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

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3 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

4 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

5 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

6 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

7 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

8 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

9 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

10 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

11 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

12 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

13 purchasing power parity exchange rate differs from the actual 1984 Third Quarter $/Pound exchange rate. The predicted relative PPP 1984 pound spot price is $ However, the actual 1984 spot price was $ Therefore, PPP implies that the pound was under-valued in September 1984 (using a 1975 base year). Analogously, the dollar was overvalued relative to the pound. The U.S. dollar value can be analyzed relative to other currencies in this manner also. Figure 3 plots the purchasing power value of the pound relative to the dollar. Using 1970 as the base year, we see from 1970 to the current time that the pound value consistently exceeded its relative purchasing power. The difference peaked in 1979, and stabilized from 1992 on at about $0.80. Part of the reason for this "overvaluation" is our choice of a 1970 base year. At that time, fixed exchange rates had prevailed for many years, and the dollar was relatively overvalued. Therefore, the initial foreign currency overvaluation, which we observe, is probably correcting for these currencies being under valued initially (in 1970.) Again, since 1992, both spot and the PPP value haven t changed markedly. Money View -11- International Finance

14 Figure 3 An alternate version of purchasing power parity can be stated in terms of the rate of change of the exchange rate and the inflation rates of the two countries. Taking logarithms of the absolute purchasing power parity relationship and totally differentiating, we find that the following equation holds: proportional change = domestic - foreign in the exchange rate inflation inflation (exchange rate change) rate rate This relation is known as the flow version of purchasing power parity. Alternatively, we can write the relation as exchange rate change = differential inflation rate or 0 = exchange rate change - differential inflation rate PPP theory states that the difference between the percentage change in the exchange rate and differential inflation (U.S. U.K.) should be zero. Figure 4 plots the necessary data to analyze this hypothesis for the U.K. and U.S. We see that the relationship does not hold. Positive bars above the zero line indicate foreign currency Money View- 12

15 appreciation over differential inflation, and the opposite for the negative bars. If PPP held exactly, there would be no bars and the dotted spot line and solid US-UK inflation line would coincide (they don t.) The PPP deviation bars are more positive than negative and all but one of the large deviations are driven by spot price changes (I.e., the pound value is more variable than the inflation differential.) Of additional relevance against the PPP hypothesis is the non-random nature of the deviations from PPP. Multiple periods of positive deviations tend to group together, and the negative deviations from also group. Such series of signed errors negate hypothesized randomness. Figure 4 Purchasing power parity can be checked, similarly, across other products and countries. Our analysis was based on the aggregate consumption basket for the U.S. and U.K. Table 2 shows how PPP stands up using the price of Big Macs as a price index. We see that PPP can be pretty far off in terms of hamburgers also. Table 2 - BurgernomicsThe Big Mac index - Jul 11th 2018 Money View -13- International Finance

16 Interactive currency comparison tool - THE Big Mac index was invented by The Economist in 1986 as a lighthearted guide to whether currencies are at their correct level. It is based on the theory of purchasing-power parity (PPP), the notion that in the long run exchange rates should move towards the rate that would equalise the prices of an identical basket of goods and services (in this case, a burger) in any two countries. Burgernomics was never intended as a precise gauge of currency misalignment, merely a tool to make exchange-rate theory more digestible. Yet the Big Mac index has become a global standard, included in several economic textbooks and the subject of dozens of academic studies. For those who take their fast food more seriously, we also calculate a gourmet version of the index for 48 countries plus the euro area. The GDP-adjusted index addresses the criticism that you would expect average burger prices to be cheaper in poor countries than in rich ones because labour costs are lower. PPP signals where exchange rates should be heading in the long run, as a country like China gets richer, but it says little about today's equilibrium rate. The relationship between prices and GDP per person may be a better guide to the current fair value of a currency. Read more about the Big Mac index in Investors are gorging on American assets from the Finance section. You can also download the data or read the methodology behind the Big Mac index here. We hope you like the improvements we have made to this tool. Please take this short survey and let us know what you think. Money View- 14

