Monetary Economics Chapter Three PDF

**CHAPTER THREE** **THE THEORY OF DEMAND FOR MONEY** **Introduction** In the first chapter we have discussed about the definition, function, evolution and measurement of money. As we have seen money basically used as medium of exchange, store of value, unit of account and source of deferred payme...

**CHAPTER THREE** **THE THEORY OF DEMAND FOR MONEY** **Introduction** In the first chapter we have discussed about the definition, function, evolution and measurement of money. As we have seen money basically used as medium of exchange, store of value, unit of account and source of deferred payment. Now let us study demand for money which is important to develop understanding of the determinant of quantity of money demanded by private agents (i.e. the amounts they choose to hold at a point in time). Money demand theories have evolved over time. And this chapter will deal with the development of different theories of money demand. We will discuss how the different theories of demand for money explain variables which determine demand for money and their policy implication. **3.1. Quantity Theory of Money** The clearest exposition of the classical quantity theory approach is found in the work of the American economist Irving Fisher, in his influential book *The Purchasing Power of* *Money*, published in 1911. Fisher wanted to examine the link between the total quantity of money *M* (the money supply) and the total amount of spending on final goods and services produced in the economy ***P*** x ***Y***, where *P* is the price level and *Y* is aggregate output (income). (Total spending ***P*** x ***Y*** is also thought of as aggregate nominal income for the economy or as nominal GDP.) The concept that provides the link between *M* and *P* x *Y* is called the **velocity of money** (often reduced to *velocity*), the rate of turnover of money; that is, the average number of times per year that a dollar is spent in buying the total amount of goods and services produced in the economy. Velocity *V* is defined more precisely as total spending *P* x *Y* divided by the quantity of money *M*: If, for example, nominal GDP (P Y) in a year is \$5 trillion and the quantity of money is \$1 trillion, velocity is 5, meaning that the average dollar bill is spent five times in purchasing final goods and services in the economy. By multiplying both sides of this definition by M, we obtain the equation of exchange, which relates nominal income to the quantity of money and velocity: ***M \* V = P \* Y*** The equation of exchange thus states that the quantity of money multiplied by the number of times that this money is spent in a given year must be equal to nominal income (the total nominal amount spent on goods and services in that year). As it stands, the above equation is nothing more than an identity---a relationship that is true by definition. It does not tell us, for instance, that when the money supply M changes, nominal income (P\*Y) changes in the same direction; a rise in M, for example, could be offset by a fall in V that leaves M \* V(and therefore P \* Y) unchanged. To convert the equation of exchange (an identity) into a theory of how nominal income is determined requires an understanding of the factors that determine velocity. Irving Fisher reasoned that velocity is determined by the institutions in an economy that affect the way individuals conduct transactions. Fisher took the view that the institutional and technological features of the economy would affect velocity only slowly over time, so velocity would normally be reasonably constant in the short run. Fisher's view that velocity is fairly constant in the short run transforms the equation of exchange into the ***quantity theory of money***, which states that nominal income is determined solely by movements in the quantity of money: When the quantity of money M doubles, M \* V doubles and so must P \* Y, the value of nominal income. To see how this works, let's assume that velocity is 5, nominal income (GDP) is initially \$5 trillion, and the money supply is \$1 trillion. If the money supply doubles to \$2 trillion, the quantity theory of money tells us that nominal income will double to \$10 trillion (=5\*\$2 trillion). Because the classical economists (including Fisher) thought that wages and prices were completely flexible, they believed that the level of aggregate output Y produced in the economy during normal times would remain at the full-employment level, so Y in the equation of exchange could also be treated as reasonably constant in the short run. The quantity theory of money then implies that if M doubles, P must also double in the short run, because V and Y are constant. In our example, if aggregate output is \$5 trillion, the velocity of 5 and a money supply of \$1 trillion indicate that the price level equals 1 because 1 times \$5 trillion equals the nominal income of \$5 trillion. When the money supply doubles to \$2 trillion, the price level must also double to 2 because 2 times \$5 trillion equals the nominal income of \$10 trillion. For the classical economists, the quantity theory of money provided an explanation of movements in the price level: ***Movements in the price level result solely from changes in the quantity of money.