Chapter 3: The Demand for Money PDF

Chapter 3 The demand for money 3.1 Introduction In Chapter 2 we saw why there was a need for money: to solve the double coincidence of wants problem associated with barter to obviate the lack of trust between the payer and the payee in a transaction. However, what determines the quantity of money...

Chapter 3 The demand for money 3.1 Introduction In Chapter 2 we saw why there was a need for money: to solve the double coincidence of wants problem associated with barter to obviate the lack of trust between the payer and the payee in a transaction. However, what determines the quantity of money that individuals and economies demand is a separate question. It is the aim of this chapter to explain what determines the quantity of money we demand and also to present a number of models (or theories) of the demand for money. The chapter is split into two main sections. The first part considers the demand for money from individuals or institutions/firms the microeconomic determinants of money demand. The second part examines the demand for money at the macroeconomic level gives a brief history of money demand, focusing on the breakdown of the macroeconomic demand for money function. 3.2 Aims The aim of the chapter is to study the money demand as one of the building blocks of the money market equilibrium. 3.3 Learning outcomes By the end of this chapter, and having completed the Essential reading and activities, you should be able to: explain why it is important to study the demand for money describe the four main microeconomic determinants of money demand outline the inventory theoretic model of Baumol–Tobin and the portfolio selection model of Tobin discuss why Tobin’s model solves the ‘plunger’ problem of the demand for money model of Keynes describe the general set-up of macroeconomic money demand equations 29 3. The demand for money discuss empirical evidence on money demand functions, especially on income and interest elasticities describe what happened and what is meant by ‘the case of the missing money’ and give reasons for the breakdown of the estimated money demand equations. 3.4 Reading advice Before embarking on this chapter, and before consulting any of the recommended reading, you should review your understanding of ‘the demand for money’ from your studies in EC2065 Macroeconomics. A very useful text on the demand for money is Laidler (1993), which is both readable and comprehensive, and should be consulted on everything covered in this chapter. Goodhart (1989) is also essential reading and should be read while you work through the chapter. 3.5 Essential reading Goodhart, C.A.E. Money, Information and Uncertainty. (London: Macmillan, 1989) Chapters 3 and 4. Laidler, D.E.W. The demand for money: Theories, evidence and problems. (New York: Harper Collins, 1993) Section II. Lewis, M.K. and P.D. Mizen Monetary Economics. (Oxford; New York: Oxford University Press, 2000) Chapters 5, 6, 11 and 12. 3.6 Further reading Books Friedman, M. ‘The quantity theory of money: a restatement’, in Friedman, M. (ed.) Studies in the quantity theory of money. (University of Chicago Press, 1956). Goldfeld, S.M. ‘Demand for money: empirical studies’, in Newman, P., M. Milgate and J. Eatwell (eds) The New Palgrave Dictionary of Money and Finance. (London: Macmillan, 1994). Goldfeld, S.M. and D.E. Sichel ‘The demand for money’, in Friedman, B. and F. Hahn (eds) Handbook of monetary economics. (Amsterdam: North-Holland, 1990). Harris, L. Monetary Theory. (New York; London: McGraw-Hill, 1985) Chapters 9 and 10. Journal articles Baumol, W. ‘The transactions demand for cash: an inventory theoretic approach’, Journal of Econometrics (1952) 66, November, pp.545–56. 30 3.7. Microeconomic determinants of the demand for money Judd, J. and J. Scadding ‘The search for a stable money demand function: a survey of the post-1973 literature’, Journal of Economic Literature 20(2) 1982, pp.993–1023. Miller, M. and D. Orr ‘A model of the demand for money by firms’, Quarterly Journal of Economics 80(3) 1966, pp.413–35. Sprenkle, C. ‘The uselessness of transactions demand models’, Journal of Finance 24(5) 1969, pp.835–47. Tobin, J. ‘The interest elasticity of transactions demand for cash’, The Review of Economics and Statistics 38(3) 1956, pp.241–47. Tobin, J. ‘Liquidity preference as behaviour towards risk’, Review of Economic Studies 25(1) 1958, pp.65–86. 3.7 Microeconomic determinants of the demand for money There are essentially four main determinants of money demand at the individual level. These are 1. interest differentials: the difference between the yield on money, commonly assumed in the literature to be zero,1 and the rate of return on other assets. The greater the rate of return on assets other than money, the greater the opportunity cost of holding money, and so the fewer money balances will be demanded. 2. cost of transfers: the costs associated with transferring between higher interest earning assets and money, needed to purchase goods and services. If the cost of transfers, known as brokerage fees, are high then it is unlikely that we will put our wealth into the higher interest earning assets as to do so will involve substantial costs. Demand for money will then be a positive function of these transfer costs. 