3. Money, Inflation, and Interest Rate Links with Currency Values

Transcription

1 3. Money, Inflation, and Interest Rate Links with Currency Values Quantity Theory of Money... 1 Real and Nominal Interest Rates - The Impact of Expected Inflation... 4 Currency Values, Inflation, and Purchasing Power Parity... 7 Purchasing Power Parity... 8 Money Growth, Inflation, and PPP Forecasting Exchange Rates with PPP Forecasting Exchange Rates from Nominal Interest Rate Differentials Liquidity Demand, Real Interest Rates, Inflation, and Velocity Real Rates, Monetary Sources of Inflation, and Nominal Rates Money Supply, Interest Rates, and Exchange Rates Conclusion Appendix - A Monetary Exchange Rate Model Optional Extension NonTraded Goods References Figure 1- U.S. Money Quantity Equation Figure 2- Cumulative U.S. Excess Money Growth, and Inflation... 4 Figure 3- Pound Spot and PPP Spot Values Figure 4- Pound Spot Change less Inflation Differential Figure 5- Pound Spot Change less Excess Money Growth Differential Figure 6- Pound Spot Change less S/T Rate Differential Figure 7- U.S. Money Velocity and S/T Rates Table 1- British Pound PPP Values Table 2- Big MAC PPP Table 3- British Pound Money Growth PPP Values Appendix Japanese Figures

2 Money, Inflation, and Interest Rate Links with Currency Values Under the monetary view, money's value comes from the quantity of transaction and liquidity services provided in trading aggregate output. This interpretation leads us, first, to the Quantity Theory of Money. The Quantity Theory is important as a long-run theory, and as a direct link from excess rates of money supply growth to inflation. Generalizing, interest rate and inflation impacts on money demand are considered. Finally, implications of the long-run monetary view for nominal interest rates and exchange rates are addressed. In this development, real interest rates and output are assumed to be unaffected by money. Quantity Theory of Money The quantity theory of money states that the stock of money available in a period, multiplied by the number of times the money turns over in the period, must equal the nominal value of all transactions in that period. Algebraically, M*V = P*gni = GNI M V P gni GNI is the money stock available for transactions in dollars is the velocity of money, the number of times money turns over in a period is the nominal price level is real income or the number of real transactions is nominal income or nominal gross national product The unmeasured variable is velocity. Based on the quantity relation, velocity can be calculated as nominal GNI divided by money stock. For example, if nominal GNI is $1 trillion a year and money stock is $500 billion, then annual velocity is two. To further illustrate this relationship, Figure 1 has been drawn to approximately represent the Quantity Theory for the U.S. in Money View -1- International Finance

3 Figure 1 The statement of the quantity theory, listed above, is known as the money demand equation. It states how much money is demanded for transactions purposes over a period of time. Under the simplest Quantity Theory of Money, velocity is assumed to be constant. 1 With this assumption, the quantity theory implies that inflation is "always and everywhere a monetary phenomenon". This implication can be seen by identifying inflation as increases in the nominal price level, P: P = M*V/gni 1 Subsequent definitions of the money demand equation will allow velocity to change. This change can be made most easily by allowing velocity to be affected by nominal interest rates, V(R). Alternatively, the two components of nominal rates, real rates and expected inflation, affect velocity. Money View- 2

4 Since velocity is assumed to be constant, P will rise and inflation will result if the money stock grows faster than real income. Died-in-the-wool monetarists assume that money supply has no effect on real income (M and gni are independent). Therefore, a no inflation condition can only result when money growth matches real income growth. Since real income varies unpredictably, monetarists, such as Friedman, have strongly advocated that money growth be fixed at the level of long-term sustainable income growth. 2 The money demand equation is stated in terms of the stock of money available. The equation can also be transformed into an equation holding in its rates of change, or flows. If the equation is to hold after changes in the variables, then the changes in the variables in the equation must net out. This transformation to rates of change is done by taking natural logarithms and totally differentiating: proportional change in + no change = money stock in velocity (money growth) (assumed) proportional change + proportional change in in prices real income (inflation) (real income growth) Assuming that velocity is constant and rearranging the equation, we have the following: inflation = money growth - real income growth Alternatively, we define the difference between money growth and real income growth as excess money growth, and inflation = excess money growth 2 An alternative, which was proposed by some supply-siders, is to expand and contract the money supply to keep the price level fixed. They believed that such a target would automatically match money growth with real GNI growth. Unfortunately, such a rule takes no account of real shocks to prices such as OPEC, or the lags in price adjustment that may follow unexpected money supply changes. Money View -3- International Finance