*** Because the quantity theory of money tells us how much money is held for a given amount of aggregate income, it is in fact a theory of the demand for money. We can see this by dividing both sides of the equation of exchange by V, thus rewriting it as: where nominal income P\*Y is written as PY. When the money market is in equilibrium, the quantity of money M that people hold equals the quantity of money demanded M^d^, so we can replace M in the equation by M^d^. Using k to represent the quantity 1/V(a constant, because Vis a constant), we can rewrite the equation as: ***M ^d^* = *k PY*** Because k is a constant, the level of transaction generated by a fixed level of nominal income PY determines the quantity of money M^d^ that people demand. Therefore, Fisher's quantity theory of money suggests that the demand for money is purely a function of income, and interest rates have no effect on the demand for money. Fisher believed that people hold money only to conduct transactions and have no freedom of action in terms of the amount they want to hold, so he came to the following conclusion. The demand for money is determined *1) by the level of transactions generated by the level of nominal income PY and* *2) by the institutions in the economy that affect the way people conduct transactions that determine velocity and hence k.* **3.2 Keynes's Liquidity Preference Theory** In his famous 1936 book The General Theory of Employment, Interest, and Money, John Maynard Keynes abandoned the classical view that velocity was a constant and developed a theory of money demand that emphasized the importance of interest rates. His theory of the demand for money, which he called the ***liquidity preference theory***, asked the question: Why do individuals hold money? He postulated that there are three motives behind the demand for money: the transactions motive, the precautionary motive, and the speculative motive. 1. ***Transactions motive*** In the classical approach, individuals are assumed to hold money because it is a medium of exchange that can be used to carry out everyday transactions. Following the classical tradition, Keynes emphasized that this component of the demand for money is determined primarily by the level of people's transactions. Because he believed that these transactions were proportional to income, like the classical economists, he took the transactions component of the demand for money to be proportional to income. 2. ***Precautionary Motive*** Keynes went beyond the classical analysis by recognizing that in addition to holding money to carry out current transactions, people hold money as a cushion against an unexpected need. Suppose that you've been thinking about buying a fancy stereo; you walk by a store that is having a 50%-off sale on the one you want. If you are holding money as a precaution for just such an occurrence, you can purchase the stereo right away; if you are not holding precautionary money balances, you cannot take advantage of the sale. Precautionary money balances also come in handy if you are hit with an unexpected bill, say for car repair or hospitalization. Keynes believed that the amount of precautionary money balances people want to hold is determined primarily by the level of transactions that they expect to make in the future and that these transactions are proportional to income. Therefore, he postulated, the demand for precautionary money balances is proportional to income. 3. ***Speculative motive*** If Keynes had ended his theory with the transactions and precautionary motives, income would be the only important determinant of the demand for money, and he would not have added much to the classical approach. However, Keynes took the view that money is a store of wealth and called this reason for holding money the speculative motive. Since he believed that wealth is tied closely to income, the speculative component of money demand would be related to income. However, Keynes looked more carefully at the factors that influence the decisions regarding how much money to hold as a store of wealth, especially interest rates. Keynes divided the assets that can be used to store wealth into two categories: money and bonds. He then asked the following question: Why would individuals decide to hold their wealth in the form of money rather than bonds? Keynes assumed that individuals believe that interest rates gravitate to some normal value (an assumption less plausible in today's world). If interest rates are below this normal value, individuals expect the interest rate on bonds to rise in the future and so expect to suffer capital losses on them. As a result, individuals will be more likely to hold their wealth as money rather than bonds and the demand for money will be high. What would you expect to happen to the demand for money when interest rates are above the normal value? In general, people will expect interest rates to fall, bond prices to rise, and capital gains to be realized. At higher interest rates, they are more likely to expect the return from holding a bond to be positive, thus exceeding the expected return from holding money. They will be more likely to hold bonds than money, and the demand for money will be quite low. From Keynes's reasoning, we can conclude that ***as interest rates rise, the demand for money falls, and therefore money demand is negatively related to the level of interest rates.