George Alogoskoufis, International Macroeconomics and Finance Chapter 3 Domestic Money Markets, Interest Rates and the Price Level Interest rates in each country are determined in the domestic money and financial markets, and adjust in order to equalize the supply of money by the central bank, with the demand for money by households and firms. The money supply (M1) is defined as the total of banknotes and coins in the hands of the public, plus deposits of households and firms in checking (current) accounts in commercial banks. Deposits of credit institutions and other institutions participating in the interbank market and the foreign exchange market are not considered as part of the money supply. A country s money supply is determined by the actions of its central bank, in its interactions with commercial banks. Households and firms demand and hold money because of its services as a means of payments and store of value, and the liquidity it provides. The demand for money is a demand for a certain amount of purchasing power which is positively dependent on the volume of economic transactions (as measured by real GDP) and negatively dependent on the opportunity cost of holding money, as measured by the rate of return of interest yielding assets, i.e the nominal interest rate. In the short run, for given prices and output, an increase in the money supply results in lower nominal interest rates. An exogenous increase in prices or output, for a given money supply, results in a higher nominal interest rate. In fact, any exogenous increase in money demand results in higher nominal interest rates in the short run, assuming that the money supply remains fixed. While in the short run increases in the money supply cause equilibrating changes in interest rates, in the long run what adjusts to equilibrate the money market is the price level. In fact the price level is the only variable that adjusts to equilibrate the money market in the long run. This property is called the long-run neutrality of money, and is a property of all consistent economic models of general equilibrium. In order to look at the determination of nominal interest rates, and the determination of the price level in the long run, we have to look at domestic money and financial markets and the role of money. 3.1 The Roles of Money Money performs three important roles in a modern economy. It is first a unit of account, second, a generally accepted means of payments, and, third, a store of value. As a unit of account, money is the unit in which all prices are measured. In a monetary economy prices are quoted in relation to money. This simplifies the calculation of values, as, otherwise,
economic agents would have to calculate too many relative prices between goods and services. For example, in an economy with N goods plus money, there are N money prices. Without money, economic agents would have to calculate N(N-1)/2 relative prices in order to make their transactions. As the number of goods increases, the number of relative prices to be calculated increases exponentially. For example, with 100 goods, one needs to know 100 money prices. Without money one would have to calculate 4950 relative prices among the various goods. With 1000 goods one would need to calculate 1000 money prices. Without money, 499500 relative prices, almost half a million would need to be calculated. Money thus helps simplify the calculation of prices and values. As a means of payment, money greatly facilitates economic transactions and limits transaction costs drastically. Without money in order to complete a transaction, the seller of a product or service would have to find a buyer who would be willing to offer in return something that the seller would also desire. Thus, for a transaction to be complete there must be a double coincidence of wants between buyers and sellers. Transactions without money are called barter, entailing huge search and other transactions costs on the part of buyers and sellers in order to ensure the double coincidence of wants. On the other hand, with money being generally accepted, there is no need for a double coincidence of wants, as all sellers accept money for payment. A modern economy would immediately cease to function if there was not a generally accepted means of payments. Money is also a store of value, and in particular the one characterized by the highest degree of liquidity. This is a key feature of money. If money was not a store of value, and it lost its value quickly, it would not be generally possible to function as a means of payments and a unit of account. Then again, since money is the only store of value which is also a means of payments, by definition it constitutes the most liquid store of value. 3.2 The Supply of Money The money supply is defined as the total of banknotes and coins in the hands of the public, plus deposits of households and firms in commercial banks. Deposits of credit institutions and other institutions participating in the interbank market and the foreign exchange market are not considered as part of the money supply. 3.2.1 The Role of Central Banks A country's money supply is eventually determined by the actions of the central bank and its interactions with commercial banks. A central bank, reserve bank, or monetary authority, is an institution that manages a state s currency, its money supply, and interest rates. Central banks also usually oversee the domestic commercial banking system. In contrast to a commercial bank, a central bank possesses a monopoly on determining the monetary base in the state, and usually also issues notes and coins, which usually serve as the state s legal tender. The primary function of a central bank is to control the nation's monetary conditions, through active duties such as issuing notes and coins, managing interest rates, setting reserve requirements for commercial banks, and acting as a lender of last resort to the banking sector, and possibly the state, during times of financial crisis. These duties usually determine a country s monetary policy. Central!2