17 Table 2 GDP - BurgernomicsThe Big Mac adjusted index - Jul 11th 2018 This adjusted index addresses the criticism that you would expect average burger prices to be cheaper in poor countries than in rich ones because labour costs are lower. PPP signals where exchange rates should be heading in the long run, as a country like China gets richer, but it says little about today's equilibrium rate. The relationship between prices and GDP per person may be a better guide to the current fair value of a currency. The adjusted index uses the line of best fit between Big Mac prices and GDP per person for 48 countries (plus the euro area). The difference between the price predicted by the red line for each country, given its income per person, and its actual price gives a supersized measure of currency under- and over-valuation. Money View -15- International Finance

18 Money Growth, Inflation, and PPP The Quantity Theory of Money defines a direct link between money growth and inflation. This link provides an alternative estimation method for purchasing power parity exchange rates. Since inflation equals excess money growth under this theory, we may substitute excess money growth for inflation in the PPP stock and flow relationships. Again, consider our U.S.-U.K. example: ACTUAL 1975 SPOT * = (1 + U.S. excess money growth) (1 + U.K. excess money growth) = PPP 1984 SPOT Table 3 lists the data necessary for calculating this formula, and the source lines from the IMF's International Financial Statistics (IFS) for the U.S. and U.K. data. Since U.S. excess money growth was % and U.K. excess money growth was 221.5%, the U.K. should have had higher inflation, and the pound should be well below it's benchmark 1975 value, $ The Quantity Money Theory - PPP implied exchange rate is $ As with the inflation differential-based PPP exchange rate, this rate is also well above the actual 1984 rate of $ In the flow PPP equation, excess money growth can be substituted for inflation: exchange = U.S. excess - U.K. excess rate change money growth money growth = differential excess money growth Money View- 16

19 Table 3 British Pound Money Growth Purchasing Power Parity Values As of September 1984, using January 1975 as the Base Period International Financial Statistics Data U.S. U.K Spot Nominal Nominal Variable S CPI MONEY GNP CPI MONEY GNP IFS Line # AR 64 5C9MB 99A 64 34B 99A Base Period 1/ End of Period /84 Inflation = 1984 CPI CPI (101.58%) (196.3%) Money Growth = 1984 M M (152.7%) (246.7%) Nominal 1984 GNP Income Growth = 1975 GNP (150.7%) (221.5%) Real Income Growth (1.507 = (2.215 = (nom. income growth ) ) inflation) Excess Money Growth (1.527 = (2.467 = (money growth - real ) ) income growth We substitute excess money growth for inflation into the 1984 PPP SPOT equation defined in Table. Again substituting for the ratio of the price level using our relative PPP assumption, and the 1975 benchmark rate, we have ACTUAL 1975 SPOT* (1+ US excess money growth) = PPP 1984 SPOT (1+ UK excess money growth) $ * ( ) = $ ( ) The predicted relative excess money growth PPP 1984 spot price is $ This price is below the inflation PPP prediction, and can be viewed as indicating that further inflation pressures existed in the U.K. relative to the U.S. However, the actual 1984 spot price was $ Therefore, both the inflation and excess money growth versions of PPP imply that the pound was under valued in September 1984 (using a 1975 base year). Money View -17- International Finance

20 Figure 5 plots this relationship. As in all other cases, we see that the excess money growth rationale for exchange rate change is inaccurate. Large mid-1980 s pound appreciation and low U.K. excess money growth dominates the relationship, which is, overall, far from zero. Persistent periods of exchange rate changes in excess of excess monetary growth (positive bars) indicate non-randomness. Figure 5 When inflation is of predominant importance, PPP can be a good exchange rate model. Hyper-inflation cases, such as Germany in the 20's, various Latin American currencies, and Israel in the early 1980's, provide good examples. In these high inflation cases, the excess money growth view of PPP will often be more useful than the measured inflation differential view. This usefulness results because countries in a hyperinflation situation often fix prices, ration goods, and print money. Therefore, true inflation will not show up in CPI changes. The inflation pressures will be manifest in excess money growth. Money View- 18