3. price uncertainty of assets: there is inevitably risk involved in holding assets. Even though there exists a risk in holding money as a store of value, since we do not know for certain how many goods a given quantity of money can buy in the future due to inflation, the risk associated with holding other, interest earning, assets is generally considered to be greater. If the price of assets is likely to vary over time then, by the time we want to sell those assets in order to obtain money to undertake transactions, we may face considerable capital loss. If we are risk-averse then our demand for money will therefore be a positive function of the riskiness or price uncertainty of alternative assets. 4. the expected pattern of expenditures and receipts: if individuals were paid their wages in lump sums weekly then average cash balances would be less than if wages were paid monthly. If the pattern of payments and receipts was uncertain then cash balances would be likely to be higher; it may be unwise to face the brokerage fees and transfer cash to bonds if there is a possibility that you will need to make a large cash payment in the near future. 1 In practice the interest paid on sight deposit accounts is positive. 31 3. The demand for money These determinants are also related to Keynes’ description of money demand motives. Keynes (1936) broke down the demand for money into three types: transactions, precautionary and speculative motives: The transaction demand for money is essentially that needed to buy goods and services where money is needed as a medium of exchange. Precautionary money balances are simply holdings of money kept in case of emergencies (an unexpectedly large tax bill or hospital treatment for example). Finally, the speculative demand for money considers money as an alternative to interest earning assets. Due to the capital loss involved with holding bonds when the interest rate increases2 if an individual expects the interest rate to rise, then he will expect to experience a capital loss on his bond holdings. Knowing that the bond price will fall, he will want to hold a larger quantity of money. In fact, Keynes originally assumed that individuals held their expectations of interest rate movements with certainty. When the interest rate was below what they expected in the long run, R∗ in Figure 3.1, then they would put all of their financial wealth in the form of money to avoid the capital loss associated with holding bonds. When the interest rate was above what was expected, then the expected interest rate fall would be associated with a capital gain from holding bonds. The individual would then hold as little money as possible, only covering the transactions and precautionary motives (T representing minimum cash required to conduct transactions). The individual’s demand for money, as a function of the interest rate, would then be a step function, shown in Figure 3.1 below. Figure 3.1: 2 This is due to the negative relationship between the price of a bond and the yield the bond earns. This is considered in more detail in Chapter 9. 32 3.8. Baumol–Tobin transactions demand for money It has become standard to model each component of the demand for money separately.3 The transaction demand for money is typically modelled by allowing money to be a function of determinants 1, 2 and 4 above (i.e. ignoring asset price uncertainty). By allowing more flexible assumptions on the expected pattern of expenditures and receipts, similar analysis can incorporate a precautionary motive for money holdings.4 Analysis of the speculative demand for money, however, concentrates on determinant 3, asset price uncertainty, while dropping one or more of the other factors for tractability. 3.8 Baumol–Tobin transactions demand for money The two papers by Baumol (1952) and Tobin (1956) explicitly model the transactions demand for money in an inventory theoretic approach. Each assumes that a cash manager (individual or firm) has to manage an inventory of cash and other interest-earning assets. In the original Baumol model, the cash manager is paid in bonds and spends money (or makes transactions) at a constant, known rate. The objective is to choose the number of times she transfers between the stock of bonds and cash that maximises profits, or equivalently minimises costs. These costs come in two forms: brokerage fees and the interest foregone by holding money. By making a large number of transfers out of bonds and into cash, she will be able to earn more interest on the bonds that are kept for longer. However, such a strategy will involve large brokerage fees. On the other hand, by making only a few transfers, she will avoid paying frequent brokerage fees but will miss out on the interest the wealth could earn if kept in the form of bonds. Let T equal the value of the cash manager’s expenditures, equal in this case to her income: i is the interest rate earned on bonds, b is the fixed cost of making a transfer between bonds and cash and Z is the value of money transferred each time, equal to the amount of bonds sold each time. If the money is spent at a constant, known rate then the average money balances will be equal to M = Z/2. The cost minimisation problem can be written as: iZ bT + . (3.1) min C = Z Z 2 Costs, C, are made up of brokerage costs, equal to the cost per transfer, b, multiplied by the number of transfers, T /Z, plus the interest foregone by (opportunity cost from) holding money. The interest rate foregone will equal the interest rate, i, multiplied by the average money holdings, Z/2. Differentiating the cost with respect to the choice variable, Z, the amount we transfer each time, gives: bT i dC =− 2 + . dZ Z 2 Setting this equal to zero and solving for M = Z/2, gives: r Z bT M= = . 