitysuch as bonds At the beginning of each month, Grant keeps $500 in cash and usesthe other $500 to buy a Treasury bond As you can see in panel (b), he starts out each

7

William J Baumol, “The Transactions Demand for Cash: An Inventory Theoretic Approach,” Quarterly Journal

of Economics 66 (1952): 545–556; James Tobin, “The Interest Elasticity of the Transactions Demand for Cash,” Review of Economics and Statistics 38 (1956): 241–247.

F I G U R E 2 Cash Balances in the Baumol-Tobin Model

In panel (a), the $1,000 payment at the beginning of the month is held entirely in cash and is spent at a constant rate until it is exhausted by the end of the month In panel (b), half of the monthly payment is put into cash and the other half into bonds At the middle of the month, cash balances reach zero and bonds must be sold to bring balances up to $500 By the end of the month, cash balances again dwindle to zero.

Cash balances ($) 1,000

500

Months (b) 1 1

month with $500 of cash, and by the middle of the month, his cash balance has rundown to zero Because bonds cannot be used directly to carry out transactions, Grantmust sell them and turn them into cash so that he can carry out the rest of the month’stransactions At the middle of the month, then, Grant’s cash balance rises back up to

$500 By the end of the month, the cash is gone When he again receives his next

$1,000 monthly payment, he again divides it into $500 of cash and $500 of bonds,and the process continues The net result of this process is that the average cash bal-ance held during the month is $500/2  $250—just half of what it was before.Velocity has doubled to $12,000/$250  48

What has Grant Smith gained from his new strategy? He has earned interest on

$500 of bonds that he held for half the month If the interest rate is 1% per month,

he has earned an additional $2.50 (1/2 $500  1%) per month

Sounds like a pretty good deal, doesn’t it? In fact, if he had kept $333.33 in cash

at the beginning of the month, he would have been able to hold $666.67 in bonds forthe first third of the month Then he could have sold $333.33 of bonds and held on

to $333.34 of bonds for the next third of the month Finally, two-thirds of the waythrough the month, he would have had to sell the remaining bonds to raise cash Thenet result of this is that Grant would have earned $3.33 per month [ (1/3 $666.67

 1%)  (1/3 $333.34  1%)] This is an even better deal His average cash ings in this case would be $333.33/2  $166.67 Clearly, the lower his average cashbalance, the more interest he will earn

hold-As you might expect, there is a catch to all this In buying bonds, Grant incurs action costs of two types First, he must pay a straight brokerage fee for the buying andselling of the bonds These fees increase when average cash balances are lower becauseGrant will be buying and selling bonds more often Second, by holding less cash, he willhave to make more trips to the bank to get the cash, once he has sold some of his bonds.Because time is money, this must also be counted as part of the transaction costs.Grant faces a trade-off If he holds very little cash, he can earn a lot of interest onbonds, but he will incur greater transaction costs If the interest rate is high, the ben-efits of holding bonds will be high relative to the transaction costs, and he will holdmore bonds and less cash Conversely, if interest rates are low, the transaction costsinvolved in holding a lot of bonds may outweigh the interest payments, and Grantwould then be better off holding more cash and fewer bonds

trans-The conclusion of the Baumol-Tobin analysis may be stated as follows: As est rates increase, the amount of cash held for transactions purposes will decline,which in turn means that velocity will increase as interest rates increase.8Put another

inter-way, the transactions component of the demand for money is negatively related to the level of interest rates.

The basic idea in the Baumol-Tobin analysis is that there is an opportunity cost

of holding money—the interest that can be earned on other assets There is also a efit to holding money—the avoidance of transaction costs When interest ratesincrease, people will try to economize on their holdings of money for transactionspurposes, because the opportunity cost of holding money has increased By using

ben-8

Similar reasoning leads to the conclusion that as brokerage fees increase, the demand for transactions money balances increases as well When these fees rise, the benefits from holding transactions money balances increase because by holding these balances, an individual will not have to sell bonds as often, thereby avoiding these higher brokerage costs The greater benefits to holding money balances relative to the opportunity cost of inter- est forgone, then, lead to a higher demand for transactions balances.

simple models, Baumol and Tobin revealed something that we might not otherwisehave seen: that the transactions demand for money, and not just the speculativedemand, will be sensitive to interest rates The Baumol-Tobin analysis presents a nicedemonstration of the value of economic modeling.9