21 Excess money growth provides a measure of pent up inflation. This measure is useful whenever price controls are in effect, as was true in the U.S. in the 1970's. For PPP to be a useful tool in these cases, it should provide a good exchange rate forecast. It can do this in three ways. Forecasting Exchange Rates with PPP The first way to use PPP as a forecasting tool, is to analyze hyperinflation cases. In this situation, expected money growth is set equal to the current money growth level, or modeled by simple (but statistically valid) procedures. Then, the expected exchange rate change is roughly equal to the expected money growth rate differential. 4 This modeling approach has been relatively successful in hyperinflation scenarios. The second way to use PPP for exchange rate forecasting is relevant for all currencies. Effectively, the PPP rate is looked upon as a long-run measure of currency value. Since in the end, a country is unlikely to run balance of payments imbalances forever, trade flows are a very, if not the most, important long-run determinant of exchange rates. PPP reflects the relative value of currencies for purchasing goods and can indicate if a currency is over or undervalued for the long-run. Some recent empirical work based on U.S. and U.K. data back through the 1800's indicates that it took four to six years for the pound rate to return halfway back to its long-run value. This aspect of PPP is particularly important when talk of fixing or managing exchange rates arises. Some method must be used to pick an appropriate fixed exchange rate. The 1985 coordinated action of the U.S., Japan, Canada, Germany and the U.K., the Group of Five, to bring down the "overvalued" dollar was in large part due to the market value of the dollar being so out of line with its purchasing power (as were the 1987 actions to bring it back up.) 4 The money demand equation is usually estimated in these applications, and a monetary exchange rate model in the appendix motivates this specification a bit more. Money View -19- International Finance

22 An important mis-evaluation of a currency's purchasing power occurred for the British pound following its float during and after World War I. In the early 1920's, the pound's value was refixed at its mighty pre-war level, even though its purchasing power had eroded badly during the war (especially relative to the dollar). Some feel that this overvalued pound rate, coupled with similar misvaluations by other countries, led first to trade barriers (to correct the resulting balance of payments problems), then led to competitive currency devaluations, and finally led directly to the 1930's depression. Current and reocuring Greek and other countries problems in the EMS Euro may, in retrospect, be partially due to the exchange rates at which these countries entered the Exchange Rate Mechanism (ERM). In the longer run, currency purchasing power is always relevant for currency valuation. This lesson is important should policy makers try to move the world monetary system back toward fixed or pegged exchange rates, or should a country enter a fixed exchange rate system, (e.g. Scandinavian countries' peg to the EMS European Currency Unit (ECU).) The third way to use PPP as an exchange rate forecasting tool is to move in to the forecasting of the determinants of purchasing power. Using this approach, the problem of forecasting exchange rates is translated into the problem of forecasting inflation and excess money growth. However, a quick review of plots of the foreign currencies and the related variables show that the variability of inflation and excess money growth, whether actual or based on forecasts derived from the data, do not explain short-term exchange rate changes very well. Forecasting Exchange Rates from Nominal Interest Rate Differentials We have already discussed why the following relationship should hold: nominal interest rates real interest rates + expected inflation Money View- 20