2 2i (3.2) (3.3) The average money demand, M , is then a positive function of both the brokerage cost, b, determinant number 2, and income/receipts, T , determinant number 4. It is also a 3 See Goodhart (1989) Chapter 3, Sections 1 and 2 for a more complete discussion of the modelling techniques. 4 See Miller and Orr (1966). 33 3. The demand for money negative function of the interest rate earned on alternative assets, i, determinant number 1. One can also show that the interest and income elasticities of money demand are −1/2 and 1/2, respectively. This is left as an exercise. So average money demand will increase by 1/2% if income increases by 1% and decreases by the same amount if the interest rate earned on alternative assets increases by 1%. The model generates a ‘saw tooth’ pattern of money holdings as shown in Figure 3.2 below. For simplicity, assume that interest payments are made at the end and do not accrue during the period. The diagram shows a situation where the optimal number of times to transfer between bonds and money is 4. At time t0 , the cash manager receives T in bonds and transfers Z to cash immediately in order to buy goods and services. The amount of bonds left is therefore B1 (the difference between T and B1 being Z). Money balances and hence financial wealth decline gradually as the cash is spent. At time t1 , another transfer is made that reduces bond holding by a further Z to B2 . The process continues until all wealth is spent and a new income is received. Money holdings are therefore shown by the saw-tooth pattern, financial wealth is shown by the straight line from T and the level of bond holdings is shown by the dashed step function. Figure 3.2: Activity 3.1 A taxi driver takes £15,000 net over the course of a year, at an approximately constant daily rate. He spends 80% of his takings on consumption goods, also at an approximately constant daily rate, but saves the remainder to pay for a world cruise at the end of the year. He can hold his savings in a deposit account in a bank paying 4% per annum, with costless deposits and withdrawals, or he can purchase bonds paying a known yield of 7%. The brokerage fee in purchasing or selling bonds is £5 per transaction. Assume the taxi driver manages his finances 34 3.9. Tobin’s model of portfolio selection optimally by making n transactions, n − 1 of these being purchases of bonds spaced equally through the year, and the n-th transaction being the sale of bonds at the end of the year to pay for the world cruise. (a) Draw the time profile of the taxi driver’s holdings of deposits and bonds. (b) What is the optimal value of n? (Note that n must be a whole number.) (c) What is the taxi driver’s ‘demand for money’, or average deposit balance? (For Feedback, see the end of this chapter.) Criticisms of the inventory theoretic model Despite the intellectual appeal and simplicity of the inventory theoretic model, it faces a number of criticisms. One argument made against such models is that they make the assumption that the pattern of expenditure and receipts is known perfectly. This is clearly not true in reality. Adding uncertainty to these processes is exactly what Miller and Orr (1966) do but, even then, these inventory theoretic models face a huge uphill struggle when faced with empirical evidence. At the micro level, the percentage of actual cash balances held by firms that is explained by the Baumol model is tiny. 3.9 Tobin’s model of portfolio selection One problem with Keynes’ original ideas of the micro level demand for money was that individuals held expectations of interest rate movements with certainty. This resulted in a step demand function given in Figure 3.1 where individuals either held no money and all long term bonds (or as little money as possible to cover transactions) or held all money and no bonds. Individuals were ‘plungers’ – all or nothing. This did not explain the empirical regularity that people held their financial wealth in both forms of assets and could only provide a downward sloping aggregate money demand function by assuming that every individual had a different expectation of the equilibrium interest rate, also assuming that each of these expectations were held with certainty. This clearly is too strong an assumption. To overcome this problem, Tobin (1958) considered the problem of how much money to hold as one where individuals maximise utility by choosing between assets in a portfolio. Money is assumed to have a zero rate of return and is considered riskless. The variance of the return on money is then also zero. Bonds, however, pay a positive rate of return, µ, but are risky due to the possibility of capital gains or losses if the bond is sold before maturity. Let the variance of the return on bonds be σ 2 . Let B be the proportion of your financial wealth held in bonds. 