Study Guide The idea that as interest rates increase, the opportunity cost of holding money

increases so that the demand for money falls, can be stated equivalently with the minology of expected returns used earlier As interest rates increase, the expectedreturn on the other asset, bonds, increases, causing the relative expected return onmoney to fall, thereby lowering the demand for money These two explanations are infact identical, because as we saw in Chapter 5, changes in the opportunity cost of anasset are just a description of what is happening to the relative expected return Theopportunity cost terminology was used by Baumol and Tobin in their work on thetransactions demand for money, and that is why we used this terminology in the text

ter-To make sure you understand the equivalence of the two terminologies, try to late the reasoning in the precautionary demand discussion from opportunity cost ter-minology to expected returns terminology

trans-Models that explore the precautionary motive of the demand for money have beendeveloped along lines similar to the Baumol-Tobin framework, so we will not go intogreat detail about them here We have already discussed the benefits of holding pre-cautionary money balances, but weighed against these benefits must be the opportu-nity cost of the interest forgone by holding money We therefore have a trade-offsimilar to the one for transactions balances As interest rates rise, the opportunity cost

of holding precautionary balances rises, and so the holdings of these money balancesfall We then have a result similar to the one found for the Baumol-Tobin analysis.10

The precautionary demand for money is negatively related to interest rates.

Keynes’s analysis of the speculative demand for money was open to several seriouscriticisms It indicated that an individual holds only money as a store of wealth whenthe expected return on bonds is less than the expected return on money and holdsonly bonds when the expected return on bonds is greater than the expected return onmoney Only when people have expected returns on bonds and money that areexactly equal (a rare instance) would they hold both Keynes’s analysis thereforeimplies that practically no one holds a diversified portfolio of bonds and moneysimultaneously as a store of wealth Since diversification is apparently a sensible strat-egy for choosing which assets to hold, the fact that it rarely occurs in Keynes’s analy-sis is a serious shortcoming of his theory of the speculative demand for money.Tobin developed a model of the speculative demand for money that attempted toavoid this criticism of Keynes’s analysis.11His basic idea was that not only do people

trans-11

James Tobin, “Liquidity Preference as Behavior Towards Risk,” Review of Economic Studies 25 (1958): 65–86.

care about the expected return on one asset versus another when they decide what tohold in their portfolio, but they also care about the riskiness of the returns from eachasset Specifically, Tobin assumed that most people are risk-averse—that they would

be willing to hold an asset with a lower expected return if it is less risky An tant characteristic of money is that its return is certain; Tobin assumed it to be zero.Bonds, by contrast, can have substantial fluctuations in price, and their returns can

impor-be quite risky and sometimes negative So even if the expected returns on bondsexceed the expected return on money, people might still want to hold money as astore of wealth because it has less risk associated with its return than bonds do.The Tobin analysis also shows that people can reduce the total amount of risk in aportfolio by diversifying; that is, by holding both bonds and money The model suggeststhat individuals will hold bonds and money simultaneously as stores of wealth Sincethis is probably a more realistic description of people’s behavior than Keynes’s, Tobin’srationale for the speculative demand for money seems to rest on more solid ground.Tobin’s attempt to improve on Keynes’s rationale for the speculative demand formoney was only partly successful, however It is still not clear that the speculativedemand even exists What if there are assets that have no risk—like money—but earn

a higher return? Will there be any speculative demand for money? No, because anindividual will always be better off holding such an asset rather than money Theresulting portfolio will enjoy a higher expected return yet has no higher risk Do suchassets exist in the American economy? The answer is yes U.S Treasury bills and otherassets that have no default risk provide certain returns that are greater than thoseavailable on money Therefore, why would anyone want to hold money balances as astore of wealth (ignoring for the moment transactions and precautionary reasons)?Although Tobin’s analysis did not explain why money is held as a store of wealth,

it was an important development in our understanding of how people should chooseamong assets Indeed, his analysis was an important step in the development of theacademic field of finance, which examines asset pricing and portfolio choice (the deci-sion to buy one asset over another)

To sum up, further developments of the Keynesian approach have attempted togive a more precise explanation for the transactions, precautionary, and speculativedemand for money The attempt to improve Keynes’s rationale for the speculativedemand for money has been only partly successful; it is still not clear that this demandeven exists However, the models of the transactions and precautionary demand formoney indicate that these components of money demand are negatively related tointerest rates Hence Keynes’s proposition that the demand for money is sensitive tointerest rates—suggesting that velocity is not constant and that nominal income might

be affected by factors other than the quantity of money—is still supported

Friedman’s Modern Quantity Theory of Money

In 1956, Milton Friedman developed a theory of the demand for money in a famousarticle, “The Quantity Theory of Money: A Restatement.”12Although Friedman fre-quently refers to Irving Fisher and the quantity theory, his analysis of the demand formoney is actually closer to that of Keynes than it is to Fisher’s

12

Milton Friedman, “The Quantity Theory of Money: A Restatement,” in Studies in the Quantity Theory of Money,

ed Milton Friedman (Chicago: University of Chicago Press, 1956), pp 3–21.