! George Alogoskoufis, International Macroeconomics and Finance Ch. 3 banks usually also have supervisory powers, intended to prevent bank runs and to reduce the risk that commercial banks and other financial institutions engage in reckless or fraudulent behavior. Central banks in most developed nations are institutionally designed to be independent from political interference. Still, limited control by the executive and legislative bodies usually exists. 3.2.2 The Monetary Base and the Money Supply The monetary base in an economy is defined as the sum of coins and banknotes held by the public, plus the reserves of commercial banks held at the central bank. Thus, the monetary base B is equal to,! B = C + R (3.1) where C is currency (coins and notes) held by the non-bank public (households and firms), and R the reserves of commercial banks. An alternative definition for the monetary base is high powered money. The monetary base is under the close control of the central bank, as the central bank decides how much currency to issue, and can also control the reserves of commercial banks either directly or indirectly. The money supply is defined as the total of coins and banknotes held by the public, plus deposits of households and firms in commercial banks. Thus, the money supply M is determined by, M = C + D (3.2) where D is deposits in checking accounts in commercial banks. If D denotes deposits in checking (current) accounts only, then the money supply is narrowly defined, a definition known as M1. If D denotes both deposits in checking accounts and savings and time deposits, the money supply is more broadly defined, a definition known as M2. If large time deposits, institutional money market funds, short-term repurchase and other liquid assets are included in deposits, then the money supply is more broadly defined, a definition known as M3. The relationship between the monetary base and the money supply can be derived by dividing (3.2) by (3.1). It follows that the money supply is proportional to the monetary base, according to, C! M = C + D (3.3) C + R B = D +1 C D + R B = c +1 c + r B = mb D where m is the so-called money multiplier. The money multiplier depends on two crucial parameters. The ratio of currency to deposits chosen by the non-bank public, c=c/d, and the reserve ratio of commercial banks, r=r/d. To the extent that these two ratios are stable, there is a stable proportional relationship between the monetary base and the money supply. Thus, by controlling the monetary base, the central bank can control the money supply. To the extent that either the ratio of currency to deposits of the non-bank public, or the reserve ratio of commercial banks are volatile, the control of the money supply by the central bank entails difficulties, because of the volatility of the money multiplier. However, the central bank can also affect the money multiplier through minimum reserve requirements for commercial banks, and other instruments,!3
such as short term interest rates, that may affect the currency deposit ratio of the non-bank public, or the reserve ratio of commercial banks. 3.2.3 Commercial Banks and the Money Supply It is clear from the discussion above that the central bank is not the only institution that affects the money supply. The behavior of the non-bank public, in choosing to hold money in the form of either currency or deposits, and the behavior of commercial banks, in deciding the ratio of their reserves to their deposits also affect the money supply. As can be seen from (3.3), a reduction in the reserve ratio of commercial banks causes an increase in the money multiplier and the money supply for a given monetary base. Thus, ultimately the money supply is determined by three factors. First, the amount of notes and coins issued by the central bank, second the choices of the non bank public between holding money in the form of notes and coins and deposits in commercial banks, and third the choices of commercial banks between holding reserves with the central bank against their deposits, versus lending to the non-bank public (households and firms) or investing in other interest yielding assets such as shares and bonds. However, since the central bank can largely determine the monetary base, and, indirectly, the cash deposit ratio of the non-bank public and the reserve ratio of commercial banks, it can, to a large extent, exert indirect control on the money supply. Thus, it is not too inaccurate to say that the money supply can in principle be controlled by the central bank. 3.3 The Demand for Money Households and firms demand and hold money because of its services as a means of payments and store of value, and the liquidity it provides. How much money households and firms wish to hold depends on the value of transactions they wish to conduct, i.e the volume of transactions and the price level. The demand for money is a demand for a certain amount of purchasing power which is positively dependent on the volume of economic transactions (as measured by real GDP) and negatively dependent on the opportunity cost of holding money, as measured by the rate of return of interest yielding assets, i.e the nominal interest rate. The demand for money function is thus assumed proportional to the price level, positively related to the volume of economic transactions, and negatively related to the nominal interest rate. It is proportional to the price level, on the presumption that an increase in the level of prices requires an analogously higher quantity of money to conduct the same volume of economic transactions. It is positively related to real output (GDP) on the presumption that an increase in output and income requires more money for transaction purposes. Finally, it is negatively related to the interest rate, as households and firms forego interest when they hold their assets in the form of money rather than interest bearing securities. The interest rate is thus the opportunity cost of holding money, and when it goes up, money holdings are expected to decline. The form of a typical demand for money function is,!4
