Macroeconomics Chapter 15: The Demand for Money PDF

C HAPTER 15 The Demand for Money CHAPTER HIGHLIGHTS Money is whatever asset is used in transactions. This varies over time and place....

C HAPTER 15 The Demand for Money CHAPTER HIGHLIGHTS Money is whatever asset is used in transactions. This varies over time and place. Money demand is a demand for real balances, the number of dollars divided by the price level. The demand for money rises with higher income and falls with higher interest rates. dor75926_ch15_376-396.indd 376 03/11/10 3:24 PM  CHAPTER 15 THE DEMAND FOR MONEY 377 What is “money” and why does anyone want it? This question is less frivolous than it appears, because economists use the term “money” in a special technical sense. By “money” we mean the medium of exchange, the stuff you use to pay for things—cash, for example. In colloquial use, “money” some- times means “income” (“I made a lot of money last year”) or “wealth” (“That guy has a lot of money”). When economists speak of the “demand for money,” we are asking about the stock of assets held as cash, checking accounts, and closely related assets, specifically not generic wealth or income. Our interest is in why consumers and firms hold money as opposed to an asset with a higher rate of return. The interaction between the demand for money and the supply of money provides the link through which the monetary authority, the Federal Reserve in the United States, affects output and prices. Money is the means of payment or medium of exchange. More informally, money is whatever is generally accepted in exchange. In the past, seashells or cocoa or gold coins served as money in different places. In the United States, M1, consisting of cur- rency plus checkable deposits, comes closest to defining the means of payment. At the start of 2010, M1 was about $5,586 per person. There is lively debate concerning whether a broader group of monetary assets—M2, (discussed below and standing at about $27,731 per person)—might better meet the definition of money in a modern payments system. Which assets constitute money? Discussions of the meaning of money are fluid for a simple reason: In the past, money was the means of payment generally accepted in exchange, but it also had the characteristic that it did not pay interest. Thus, the sum of currency and demand deposits (which did not earn interest in the United States) was the accepted definition of money for a long time. This aggregate is now known as M1. In the course of the 1980s, however, a widening range of interest-bearing assets also be- came checkable. That has forced an ongoing review on where to draw the line between assets that form part of our definition of money and those that are just financial assets and not money proper. The issue is important not only conceptually but also for the evaluation of which monetary aggregate the Fed should try to control. Recall that aggregate demand rises when money supply increases faster than money demand—with a concomitant rise in output or the price level. When the demand for money rises the LM curve shifts left, reducing aggregate demand unless the monetary authority recognizes the increase in time to push up the money supply by an equal amount. Under- standing money demand, and how various factors affect that demand, is therefore a first step in setting a target for the monetary authority. And while it’s easy in setting out macro theory to simply have an asset labeled M, we’ll see in this chapter that measuring and understanding money in the complex, many-asset world in which we live is considerably more difficult. 15-1 COMPONENTS OF THE MONEY STOCK There is a vast array of financial assets in any economy, from currency to complicated claims on other financial assets. Which part of these assets is called money? In the United States, there are two main monetary aggregates: M1 and M2. Box 15-1 describes the components of the different measures of money. dor75926_ch15_376-396.indd 377 03/11/10 3:24 PM  378 PART 4 BEHAVIORAL FOUNDATIONS BOX 15-1 Components of the Monetary Aggregates We briefly describe here the components of the monetary aggregates. 1. Currency: Consists of coins and notes in circulation.* 2. Demand deposits: Non-interest-bearing checking accounts at commercial banks, excluding deposits of other banks, the government, and foreign governments. 3. Traveler’s checks: Only those checks issued by nonbanks (such as American Express). Traveler’s checks issued by banks are included in demand deposits. 4. Other checkable deposits: Interest-earning checking accounts, with a variety of legal arrangements and marketing names. M1 ⫽ (1) ⫹ (2) ⫹ (3) ⫹ (4) 5. Money market mutual fund (MMMF) shares: Interest-earning checkable deposits in mutual funds that invest in short-term assets. Some MMMF shares are held by institu- tions; these are excluded from M2. 6. Money market deposit accounts (MMDAs): MMMFs run by banks, with the advan- tage that they are insured up to $100,000. They were introduced at the end of 1982 to allow banks to compete with MMMFs. 7. Savings deposits: Deposits at banks and other thrift institutions that are not transfer- able by check and are often recorded in a separate passbook kept by the depositor. 8. Small time deposits: Interest-bearing deposits with a specific maturity date. Before that date they can be used only if a penalty is paid. “Small” means less than $100,000. M2 ⫽ M1 ⫹ (5) ⫹ (6) ⫹ (7) ⫹ (8) *A picture tour of the history of American currency can be found at www.frbsf.org/currency. Source: Federal Reserve Bulletin, which reports the data and definition in each monthly issue. M1 comprises those claims that can be used directly, instantly, and without restric- tions to make payments. These claims are liquid. An asset is liquid if it can immedi- ately, conveniently, and cheaply be used for making payments. M1 corresponds most closely to the traditional definition of money as the means of payment. M2 includes, in addition, claims that are not instantly liquid—withdrawal of time deposits, for example, may require notice to the depository institution; money market mutual funds may set a minimum on the size of checks drawn on an account.1 1 Historically, the Fed also tracked M3, which includes certain additional large, liquid accounts. M3 tracking was discontinued in March 2006, based on the Fed’s judgment that it provided no useful information once one knew M1 and M2. dor75926_ch15_376-396.indd 378 03/11/10 3:24 PM  CHAPTER 15 THE DEMAND FOR MONEY 379 As we move from the top to the bottom of the list in Box 15-1, the liquidity of the assets decreases, while their interest yield increases. Currency earns zero interest, check- ing accounts earn less than money market deposit accounts, and so on. This is a typical economic tradeoff—in order to get more liquidity, asset holders have to give up yield. M2 AND OTHER MONETARY AGGREGATES All the assets described in Box 15-1 are to some extent substitutes for one another, and