*** In putting the three motives for holding money balances together into a demand for money equation, Keynes was careful to distinguish between nominal quantities and real quantities. Money is valued in terms of what it can buy. If, for example, all prices in the economy double (the price level doubles), the same nominal quantity of money will be able to buy only half as many goods. Keynes thus reasoned that people want to hold a certain amount of real money balances (the quantity of money in real terms)---an amount that his three motives indicated would be related to real income Y and to interest rates i. Keynes wrote down the following demand for money equation, known as the ***liquidity preference function***, which says that the demand for real money balances M^d^/P is a function of (related to) i and Y: The minus sign below i in the liquidity preference function means that the demand for real money balances is negatively related to the interest rate i, and the plus sign below Y means that the demand for real money balances and real income Yare positively related. By deriving the liquidity preference function for velocity PY/M, we can see that Keynes's theory of the demand for money implies that velocity is not constant, but instead fluctuates with movements in interest rates. The liquidity preference equation can be rewritten as: And multiplying both sides by '*Y'* will give us the following: At equilibrium money demand (*M^d^*) and money supply (*M*) are equal and hence by substitution: This equation implies that because interest rates have substantial fluctuations, the liquidity preference theory of the demand for money indicates that velocity has substantial fluctuations as well. **3.3 Post Keynesian developments in monetary theory** After World War II, economists began to take the Keynesian approach to the demand for money even further by developing more precise theories to explain the three Keynesian motives for holding money. Because interest rates were viewed as a crucial element in monetary theory, a key focus of this research was to understand better the role of interest rates in the demand for money. ***Transactions motive*** William Baumol and James Tobin independently developed similar demand for money models, which demonstrated that even money balances held for transactions purposes are sensitive to the level of interest rates. ***Simplifying assumptions:*** In developing their models, they considered a hypothetical individual who receives a payment once a period and spends it over the course of this period. More specifically: - The individual finances his consumption fully on the basis of earned income, with no savings. - The individual's nominal income, (y = PY), arrives once -- at the beginning of every month. - The consumer's income is divided between cash on hand and purchased bonds. - The bond pays interest at rate i, while cash pays no nominal interest. To refine this analysis, let us say that you receive 1,000 Birr at the beginning of the month and spend it on transactions that occur at a constant rate during the course of the month. If you keep the 1,000 Birr in cash in order to carry out your transactions, your money balances will be: - 1,000 Birr at the beginning of the month, and - zero (no cash left because you have spent it all) by the end of the month. Over the course of the month, your holdings of money will on average be 500 Birr (your holdings at the beginning of the month, 1,000 Birr, plus your holdings at the end of the month, 0 Birr, divided by 2). At the beginning of the next month, you receive another 1,000 Birr payment, which you hold as cash, and the same decline in money balances begins again. This process repeats monthly, and your average money balance during the course of the year is 500 Birr. Since your yearly nominal income is 12,000 Birr (= 1,000 Birr per month x 12 months) and your holdings of money average 500 Birr \[the average of averages = (12x500)/12)\], the velocity of money (V = PY/M) is 12,000/500 = 24. *In panel (a), the 1,000 Birr payment at the beginning of the month is held entirely in cash and is spent at a constant rate until it is exhausted by the end of the month. In panel (b), half of the monthly payment is put into cash and the other half into bonds. At the middle of the month, cash balances reach zero and bonds must be sold to bring balances up to 500 Birr. By the end of the month, cash balances again dwindle to zero.