CHAPTER 16

THE DEMAND FOR MONEY

Chapter Outline

  • The Components of the Money Stock
  • Financial Innovation
  • The Functions of Money
  • The Demand for Money: Theory
  • Transactions Demand
  • The Precautionary Motive
  • The Speculative Demand for Money
  • Empirical Results for M2 Demand
  • The Income Velocity of Money
  • Working With Data

Changes from the Previous Edition

The material in this chapter has been updated, but the basic organization has not changed.

Learning Objectives

  • Students should be able to identify the different functions of money.
  • Students should be familiar with the concept of money illusion.
  • Students should be able to identify the different monetary aggregates, especially M1 and M2, and they should know the approximate current values for M1, M2, V1, and V2.
  • Students should be able to identify some of the possible explanations for the increased instability of money demand the income velocity of money.
  • Students should be able to distinguish between the three different motives for holding money balances (transaction, precaution, and speculation).
  • Students should understand why the demand for money decreases with an increase in the interest rate and increases with an increase in income.
  • Students should know the implications of the square-root formula that is derived from the Baumol-Tobin transactions demand model.
  • Students should be aware that holding money has an opportunity cost.
  • Students should know that portfolio diversification involves a tradeoff between risk and expected return and that money is held because it is the asset with the lowest risk.

Accomplishing the Objectives

It is impossible to imagine a modern economy functioning without the use of money as a means of payments. Money is defined as anything that is generally accepted in transactions. Its four basic functions are:

  • a medium of exchange
  • a store of value
  • a unit of account
  • a standard of deferred payment.

It is the first function of money that deserves most of our attention. The assets that are included in M1 are used most often for transaction purposes, since they can be used almost instantly and without restrictions in third party payments. The assets that are not included in M1 but are part of M2 or M3 tend to serve more as a store of value. However, financial innovations have blurred the distinctions between the different components of the monetary aggregates to some degree. Technology and the structure of the financial system are constantly changing, affecting the way in which money is held. Some assets included in M2 can now almost be considered a medium of exchange.

Financial markets are forever changing and banks respond by changing the nature of their assets and liabilities. It has become more difficult to assess which bank liabilities constitute what component of money and less clear which definition of money is most useful for policy purposes. M1 used to be the prime monetary aggregate, not only because it came closest to the definition of money as medium of exchange but also because its demand function was reasonably stable. However, as the assets included in M1 and M2 became much closer substitutes for one another, the demand for M1 became much more difficult to predict. As a result, the focus shifted from the more narrowly defined M1 to the broader M2 as a guide for monetary policy. However, over the last few years M2 also has become less predictable and other aggregates have not fared much better, creating difficulties for the Bank of Canada in conducting its monetary policy on the basis of money supply control.

The demand for M1 was fairly stable until 1973, but has shifted several times since. The demand for M2, on the other hand, has displayed a fairly stable long-run trend throughout most of the last three decades, until quite recently. But just as the Bank of Canada began to place more emphasis on M2, the demand for M2 also became somewhat less stable. A truly satisfying explanation for the shifts in money demand has not yet been found and this topic will no doubt remain a focus of much further economic research. But the question of how stable money demand actually is provides a crucial element in the discussion of how monetary stabilization policy should be employed. A stable money demand function would provide the Bank of Canada with a good guide for making decisions on how fast to expand money supply in order to hit its inflation targets while supporting a desired growth path of GDP. A stable demand function also provides the opportunity for management of the money supply through short-run interest rate control policy.

The theory of money demand generally is built around the tradeoff between the benefits and costs of holding money. Keynes originally proposed three basic motives underlying the demand for money:

  • transaction demand, which is the demand for money to make regular payments,
  • precautionary demand, which is the demand for money to meet unforeseen payments, and
  • speculative demand, which is the demand for money to avoid capital losses from holding less liquid assets as interest rates rise.

In deciding how much money to hold for transactions, people are primarily concerned with weighing the inconvenience that results from holding too little money for making regular payments against the interest loss that results from holding too much. This dilemma is addressed by the Baumol-Tobin transactions demand model. From this approach, the following square-root formula is derived,

m* = [(tcY)/(2i)]1/2.

This square-root formula does not imply any money illusion, since it shows the elasticity of demand for real money balances with respect to real income. The assumptions made in deriving the formula are somewhat restrictive, but this approach nonetheless establishes important facts. For one, real money demand increases less than proportionally with the level of real income (Y). It increases as the transaction costs (tc) of transferring funds from interest bearing accounts into cash increases, and decreases with lower levels of the interest rate (i). From the above formula one can calculate the elasticity of money demand in respect to the interest rate as - 1/2 and the elasticity with respect to income as + 1/2. An income elasticity of less than one would explain why velocity increases with income growth.