5 This relationship shows clearly why inflation may be interpreted as a monetary phenomenon. Regarding this point, some rudimentary evidence for the U.S. is presented in Figure 2. Figure 2 As suggested by the monetary view, we can see that accumulated U.S. inflation and excess money growth do trend upward together. Real and Nominal Interest Rates - The Impact of Expected Inflation The real interest rate, r, is the discount rate that determines the present value of a unit of future output, b. On an annualized basis, this present value is the price of a real discount bond, b: b = 1 unit/(1+r) or r = 1 unit/b - 1 The present value (or price) is quoted in units of output, not currency. Since the value of a unit of output a year from now will generally be worth less that the value of a unit of output today, the real rate is generally positive. For example at a real rate of 2.5%, only units of current output are equivalent to one unit of output in a year. Money View- 4

6 Under the strict monetarist view, real interest rates and money supply are assumed to be independent. Under this assumption, inflation does not affect real interest rates. Nevertheless, nominal interest rates, R, are obviously affected by inflation. Approximately, R r + expected inflation (+ inflation risk premium) Nominal rates equal real rates plus expected inflation (plus possibly - a potential inflation risk premium). To illustrate this link, we continue to define excess money growth to be the source of inflation. In our example, we assume that 5% money growth is expected, while real gni is constant. This expected money growth rate will induce 5% expected inflation. The 5% expected inflation should cause a 5% inflation premium in the nominal rate in excess of the real rate. More specifically, assume that real gnp is one trillion units of output and the price level (or price per output unit) is one dollar. Nominal GNP is also $1 trillion. The money stock is $500 billion, so that the money stock must turnover twice to transact gni. Money velocity is two. The money quantity equation holds: 1 trillion units * ($1 per unit) = $500 billion * 2 Expecting 5% money growth, the expected money stock level is $525 billion. With real gni and velocity constant, we solve for the expected price level: 1 trillion units * ($? per unit) = $525 billion * 2 The new dollar price per unit of real output is $1.05. With 5% expected excess money growth and constant velocity, the price level is expected to rise 5%. Money View -5- International Finance

7 Expecting a 5% increase in prices, investors require greater nominal returns than real returns. If investors are insensitive to inflation risk, then the nominal return must compensate for expected inflation: 1+R = (1+r)*(1+expected inflation) = r + expected inflation + r*expected inflation +1 And approximately, R r + expected inflation Given a 2.5% real rate and 5% expected inflation, the nominal rate should be 7.625%. As an approximation, we overlook the real rateexpected inflation product term, and the nominal rate should be 7.5%, the sum of the real rate and expected inflation. 3 Under this approximation, the level of nominal interest rates is determined by two factors, the level of real interest rates and expected inflation. As a stronger approximation, expected excess money growth may be taken to be the only source of inflation, and nominal rates will equal the real rate plus expected excess money growth. To really model nominal rates, however, we should look more deeply into the sources of inflation and also to the impacts of investor risk sensitivity. This second factor motivates our parenthetical inclusion of an inflation risk premium in the original relationship between nominal rates and real rates. Unfortunately, we can never know expected inflation (or the inflation risk premium). The U.S., Canada, U.K. and Australian governments issue real bonds. Unfortunately, the payments on these bonds are more complicated than just being a real rate plus realized inflation. Nonetheless, these bonds are a useful source of expected inflation information. 3 The real rate can also be calculated directly as a discount rate. In our example, the expected price of a unit of output is $1.05. Therefore, $1.05 will be needed to pay for a unit of output in a year. The real present value of a unit of output in a year is units or $ at the current price level, $1. Therefore, the nominal rate must solve the following nominal discounting relationship. $.97561= $1.05/(1+R). On solution, the nominal rate, R, equals 7.625%. Money View- 6

8 A reasonable way to forecast nominal rate levels is to forecast the rate component changes. These expected changes should aggregate to the expected nominal rate change. The nominal rate forecast is this change plus the current nominal rate. We know that the nominal rate has two major components, the real rate and expected inflation, and one minor component, the risk premium. Given the current state of these three quantities, we should have a pretty good idea on whether they are going up, down or sideways. If all three are expected to rise, then so too are nominal rates. Mixed effects must by weighted analytically or heuristically. In the end, we suggest an expected nominal rate change minichecklist: Expected Increase in Expected Nominal Nominal Rate Effect Impact Real Rate + Excess Money Growth + Inflation + (Inflation risk premium) (+) Currency Values, Inflation and Purchasing Power Parity Just as real interest rates are determined by the relative value of current and future real output, currency exchange rates are set by the cost of current and future output in one country relative to another. In a world of fixed exchange rates, domestic country price changes imply real price changes. However, when exchange rates float, price changes in one country may be directly offset by an equivalent change in the exchange rate. For example, if U.S. export prices fall by 10% and import prices rise by 10%, or the dollar drops by 10%, the effective domestic price of U.S. and foreign goods is the same. Given unrestricted and low-cost international trade, goods should be priced similarly world-wide. Exchange rates should adjust to keep relative prices of import and export goods equal across Money View -7- International Finance