23 This relationship is especially important because it is forward looking. Effectively, it says that if investors expect more inflation (less purchasing power), then they will require a higher nominal return on their nominal investments in order to offset their expected purchasing power loss. To apply this insight, let us make another strong assumption: real interest rates are relatively constant and equal across countries. Under this assumption, changing nominal interest rate levels provide expected inflation information. Higher nominal rates forecast higher inflation, and vice versa. Under this simplifying assumption, nominal interest rates can also be used to forecast currency values. Specifically, the nominal interest rate differential across two countries should equal their expected differential inflation rate. Under PPP, this expected differential inflation rate should equal the expected exchange rate change. Therefore, PPP and a simple view of real and nominal interest rates, together, imply expected exchange = differential expected = differential nominal rate change inflation interest rates For the U.S. and a foreign country, expected foreign = U.S. nominal - foreign nominal currency value change interest rate interest rate Higher U.S. nominal rates mean higher expected U.S. inflation, and less expected U.S. purchasing power, and a more valuable foreign currency. Figure 6 provides a graphical analysis of this relation. If our PPP and real rate assumptions are true, then the average of the deviations around the X-axis should be close to zero, and be uncorrelated across time. This plot tends to show that the nominal interest rate differential forecast of exchange rate change is not very good. As with the other PPP exchange rate measures, the grouping of positive errors is problematic for forecast error independence. Money View -21- International Finance

24 However, this finding does not necessarily mean that this measure of expected inflation is useless for forecasting exchange rates. FIGURE 6 Even though a lot of inflation may be expected, it may not occur. For example in 1980, inflation rates of 15-20% were viewed as quite possible. However, they did not occur. Estimates of expected inflation based only on realized inflation levels did not account for this possibility. However, nominal interest rate differentials might have reflected this possibility. Therefore, market-based nominal interest rate differential expected inflation estimates can provide useful information. Both short-term and long-term nominal interest rate differentials can be used for this purpose. Nevertheless, Figure 6 shows that much is still left unexplained. The quantity theory has a remaining component which may explain some of this error. This component is velocity, and modeling velocity may or may not provide better forecasts. Liquidity Demand, Interest Rates, Inflation, and Velocity Real money supply is defined as the stock of money divided by the price level, m = M/P. Given a fixed money velocity, the simple Money View- 22

25 Quantity Theory identifies real money supply as an absolute brake on the potential level of real gnp. This implication of the Quantity Theory is not true, and is adjusted by allowing the stock of money available for transactions to be affected by interest rates and inflation. Therefore, this model has been extended to incorporate a second interest rate and inflation-sensitive component of money demand. This component is liquidity demand, which leads to changing velocity. Since the nominal interest rate can be viewed as the opportunity cost of holding money balances, a higher opportunity cost (interest rate) implies that less money is held. The higher rate can be caused by high real rates or high expected inflation. In either case, there is less liquidity demand for money. At very high rate levels, only money necessary for transactions will be held, and liquidity demand goes to almost nothing. Therefore, money will turn over quickly, liquidity demand would be very low, and its velocity will be high. Another way to state this concept is that at high rate levels, a large number of transactions (high real gnp) can by accommodated by a relatively low real money stock. To highlight this liquidity demand factor, we can split total money stock into two components, transaction money and liquidity money. Liquidity money is the money kept in checking and other short-term accounts, which is relatively available for transactions. Because the cost of keeping money balances is low at low interest rates, liquidity money demand is higher at low interest rate levels, and lower at high rate levels. We write the liquidity demand for money as a general function of nominal interest rates, M L (R). Also defining transaction money as M T, we have total money demand: M = M T + M L (R) Money View -23- International Finance