Uncertainty about payments, receipts, and potential costs associated with illiquidity gives rise to the precautionary demand for money. As the probability of illiquidity and the expected costs associated with it increase, so does precautionary money demand. The more money individuals or firms hold, the less likely they are to incur the cost of liquidity. The marginal benefits from lower expected costs of illiquidity have to be weighed against the marginal costs from foregone interest income.

The speculative demand for money arises from the need for a diversified portfolio. Some money is always held as insurance against the decreases in the value of less liquid assets that occur when interest rates increase. The relevant considerations for including an asset in a portfolio are the perceived returns and anticipated risks of that asset. The degree of an investor's aversion to risk ultimately determines what portion of the total portfolio is held in money. Portfolio holdings are shifted towards more risky assets only if a higher return can be expected, which means that less money is held as yields on non-money assets rise.

Knowledge of the approximate size of both the interest elasticity and the income elasticity of money demand is important to the Bank of Canada in conducting its monetary policy. The empirical work done on the money demand function has established that money demand adjusts to changes in income or interest rates, but only with a lag. The reasons for the lag lie in either the cost of adjusting money holdings or the slow adjustment of expectations. In 1973, a comprehensive study by Stephen Goldfeld established that the money demand response to changes in interest rates and income is considerably lower in the short run than in the long run. Goldfeld also found that changes in the demand for nominal money balances are proportional to changes in the price level, that is, there is no money illusion.

The instability of the demand for M1 and M2 raises many questions about the correct form of the money demand function. Therefore it is important to analyze how the demand for money is influenced by changes in other variables, such as inflationary expectations, consumers' wealth, and the cost of making financial transactions. Furthermore, since different assets have a different degree of "moneyness," the demand for a particular monetary aggregate should probably be adjusted by weighing the different components. In well-developed financial markets, nominal interest rates will reflect inflationary expectations, so one can choose to rely on either interest rates or inflation as a measure for the opportunity cost of holding money. However, if there are restrictions in financial markets, the right measure for the opportunity cost of holding money should be the higher of these two variables.

The discussion of the behaviour of the income velocity of money is closely related to the discussion of money demand, as we can see from the equations below. The money market is in equilibrium when real money supply is equal to real money demand, that is,

M/P = ms = md = L(i,Y).

From the quantity theory of money equation, that is, MV = PY, it follows that

V =Y/(M/P) = Y/L(i,Y) ==> V = V(i,Y).

It is evident that the income velocity of money is affected by the same factors, namely income and the interest rate, as money demand. Velocity (V) increases as the interest rate (i) increases (since money demand decreases). But the way velocity is affected by an income change depends on the income elasticity of money. If the long-run income elasticity of money is less than 1, the income velocity of money increases with increases in income. But if the long-run income elasticity of money is approximately equal to 1, changes in income do not change the income velocity of money. If the income velocity of money is constant or at least highly predictable, the Bank of Canada can use the equation M = (PY)/V, as a guide for its monetary policy, since nominal GDP (PY) is directly linked to changes in money supply (M). If velocity (V) is constant, changes in money supply translate into proportional changes in nominal GDP (PY) and, if the level of output (Y) is fixed, into proportional changes in the price level (P). This can be seen, since P = (VM)/Y.

Suggestions and Pitfalls

While most students will already be familiar with the four functions of money from their introductory economics courses, many may be unfamiliar with the way monetary aggregates are defined. Some attention should therefore be paid to Table 16-1 and the way in which M1, M2, M2+ and M3 are defined. To understand the magnitude of monetary aggregates (at least M1 and M2), students may be asked to look for their current values as well as the value of nominal GDP, so they can calculate the values for V1 and V2.