there is therefore no clear point at which to draw the line in defining money. M2 adds to M1 assets that are close to being usable as a medium of exchange. The largest part of M2 consists of savings and small (less than $100,000) time deposits at banks and thrift institutions. These can be used with little difficulty for making payments. In the case of a savings deposit, the bank has to be notified to transfer funds from the savings deposit to a checking account; for time deposits, it is in principle necessary to wait until the time deposit matures or else to pay an interest penalty. The second-largest category of assets in M2 consists of money market mutual funds and deposit accounts. A money market mutual fund (MMMF) invests its assets in short-term interest-bearing securities, such as negotiable certificates of deposit (CDs) and Treasury bills.2 MMMFs pay interest and permit the owner of the account to write checks against the account. Money market deposit accounts (MMDAs) are MMMFs held in commercial banks. A limited number of checks can be written against MMDAs each month. Obviously, MMDAs and MMMFs are close to being checkable deposits— but they also serve as financial investments. Until 1987, M1 was the most closely watched money stock, both because it comes closest to the theoretical definition of money as a medium of exchange and because its demand function was reasonably stable. But after the demand for M1 became difficult to predict,3 many economists, including those at the Federal Reserve Board, began to pay more attention to the behavior of M2. Since the early 1990s, the behavior of M2 has also become unpredictable. Unpredictability of the demand for the monetary aggregates complicates the task of monetary policy, as we shall see in Chapter 16. FINANCIAL INNOVATION Changes in the definitions of the monetary aggregates followed financial innovations, frequently a result of attempts to get around government regulations. For instance, thrifts, which pay interest on deposits and had been forbidden to have checkable accounts, invented negotiable order of withdrawal (NOW) accounts as a way of getting around the prohibition. A NOW looks and smells like a check but is not, legally speaking, a check. Similarly, money market mutual funds were invented only in 1973. 2 Negotiable CDs are liabilities of the banks that can be bought and sold in the open market like other securi- ties. Typically, they come in large denominations of $100,000 or more. 3 Yoshihisa Baba, David Hendry, and Ross Starr provide a detailed investigation of the instability of M1 in “The Demand for M1 in the U.S.A., 1960–1988,” Review of Economic Studies, January 1992. dor75926_ch15_376-396.indd 379 03/11/10 3:24 PM  380 PART 4 BEHAVIORAL FOUNDATIONS Until 1982, banks were not allowed to issue money market deposit accounts, but as soon as they were permitted to do so, there was a rapid inflow of such deposits to banks: MMDA deposits rose from zero in November 1982 to $320 billion in March 1983. Clearly, there is no unique set of assets that will always constitute the money supply, nor are present definitions beyond question. For instance, there is a question of whether credit cards should be regarded as a means of making payment. And there are even argu- ments for using a less broad definition than M1—for example, should $1,000 bills, which are not easily used to buy groceries, be included? What is certain is that over the course of time, the particular assets that serve as a medium of exchange, or means of payment, will change further, and so will the definitions of the monetary aggregates. 15-2 THE FUNCTIONS OF MONEY Money is so widely used that we rarely step back to think how remarkable a device it is. It is impossible to imagine a modern economy operating without the use of money or something very much like it. In a mythical barter economy in which there is no money, every transaction has to involve an exchange of goods (and/or services) on both sides of the transaction. The examples of the difficulties of barter are endless. The economist wanting a haircut would have to find a barber wanting to listen to a lec- ture on economics; the actor wanting a suit would have to find a tailor wanting to watch a performance; and so on. Without a medium of exchange, modern economies could not operate. Money, as a medium of exchange, makes it unnecessary for there to be a “double coincidence of wants,” such as the barber and economist bumping into each other at just the right time. There are four traditional functions of money, of which medium of exchange is the first.4 The other three are store of value, unit of account, and standard of deferred pay- ment. These stand on a different footing from the medium-of-exchange function. A store of value is an asset that maintains value over time. Thus, an individual holding a store of value can use that asset to make purchases at a future date. If an asset were not a store of value, it would not be used as a medium of exchange. Imagine trying to use ice cream as money in the absence of refrigerators. There would hardly ever be a good reason for anyone to give up goods for money (ice cream) if the money were sure to melt within the next few minutes. To be useful as money, an asset must be a store of value, but there are many stores of value other than money—such as bonds, stocks, and houses. The unit of account is the unit in which prices are quoted and books kept. Prices are quoted in dollars and cents, and dollars and cents are the units in which the money stock is measured. Usually, the money unit is also the unit of account, but that is not essential. In many high-inflation countries, dollars become the unit of account even though the local money continues to serve as the medium of exchange. 4 For the classic statement of the functions of money, see W. S. Jevons, Money and the Mechanism of Exchange (London: Kegan Paul, 1875). dor75926_ch15_376-396.indd 380 03/11/10 3:24 PM  CHAPTER 15 THE DEMAND FOR MONEY 381 BOX 15-2 Who’s Got the Cash? A 1995 survey of cash holdings of U.S. households, undertaken for the Federal Reserve System, showed that the average amount of currency held per person surveyed then was about $100.* At that time, total currency outstanding divided by population was $1,375. Thus, the vast majority of the currency outstanding is not held by U.S. households—or at least they do not admit to holding it. Some currency is held by legiti- mate businesses, but large amounts must be held to finance illegal activities, particularly drug-related ones, or are held outside the United States. In many countries undergoing severe financial distress, U.S. currency circulates in preference to local currency. Since 1990, there has been a dramatic upswing in the proportion of U.S. currency held outside the United States. Richard Porter and Ruth Judson estimated that over $8 billion per year in currency was flowing abroad in 1995. More recent estimates show that even more currency is now held abroad. As Figure 1 shows, about half of U.S. currency is held outside the United States. 