1 − B is therefore the proportion held in the form of money if we assume a two-asset world. The distribution of money and bonds are given below: Money ∼ (0, 0) Bonds ∼ (µ, σ 2 ). (3.4) (3.5) 35 3. The demand for money A portfolio containing a share B of bonds and 1 − B of money therefore has a distribution: Portfolio ∼ (0 · (1 − B) + µ · B, 0 · (1 − B)2 + σ 2 B 2 ) = (µB, σ 2 B 2 ). (3.6) Let the mean return of this portfolio be µp and the variance be σp2 . µp = µB σp2 = σ 2 B 2 . (3.7) (3.8) Writing B in terms of σ and σp from (3.8) and substituting into (3.7) gives a budget constraint relating the maximum return on a portfolio to the standard deviation, which we assume is a proxy for risk. µσp . (3.9) µp = σ Assuming that agents are risk-averse, the indifference curves will be convex and upward sloping, as shown in Figure 3.3. The top part of the figure shows the budget constraint and indifference curves of the agent. Note that there is an upper bound on the return and risk of the portfolio, µ0p and σp0 , respectively, where the individual has put all of their financial wealth in bonds; B = 1. At this point it is impossible to increase the return or risk of the portfolio by substituting between money and bonds. The bottom part of the figure simply shows the share of the portfolio held in bonds and the corresponding risk of the portfolio. As can be seen in the figure, the individual maximises utility by being at the point where the indifference curve is tangential to the portfolio budget constraint, point E. The share of wealth held in bonds is B ∗ and the share held in money is 1 − B ∗ . By using portfolio analysis, Tobin showed how individuals can diversify their wealth into more than just one asset. By changing the return earned on bonds, µ, this will shift the lines in the figure, resulting in a new equilibrium and different bond/money allocation (see ‘Feedback to the Activity’ at the end of this chapter). 3.10 Macroeconomic determinants of money demand As seen in the previous section and the models referenced there, money demand at the micro level is modelled as a function of a number of variables: interest differentials, cost of transfers, asset price uncertainty and the pattern of expenditures and receipts. At the macro level, however, the demand for money is modelled under, arguably, a simpler framework. That is not to say that the analysis is simpler or there are fewer complications to overcome. Indeed, the econometric techniques used to model the aggregate demand for money are complex and have needed to be after the breakdown of the demand for money functions starting in the 1970s. The demand for money is one of the most thoroughly researched topics in the field of economics but why has it attracted so much attention? We study the demand for something in order to be able to predict the consequences of changes in its supply, and this is as true of money as of anything else. Changes in the supply of any good, service or asset will alter at least one of the variables upon which the demand for that good, 36 3.10. Macroeconomic determinants of money demand Figure 3.3: service or asset depends. For example, assume that the demand for apples depends primarily on the following: 1. their price 2. the price of pears 3. the incomes of consumers, and 4. the tastes and preferences of consumers. Then a change in the supply of apples will be expected to alter one of these factors influencing demand. In this case most probably the price of apples. In a similar fashion, changes in the supply of money can be expected to bring about a change in the value of one or more of the determinants of the demand for money. The possibility that these determinants may include interest rates, real income and the general level of prices – themselves important macroeconomic variables – gives the study of the demand for money a particular importance. A particular aggregate money demand function takes the form: M d = f (Y, Ri , W ). (3.10) M d is the demand for nominal money balances, Y is nominal income and Ri is the rate of return on asset i. Since the rate of return on a number of assets will determine the demand for money, including that on money itself, i can represent a number of assets. The Ri s represent the opportunity cost of holding money and Y acts as a proxy for the level of transactions undertaken. Wealth (W ) is included as it forms the budget constraint on which the choice of money holdings depends but since wealth is capitalised current and future income, it is not independent of Y . For this reason, and 37 3. The demand for money also because data on wealth levels of nations are very difficult to obtain, W is often dropped from the analysis. If money demand is homogenous of degree one in prices (i.e. a doubling of the price level leads to a doubling of the demand for nominal money balances), (3.10) can be re-written as:  d