M! M = PL(Y,i), or! = L(Y,i) (3.4) P where M is the nominal stock of money, P the price level, Y is real income and i is the nominal interest rate. L denotes the demand for real money balances function, which depends positively on real income and negatively on the nominal interest rate. A special case of (3.4) is the so call quantity theory equation, which assumes a unitary income elasticity of money demand, i.e that money demand is proportional to real output and income. This takes the form, M! (3.5) P = k(i)y where k is a negative function of the nominal interest rate. The demand for money schedule, as a negative function of the nominal interest rate is depicted in Figure 3.1. An increase in real income causes this demand for money schedule to shift upwards and to the right, as with higher real income, more money is demanded at given nominal interest rates. This shift is depicted in Figure 3.2. 3.4 Equilibrium in the Money Market and the Short Run Determination of Interest Rates Equilibrium in the money market occurs when the supply of money, as determined by the central bank, is equal to the demand for money, as determined by the behavior of households and firms. What adjusts in the short run to bring about equilibrium is the nominal interest rate, which can move much more quickly than aggregate income or the price level. The determination of the nominal interest rate is depicted in Figure 3.3. In the short run, the nominal interest rate moves to equilibrate the money market, in the sense of equating the demand with the supply of money. If the nominal interest rate is higher than the equilibrium interest rate i0 there is an excess supply of money. As agents try to buy interest yielding securities instead of holding money, the price of these securities rises and their yield, the nominal interest rate, falls. The opposite happens if the interest rate is lower than the equilibrium interest rate i0. These equilibrating interest rate shifts happen very quickly, as traders in financial markets engage in arbitrage between money and interest bearing securities. In Figure 3.4 we examine the effects of a short run increase in the money supply by the central bank. This shifts the money supply to the right, and causes nominal interest rates to fall. This negative short run effect of an increase in the money supply on domestic money markets is called the liquidity effect. Thus, central banks can reduce interest rates in the short run by increasing the money supply, and increase interest rates by reducing the money supply. Hence, central banks can control interest rates in the short run through injections of withdrawals of liquidity from the market. In Figure 3.5 we examine the effects of a short run increase in money demand because of an increase in output. This shifts the money demand schedule to the right, and causes nominal interest rates to rise. This is because the demand for money for transaction purposes increases, and a rise in nominal interest rates is required in order to equate money demand with the money supply which!5
has not changed. Similar effects on interest rates would apply if the increase in money demand was autonomous, rather than induced by an increase in real output. We next turn to the long run effects of money and monetary policy. While in the short run what adjusts to equilibrate the money market is the level of nominal interest rates, in the long run it is the price level that adjusts to equilibrate the money market. 3.5 Long Run Effects of Money and Monetary Policy Permanent changes in the money supply eventually affect the level of prices of goods and services. Thus, a permanent increase in the money supply may affect interest rates in the short run, by creating an excess supply of money, but gradually the price level starts rising. The rise in the price level reduces the excess supply of real money balances, bringing interest rates back to their original level. Eventually, the price level rises by the same proportion as the money supply, and nominal interest rates return to their original level. Real income is not affected by the level of the money supply either. Thus, the only variable that is affected by a permanent change in the money supply in the long run is the price level, and not real income or interest rates. 3.5.1 A Permanent Increase in the Money Supply This can be shown by equating the money demand equation (3.4) with the money supply, and solving for the price level. M! P = (3.6) L(Y,i) What determines the long-term level of real output Y are real and not monetary variables, such as the stocks of natural resources, capital and labor, productivity, savings and the functioning of markets and other economic institutions. Real output does not depend on the stock of the money supply in the long run. Nominal interest rates do not depend on the stock of the money supply in the long run either. In the absence of long run inflation, the nominal interest rate is equal to the productivity of capital in the long run. This depends only on real and not monetary factors. Thus, the only variable affecting money demand that can adjust to equilibrate the money market in the long run is the price level. In the long run, the money supply is merely a "veil" for the real economy and just determines the price level. This is called the long-run neutrality of money, and is a property of all theoretically consistent general equilibrium economic models. Thus, while in the short run an increase in the money supply causes equilibrating changes in nominal interest rates, in the long-term what adjusts to equilibrate the money market is the price level, as interest rates return to their long-run equilibrium. 3.5.2 Monetary Growth, Inflation and Nominal Interest Rates in the Long Run In the same way that a permanent increase in the money supply causes a long run increase in the price level by the same proportion, monetary growth, in the form of continuous increases in the!6