Like his predecessors, Friedman pursued the question of why people choose tohold money Instead of analyzing the specific motives for holding money, as Keynesdid, Friedman simply stated that the demand for money must be influenced by thesame factors that influence the demand for any asset Friedman then applied the the-ory of asset demand to money.

The theory of asset demand (Chapter 5) indicates that the demand for moneyshould be a function of the resources available to individuals (their wealth) and theexpected returns on other assets relative to the expected return on money LikeKeynes, Friedman recognized that people want to hold a certain amount of realmoney balances (the quantity of money in real terms) From this reasoning, Friedmanexpressed his formulation of the demand for money as follows:

(6)

where M d /P  demand for real money balances

Y p  Friedman’s measure of wealth, known as permanent income

(techni-cally, the present discounted value of all expected future income, butmore easily described as expected average long-run income)

r m expected return on money

r b expected return on bonds

r e expected return on equity (common stocks)

e expected inflation rate

and the signs underneath the equation indicate whether the demand for money ispositively () related or negatively () related to the terms that are immediatelyabove them.13

Let us look in more detail at the variables in Friedman’s money demand functionand what they imply for the demand for money

Because the demand for an asset is positively related to wealth, money demand ispositively related to Friedman’s wealth concept, permanent income (indicated by theplus sign beneath it) Unlike our usual concept of income, permanent income (whichcan be thought of as expected average long-run income) has much smaller short-runfluctuations, because many movements of income are transitory (short-lived) Forexample, in a business cycle expansion, income increases rapidly, but because some

of this increase is temporary, average long-run income does not change very much.Hence in a boom, permanent income rises much less than income During a reces-sion, much of the income decline is transitory, and average long-run income (hencepermanent income) falls less than income One implication of Friedman’s use of theconcept of permanent income as a determinant of the demand for money is that thedemand for money will not fluctuate much with business cycle movements

M d

P  f (Y p , r b  r m , r e  r m, e r m)

   

13

Friedman also added to his formulation a term h that represented the ratio of human to nonhuman wealth He

reasoned that if people had more permanent income coming from labor income and thus from their human ital, they would be less liquid than if they were receiving income from financial assets In this case, they might

cap-want to hold more money because it is a more liquid asset than the alternatives The term h plays no essential

role in Friedman’s theory and has no important implications for monetary theory That is why we ignore it in the money demand function.

An individual can hold wealth in several forms besides money; Friedman rized them into three types of assets: bonds, equity (common stocks), and goods Theincentives for holding these assets rather than money are represented by the expectedreturn on each of these assets relative to the expected return on money, the last threeterms in the money demand function The minus sign beneath each indicates that aseach term rises, the demand for money will fall.

catego-The expected return on money r m, which appears in all three terms, is influenced

by two factors:

1 The services provided by banks on deposits included in the money supply, such asprovision of receipts in the form of canceled checks or the automatic paying of bills.When these services are increased, the expected return from holding money rises

2 The interest payments on money balances NOW accounts and other depositsthat are included in the money supply currently pay interest As these interestpayments rise, the expected return on money rises

The terms r b  r m and r e  r mrepresent the expected return on bonds and equityrelative to money; as they rise, the relative expected return on money falls, and thedemand for money falls The final term, e  r m, represents the expected return ongoods relative to money The expected return from holding goods is the expected rate ofcapital gains that occurs when their prices rise and hence is equal to the expected infla-tion rate e If the expected inflation rate is 10%, for example, then goods’ prices areexpected to rise at a 10% rate, and their expected return is 10% When e r mrises,the expected return on goods relative to money rises, and the demand for money falls

Distinguishing Between the Friedman and Keynesian Theories

There are several differences between Friedman’s theory of the demand for money andthe Keynesian theories One is that by including many assets as alternatives to money,Friedman recognized that more than one interest rate is important to the operation ofthe aggregate economy Keynes, for his part, lumped financial assets other than moneyinto one big category—bonds—because he felt that their returns generally movetogether If this is so, the expected return on bonds will be a good indicator of theexpected return on other financial assets, and there will be no need to include themseparately in the money demand function

Also in contrast to Keynes, Friedman viewed money and goods as substitutes; that

is, people choose between them when deciding how much money to hold That is whyFriedman included the expected return on goods relative to money as a term in hismoney demand function The assumption that money and goods are substitutes indicatesthat changes in the quantity of money may have a direct effect on aggregate spending