50% 45 40 35 30 25 20 15 10 5 0 1965 1970 1975 1980 1985 1990 1995 2000 FIGURE 1 RATIO OF U.S. CURRENCY HELD ABROAD TO TOTAL U.S. CURRENCY IN CIRCULATION. (Source: Richard G. Anderson, “Some Tables of Historical U.S. Currency and Monetary, Aggregates Data,” Working Paper 2003-006A, Federal Reserve Bank of St. Louis, April 2003.) *Richard D. Porter and Ruth A. Judson, “The Location of U.S. Currency: How Much Is Abroad?” Federal Reserve Bulletin, October 1996. dor75926_ch15_376-396.indd 381 03/11/10 3:24 PM  382 PART 4 BEHAVIORAL FOUNDATIONS Finally, as a standard of deferred payment, money units are used in long-term transactions, such as loans. The amount that has to be paid back in 5 or 10 years is specified in dollars and cents. Dollars and cents are acting as the standard of deferred pay- ment. Once again, though, it is not essential that the standard of deferred payment be the money unit. For example, the final payment of a loan may be related to the behavior of the price level, rather than being fixed in dollars and cents. This is known as an indexed loan. The last two of the four functions of money are, accordingly, functions that money usually performs but not functions that it necessarily performs. And the store-of-value function is one that many assets perform. There is one final point we want to reemphasize: Money is whatever is generally accepted in exchange. In the past an astounding variety of monies have been used: simple commodities such as seashells, then metals, pieces of paper representing claims on gold or silver, pieces of paper that are claims only on other pieces of paper, and then paper and electronic entries in banks’ accounts.5 However magnificently a piece of paper may be engraved, it is not money if it is not accepted in payment. And however unusual the mate- rial of which it is made, anything that is generally accepted in payment is money. There is thus an inherent circularity in the acceptance of money. Money is accepted in payment only because of the belief that it will later also be accepted in payment by others. 15-3 THE DEMAND FOR MONEY: THEORY In this section we review the three major motives underlying the demand for money, and we concentrate on the effects of changes in income and the interest rate on money de- mand. Before we take up the discussion, we must make an essential point about money demand: The demand for money is a demand for real balances. In other words, peo- ple hold money for its purchasing power, for the amount of goods they can buy with it. They are not concerned with their nominal money holdings, that is, the number of dollar bills they hold. Two implications follow: 1. Real money demand is unchanged when the price level increases, and all real vari- ables, such as the interest rate, real income, and real wealth, remain unchanged. 2. Equivalently, nominal money demand increases in proportion to the increase in the price level, given the real variables just specified. In other words, we are interested in a money demand function that tells us the de- mand for real balances, M兾P, not nominal balances, M. There is a special name for the behavior described here. An individual is free from money illusion if a change in the level of prices, holding all real variables constant, leaves the person’s real behavior, including real money demand, unchanged.6 5 See Glyn Davies, A History of Money from Ancient Times to the Present (Aberystwyth: University of Wales Press, 1994). 6 Mixing economics and psychology, Eldar Shafir, Peter Diamond, and Amos Tversky describe fun experi- ments about money illusion in “Money Illusion,” Quarterly Journal of Economics, May 1997. dor75926_ch15_376-396.indd 382 03/11/10 3:24 PM  CHAPTER 15 THE DEMAND FOR MONEY 383 The theories we are about to review correspond to Keynes’s famous three motives for holding money:7 The transactions motive, which is the demand for money arising from the use of money in making regular payments. The precautionary motive, which is the demand for money to meet unforeseen con- tingencies. The speculative motive, which arises from uncertainties about the money value of other assets that an individual can hold. In discussing the transactions and precautionary motives, we are mainly discussing M1, whereas the speculative motive refers more to M2 as well as nonmoney assets, as we shall see.8 These theories of money demand are built around a tradeoff between the bene- fits of holding more money versus the interest costs of doing so. Money (M1, that is, currency and some checkable deposits) generally earns no interest or less interest than other assets. The higher the interest loss from holding a dollar of money, the less money we expect the individual to hold. In practice, we can measure the cost of holding money as the difference between the interest rate paid on money (perhaps zero) and the interest rate paid on the most nearly comparable other asset, such as a savings deposit or, for corporations, a certificate of deposit or commercial paper. The interest rate on money is referred to as the own rate of interest, and the opportunity cost of holding money is equal to the difference between the yield on other assets and the own rate. TRANSACTIONS DEMAND The transactions demand for money arises from the lack of synchronization of receipts and disbursements. In other words, you aren’t likely to get paid at the exact instant you need to make a payment, so between paychecks you keep some money around in order to buy stuff. In this section we examine a simple model of how much money an indi- vidual will hold to make purchases. The tradeoff here is between the amount of interest an individual forgoes by holding money and the costs and inconveniences of holding a small amount of money. To make the problem concrete, consider someone who is paid, say, $1,800 each month. Assume the person spends the $1,800 evenly over the course of the month, at the rate of $60 per day. Now at one extreme, the individual could simply leave the $1,800 in cash and spend it at the rate of $60 per day. Alternatively, on the first day of the month the individual could take $60 to spend that day and put the remaining $1,740 in a daily-interest savings 7 J. M. Keynes, The General Theory of Employment, Interest and Money (New York: Macmillan, 1936), Chap. 13. 