Forecasting Exchange Rates with PPP

Transcription

1 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

2 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

3 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

4 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

5 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

6 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

7 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

8 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

9 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

10 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

11 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

12 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

13 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

14 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

15 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

16 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

17 References Branson, William H., Macroeconomic Theory and Policy, New York, Harper & Row, Dornbusch, Rudiger, Monetary Policy Exchange Rate Flexibility, in D. Lessard, ed. International Financial Management: Theory and Application, Boston, Warren, Gorham and Lamont, Frenkel, Jacob, A. "A Monetary Approach to the Exchange Rate: Doctrinal Aspects and Empirical Evidence," in J.A. Frenkel and H.G. Johnson (eds.), The Economics of Exchange Rates: Selected Readings, Reading, Addison-Wesley, Friedman, Milton, and Anna J. Schwartz, A Monetary History of the United States, , Princeton, N.J., Princeton University Press, Krugman, Paul R., and Maurice Obstfeld, International Economics, Boston, Scott, Foresman and Company, 1988, Chapter 14. Laidler, David E.W., The Demand for Money, New York, Harper and Row, Lucas, Jr., R.E., Interest Rates and Currency Prices in a Two Country World, Journal of Monetary Economics, November 1982, p MacKinnon, Ronald, Money in International Exchange, 1976, chapter 6, p Mark, Nelson, International Macroeconomics and Finance : Theory and Econometric Methods, Oxford, John Wiley and Sons Ltd, Mankiw, Gregory, Macroeconomics, Stamford, CT, Cenpage Learning, 2014, ISBN-13: , ISBN-10: Money View -35- International Finance