In addition, Friedman stressed two issues in discussing his demand for moneyfunction that distinguish it from Keynes’s liquidity preference theory First, Friedmandid not take the expected return on money to be a constant, as Keynes did Wheninterest rates rise in the economy, banks make more profits on their loans, and theywant to attract more deposits to increase the volume of their now more profitableloans If there are no restrictions on interest payments on deposits, banks attractdeposits by paying higher interest rates on them Because the industry is competitive,the expected return on money held as bank deposits then rises with the higher inter-est rates on bonds and loans The banks compete to get deposits until there are no

excess profits, and in doing so they close the gap between interest earned on loansand interest paid on deposits The net result of this competition in the banking indus-

try is that r b  r m stays relatively constant when the interest rate i rises.14

What if there are restrictions on the amount of interest that banks can pay on theirdeposits? Will the expected return on money be a constant? As interest rates rise, will

r b  r mrise as well? Friedman thought not He argued that although banks might berestricted from making pecuniary payments on their deposits, they can still compete

on the quality dimension For example, they can provide more services to depositors

by hiring more tellers, paying bills automatically, or making more cash machines able at more accessible locations The result of these improvements in money services

avail-is that the expected return from holding deposits will ravail-ise So despite the restrictions

on pecuniary interest payments, we might still find that a rise in market interest rates

will raise the expected return on money sufficiently so that r b  r mwill remain tively constant.15 Unlike Keynes’s theory, which indicates that interest rates are an important determinant of the demand for money, Friedman’s theory suggests that changes in interest rates should have little effect on the demand for money.

rela-Therefore, Friedman’s money demand function is essentially one in which manent income is the primary determinant of money demand, and his moneydemand equation can be approximated by:

In Friedman’s view, the demand for money is insensitive to interest rates—not because

he viewed the demand for money as insensitive to changes in the incentives for ing other assets relative to money, but rather because changes in interest rates shouldhave little effect on these incentive terms in the money demand function The incen-tive terms remain relatively constant, because any rise in the expected returns onother assets as a result of the rise in interest rates would be matched by a rise in theexpected return on money

hold-The second issue Friedman stressed is the stability of the demand for moneyfunction In contrast to Keynes, Friedman suggested that random fluctuations in thedemand for money are small and that the demand for money can be predicted accu-rately by the money demand function When combined with his view that thedemand for money is insensitive to changes in interest rates, this means that velocity

is highly predictable We can see this by writing down the velocity that is implied bythe money demand equation (Equation 7):

Friedman does suggest that there is some increase in r b  r m when i rises because part of the money supply

(espe-cially currency) is held in forms that cannot pay interest in a pecuniary or nonpecuniary form See, for example,

Milton Friedman, “Why a Surge of Inflation Is Likely Next Year,” Wall Street Journal, September 1, 1983, p 24.

15

Competing on the quality of services is characteristic of many industries that are restricted from competing on price For example, in the 1960s and early 1970s, when airfares were set high by the Civil Aeronautics Board, airlines were not allowed to lower their fares to attract customers Instead, they improved the quality of their service

by providing free wine, fancier food, piano bars, movies, and wider seats.

demand for money accurately) implies that velocity is predictable as well If we canpredict what velocity will be in the next period, a change in the quantity of moneywill produce a predictable change in aggregate spending Even though velocity is nolonger assumed to be constant, the money supply continues to be the primary deter-minant of nominal income as in the quantity theory of money Therefore, Friedman’stheory of money demand is indeed a restatement of the quantity theory, because itleads to the same conclusion about the importance of money to aggregate spending.You may recall that we said that the Keynesian liquidity preference function (inwhich interest rates are an important determinant of the demand for money) is able toexplain the procyclical movements of velocity that we find in the data Can Friedman’smoney demand formulation explain this procyclical velocity phenomenon as well?The key clue to answering this question is the presence of permanent incomerather than measured income in the money demand function What happens to per-manent income in a business cycle expansion? Because much of the increase inincome will be transitory, permanent income rises much less than income Friedman’smoney demand function then indicates that the demand for money rises only a smallamount relative to the rise in measured income, and as Equation 8 indicates, velocityrises Similarly, in a recession, the demand for money falls less than income, becausethe decline in permanent income is small relative to income, and velocity falls In thisway, we have the procyclical movement in velocity.