8 Although we examine the demand for money by looking at the three motives for holding it, we cannot sepa- rate a particular person’s money holdings, say, $500, into three neat piles of, say, $200, $200, and $100, each being held for a different motive. Money being held to satisfy one motive is always available for another use. The person holding unusually large balances for speculative reasons also has those balances available to meet an unexpected emergency, so they serve, too, as precautionary balances. All three motives influence an indi- vidual’s holdings of money. dor75926_ch15_376-396.indd 383 03/11/10 3:24 PM  384 PART 4 BEHAVIORAL FOUNDATIONS BOX 15-3 A Back-of-the-Envelope Calculation Using Income Elasticity You are now the monetary authority of the small country of Baumol - Tobania. Real growth reliably averages 3 percent per year. How fast should you increase the money supply to stabilize the price level? According to equation (1), 3 percent growth in GDP raises money demand 1.5 percent per year. If you increase the nominal money supply by the same 1.5 percent, real money supply and demand will stay in balance with a constant price level. If you had thought the income elasticity was 1 instead of 1兾2 you would have created money at 3 percent per year, in the erroneous belief that money demand was rising 3 percent per year, leading to a small but steady inflation. account. Then every morning the person could go to the bank and withdraw that day’s $60 from the savings account. By the end of the month the depositor would have earned interest on the money retained each day in the savings account. That would be the benefit of keeping the money holdings down as low as $60 at the beginning of each day. The cost of keeping money holdings down is simply the cost and inconvenience of the trips to the bank to withdraw the daily $60. The greater the number of trips to the bank, the larger the amount earning interest in the savings account. With one trip—everything taken as cash on the first day—no interest is earned. The cash balance falls smoothly from $1,800 on the first day to $0 at the end of the month for an average balance of ($1,800 ⫺ $0)兾2 ⫽ $900, forgoing inter- est of i ⫻ $900. For two trips, the cash balance falls from $1,800兾2 to zero at midmonth and then repeats, for an average cash balance of ($1,800兾2 ⫺ $0)兾2 ⫽ $450. We show in the appendix to this chapter that this generalizes so that starting with income Y, if n trips are made, the average cash balance is Y兾2n. If each trip costs tc, the combined cost of trips plus forgone interest is (n ⫻ tc) ⫹ i ⫻ (Y/2n). Choosing n to minimize costs and computing the implied average money holdings leads to the famous square-root Baumol-Tobin formula for the demand for money:9 _ tc ⫻ Y ⫽ _ M  P √ 2i (1) 9 The theory has quite general applicability for determining optimal inventories of goods as well as money. This inventory-theoretical approach to the demand for money is associated with the names of William Baumol and James Tobin: William Baumol, “The Transactions Demand for Cash: An Inventory Theoretic Approach,” Quarterly Journal of Economics, November 1952; James Tobin, “The Interest Elasticity of Transactions Demand for Cash,” Review of Economics and Statistics, August 1956. dor75926_ch15_376-396.indd 384 03/11/10 3:24 PM  CHAPTER 15 THE DEMAND FOR MONEY 385 Equation (1) shows that the demand for money decreases with the interest rate and increases with the cost of transacting. Money demand increases with income, but less than proportionately. This point is sometimes put in different words by saying that there are economies of scale in cash management. Equation (1) makes two very strong predictions: The income elasticity of money demand is 1⁄2, and the interest elasticity is ⫺1⁄2.10 Empirical evidence supports the signs of these predictions but suggests that the income elasticity is somewhat closer to 1 and that the interest elasticity is somewhat closer to zero. THE PRECAUTIONARY MOTIVE In discussing the transactions demand for money, we focused on transactions costs and ignored uncertainty. In this section, we concentrate on the demand for money that arises because people are uncertain about the payments they might want, or have, to make.11 Realistically, an individual does not know precisely what payments she will be receiving in the next few weeks and what payments will have to be made. The person might decide to have a hot fudge sundae, or need to take a cab in the rain, or have to pay for a prescrip- tion. If the person does not have money with which to pay, she will incur a loss. The more money an individual holds, the less likely he or she is to incur the costs of illiquidity (that is, not having money immediately available). But the more money the person holds, the more interest he or she is giving up. We are back to a tradeoff similar to that examined in relation to the transactions demand. The added consideration is that greater uncertainty about receipts and expenditures increases the demand for money. Technology and the structure of the financial system are important determinants of precautionary demand. In times of danger, families may keep hidden hordes of cash in case they need to flee. In contrast, in much of the developed world credit cards, debit cards, and smart cards reduce precautionary demand. THE SPECULATIVE DEMAND FOR MONEY The transactions demand and the precautionary demand for money emphasize the medium-of-exchange function of money, for each refers to the need to have money on hand to make payments. Each theory is most relevant to the M1 definition of money, though the precautionary demand could certainly explain some of the holding of sav- ings accounts and other relatively liquid assets that are part of M2. Now we move over to the store-of-value function of money and concentrate on the role of money in the in- vestment portfolio of an individual. 10 Meaning that if income rises 1 percent, money demand should rise 1兾2 of 1 percent, and so forth. Be careful about the definition of percentage change with interest rates. If the interest rate goes from 10 percent per year to 10.5 percent per year, it has gone up by 5 percent of its original level, so money demand should drop by 2.5 percent. 11 See Edward H. Whalen, “A Rationalization of the Precautionary Demand for Cash,” Quarterly Journal of Economics, May 1966. dor75926_ch15_376-396.indd 385 03/11/10 3:24 PM  386 PART 4 BEHAVIORAL FOUNDATIONS An individual who has wealth has to hold that wealth in specific assets. Those assets make up a portfolio. One would think an investor would want to hold the asset that provides the highest returns. However, given that the return on most assets is uncertain, it is unwise to hold the entire portfolio in a single risky asset. You may have a hot tip that a certain stock will surely double within the next two years, but you would be wise to recognize that hot tips are far from infallible. The typical inves- tor will want to hold some amount of a safe asset as insurance against capital losses on assets whose prices change in an uncertain manner. Money is a safe asset in that its nominal value is known with certainty.12 In a famous article, James Tobin argued that money would be held as the safe asset in the portfolios of investors.13 The title of the article, “Liquidity Preference as Behavior towards Risk,” explains the essential notion. In this framework, the demand for money—the safest asset—depends on the expected yields as well as on the riskiness of the yields on other assets. Tobin showed that an increase in the expected return on other assets—an increase in the opportunity cost of holding money (that is, the return lost by holding money)—lowers money demand. By contrast, an increase in the riskiness of the returns on other assets increases money demand. An investor’s aversion to risk certainly generates a demand for a safe asset. How- ever, that asset is not likely to be M1. From the viewpoint of the yield and risks of hold- ing money, it is clear that time or savings deposits or MMDAs have the same risks as currency or checkable deposits. However, the former generally pay a higher yield. Given that the risks are the same, and with the yields on time and savings deposits higher than those on currency and demand deposits, portfolio diversification explains the demand for assets such as time and savings deposits, which are part of M2, better than the demand for M1. 