Slides prepared by Thomas Bishop Chapter 15 Price Levels and the Exchange Rate in the Long Run

Copyright © 2006 Pearson Addison-Wesley. All rights reserved Preview Law of one price Purchasing power parity Long run model of exchange rates: monetary approach Relationship between interest rates and inflation: Fisher effect Shortcomings of purchasing power parity Long run model of exchange rates: real exchange rate approach Real interest parity

Copyright © 2006 Pearson Addison-Wesley. All rights reserved Introduction Consider how the exchange rate (eg. euro-dollar or yen-dollar) have changed over the years (decades). How can we predict long run exchange rate change?  In previous chapters, we developed a model showing that exchange rate is determined by interest rate and expectation about the future, which are in turn influenced by the money supply.  In this chapter, we develop models of explaining the long run behavior of exchange rate, extending the previous model.  The model of long-run exchange rate behavior provides the framework that actors in asset markets use to forecast future exchange rates.  In the long run, national price levels play a key role in determining both interest rates and exchange rate.

Copyright © 2006 Pearson Addison-Wesley. All rights reserved Law of One Price The law of one price simply says that the same good in different competitive markets must sell for the same price,  If transportation costs and barriers between markets are not important.  Why? Suppose the price of pizza at one restaurant is $20, while the price of the same pizza at another similar restaurant is $40.  What do you predict to happen? Many people would buy the $20 pizza, few would buy the $40, ultimately having the same price for both restaurants between $20 and $40.

Copyright © 2006 Pearson Addison-Wesley. All rights reserved Law of One Price (cont.) Consider a pizza restaurant in Seattle and one across the border in Vancouver. The law of one price says that the price of the same pizza in the two restaurants must be the same,  using a common currency to measure the price  if barriers between markets and transportation costs are negligible: P pizza US = (E US$/Canada$ ) x (P pizza Canada ) where P pizza US = price of pizza in Seattle P pizza Canada = price of pizza in Vancouver E US$/Canada$ =US$/Canadian$ exchange rate In trade theory, we saw that prices are equalized between the countries under free trade.

Copyright © 2006 Pearson Addison-Wesley. All rights reserved Purchasing Power Parity Purchasing power parity (PPP) is the application of the law of one price across the countries  for all goods and services,  Or for representative “baskets” of goods and services. P US = (E US$/Canada$ ) x (P Canada ) P US = price level of (reference basket of) goods and services in the US P Canada = price level of (the same basket of) goods and services in Canada E US$/Canada$ = US$/Canada$ exchange rate The PPP asserts that all countries price levels are equal when measured in terms of the same currency.

Copyright © 2006 Pearson Addison-Wesley. All rights reserved Purchasing Power Parity (cont.) PPP (Purchasing power parity) implies that E US$/Canada$ = P US /P Canada  The exchange rate between two countries ’ currencies equals the ratio of the counties ’ price levels..  If the price level in the US is US$200 per basket, while the price level in Canada is C$400 per basket, PPP implies that the US$/C$ exchange rate would be US$200/C$400 = US$1/C$ 2  PPP suggests that each country ’ s exchange rate adjusted currency has the same purchasing power: 2 Canadian dollars buy the same amount of goods and services as does 1 US dollar, since prices in Canada are twice as high.

Copyright © 2006 Pearson Addison-Wesley. All rights reserved Purchasing Power Parity (cont.) The Relationship Between PPP and the Law of One Price  The law of one price applies to individual commodity, while PPP applies to the overall price level.  If the law of one price holds true for every commodity, PPP must hold automatically.  Proponents of PPP theory argue its validity does not require the law of one price to hold exactly. Prices and exchange rate should not stray too far from the relation predicted by PPP, even when the law of one price fails to hold for all commodities.

Copyright © 2006 Pearson Addison-Wesley. All rights reserved Purchasing Power Parity (cont.) Purchasing power parity comes in two forms: Absolute PPP: PPP that has already been discussed. Exchange rates equal price levels across countries. E $/€ = P US /P EU Absolute PPP implies Relative PPP Relative PPP: percentage change in exchange rates equals difference in the percentage changes in prices (i.e. difference in inflation rate) between two countries: (E $/€,t - E $/€, t –1 )/E $/€, t –1 =  US, t -  EU, t where  t = inflation rate from period t-1 to t

Copyright © 2006 Pearson Addison-Wesley. All rights reserved A long-run exchange rate model based on PPP: Monetary Approach to Exchange Rate Monetary approach to the exchange rate: uses monetary factors to predict how exchange rates adjust in the long run.  Combine the money market framework of Ch 14 and the PPP.  It uses the absolute version of PPP.  It assumes that prices fully adjust in the long run.  In particular, price levels adjust to equate real (aggregate) money supply with real (aggregate) money demand. This implies: P US = M s US /L (R $, Y US ) P EU = M s EU /L (R €, Y EU )