To summarize, Friedman’s theory of the demand for money used a similar approach

to that of Keynes but did not go into detail about the motives for holding money.Instead, Friedman made use of the theory of asset demand to indicate that the demandfor money will be a function of permanent income and the expected returns on alter-native assets relative to the expected return on money There are two major differencesbetween Friedman’s theory and Keynes’s Friedman believed that changes in interestrates have little effect on the expected returns on other assets relative to money Thus,

in contrast to Keynes, he viewed the demand for money as insensitive to interest rates

In addition, he differed from Keynes in stressing that the money demand function doesnot undergo substantial shifts and is therefore stable These two differences also indicatethat velocity is predictable, yielding a quantity theory conclusion that money is the pri-mary determinant of aggregate spending

Empirical Evidence on the Demand for Money

As we have seen, the alternative theories of the demand for money can have very ent implications for our view of the role of money in the economy Which of these theo-ries is an accurate description of the real world is an important question, and it is thereason why evidence on the demand for money has been at the center of many debates

differ-on the effects of mdiffer-onetary policy differ-on aggregate ecdiffer-onomic activity Here we examine theempirical evidence on the two primary issues that distinguish the different theories ofmoney demand and affect their conclusions about whether the quantity of money is theprimary determinant of aggregate spending: Is the demand for money sensitive tochanges in interest rates, and is the demand for money function stable over time?16

16

If you are interested in a more detailed discussion of the empirical research on the demand for money, you can find it in an appendix to this chapter on this book’s web site at www.aw.com/mishkin.

Earlier in the chapter, we saw that if interest rates do not affect the demand for money,velocity is more likely to be a constant—or at least predictable—so that the quantitytheory view that aggregate spending is determined by the quantity of money is morelikely to be true However, the more sensitive the demand for money is to interestrates, the more unpredictable velocity will be, and the less clear the link between themoney supply and aggregate spending will be Indeed, there is an extreme case of

ultrasensitivity of the demand for money to interest rates, called the liquidity trap, in

which monetary policy has no effect on aggregate spending, because a change in themoney supply has no effect on interest rates (If the demand for money is ultrasensi-tive to interest rates, a tiny change in interest rates produces a very large change in thequantity of money demanded Hence in this case, the demand for money is com-pletely flat in the supply and demand diagrams of Chapter 5 Therefore, a change inthe money supply that shifts the money supply curve to the right or left results in itintersecting the flat money demand curve at the same unchanged interest rate.)The evidence on the interest sensitivity of the demand for money found by dif-ferent researchers is remarkably consistent Neither extreme case is supported by thedata: The demand for money is sensitive to interest rates, but there is little evidencethat a liquidity trap has ever existed

If the money demand function, like Equation 4 or 6, is unstable and undergoes stantial unpredictable shifts, as Keynes thought, then velocity is unpredictable, andthe quantity of money may not be tightly linked to aggregate spending, as it is in themodern quantity theory The stability of the money demand function is also crucial towhether the Federal Reserve should target interest rates or the money supply (seeChapter 18 and 24) Thus it is important to look at the question of whether themoney demand function is stable, because it has important implications for howmonetary policy should be conducted

sub-By the early 1970s, evidence strongly supported the stability of the moneydemand function However, after 1973, the rapid pace of financial innovation, whichchanged what items could be counted as money, led to substantial instability in esti-mated money demand functions The recent instability of the money demand func-tion calls into question whether our theories and empirical analyses are adequate Italso has important implications for the way monetary policy should be conducted,because it casts doubt on the usefulness of the money demand function as a tool toprovide guidance to policymakers In particular, because the money demand functionhas become unstable, velocity is now harder to predict, and as discussed in Chapter

21, setting rigid money supply targets in order to control aggregate spending in theeconomy may not be an effective way to conduct monetary policy

1. Irving Fisher developed a transactions-based theory of

the demand for money in which the demand for real

balances is proportional to real income and is

insensitive to interest-rate movements An implication

of his theory is that velocity, the rate of turnover of

money, is constant This generates the quantity theory

of money, which implies that aggregate spending isdetermined solely by movements in the quantity ofmoney

2.The classical view that velocity can be effectively treated

as a constant is not supported by the data Thenonconstancy of velocity became especially clear to the

economics profession after the sharp drop in velocity

during the years of the Great Depression

3.John Maynard Keynes suggested three motives for

holding money: the transactions motive, the

precautionary motive, and the speculative motive His

resulting liquidity preference theory views the

transactions and precautionary components of money

demand as proportional to income However, the

speculative component of money demand is viewed as

sensitive to interest rates as well as to expectations

about the future movements of interest rates This

theory, then, implies that velocity is unstable and

cannot be treated as a constant

4.Further developments in the Keynesian approach

provided a better rationale for the three Keynesian

motives for holding money Interest rates were found to

be important to the transactions and precautionary

components of money demand as well as to the

speculative component

5. Milton Friedman’s theory of money demand used asimilar approach to that of Keynes Treating money likeany other asset, Friedman used the theory of assetdemand to derive a demand for money that is afunction of the expected returns on other assets relative

to the expected return on money and permanentincome In contrast to Keynes, Friedman believed thatthe demand for money is stable and insensitive tointerest-rate movements His belief that velocity ispredictable (though not constant) in turn leads to thequantity theory conclusion that money is the primarydeterminant of aggregate spending