15-4 EMPIRICAL EVIDENCE This section examines the empirical evidence—the studies made using actual data—on the demand for money. We know from Chapter 11 that the interest elasticity of the de- mand for money plays an important role in determining the effectiveness of monetary and fiscal policies. We showed in Section 15-3 that there are good theoretical reasons for believing that the demand for real balances should depend on the interest rate. The empirical evidence supports that view. Empirical studies have established that the demand for money is negatively related to the interest rate. 12 Of course, when the rate of inflation is uncertain, the real value of money is also uncertain, and money is no longer a safe asset. Even so, the uncertainties about the values of equity are so much larger than the uncertain- ties about the rate of inflation that money can be treated as a relatively safe asset (countries at risk of hyperin- flation excepted). 13 James Tobin, “Liquidity Preference as Behavior towards Risk,” Review of Economic Studies, February 1958. dor75926_ch15_376-396.indd 386 03/11/10 3:24 PM  CHAPTER 15 THE DEMAND FOR MONEY 387 The theory of money demand also predicts that the demand for money should de- pend on the level of income. The response of the demand for money to the level of in- come, as measured by the income elasticity of money demand, is also important from a policy viewpoint. As we shall see below, the income elasticity of money demand pro- vides a guide for the Fed as to how fast to increase the money supply in order to support a given rate of GDP growth without changing the interest rate. LAGGED ADJUSTMENT The empirical work on the demand for money has introduced one complication that we did not study in the theoretical section—that the demand for money adjusts to changes in income and interest rates with a lag. When the level of income or the interest rate changes, there is first only a small change in the demand for money. Then, over the course of time, the change in the demand for money increases, slowly building up to its full long-run change. There are two basic reasons for these lags. First, there are costs of adjusting money holdings; second, money holders’ expectations are slow to adjust. The costs of adjust- ment include the costs of figuring out the new best way to manage money and the cost of opening up a new type of account if that is needed. On the expectations side, if peo- ple believe that a given change in the interest rate is temporary, they may be unwilling to make a major change in their money holdings. As time passes and it becomes clearer that the change is not transitory, they are willing to make a larger adjustment. EMPIRICAL RESULTS FOR M1 DEMAND Estimates of the response of M1 demand to income and interest rate changes are reported in Table 15-1.14 In the short run (one quarter), the elasticity of demand with respect to real income is.11. This means that a 1 percent increase in real income raises money demand by.11 percent, which is considerably less than proportionately. The table shows that an increase in interest rates reduces money demand. The short-run interest responses are quite small. A 1 percentage point increase in the Treasury bill rate reduces the demand for money by only.8 percent. The long-run responses exceed the short-run responses by a factor of 5, as Table 15-1 shows. The long-run real income elasticity is.53, meaning that in the long run the increase in real money demand occurring as a result of a given increase in real income is only.53 percent as large as the proportional increase in income. Real money demand thus rises less than proportionately to the rise in real income. A 1 percentage point increase in the Treasury bill rate reduces money demand by 4 percent in the long run. 14 Laurence Ball, “Short-Run Money Demand,” NBER working paper no. W9235, October 2002. For a sum- mary of earlier work on money demand, see Stephen Goldfeld and Daniel Sichel, “The Demand for Money,” in B. M. Friedman and F. H. Hahn (eds.), Handbook of Monetary Economics, vol. 1 (Amsterdam: North- Holland, 1990), Chap. 8. dor75926_ch15_376-396.indd 387 03/11/10 3:24 PM  388 PART 4 BEHAVIORAL FOUNDATIONS TABLE 15-1 Response of Real M1 Money Demand INCOME ELASTICITY INTEREST RATE SEMI-ELASTICITY Short run.109 −.008 Long run.532 −.040 Source: Laurence Ball, “Short-Run Money Demand,” NBER working paper no. W9235, October 2002; and authors’ calculations. Empirical work thus establishes four essential properties of money demand: The demand for real money balances responds negatively to the rate of interest. An increase in interest rates reduces the demand for money. The demand for money increases with the level of real income. The short-run responsiveness of money demand to changes in interest rates and income is considerably less than the long-run response. The long-run responses are estimated to be about 5 times the size of the short-run responses. The demand for nominal money balances is proportional to the price level. There is no money illusion; in other words, the demand for money is a demand for real balances. In the past, the demand for real money balances was considered one of the best understood and most highly stable equations in the U.S. macroeconomy, and indeed in other countries too. Since then, M1 demand has been shifting and has not yet settled down to the extent that there is agreement on the empirically correct form of the money demand function. However, there is general agreement on the fact that money demand is affected primarily by income and interest rates. M2 MONEY DEMAND Innovation in the financial system has made it easier to move back and forth between M1 and other assets. For example, automatic teller machines typically allow cash with- drawals from savings accounts. We would say that savings accounts are now better sub- stitutes for M1 than they were in the past. When money flows between savings accounts and cash, as an example, M1 changes but M2 does not. For this reason, financial innova- tion has made the demand for M2 more stable than the demand for M1.15 We would expect real money demand to depend negatively on the opportunity cost of holding M2, the difference between a market interest rate, such as the Treasury bill rate, and a weighted average of the interest rates paid on various kinds of deposits con- stituting M2. We also expect real M2 money demand to depend positively on the level of income. 