1 trillion units * ($1 per unit) = $500 billion * 2

Transcription

1 Under the strict monetarist view, real interest rates and money supply are assumed to be independent. Under this assumption, inflation does not affect real rates. Nevertheless, nominal 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

2 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

3 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

4 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 = $.5 per DM Since consumption baskets differ greatly world-wide, applying absolute PPP is very difficult in practice. Construction of a price Money View- 8

5 index for one country is difficult enough. (As evidenced by U.S. experience with 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 subtract 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

6 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 IFS Line # S AR CPI 64 CPI 64 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 our relative PPP assumption, and the 1975 benchmark rate, we have 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 purchasing power parity exchange rate differs from the actual Third Quarter 1984 exchange rate. Money View- 10

7 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, 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

8 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

9 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. Money View -13- International Finance

10 The Big Mac index Table 2 - July 2016 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. For example, the average price of a Big Mac in America in July 2016 was $5.04; in China it was only $2.79 at market exchange rates. So the "raw" Big Mac index says that the yuan was undervalued by 45% at that time. (Pound ~ -22%, $3.93, Yen ~ -32, $3.43). 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 at least 20 academic studies. For those who take their fast food more seriously, we have also calculated a gourmet version of the index. 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- 14

11 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 -15- International Finance

12 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 (nom. income growth ) = ( ) = inflation) Excess Money Growth (1.527 (money growth - real ) = (2.467 = ) 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- 16

13 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, but will be manifest in excess money growth. Excess money growth provides a measure of pent up inflation pressure. This measure is useful whenever price controls are in effect, even the U.S. in the 1970's. For PPP to be a useful tool for Money View -17- International Finance