* Suppose that as a result of taking a Money and Banking Course (Assumed), you realize that you can improve your situation by not always holding cash. Then, you decide to hold part of your 1,000 Birr in cash and put part of it into an income-earning asset (say, bonds). At the beginning of each month, you keep 500 Birr in cash and the other 500 Birr to buy a bond. You start out each month with 500 Birr of cash, and by the middle of the month; your cash balance has run down to zero. Because bonds cannot be used directly to carry out transactions, you must turn them into cash so that you can carry out the rest of the month's transactions. At the middle of the month, then, your cash balance rises back up to 500 Birr. By the end of the month, the cash is gone. When you again receive your next 1,000 Birr monthly payment, you again divide it into 500 Birr of cash and 500 Birr of bonds, and the process continues. The net result of this process is that the average cash balance held during the month is 500 Birr/2 =250Birr---just half of what it was before. Velocity has doubled to 12,000 Birr/250 Birr =48. What have you gained from your new strategy? You have earned interest on \$500 of bonds that you held for half the month. If the interest rate is 1% per month, you have earned an additional 2.50 Birr (=1/2\*500 Birr \*1%) per month. As you might expect, there is a catch to all this. In buying bonds, you incur transaction costs of two types. First, you must pay a straight brokerage fee for the buying and selling of the bonds. These fees increase when average cash balances are lower because you will be buying and selling bonds more often. Second, by holding less cash, you will have to make more trips to the bank to get the cash, once you have sold some of your bonds. Because time is money, this must also be counted as part of the transaction costs. You face a trade-off. If you hold very little cash, you can earn a lot of interest on bonds, but you will incur greater transaction costs. If the interest rate is high, the benefits of holding bonds will be high relative to the transaction costs, and you will hold more bonds and less cash. Conversely, if interest rates are low, the transaction costs involved in holding a lot of bonds may outweigh the interest payments, and you would then be better off holding more cash and fewer bonds. The conclusion of the Baumol-Tobin analysis may be stated as follows: ***As interest rates increase, the amount of cash held for transactions purposes will decline, which in turn means that velocity will increase as interest rates increase. Put another way, the transactions component of the demand for money is negatively related to the level of interest rates.*** The basic idea in the Baumol-Tobin analysis is that there is an opportunity cost of holding money---the interest that can be earned on other assets. There is also a benefit to holding money---the avoidance of transaction costs. When interest rates increase, people will try to economize on their holdings of money for transactions purposes, because the opportunity cost of holding money has increased. ***Precautionary motive*** Models that explore the precautionary motive of the demand for money have been developed along lines similar to the Baumol-Tobin framework, so we will not go into great detail about them here. We have already discussed the benefits of holding precautionary money balances, but weighed against these benefits must be the opportunity cost of the interest forgone by holding money. We therefore have a trade-off similar to the one for transactions balances. As interest rates rise, the opportunity cost of holding precautionary balances rises, and so the holdings of these money balances fall. We then have a result similar to the one found for the Baumol-Tobin analysis. ***The precautionary demand for money is negatively related to interest rates.*** ***Speculative motive*** Keynes's analysis of the speculative demand for money was open to several serious criticisms. It indicated that an individual holds only money as a store of wealth when the expected return on bonds is less than the expected return on money and holds only bonds when the expected return on bonds is greater than the expected return on money. Only when people have expected returns on bonds and money that are exactly equal (a rare instance) would they hold both. Keynes's analysis therefore implies that practically no one holds a diversified portfolio of bonds and money simultaneously as a store of wealth. Since diversification is apparently a sensible strategy for choosing which assets to hold, the fact that it rarely occurs in Keynes's analysis is a serious shortcoming of his theory of the speculative demand for money. Tobin developed a model of the speculative demand for money that attempted to avoid this criticism of Keynes's analysis. His basic idea was that not only do people care about the expected return on one asset versus another when they decide what to hold in their portfolio, but they also care about the riskiness of the returns from each asset. Specifically, Tobin assumed that most people are risk-averse---that they would be willing to hold an asset with a lower expected return if it is less risky. An important characteristic of money is that its return is certain; Tobin assumed it to be zero. Bonds, by contrast, can have substantial fluctuations in price, and their returns can be quite risky and sometimes negative. So even if the expected returns on bonds exceed the expected return on money, people