15 See Robert Hetzel and Yash Mehra, “The Behavior of Money Demand in the 1980s,” Journal of Money, Credit and Banking, November 1989; and R. W. Hafer and Dennis Jansen, “The Demand for Money in the United States: Evidence from Cointegration Tests,” Journal of Money, Credit and Banking, May 1991. dor75926_ch15_376-396.indd 388 03/11/10 3:24 PM  CHAPTER 15 THE DEMAND FOR MONEY 389 BOX 15-4 Money Demand and High Inflation The demand for real balances depends on the alternative cost of holding money. That cost is normally measured by the yield on alternative assets, say, Treasury bills, commer- cial paper, or money market funds. But there is another margin of substitution. Rather than holding their wealth in financial assets, households or firms can also hold real assets: stocks of food or houses or machinery. This margin of substitution is particularly important in countries in which inflation is very high and capital markets do not function well. In that case it is quite possible that the return on holding goods can even be higher than that on financial assets. Consider a household deciding whether to hold $100 in currency or a demand deposit or to hold its wealth in the form of groceries on the shelf. The advantage of hold- ing groceries is that, unlike money, they maintain their real value. Rather than having the purchasing power of money balances eroded by inflation, the household gets rid of money, buying goods and thus avoiding a loss. This flight out of money occurs systematically when inflation rates become high. In a famous study of hyperinflations (defined in the study as inflation rates of more than 50 percent per month), Phillip Cagan of Columbia University found large changes in real balances taking place as inflation increased.* In the most famous hyperinflation, that in Germany in 1922–1923, the quantity of real balances at the height of the hyperinflation had fallen to 1兾20th of its preinflation level. The increased cost of holding money leads to a reduction in real money demand and, with it, to changes in the public’s payment habits as everybody tries to pass money on like a hot potato. In well-developed capital markets, interest rates will reflect expectations of infla- tion, and hence it will not make much difference whether we measure the alternative cost of holding money by interest rates or inflation rates. But when capital markets are not free because interest rates are regulated or have ceilings, it is often appropriate to use inflation, not interest, rates as the measure of the alternative cost. Franco Modigliani has offered the following rule of thumb: The right measure of the opportunity cost of holding money is the higher of the two, interest rates or inflation. *Phillip Cagan, “The Monetary Dynamics of Hyperinflation,” in Milton Friedman (ed.), Studies in the Quantity Theory of Money (Chicago: University of Chicago Press, 1956). These hypotheses are, indeed, confirmed by the empirical evidence. An estimate with quarterly data for the period 1953–1991 yields the elasticities shown in Table 15-2. The table confirms that the elasticity with respect to the opportunity cost is negative. The short-run elasticities are smaller than the long-run elasticities. The long-run income elasticity of M2 is clearly positive and is approximately equal to unity. This implies that, other things equal, the ratio of real balances, measured by M2, to real GNP will remain constant over time. dor75926_ch15_376-396.indd 389 03/11/10 3:24 PM  390 PART 4 BEHAVIORAL FOUNDATIONS TABLE 15-2 Elasticities of Real M2 Money Demand, 1953–1991 INCOME OPPORTUNITY COST* Short run.39 −.017 Long run.98 −.08 *Six-month commercial paper rate less own rate on M2. Source: Yash P. Mehra, “The Stability of the M2 Demand Function: Evidence from an Error-Correction Model,” Journal of Money, Credit, and Banking, August 1993. 15-5 THE INCOME VELOCITY OF MONEY The income velocity of money is the number of times the stock of money is turned over per year in financing the annual flow of income. It is equal to the ratio of nominal GDP to the nominal money stock. Thus, in 2009 GDP was about $14,256 billion, the M2 money stock averaged $8,424 billion, and M2 velocity was there- fore about 1.7. The average dollar of M2 money balances financed $1.70 of spending on final goods and services, or the public held an average of 59 cents of M2 per dollar of income. Income velocity (from now on, we shall refer to “velocity” rather than “income velocity”)16 is defined as P⫻Y _ _ Y V⬅ ⫽ (2) M M兾P that is, the ratio of nominal income to the nominal money stock or, equivalently, the ratio of real income to real balances. The concept of velocity is important largely because it is a convenient way of talking about money demand. Let the demand for real balances be written M兾P ⫽ L(i, Y ). Substi- tuting into equation (2), velocity can be rewritten as V ⫽ Y兾L(i, Y ). This is especially convenient if money demand is proportional to income, as is roughly true for long-run M2 demand, so money demand can be written as L(i, Y ) ⫽ Y ⫻ l(i). In this case equation (2) is simply V ⫽ 1兾l(i), so velocity is a quick way to summarize the effect of interest rates on money demand—remembering that high velocity means low money demand.17 Figure 15-1 shows M2 velocity (left scale) and the Treasury bill interest rate (right scale). M2 velocity is relatively stable—the left-hand scale is only between 1.5 and 2.2 16 Why do we say “income velocity” and not plain “velocity”? There is another concept, transactions velocity, which is the ratio of total transactions to money balances. Total transactions far exceed GDP for two reasons. First, many transactions involving the sale and purchase of assets do not contribute to GDP. Second, a particu- lar item in final output typically generates total spending on it that exceeds the contribution of that item to GDP. For instance, a dollar’s worth of wheat generates transactions as it leaves the farm, as it is sold by the miller, and so forth. Transactions velocity is thus higher than income velocity. 