M = g(y, Ri ) (3.11) P where y is real income. A common log linear form of this equation is: mt − pt = ayt − bRt (3.12) where mt , pt and yt are log values of the nominal money supply, price level and income at time t respectively and Rt is ‘the’ nominal interest rate at time t. Two important parameters of the money demand function are the elasticities with respect to income and the interest rate. For a summary of the empirical evidence on these estimates, see Lewis and Mizen, especially Chapter 11. This chapter also explains in detail the methods used to estimate such money demand functions.5 The interest elasticity of money demand is important in the debate over whether monetary or fiscal policy is more powerful. A low value of b implies a relatively steep LM curve and, other things being equal, monetary policy has a larger effect on output than fiscal policy. Keynesians on the other hand argue the opposite: a high value of b and therefore a relatively shallow LM curve, implying a greater role for fiscal policy. Of equal importance is whether or not the money demand equation is stable. If the monetary authorities decide to target the money supply then an unstable money demand function can lead to unexpected and adverse changes in nominal and possibly real factors in the economy. The stability of money demand can only be determined by statistical analysis of the relevant data – hence the enormous number of empirical studies relating to the demand for money. 3.11 The stability of the money demand function Relatively simple functional forms of money demand were estimated until the early 1970s and these appeared to work reasonably well at explaining the demand for money. One such specification was used by Goldfeld (1973) and is similar to (3.12).     M M ln = b0 + b1 yt + b2 Rt + b3 ln + ut (3.13) P t P t−1 where ut is a random error term and a lagged dependent variable, ln(M/P )t−1 , is also included. Goldfeld himself suggested: ‘Perhaps most interesting is the apparent sturdiness of a quite conventional formulation of the money demand function, however scrutinised. . . (T)he conventional equation exhibits no marked instabilities, in either the short run or the long run.’6 5 6 For a more technical review, see also Goldfeld and Sichel listed in the ‘Further reading’ section. Goldfeld, 1973, quoted by Goodhart, 1989. 38 3.12. Reasons for the breakdown of the money demand functions However, from 1974 Goldfeld’s equation overpredicted real money balances, M1, in the US. This was known as ‘the case of the missing money’ (Goldfeld, 1976). Basically, for any given level of real income and interest rates, the above equation suggested that there should be more money in circulation than there actually was.7 Such demand for money functions were breaking down, not only in the US but also elsewhere, such as the UK – see Hacche (1974) who examined a broader measure of money, M3. Whereas Goldfeld’s equation overpredicted the amount of money in the US, money demand equations for the broader M3 aggregate in the UK were underpredicting the amount of money. 3.12 Reasons for the breakdown of the money demand functions A common reason quoted for why the money demand equations broke down in the 1970s was greater financial innovation. The oil shocks of the mid-1970s and the resulting high inflation caused interest rates to increase substantially. This meant that the opportunity cost of holding money increased and was eventually so large that it became worthwhile for cash managers to find more efficient ways of holding cash balances, allowing more wealth to be put into interest-earning assets. Hence for any level of income and interest rate, the demand for money would be reduced, explaining the ‘missing money.’ Another possible explanation for the negative results of the 1970s is the fact that a single equation money demand function may be misspecified. An equation relating real money balances, income and interest rates may not represent a true money demand equation, but a reduced form equation; a mixture of both money demand and supply equations, especially if the money supply set by the authorities is dependent on conditions in the economy such as inflation and output. A changing policy stance by the authorities, as was the case from 1979 to 1982 in the US,8 will cause the reduced form relationship to alter, explaining the breakdown of the estimated ‘demand’ function. Overly simplified econometrics was also used up until the last couple of decades. Issues including stationarity, spurious regressions and co-integration need to be addressed before any meaningful interpretation can be taken from empirical results. See Lewis and Mizen (2000), Chapter 11. 3.13 A reminder of your learning outcomes By the end of this chapter, and having completed the Essential reading and activities, you should be able to: explain why it is important to study the demand for money describe the four main microeconomic determinants of money demand outline the inventory theoretic model of Baumol–Tobin and the portfolio selection model of Tobin 7 8 For a review of the stability of the demand for money function, see Judd and Scadding (1982). See Goodhart (1989), Chapter 10. 39