9 countries. This view led to an early theory of exchange rate determination called purchasing power parity. When exchange rates change to exactly offset price differences across countries, no real price effects occur, and the Purchasing Power Parity (PPP) Theory holds. In this case, the real volume of trade is unaffected by exchange rate change. However, if exchange rate changes do not exactly compensate for commodity prices changes across two countries, then the real price of traded goods will differ internationally. Lower priced goods, which are produced in the domestic country, will be exported and/or imported less. The volume of real trade will be affected. In this case, deviations from the PPP Theory provide an estimate of real price differences across countries. Purchasing Power Parity Purchasing Power Parity (PPP) theory states that the commodity purchasing power of one currency relative to another currency determines the exchange rate. There are two versions of the theory, absolute and relative. Absolute Purchasing Power Parity theory is straight-forward, but hard to implement. It states that at any point in time, the ratio of the price levels in two countries, where the price levels of the two countries reflect the cost of purchasing a representative basket of goods, determines the exchange rate. Under the absolute PPP theory, if two Deutschemarks (DM) are required to buy the same representative commodity or basket of commodities that one dollar does, then the DM is worth half a dollar. Algebraically, Domestic price/foreign price = foreign currency value or Price in US/Price in Germany = $1/2 DM = $0.5 per DM Since consumption baskets differ greatly world-wide, applying absolute PPP is difficult in practice. Construction of a price index for Money View- 8

10 one country is difficult enough. (As evidenced by U.S. experience with calculating its consumer price index (CPI).) Therefore, the relative view of PPP has been proposed as a means to implement PPP theory. Under this alternative, a representative point in time is chosen when the exchange rate is believed to fairly reflect the relative purchasing powers of the two currencies. The exchange rate prevailing at this time provides the PPP benchmark value. Since any change in the price level is inflation, differential inflation rates across the two countries will cause the currencies' purchasing power to change. Over time, accumulated inflation differentials are added to the benchmark exchange rate to determine the PPP exchange rates. To illustrate this relative version of PPP, we construct a U.S. dollar-british pound example. We choose January 1975 as the base period. The January 1975 pound exchange rate was $ From January 1975 until the end of third quarter 1984, U.S. inflation (as measured by the CPI) was %, and U.K. inflation was 196.3%. Since U.S. inflation was less than U.K. inflation, PPP implies that the pound should have been worth less in 1984, than it was in Given these levels of inflation, what should the pound's value have been? To work this value out, we start with the assumed PPP relation for 1975 and scale this value by the accumulated inflation differential. PPP Spot = Base year Spot x 1 + accumulated U.S. Inflation 1 + accumulated U.K. Inflation Table 1 illustrates this and other necessary calculations. Money View -9- International Finance

11 Table 1 British Pound Purchasing Power Parity Values As of September 1984, using January 1975 as the Base Period International Financial Statistics Data Spot Price Level U.S. U.K Variable S CPI CPI IFS Line # AR Base Period /75 End of Period /84 Inflation = 1984 CPI CPI (101.58%) (196.26%) Substituting these definitions of the 1984 price levels into the 1984 PPP SPOT equation. And substituting for the ratio of the price level using the relative PPP assumption, and the 1975 benchmark rate, ACTUAL 1975 SPOT* (1+ US inflation) = PPP 1984 SPOT (1+ UK inflation) $ * ( ) = $ ( ) To calculate the PPP spot price, we work through the following relationships and calculations: US 1975 PRICE LEVEL = ACTUAL 1975 SPOT = $ ) UK 1975 PRICE LEVEL and the unknown PPP 1984 spot price is US 1984 PRICE LEVEL = PPP 1984 SPOT = $? 2) UK 1984 PRICE LEVEL The rd quarter price level is the 1975 price level plus inflation, and US 1975 PRICE LEVEL* (1+ US inflation) = US 1984 PRICE LEVEL 3) UK 1975 PRICE LEVEL* (1+ UK inflation) = UK 1984 PRICE LEVEL 4) Dividing 3) by 4) and substituting 1) and 2) into this new equation yields the desired result. Generally, this method can be used to determine currency purchasing powers. Nevertheless, we find that the calculated Money View- 10