might still want to hold money as a store of wealth because it has less risk associated with its return than bonds do. The Tobin analysis also shows that people can reduce the total amount of risk in a portfolio by diversifying; that is, by holding both bonds and money. The model suggests that individuals will hold bonds and money simultaneously as stores of wealth. Since this is probably a more realistic description of people's behavior than Keynes's, Tobin's rationale for the speculative demand for money seems to rest on more solid ground. To sum up, further developments of the Keynesian approach have attempted to give a more precise explanation for the transactions, precautionary, and speculative demand for money. The attempt to improve Keynes's rationale for the speculative demand for money has been only partly successful; it is still not clear that this demand even exists. However, the models of the transactions and precautionary demand for money indicate that these components of money demand are negatively related to interest rates. Hence Keynes's proposition that the demand for money is sensitive to interest rates---suggesting that velocity is not constant and that nominal income might be affected by factors other than the quantity of money---is still supported. **3.4 Friedman's Modern Quantity Theory of Money** In 1956, Milton Friedman developed a theory of the demand for money in a famous article, "The Quantity Theory of Money: A Restatement." Although Friedman frequently refers to Irving Fisher and the quantity theory, his analysis of the demand for money is actually closer to that of Keynes than it is to Fisher's. Like his predecessors, Friedman pursued the question of why people choose to hold money. Instead of analyzing the specific motives for holding money, as Keynes did, Friedman simply stated that the demand for money must be influenced by the same factors that influence the demand for any asset. Friedman then applied the theory of asset demand to money. The theory of asset demand indicates that the demand for money should be a function of the resources available to individuals (their wealth) and the expected returns on other assets relative to the expected return on money. Like Keynes, Friedman recognized that people want to hold a certain amount of real money balances (the quantity of money in real terms). From this reasoning, Friedman expressed his formulation of the demand for money as follows:  Where demand for real money balances Friedman\'s measure of wealth, known as *permanent income* (technically, the present discounted value of all expected future income, but more easily described as expected average long-run income) = expected inflation rate and the signs underneath the equation indicate whether the demand for money is positively (+) related or negatively (-) related to the terms that are immediately above them. Let us look in more detail at the variables in Friedman's money demand function and what they imply for the demand for money. Because the demand for an asset is positively related to wealth, money demand is positively related to Friedman's wealth concept, permanent income (indicated by the plus sign beneath it). Unlike our usual concept of income, permanent income (which can be thought of as expected average long-run income) has much smaller short-run fluctuations, because many movements of income are transitory (short-lived). For example, in a business cycle expansion, income increases rapidly, but because some of this increase is temporary, average long-run income does not change very much. Hence in a boom, permanent income rises much less than income. During a recession, much of the income decline is transitory, and average long-run income (hence permanent income) falls less than income. One implication of Friedman's use of the concept of permanent income as a determinant of the demand for money is that the demand for money will not fluctuate much with business cycle movements. An individual can hold wealth in several forms besides money; Friedman categorized them into three types of assets: bonds, equity (common stocks), and goods. The incentives for holding these assets rather than money are represented by the expected return on each of these assets relative to the expected return on money, the last three terms in the money demand function. The minus sign beneath each indicates that as each term rises, the demand for money will fall. The terms r~b~-r~m~ and r~e~ --r~m~ represent the expected return on bonds and equity relative to money; as they rise, the relative expected return on money falls, and the demand for money falls. The final term, π^e^ -r~m~, represents the expected return on goods relative to money. The expected return from holding goods is the expected rate of capital gains that occurs when their prices rise and hence is equal to the expected inflation rate π^e^. If the expected inflation rate is 10%, for example, then goods' prices are expected to rise at a 10% rate, and their expected return is 10%. When π^e^ -r~m~ rises, the expected return on goods relative to money rises, and the demand for money falls. **3.5 Empirical Evidence on the Demand