17 In fact, while academic economists use velocity and money demand more or less interchangeably, Wall Street tends to focus directly on velocity. dor75926_ch15_376-396.indd 390 03/11/10 3:24 PM  CHAPTER 15 THE DEMAND FOR MONEY 391 2.2 20 Velocity of money 2.1 T-bill rate 15 2.0 T-bill rate 1.9 Velocity of money 10 1.8 1.7 5 1.6 1.5 0 1959 1964 1969 1974 1979 1984 1989 1994 1999 2004 2009 FIGURE 15-1 VELOCITY OF MONEY (LEFT SCALE) AND TREASURY BILL RATES (RIGHT SCALE). (Source: Federal Reserve Economic Data [FRED II ].) over a 50-year period—and velocity has a strong tendency to rise and fall with market interest rates. Figure 15-1 also shows that in the last decade M2 velocity has become much less stable than in the past. When the monetary aggregates all become relatively unstable, the monetary authority should use the interest rate rather than the money supply as the direct operating target. In the next chapter we’ll see why this is so. THE QUANTITY THEORY The quantity theory of money, which we met in Chapter 5, provides a very simple way to organize thinking about the relation between money, prices, and output: M⫻V⫽P⫻Y (3) Equation (3) is the famous quantity equation, linking the price level and the level of output to the money stock. The quantity equation became the classical quantity theory of money when it was argued that both V, the income velocity of money, and Y, the level of output, were fixed. Real output was taken to be fixed because the economy was at full employment, and velocity was assumed not to change much. Neither of these assumptions holds in fact, but it is, nonetheless, interesting to see where they lead. If both V and Y are fixed, it follows that the price level is proportional to the money stock. Thus, the classical quantity theory was a theory of inflation. The classical quantity theory is the proposition that the price level is propor- tional to the money stock: V⫻M P⫽_ (3a) Y If V is constant, changes in the money supply translate into proportional changes in nominal GDP, P ⫻ Y. When the classical case (vertical) supply function examined in dor75926_ch15_376-396.indd 391 03/11/10 3:24 PM  392 PART 4 BEHAVIORAL FOUNDATIONS Chapter 5 applies, Y is fixed and changes in money translate into changes in the overall price level, P. SUMMARY 1. The demand for money is a demand for real balances. It is the purchasing power, not the number of dollar bills, that matters to holders of money. 2. The money supply, M1, is made up of currency and checkable deposits. A broader measure, M2, also includes savings and time deposits at depository institutions as well as some other interest-bearing assets. 3. The chief characteristic of money is that it serves as a means of payment. The three classic reasons to hold money are for transactions purposes (M1) and for precau- tionary (M1 and M2) and speculative reasons (M2). 4. Decisions to hold money are based on a tradeoff between the liquidity of money and the opportunity cost of holding it when other assets have a higher yield. 5. The inventory-theoretic approach shows that an individual will hold a stock of real balances that varies inversely with the interest rate but increases with the level of real income and the cost of transactions. According to the inventory approach, the income elasticity of money demand is less than unity, implying that there are economies of scale. 6. Uncertainty about payments and receipts in combination with transactions costs gives rise to a precautionary demand for money. Precautionary money holdings are higher the greater the variability of net disbursements, the higher the cost of illiquidity, and the lower the interest rate. 7. Some assets that are in M2 form part of an optimal portfolio because they are less risky than other assets—their nominal value is constant. Because they earn inter- est, assets such as savings or time deposits and MMMF shares dominate currency and demand deposits for portfolio diversification purposes. 8. The empirical evidence provides support for a negative interest elasticity of money demand and a positive income elasticity. Because of lags, short-run elasticities are much smaller than long-run elasticities. 9. The demand function for M1 started showing instability in the mid-1970s. The demand function for M2 appears to be somewhat more stable, showing a unit in- come elasticity, a positive elasticity with respect to the own rate, and a negative elasticity with respect to the commercial paper rate. 10. The income velocity of money is defined as the ratio of income to money or the rate of turnover of money. The behavior of velocity is closely tied to the demand for money, so an increase in the opportunity cost of holding money leads to an increase in velocity. 11. The velocity of M2 was roughly constant for many years. The constancy is a reflec- tion of small changes in the opportunity cost of holding money and of a unit income elasticity of demand for M2. In recent years, M2 velocity has varied considerably. 12. Inflation implies that money loses purchasing power, and inflation thus creates a cost of holding money. The higher the rate of inflation, the lower the amount of real balances that will be held. Hyperinflations provide striking support for this dor75926_ch15_376-396.indd 392 03/11/10 3:24 PM  CHAPTER 15 THE DEMAND FOR MONEY 393 prediction. Under conditions of very high expected inflation, money demand falls dramatically relative to income. Velocity rises as people use less money in relation to income. KEY TERMS classical quantity theory medium of exchange quantity theory of money flight out of money money real balances income elasticity money illusion risky asset income velocity of money opportunity cost speculative motive interest elasticity own rate of interest standard of deferred payment liquid (assets) portfolio store of value M1 precautionary motive transactions motive M2 quantity equation unit of account PROBLEMS Conceptual 1. What is money, and why does anyone want it? 2. To what extent would it be possible to design a society in which there was no money? What would the problems be? Could currency at least be eliminated? How? (Lest all this seem too unworldly, you should know that some people are beginning to talk of a “cashless economy” in this century.) 3. Do you think credit card credit limits should be counted in the money stock? Why or why not? 4. Discuss the various factors that go into an individual’s decision regarding how many traveler’s checks to take on a vacation. 5. Explain the concept of the opportunity cost of holding money. 6. The demand for nominal balances rises with the price level. At the same time, inflation causes the real demand to fall. Explain how these two assertions can both be correct. 7. “Muggers favor deflation.” Comment. Technical 1. Evaluate the effects of the following changes on the demand for M1 and M2. Which of the functions of money do they relate to? a. “Instant-cash” machines that allow 24-hour withdrawals from savings accounts at banks. b. The employment of more tellers at your bank. c. An increase in inflationary expectations. d. Widespread acceptance of credit cards. e. Fear of an imminent collapse of the government. f. A rise in the interest rate on time deposits. g. The rise of e-commerce. 2. a. Is velocity high or low relative to trend during recessions? Why? b. How can the Fed influence velocity? dor75926_ch15_376-396.indd 393 03/11/10 3:24 PM  394 PART 4 BEHAVIORAL FOUNDATIONS The next two questions are related to the material in the appendix. 3.