26 Since we assume that total money stock is controlled by the central bank, the money available for transaction purposes is a residual component of money demand, after "liquidity money" is accounted for: M T = M - M L (R) Therefore, the stock of money that is available for transactions is also a positive function of nominal interest rates. As rates rise, liquidity money demand falls, and the money stock available for transactions rises. We already interpreted the quantity theory in terms of money's transaction services. Our discussion of liquidity demand indicates that all money is not available for transactions, and that the money stock which is available for transactions varies with the level of nominal interest rates. Therefore, we amend the quantity theory as follows: M T *V = P*gnp [M-M L (R)]*V = P*gnp Since our major concern is the impact of money stock on inflation, we re-define the price level: P = (M - M L (R))*V/gnp In this case, price level changes occur not only when total money stock growth differs from gnp growth, but also when nominal interest rates change. In approximate rate of change terms, inflation % change in - % change in - % change in total money liquidity demand real gnp supply (due to rate changes) To review this definition, we assume that excess money growth, which is total money supply growth less real gnp growth, is zero. What are the inflationary effects of interest rate changes? Lower rates increase liquidity demand, so that a lower transaction money stock is available. All else equal, lower rates should result in lower inflation. With high rates, liquidity balances are kept low, and Money View- 24

27 a relatively large stock of transaction money is available. Hence, inflation should rise with higher rates. To analyze the hypothesized links, we can examine velocity and its relation to interest rates. Under the simple quantity theory, velocity is constant and may be estimated as nominal GNP divided by money stock. With additional consideration of liquidity money demand, velocity will not remain constant. However, it will be equal to nominal gnp divided by transaction money stock. Unfortunately, transaction money stock is unobservable. In terms of total money stock (which we do know), measured velocity is also not constant. At high real rates or high levels of expected inflation, nominal rates are higher, and liquidity demand is low. Therefore, money stock velocity is high. At low real rates or low levels of expected inflation, liquidity demand is high and money sits around in pockets at low cost with low velocity. To see how these links hold in reality, Figure 7 plots U.S. money velocity against U.S. nominal interest rate levels. Clearly, velocity is not constant. Interestingly, velocity does seem to move roughly in line with nominal interest rate levels. Most recently, the significant drop in U.S. rates is matched with a marked decline in velocity. Money View -25- International Finance

28 FIGURE 7 Real Rates, Monetary Sources of Inflation, and Nominal Rates Initially, we defined the nominal rate as the real rate plus expected inflation (plus an inflation risk premium). Now, we have identified factors that lead to inflation. In a business context, gaining this deeper understanding is important because it provides a mechanism for forecasting inflation and nominal interest rates. If a factor that causes inflation is expected to pick up, then inflation and nominal rates should rise, and our planning should incorporate this expectation. For example, a higher general price level is more likely to occur with higher interest rates, and, under the monetary view, a lower currency value. Actually, under the pure neutrality of money view, all of these changes could (should?) combine to have no impact on real business decisions and economic activity. Money View- 26

29 In review, we summarize the factors that have been hypothesized to affect nominal rates: Increase in Nominal Rate Effect Real Rate + (also leads to lower liquidity money demand and more transaction money) (+) Expected inflation + (also leads to lower liquidity demand and more transaction money) (+) Money growth + Real gnp growth - Excess money growth + (inflation risk premium) (+) Money Supply, Interest Rates, and Exchange Rates Under Purchasing Power Parity (PPP), interest rates affect excess money growth. Therefore, rates will also affect currency values. As before, expected exchange = U.S. excess money - foreign excess money rate change growth (U.S. real rate) growth (foreign real rate) = differential excess money growth (U.S. foreign rate) In this expanded definition, we have incorporated interest rate effects into U.S. and foreign excess money growth. Without considering real rate effects on liquidity demand, low money growth and high real income growth in a country lead to an appreciation of its own (domestic) currency. If at the same time nominal rates rise, then liquidity demand falls, velocity increases and excess transaction money is available. This extra money yields relatively more inflation, and less appreciation of the domestic currency than would otherwise be the case. Dependent on the interest rate sensitivity of liquidity demand, tight money may not lead to low inflation and a rising domestic currency because associated higher rates may lower liquidity money Money View -27- International Finance