money supply that exceed the long run growth rate of output cause continuous price inflation. Inflation in the long run is determined by the difference between the long run rate of growth of the money supply and the long run rate of growth of money demand, which is equal to the long run rate of growth of output. Thus, long run inflation is determined by,! π = µ g (3.7) where π is inflation, µ the rate of growth of the money supply, and g the rate of growth of output and demand for real money balances, assumed exogenous. (3.7) is derived by taking the rates of growth of prices, money and output in the quantity theory equation (3.5), assuming a constant long run nominal interest rate. The positive one to one relation between monetary growth and inflation implied by (3.7) is related to the so called long run super-neutrality of money. A high rate of growth of the money supply by the central bank results in long run inflation, without affecting either the rate of growth of output or real interest rates. However, long run inflation affects the level of nominal interest rates, as investors in bonds and other interest yielding nominal securities seek to be compensated for the loss in the real value of their assets through inflation. Thus, in an economy with a non zero long run inflation, nominal interest rates are determined by the so-called Fisher equation, which states that the nominal interest rate is equal to the real rate of return on capital, plus expected inflation. The Fisher equation takes the form,! i = ρ + π (3.8) where ρ is the equilibrium real interest rate, equal to the real rate of return on capital. As there is a one to one relationship between long run monetary growth and inflation in the quantity theory equation (3.5), so there is a one to one relationship between long run inflation and nominal interest rates in the Fisher equation (3.8). Thus, high monetary growth economies will tend to have high long run inflation, and high long run inflation economies will tend to have high long run nominal interest rates. 3.5.3 The Welfare Cost of Inflation What is the cost of high long run inflation? High inflation economies will tend to have high nominal interest rates. High nominal interest rates will result in a reduction in money demand. Thus, high inflation economies will be associated with lower real money balances in the long run. This will result in a loss of consumer surplus from the use of money, which is the welfare cost of inflation. The welfare cost of inflation is depicted in Figure 3.6. A positive rate of long run inflation causes nominal interest rates to increase from i0 to i1. This reduces money demand and the real money balances in the long run, and creates a welfare cost in the form of loss of consumer surplus, which is depicted by the colored area. This colored area is the welfare cost of inflation. Essentially, in high inflation economies households and firms hold smaller quantities of money for their transactions, because of the higher opportunity cost of holding money implied by higher!7
inflation. This forces them to make more trips to the bank in order to convert interest yielding assets into money, and thus implies a welfare cost in the form of higher transactions costs. 3.6 Conclusions In the short run, nominal interest rates adjust to equilibrate the money market. An increase in the money supply results in a fall in nominal interest rates, and a decrease in the money supply results in a rise in nominal interest rates. An increase in money demand, either autonomously, or because of an increase in output, results in a rise in nominal interest rates. A fall in money demand, either autonomously or because of a decrease in output, results in a reduction in nominal interest rates. In the long run, what adjusts to equilibrate the money market is the price level. Permanent increases in the money supply push prices to a higher level in the long run, but do not affect the level of real income or interest rates. Higher rates of monetary growth results in higher inflation rates and higher nominal interest rates, but do not affect the growth rate of output or real interest rates. Thus, in the long run money is neutral with respect to the real economy. The level of the money supply only affects the price level in the long run, and the rate of growth of the money supply only affects inflation and nominal interest rates in the long run. No real variables are affected by the level or the rate of growth of the money supply in the long run, with the exception of the demand for real money balances, which depends negatively on the level of nominal interest rates. Thus higher monetary growth and inflation, by causing higher nominal interest rates result in a long run reduction in the demand for real money balances and this implies a welfare cost.!8
Figure 3.1 The Demand for Money and the Nominal Interest Rate!9
Figure 3.2 An Increase in Real Output and the Demand for Money Schedule!10
Figure 3.3 Equilibrium in the Money Market and the Determination of Interest Rates!11
Figure 3.4 An Increase in the Money Supply and Nominal Interest Rates The Short Run Liquidity Effect!12
Figure 3.5 An Increase in Money Demand and Nominal Interest Rates!13
Figure 3.6 An Increase in Inflation, Long Run Nominal Interest Rates and Money Demand!14