Since money is "whatever is generally accepted in exchange," some discussion may be devoted to the possibility of substituting items other than currency or deposits for money. For example, American cigarettes were used to facilitate transactions during the hyperinflation in Germany in 1922/23, in P.O.W. camps after World War II, and even in the 1990s in countries with very weak currencies. There is also increased talk of a cashless society in which all payments are made through credit or debit cards. As many more people have begun to purchase items or trade stocks on the Internet, some banks have begun to offer "e-cash" and transaction accounts solely devoted to e-commerce. Students always find it interesting to talk about these issues. It also may be of interest to discuss why holding cash may be important to people even if other means of payment are easily available to them

Chapter 17 provides an opportunity to discuss in greater detail the three basic motives for holding money. Some emphasis should be given to the Baumol-Tobin approach, since it not only deals with the interest rate as the opportunity cost of holding money, but also introduces the notion of a transaction cost. From this approach, the square-root formula can be derived easily by minimizing the total cost of holding money with respect to the number of transactions (n) needed to transfer funds from an interest bearing account to cash. This total cost is the sum of the "brokerage cost" (ntc) and the interest cost of holding cash (imd, where md = M/P). Since it can be shown that md = Y/(2n) is the average cash balance held, the total cost of holding money is

C = ntc + (iY)/(2n).

By taking the derivative with respect to n and setting it equal to zero, one can get the minimum cost as follows:

C/n = tc - (iY)/(2n2) = 0 ==> tc = (iY)/(2n2) ==> (tcY)/(2i) = [Y/(2n)]2 = md2

==> md = [(tcY)/(2i)]1/2.

From this square-root formula, the income elasticity of money demand can be derived as being equal to + 1/2 and the interest elasticity of money demand as being equal to - 1/2, as follows:

md/Y = [(1/2)[(tcY)/(2i)]-1/2(tc/2i) = (1/2)(1/Y)md

==> [(md/md)]/[(Y/Y)] = (md/Y)(Y/md) = + 1/2

md/i = -[(1/2)[(tcY)/(2i)]-1/2(tcY/2i2) = - (1/2)(1/i)md

==> [(md/md)]/[(i/i)] = (md/i)(i/md) = - 1/2.

1

Students with a weak math background may not gain new insights from the derivation of the square-root formula and the income and interest elasticities of money demand implied by it. It is nonetheless important to discuss the formula's implications. The fact that the transaction cost (tc) may not just be a specific charge for withdrawals but may also include time costs, inconvenience, etc., should be stressed. Likewise, the fact that the formula implies the existence of economies of scale in cash management deserves some attention, since the average cost of transaction is lower for large-size transactions. High-income individuals have easier access to financial markets and thus have a low probability of becoming illiquid. This means that high-income individuals on average can hold a lower proportion of their income in money assets than low-income people. Similarly, industrialized countries with a large GDP and very efficient financial markets need proportionally less money to run their economy than countries that lack a well-functioning banking system.

This leads to the discussion of precautionary money demand. Precautionary money is not just held for emergencies but for unforeseen opportunities to make potentially profitable purchases as well. It is helpful to give some real life examples of precautionary balances and to point out that precautionary money holdings increase as the potential cost and the probability of cash flow problems go up. Businesses always have extra cash (or money that is easily accessible) on hand, since cash flow problems can easily lead to bankruptcy.

The speculative demand for money is likely to be the most confusing to students, and it should be stressed that the amount of money balances held is determined by expectations about interest rates movements. In times of high interest rates, people may expect a drop in interest rates in the near future and thus expect bond prices to increase. This makes it much more attractive to hold bonds, so less money is held. On the other hand, if interest rates are very low, people may expect them to increase soon and thus expect bond prices to decrease. In such a case, people prefer to hold money rather than bonds to avoid a potential capital loss.

Those instructors who have already discussed the principle of discounting and derived the present value (price) of a consol as PV = b = R/i, can easily show that bond prices will fall when interest rates rise. Some instructors may use this simple formula for the price of a consol to derive Keynes' notion of a "critical interest rate." Others may want to stress Tobin's more complicated portfolio approach. The portfolio approach generally creates more interest, but it is much more involved and requires a larger commitment of class time. In either case, students should understand that portfolio diversification involves the tradeoff between risk and expected yield and that some money is always held since it is the least risky asset. However, since Chapter 18 covers financial markets and discusses the relationship between bond prices and interest rates, instructors may wish to wait until then to derive the price of a consol.

Some class time should be devoted to the discussion of the financial innovations that have taken place since the 1970s and how they have contributed to the instability of the demand for and thus the velocity of M1. The "unexpected" decrease in the income velocity of M1 in the early 1980s provides a good starting point for such a discussion. This drop was caused by financial innovation and the recession of 1981/82. The concept of the income velocity of money is also very important since it reflects to a large degree the behaviour of money demand. Velocity is the turnover rate of money and is defined simply as the ratio of nominal GDP to nominal money supply. The behaviour of income velocity has important policy implications and instructors should draw attention to the implications of the quantity theory of money.