30 demand. Analogously, if associated with a fall in interest rates and money velocity, high money growth and low income growth may not lead to a falling currency value. Two final cases of interest concern high money growth coupled with high real income growth, and low growth in both money and real income. Should high rates result from either of these combinations, then the rise in velocity is likely to predominate. In this case, inflation and a falling domestic currency value should result. Analogously, combinations that yield lower interest rates and lower velocity should yield limited inflation and a rising domestic currency value. Just as we summarized the affects of certain factors on nominal interest rates, we can summarize certain factors affects on the exchange rates: % change in = % differential - % differential + v* (differential foreign currency money growth real income nominal rate value growth change) The final velocity change term incorporates the impact of interest rates on liquidity demand and velocity. For currency values, differential factors across countries are important. If U.S. rates are much higher than foreign rates, then U.S. velocity is higher, and (all else equal) U.S. inflation is higher. In this case, the foreign currency should appreciate. Analogously, higher foreign rates imply relatively more transaction money abroad, and the foreign currency should depreciate. Money View- 28

31 Across all of the hypothesized factors considered, we posit the following links: U.S. Inflation Implications Relative Exchange Rate to Foreign Dollar ($ Foreign Forecast Increase in Inflation Value Currency Value) U.S. Money Stock Up Down Up Foreign Money Stock Down Up Down U.S. Real Income Down Up Down Foreign Real Income Up Down Up U.S. Real Rate Up Down Up Foreign Real Rate Down Up Down U.S. Expected Inflation Up Down Up Foreign Expected Inflation Down Up Down Differential Money Growth Up Down Up Differential Real Income Growth Down Up Down Differential Real Rates Up Down Up Conclusion The monetary model suggests that interest rate and exchange rate changes, as well as the variability of these changes, should be related to changes and variability of other quantities. These quantities are excess money growth, income growth, real interest rates and expected inflation. Under the monetary model hypothesis, the problem of forecasting interest rates and exchange rates is transformed into the interrelated problem of forecasting these quantities. Under the monetary view, higher money growth leads to inflation. Inflation raises nominal interest rates and lowers the domestic currency value. Higher domestic real income means higher money demand and lower nominal prices. As a result, the domestic currency value rises. Higher domestic real interest rates mean higher domestic nominal interest rates and a lower currency value under the monetary model. Increases in nominal interest rates come from two sources. First, the base real rate component may rise. Second, expectations of future inflation rise. Expected inflation may increase directly with expectations of future price increases or may increase with a money velocity increase associated with expectations of rising interest rates. The velocity increase raises future excess money growth and Money View -29- International Finance

32 inflation. As increased velocity raises the expected transaction supply of domestic currency available, and the home currency depreciates. Finally, a short appendix is provided. It develops a simple monetary exchange rate model, which has been relatively successful in hyperinflation cases, and also links the monetary model to the long-run view of the real economy. Money View- 30

33 Appendix - A Monetary Exchange Rate Model The monetary model states that the exchange rate equilibrates currency purchasing power. Under PPP and the quantity theory of money, a currency's relative purchasing power (Pus/ Pf)is set by the money stock, real income, and money velocity (the Quantity Theory, P = M V gnp). Defining the U.S.-foreign currency spot exchange rate, S, in these terms, S = P us (M us* V us /gnp us ) P = f (M f* V f /gnp f ) Taking natural logs, and indicating logs by a prime over a variable, S = P us - P f = M us - M f - (gnp us - gnp f ) + V us - V f If we additionally define both countries' money velocity as an exponential function of their nominal interest rate, V = e vr, then V = vr. We have S = M us - M f - (gnp us - gnp f ) +v * (R us - R f ) The log exchange rate is hypothesized to be equal to the difference in log money stocks, less the difference in log real incomes, plus a positive constant times the interest rate differential. 5 Rewriting the nominal interest rate in its component parts (real rate and expected inflation), S = M us - M f - (gnp us - gnp f ) + v * (r us - r f ) + v*(expected inflation differential) This model allows us to summarize the effects of money, real income, expected inflation and real rates on the exchange rate. 5 For a domestic, d, country and a foreign, f, country, the model can be fitted and tested by a regression: ' ' ' ' ' ' S = a + b(m M ) c(gnp gnp ) + v * (R R ) + e t dt ft dt ft dt ft t b, c and v all greater than zero. Money View -31- International Finance