6. There are two main conclusions from the research onthe demand for money: The demand for money issensitive to interest rates, but there is little evidence thatthe liquidity trap has ever existed; and since 1973,money demand has been found to be unstable, with themost likely source of the instability being the rapid pace

real money balances, p 523velocity of money, p 518

Questions and Problems

Questions marked with an asterisk are answered at the end

of the book in an appendix, “Answers to Selected Questions

and Problems.”

*1. The money supply M has been growing at 10% per

year, and nominal GDP PY has been growing at 20%

per year The data are as follows (in billions of dollars):

2. Calculate what happens to nominal GDP if velocity

remains constant at 5 and the money supply increases

from $200 billion to $300 billion

*3. What happens to nominal GDP if the money supplygrows by 20% but velocity declines by 30%?

4. If credit cards were made illegal by congressional islation, what would happen to velocity? Explain youranswer

leg-*5. If velocity and aggregate output are reasonably stant (as the classical economists believed), what hap-pens to the price level when the money supplyincreases from $1 trillion to $4 trillion?

con-6. If velocity and aggregate output remain constant at 5and 1,000, respectively, what happens to the pricelevel if the money supply declines from $400 billion

to $300 billion?

*7. Looking at Figure 1 in the chapter, when were the twolargest falls in velocity? What do declines like this sug-

QUIZ

gest about how velocity moves with the business

cycle? Given the data in Figure 1, is it reasonable to

assume, as the classical economists did, that declines

in aggregate spending are caused by declines in the

quantity of money?

8.Using data from the Economic Report of the President,

calculate velocity for the M2 definition of the money

supply in the past five years Does velocity appear to

be constant?

*9.In Keynes’s analysis of the speculative demand for

money, what will happen to money demand if people

suddenly decide that the normal level of the interest

rate has declined? Why?

10.Why is Keynes’s analysis of the speculative demand for

money important to his view that velocity will

undergo substantial fluctuations and thus cannot be

treated as constant?

*11.If interest rates on bonds go to zero, what does the

Baumol-Tobin analysis suggest Grant Smith’s average

holdings of money balances should be?

12.If brokerage fees go to zero, what does the Tobin analysis suggest Grant Smith’s average holdings

Baumol-of money should be?

*13.“In Tobin’s analysis of the speculative demand formoney, people will hold both money and bonds, even

if bonds are expected to earn a positive return.” Is thisstatement true, false, or uncertain? Explain youranswer

14.Both Keynes’s and Friedman’s theories of the demandfor money suggest that as the relative expected return

on money falls, demand for it will fall Why doesFriedman think that money demand is unaffected bychanges in interest rates, but Keynes thought that it isaffected?

*15.Why does Friedman’s view of the demand for moneysuggest that velocity is predictable, whereas Keynes’sview suggests the opposite?

Web Exercises

1. Refer to Figure 1 The formula for computing the

velocity of money is GDP/M1 Go to www.research

.stlouisfed.org/fred/data/gdp.htmland look up the GDP

Next go to www.federalreserve.gov/Releases/h6/Current/

and find M1 Compute the most recent year’s velocity of

money and compare it to its level in 2002 Has it risen

or fallen? Suggest reasons for its change since that time

2.John Maynard Keynes is among the most well knowneconomic theorists Go to www-gap.dcsn.st-and.ac.uk/~history/Mathematicians/Keynes.htmland write

a one-page summary of his life and contributions

Baumol-Tobin Model of Transactions Demand for Money

The basic idea behind the Baumol-Tobin model was laid out in the chapter Here weexplore the mathematics that underlie the model The assumptions of the model are

as follows:

1 An individual receives income of T0at the beginning of every period

2 An individual spends this income at a constant rate, so at the end of the period,

all income T0has been spent

3 There are only two assets—cash and bonds Cash earns a nominal return of zero,

and bonds earn an interest rate i

4 Every time an individual buys or sells bonds to raise cash, a fixed brokerage fee

of b is incurred

Let us denote the amount of cash that the individual raises for each purchase or

sale of bonds as C, and n the number of times the individual conducts a

transac-tion in bonds As we saw in Figure 3 in the chapter, where T0 1,000, C  500, and

n 2:

Because the brokerage cost of each bond transaction is b, the total brokerage costs for

a period are:

Not only are there brokerage costs, but there is also an opportunity cost to holding

cash rather than bonds This opportunity cost is the bond interest rate i times

aver-age cash balances held during the period, which, from the discussion in the chapter,

we know is equal to C/2 The opportunity cost is then:

Combining these two costs, we have the total costs for an individual equal to:

COSTS bT0

C iC2

to chapter

22

1

The individual wants to minimize costs by choosing the appropriate level of C This is accomplished by taking the derivative of costs with respect to C and setting it

to zero.1That is:

Solving for C yields the optimal level of C:

Because money demand M d is the average desired holding of cash balances C/2,

(1)

This is the famous square root rule.2 It has these implications for the demand formoney:

1 The transactions demand for money is negatively related to the interest rate i

2 The transactions demand for money is positively related to income, but there areeconomies of scale in money holdings—that is, the demand for money rises less

than proportionally with income For example, if T0quadruples in Equation 1,the demand for money only doubles

3 A lowering of the brokerage costs due to technological improvements woulddecrease the demand for money

4 There is no money illusion in the demand for money If the price level doubles,

T0and b will double Equation 1 then indicates that M will double as well Thus

the demand for real money balances remains unchanged, which makes sensebecause neither the interest rate nor real income has changed

d2COSTS

dC2 
2

C3 (
bT0 ) 2bT0

C3

Tobin Mean-Variance Model

Tobin’s mean-variance analysis of money demand is just an application of the basicideas in the theory of portfolio choice Tobin assumes that the utility that peoplederive from their assets is positively related to the expected return on their portfolio

of assets and is negatively related to the riskiness of this portfolio as represented bythe variance (or standard deviation) of its returns This framework implies that anindividual has indifference curves that can be drawn as in Figure 1 Notice that theseindifference curves slope upward because an individual is willing to accept more risk

if offered a higher expected return In addition, as we go to higher indifference curves,utility is higher, because for the same level of risk, the expected return is higher Tobin looks at the choice of holding money, which earns a certain zero return, orbonds, whose return can be stated as:

R B  i  g where i interest rate on the bond

g capital gainTobin also assumes that the expected capital gain is zero3and its variance is g2 That is,

E(g)  0 and so E(R B)  i  0  i

Var(g)  E[g
E(g)]2 E(g2)  g2

F I G U R E 1 Indifference Curves

in a Mean-Variace Model

The indifference curves are

upward-sloping, and higher

indif-ference curves indicate that utility

is higher In other words,

Expected Return

Higher Utility

Standard Deviation of Returns 

U3

U2

U1

3

This assumption is not critical to the results If E(g) ≠ 0, it can be added to the interest term i, and the

analy-sis proceeds as indicated

where E expectation of the variable inside the parentheses

Var variance of the variable inside the parentheses

If A is the fraction of the portfolio put into bonds (0 ≤ A ≤ 1) and 1
A is the fraction of the portfolio held as money, the return R on the portfolio can be writ-

ten as:

R  AR B  (1
A)(0)  AR B  A(i  g)

Then the mean and variance of the return on the portfolio, denoted respectively as and 2, can be calculated as follows:

 E(R)  E(AR B)  AE(RB)  Ai

2 E(R
)2 E[A(i  g)
Ai]2 E(Ag)2 A 2 E(g2)  A2g2

Taking the square root of both sides of the equation directly above and solving for A

yields:

(2)

Substituting for A in the equation  Ai using the preceding equation gives us:

(3)

Equation 3 is known as the opportunity locus because it tells us the combinations

of and  that are feasible for the individual This equation is written in a form inwhich the variable corresponds to the Y axis and the  variable to the X axis The

opportunity locus is a straight line going through the origin with a slope of i/ g It isdrawn in the top half of Figure 2 along with the indifference curves from Figure 1 The highest indifference curve is reached at point B, the tangency of the indiffer-ence curve and the opportunity locus This point determines the optimal level of risk

* in the figure As Equation 2 indicates, the optimal level of A, A*, is:

This equation is solved in the bottom half of Figure 2 Equation 2 for A is a straight

line through the origin with a slope of 1/g Given *, the value of A read off this line

is the optimal value A* Notice that the bottom part of the figure is drawn so that as

we move down, A is increasing

Now let’s ask ourselves what happens when the interest rate increases from i1to

i2 This situation is shown in Figure 3 Because gis unchanged, the Equation 2 line

in the bottom half of the figure does not change However, the slope of the

opportu-nity locus does increase as i increases Thus the opportuopportu-nity locus rotates up and we

move to point C at the tangency of the new opportunity locus and the indifferencecurve As you can see, the optimal level of risk increases from *and *the optimal

fraction of the portfolio in bonds rises from A*to A* The result is that as the interest

rate on bonds rises, the demand for money falls; that is, 1
A, the fraction of the

portfolio held as money, declines.4

Tobin’s model then yields the same result as Keynes’s analysis of the speculativedemand for money: It is negatively related to the level of interest rates This model,however, makes two important points that Keynes’s model does not:

1 Individuals diversify their portfolios and hold money and bonds at the same time

2 Even if the expected return on bonds is greater than the expected return onmoney, individuals will still hold money as a store of wealth because its return ismore certain

F I G U R E 2 Optimal Choice of

the Fraction of the Portfolio in Bonds

The highest indifference curve is

reached at a point B, the tangency

of the indifference curve with the

opportunity locus This point

determines the optimal risk *,

and using Equation 2 in the

bot-tom half of the figure, we solve for

the optimal fraction of the

portfo-lio in bonds A*.



Eq 2

4

The indifference curves have been drawn so that the usual result is obtained that as i goes up, A* goes up as

well However, there is a subtle issue of income versus substitution effects If, as people get wealthier, they are willing to bear less risk, and if this income effect is larger than the substitution effect, then it is possible to get

the opposite result that as i increases, A* declines This set of conditions is unlikely, which is why the figure is

drawn so that the usual result is obtained For a discussion of income versus substitution effects, see David

Laidler, The Demand for Money: Theories and Evidence, 4th ed (New York: HarperCollins, 1993)

F I G U R E 3 Optimal Choice of

the Fraction of the Portfolio in Bonds

as the Interest Rate Rises

The interest rate on bonds rises

from i1to i2 , rotating the

opportu-nity locus upward The highest

indifference curve is now at point

C, where it is tangent to the new

opportunity locus The optimal

level of risk rises from  1 to  2 ,

and then Equation 2, in the

bot-tom haf of the figure, shows that

the optimal fraction of the

portfo-lio in bonds rises from A1to A2.



Here we examine the empirical evidence on the two primary issues that distinguishthe different theories of money demand and affect their conclusions about whetherthe quantity of money is the primary determinant of aggregate spending: Is thedemand for money sensitive to changes in interest rates, and is the demand for moneyfunction stable over time?

James Tobin conducted one of the earliest studies on the link between interest ratesand money demand using U.S data.1 Tobin separated out transactions balances fromother money balances, which he called “idle balances,” assuming that transactionsbalances were proportional to income only, and idle balances were related to interestrates only He then looked at whether his measure of idle balances was inverselyrelated to interest rates in the period 1922–1941 by plotting the average level of idlebalances each year against the average interest rate on commercial paper that year.When he found a clear-cut inverse relationship between interest rates and idle bal-ances, Tobin concluded that the demand for money is sensitive to interest rates.2

Additional empirical evidence on the demand for money strongly confirmsTobin’s finding.3Does this sensitivity ever become so high that we approach the case

of the liquidity trap in which monetary policy is ineffective? The answer is almost

cer-tainly no Keynes suggested in The General Theory that a liquidity trap might occur

when interest rates are extremely low (However, he did state that he had never yetseen an occurrence of a liquidity trap.)

Typical of the evidence demonstrating that the liquidity trap has never occurred

is that of David Laidler, Karl Brunner, and Allan Meltzer, who looked at whether theinterest sensitivity of money demand increased in periods when interest rates were

Interest Rates

and Money

Demand

Empirical Evidence on the Demand for Money

A problem with Tobin’s procedure is that idle balances are not really distinguishable from transactions balances.

As the Baumol-Tobin model of transactions demand for money makes clear, transactions balances will be related

to both income and interest rates, just like idle balances.

3See David E W Laidler, The Demand for Money: Theories and Evidence, 4th ed (New York: HarperCollins, 1993).

Only one major study has found that the demand for money is insensitive to interest rates: Milton Friedman,

“The Demand for Money: Some Theoretical and Empirical Results,” Journal of Political Economy 67 (1959):

327–351 He concluded that the demand for money is not sensitive to interest-rate movements, but as later work

by David Laidler (using the same data as Friedman) demonstrated, Friedman used a faulty statistical procedure that biased his results: David E W Laidler, “The Rate of Interest and the Demand for Money: Some Empirical

Evidence,” Journal of Political Economy 74 (1966): 545–555 When Laidler employed the correct statistical

pro-cedure, he found the usual result that the demand for money is sensitive to interest rates In later work, Friedman has also concluded that the demand for money is sensitive to interest rates.

1