* The transactions demand-for-money model can also be applied to firms. Suppose a firm sells steadily during the month and has to pay its workers at the end of the month. Explain how the firm would determine its money holdings. 4.* a. Determine the optimal strategy for cash management for a person who earns $1,600 per month, can earn.5 percent interest per month in a savings account, and has a transaction cost of $1. (Hint: Integer constraints matter here.) b. What is the individual’s average cash balance? c. Suppose income rises to $1,800. By what percentage does the individual’s demand for money change? Empirical 1. The chapter reviewed the different measures of money stock (M1 and M2). You can use any of these money stock measures in order to determine the velocity of money. What is the rela- tionship between M1 velocity and M2 velocity? Which is the largest and which is the small- est? Go to http://research.stlouisfed.org/fred2. Download data for M1 and M2 stock by clicking on “Monetary Aggregates.” Then, download GDP data (click on “Gross Domestic Product (GDP) and Components”). Divide the GDP series by the M1 (or M2) series, since velocity of M1 (or M2) is simply GDP divided by M1 (or M2) stock. Then, take a look at these two alternative velocity measures in order to confirm the answer you got for the previ- ous question. 2. Is there today in real terms more U.S. currency outstanding per capita than 30 years ago? To an- swer this question, go to http://research.stlouisfed.org/fred2 and get the data in order to fill in the first three columns of the table. To get the currency data, click on “Monetary Aggregates,” then on “M1 and Components,” and on “CURRNS.” Population can be found under “Employment and Population” and CPI data can be found under “Consumer Price Indexes (CPI).” CURRENCY U.S. POPULATION CPI (1982− PER CAPITA REAL ($ BILLION) (THOUSANDS) 84 ⫽ 100) CURRENCY April 1980 April 2010 ◆OPTIONAL◆ APPENDIX: THE BAUMOL-TOBIN TRANSACTIONS DEMAND MODEL The assumptions of the Baumol-Tobin transactions demand model are set out in the text and summarized here. An individual receives a payment, Y, at the beginning of each month and spends it at an even pace during the month. He or she can earn interest at the rate i per month by holding money in a savings account (equivalently, bonds). There is a cost of tc per transaction for moving between bonds and money. We denote by n the number of transactions per month between bonds and money, and we assume, *An asterisk denotes a more difficult problem. dor75926_ch15_376-396.indd 394 03/11/10 3:24 PM  CHAPTER 15 THE DEMAND FOR MONEY 395 Z = Yn Money holding Z = Yn /2 1/2 1 0 1/2 1 0 Time Time (a) (b) FIGURE 15A-1 AMOUNT OF CASH HELD BY THE PUBLIC RELATED TO NUMBER OF TRANSACTIONS. for convenience, that monthly income is paid into the savings account or paid in the form of bonds. The individual minimizes the cost of money management during the month. Those costs consist of the transactions cost, (n ⫻ tc), plus the interest forgone by holding money instead of bonds during the month. The interest cost is (i ⫻ M), where M is the average holdings of money during the month. M, the average holdings of money, depends on n, the number of transactions. Sup- pose that each time the individual makes a transaction, she transfers amount Z from bonds into money.18 If the individual makes n equal-size withdrawals during the month, the size of each transfer is Y兾2n, since a total of Y has to be transferred. Thus, nZ ⫽ Y (A1) Now, how is the average cash balance related to n? Figure 15A-1 helps answer the question. In Figure 15A-1a (n ⫽ 1), the average cash balance held during the month is Y兾2 ⫽ Z兾2, since the cash balance starts at Y and runs down in a straight line to zero.19 In the case of Figure 15A-1b (n ⫽ 2), the average cash balance for the first half of the month is Y兾4 ⫽ Z兾2, and the average cash balance for the second half of the month is also Z兾2. Thus, the average cash balance for the entire month is Y兾4 = Z兾2. In general, the average cash balance is Z兾2, as you might want to confirm by drawing diagrams similar to Figure 15A-1 for n ⫽ 3 or other values of n. Using equation (A1), it follows that the average cash balance is Y兾2n. 18 With simple interest being paid on the savings account, the individual’s transactions between bonds and cash should be evenly spaced over the month. 19 The average cash balance is the average of the amount of cash the individual holds at each moment during the month. For instance, if the balance held is $400 for three days and zero for the rest of the month, the aver- age cash balance would be $40, or 1兾10th (3 days ⫼ 30 days) of the month times $400. dor75926_ch15_376-396.indd 395 03/11/10 3:24 PM  396 PART 4 BEHAVIORAL FOUNDATIONS The total cost of cash management is, accordingly, Total cost ⫽ (n ⫻ tc) ⫹ _ iY (A2) 2n The optimum number of transactions is found by minimizing total cost with respect to n.20 That implies n* ⫽ √ _ iY 2tc (A3) where n* is the optimal number of transactions. As we should expect, the individual makes more transactions the higher the interest rate, the higher the income, and the lower the transactions cost. The Baumol-Tobin result, equation (1) in the text, is obtained using equation (A3) and the fact that M兾P = Y兾2n. In addition to deriving the square-root formula, we want also to show why, for many people, it is optimal to make only one transaction between bonds and money. Consider the example in the text of an individual who receives $1,800 per month. Sup- pose that the interest rate on deposits is as high as.5 percent per month. The individual cannot avoid making one initial transaction, since income is paid into the savings ac- count to start with. Does it pay to make a second transaction? For n ⫽ 2, the average cash balance is $1,800兾2n ⫽ $450, so interest earned would be (.005 ⫻ $450) ⫽ $2.25. If the transaction cost exceeds $2.25, the individual will not bother to make more than one transaction. And $2.25 is not an outrageous cost in terms of the time and nui- sance of making a transfer between bonds (or a savings account) and money. For anyone making only one transaction, the average cash balance is half his or her income. That means the interest elasticity of money demand for that person is zero—up to the point that the interest rate becomes high enough to make a second transaction worthwhile. And the income elasticity is 1, up to the point that income rises high enough to make a second transaction worthwhile. Since for some people the income elasticity is 1 and for others the Baumol-Tobin formula is closer to applying, we expect the in- come elasticity to be between 1⁄2 and 1; similarly, since for some the interest elasticity is zero while for others it is closer to ⫺1⁄2, we expect the interest elasticity to be between ⫺1⁄2 and zero. 20 If you can handle calculus, derive equation (A3) by minimizing the total cost with respect to n in equation (A2). dor75926_ch15_376-396.indd 396 03/11/10 3:24 PM