34 Higher money growth in the U.S., M us, implies that the log exchange rate, S, rises (note the plus in front of M us in the equation.) Thus, higher U.S. money growth (with real income growth constant) leads to a rising foreign currency value. Analogously, increases in the foreign money stock, M f, lower foreign currency value. Increases in U.S. real income, gnp us, increase transactions demand for the dollar,and lower the value of the foreign currency. Increases in foreign real income, gnp f, raise the foreign currency value. Increases in the real interest rate differential, r d - r f, implying higher real rates in the U.S. than abroad, lead to relatively less U.S. liquidity demand and larger transaction money balances in the U.S. relative to the foreign country. This action frees up relatively more dollars for transaction purposes (U.S. inflation picks up), and the foreign currency rises in value, as the dollar falls. Increases in the expected inflation differential mean that U.S. inflation is expected to be higher than foreign inflation. U.S. liquidity demand falls and, again, the foreign currency rises in value. To use the monetary model for forecasting exchange rates, we see that it simply translates our problem into one of measuring money stock and real income, and estimating real interest rates and expected inflation. Under three more assumptions, a specific monetary model follows: 1) gnp growth is exogenous, i.e. unaffected by money stock, exchange rates or expected inflation 2) real rates are equivalent across countries 3) The best estimate of next period money growth is the current level of money growth. Under these assumptions, the only source of expected inflation is expected money growth. Furthermore, the best estimate of expected Money View- 32

35 money growth is just the current money growth level. The following forecasting relation results: expected exchange rate = difference in log money stock - difference in log gnp + v * current differential money growth This model has been found to work relatively well for countries suffering from hyperinflation. 6 Optional Extension: Non-Traded Goods Since the model assumes that PPP holds for the countries' price levels, it embodies the implicit assumption that all goods are traded. If, instead, some are non-traded, then the exchange rate should only equate the purchasing power of the traded goods. Defining the price level of traded goods as P T, we relate these prices to the aggregate price level P: P T us = θ us P us, PT f = θ f P f On substitution, the PPP relation is agumented: S = P T us / PT f = P us / P f * (θ us / θ f ) Substituting for both aggregate price levels with the quantity definition, P = MV/gnp, S = (M us* V us /gnp us ) (M f* V f /gnp f ) = θ us θ f Taking logs, and substituting for velocity, S' = M ' us - M' f - (gnp' us - gnp ' f ) + V * (R us - R f ) + (θ us - θ f ) 6 For a domestic, d, country and a foreign, f, country, the model can be fitted and tested by a regression: ' ' ' ' ' ' ' ' S = a + b(m M ) c(gnp gnp ) + v * (dm dm ) + e t dt ft dt ft dt ft t dm is money growth, b, c and v all greater than zero. Money View -33- International Finance

36 With non-traded goods, monetary factors affect exchange rates as previously. However, the relative prices of the non-traded goods in both countries also affect the exchange rate. For example, increased demand by U.S. consumers for traded goods raises the relative price of these goods, (θ us ). The price of U.S. traded goods rises (P us T ) and the PPP relation identifies the resultant rising foreign currency value (S ) and domestic currency depreciation. Traded-good production technology improvements lead to price, interest rate and real income effects. The relative price of traded goods falls, real interest rates rise, and real income rises. The traded good price effect (P us T ) tends to raise the relative price of traded goods. However, the income effect on money demand lowers the general price level. Dependent on the responsiveness of money demand to income and interest rate changes (V = e Rv ), the overall effect of technology change is not fully determined. Generally, it should be positive with the direct relative price effect (θ T us ) being negative and money demand being increased on net (the income effect being greater than the interest rate effect.) Money View- 34