for Money** As we have seen, the alternative theories of the demand for money can have very different implications for our view of the role of money in the economy. Which of these theories is an accurate description of the real world is an important question, and it is the reason why evidence on the demand for money has been at the center of many debates on the effects of monetary policy on aggregate economic activity. Here we examine the empirical evidence on the two primary issues that distinguish the different theories of money demand and affect their conclusions about whether the quantity of money is the primary determinant of aggregate spending: Is the demand for money sensitive to changes in interest rates, and is the demand for money function stable over time? ***Interest Rates and Money Demand*** Earlier in the chapter, we saw that if interest rates do not affect the demand for money, velocity is more likely to be a constant---or at least predictable---so that the quantity theory view that aggregate spending is determined by the quantity of money is more likely to be true. However, the more sensitive the demand for money is to interest rates, the more unpredictable velocity will be, and the less clear the link between the money supply and aggregate spending will be. Indeed, there is an extreme case of ultra sensitivity of the demand for money to interest rates, called the liquidity trap, in which monetary policy has no effect on aggregate spending, because a change in the money supply has no effect on interest rates. (If the demand for money is ultrasensitive to interest rates, a tiny change in interest rates produces a very large change in the quantity of money demanded. Hence in this case, the demand for money is completely flat in the supply and demand diagrams. Therefore, a change in the money supply that shifts the money supply curve to the right or left results in it intersecting the flat money demand curve at the same unchanged interest rate.) The evidence on the interest sensitivity of the demand for money found by different researchers is remarkably consistent. Neither extreme case is supported by the data: The demand for money is sensitive to interest rates, but there is little evidence that a liquidity trap has ever existed. ***Stability of Money Demand*** If the money demand function, like Equation 4 or 6, is unstable and undergoes substantial unpredictable shifts, as Keynes thought, then velocity is unpredictable, and the quantity of money may not be tightly linked to aggregate spending, as it is in the modern quantity theory. The stability of the money demand function is also crucial to whether the Federal Reserve should target interest rates or the money supply. Thus it is important to look at the question of whether the money demand function is stable, because it has important implications for how monetary policy should be conducted. By the early 1970s, evidence strongly supported the stability of the money demand function. However, after 1973, the rapid pace of financial innovation, which changed what items could be counted as money, led to substantial instability in estimated money demand functions. The recent instability of the money demand function calls into question whether our theories and empirical analyses are adequate. It also has important implications for the way monetary policy should be conducted, because it casts doubt on the usefulness of the money demand function as a tool to provide guidance to policymakers. In particular, because the money demand function has become unstable, velocity is now harder to predict, and setting rigid money supply targets in order to control aggregate spending in the economy may not be an effective way to conduct monetary policy. **Review Questions** 1. According to Fisher's classical theory the velocity of money remain constant at least in the short run. On what basis do the classical introduces this assumption to their theory of demand analysis? 2. If the assumption of constant velocity of money and predetermined level of output at full employment is correct, discus with your friend how classical economists explain the determinant of price level. 3. What determines demand for money according to Fisher explanation using quantity equation of money? Among the four functions of money, for what purpose do money is used for Fisher? 4. Identify and describe the contribution of Keynesian over classical theory of money demand. 5. Demand for money depends on the current income, future income and the return on alternative asset. Explain how the demand for money depends on the indicated variables. 6. Keynes use two asset portfolios; bond and money in order to develop the speculative demand for money. Explain how the determinant of money demand is identified using this approach? Discus the practical feasibility of this approach. 7. Identify and describe the advancement of Baumol-Tobin theory of transaction, precautionary and speculative demand form money over Keynesian transaction, precautionary and speculative demand for money. 8. On what ground Keynesian theory of money demand is criticized. 9. Analyze Friedman's modern quantity theory of money.