Copyright © 2006 Pearson Addison-Wesley. All rights reserved Monetary Approach to Exchange Rates (cont.) We have the following prediction,  (to the degree that PPP holds and to the degree that prices adjust to equate real money supply with real money demand) :  The exchange rate is determined in the long run by prices, which are determined by the relative supply of money and the relative real demand of money across countries. E $/€ = P US /P EU, where P US = M s US /L (R $, Y US ) & P EU = M s EU /L (R €, Y EU )

Copyright © 2006 Pearson Addison-Wesley. All rights reserved Monetary Approach to Exchange Rates (cont.) In this model, 1.Money supply increase (a permanent rise in the domestic money supply)  causes a proportional increase in the domestic price level,  causing a proportional depreciation in the domestic currency (through PPP). Same prediction as the long run model (of Ch 14) without PPP 2.A rise in domestic Interest rate (R)  lowers domestic money demand,  increasing the domestic price level,  causing a proportional depreciation of the domestic currency (through PPP). Different prediction from the long run model without PPP

Copyright © 2006 Pearson Addison-Wesley. All rights reserved Monetary Approach to Exchange Rates (cont.) 3.A rise in the domestic output level (Y)  raises domestic money demand,  decreasing the domestic price level,  causing a proportional appreciation of the domestic currency (through PPP). All the above 3 changes affect money supply or money demand, causing prices to adjust to maintain equilibrium in the money market  thereby causing exchange rates to adjust to maintain PPP.

Copyright © 2006 Pearson Addison-Wesley. All rights reserved Monetary Approach to Exchange Rates (cont.) The monetary approach assumes price levels adjust as quickly as exchange rates do.  Same as any other long-run theory (such as in Ch 14).  Eg. Output rise- real demand for money increase- price drops immediately- exchange rate change follows immediately. The monetary approach leads to the following effects for exchange rate.  Same effect of the change in money supply with Ch 14.  Opposite effect of the change in interest rate with Ch 13, 14. Does a rise in interest rate depreciates the currency? A puzzle for the relation between interest rate & exchange rate. To resolve the puzzle, close examination is needed on the relations between money supply & interest rate in the long-run.

Copyright © 2006 Pearson Addison-Wesley. All rights reserved Monetary Approach to Exch Rate (cont.): Ongoing Inflation, interest parity, and PPP A change in the level of the money supply results in a change in the price level  Not a realistic method of implementing monetary policy. A change in the growth rate of money supply results in a change in the growth rate of prices (inflation).  A constant growth rate in the money supply eventually results in an ongoing inflation at the same constant rate, other things being equal (Ch 14). Changes in inflation does not affect the full-employment output level or the long-run relative prices. Inflation, however, does affect the interest rate. While the long-run interest rate does not depend on the level of money supply, continuing growth in the money supply affect the interest rate. How?

Copyright © 2006 Pearson Addison-Wesley. All rights reserved Monetary Approach to Exch Rate (cont.): Ongoing Inflation, interest parity, and PPP One way to see how a permanent increase in inflation affects the long-run interest rate is combining PPP with the interest parity condition.  Interest parity condition: R $ = R € + (E e $/€ - E $/€ )/E $/€ (1) Hold both in the short run and in the long run.  Relative PPP (a long-run relationship) implies, (E $/€,t - E $/€, t –1 )/E $/€, t –1 =  US, t -  EU, t  It implies that (E e $/€ - E $/€ )/E $/€ =  e US -  e EU (2) where  e = (P e – P)/P (expected inflation rate) This is the expected version of relative PPP, holding because market participants understand the relative PPP.

Copyright © 2006 Pearson Addison-Wesley. All rights reserved The Fisher Effect From the above relations (combining (1) & (2)), we can derive the following:  R $ - R € =  e US -  e EU  The interest rate difference must equal the expected inflation difference (called the Fisher effect) The Fisher effect (named after Irving Fisher) describes the (long-run) relationship between interest rates and ongoing inflation.  A rise in the domestic expected inflation rate causes an equal rise in the interest rate (on domestic currency deposit) in the long run, (all other things being constant).

Copyright © 2006 Pearson Addison-Wesley. All rights reserved The Fisher Effect The Fisher effect is another example that purely monetary change should have no effect on the economy ’ s relative price.  If expected inflation jump by 5% (from 5% to 10%) in US, then dollar interest rate will also jump by 5%. But the real rate of return on dollar asset being constant 5%. The Fisher effect is behind the paradoxical monetary approach prediction that a currency depreciates when its interest rate rises relative to foreign currency interest rate in the long run.  In the long run equilibrium (of monetary approach), a rise in the difference in interest rates between the two countries occurs only when expected inflation increases more in one country.  In the SR, when domestic money supply falls interest rate rises due to excess demand for real money balance (under sticky price ); * M s /P = L(R,Y)

Copyright © 2006 Pearson Addison-Wesley. All rights reserved Monetary Approach to Exchange Rates: an example. We can better understand how interest rates and exchange rate interact using an example. Suppose that the Federal Reserve (central bank) unexpectedly increases the money supply growth rate at time t 0.  From π before t 0 to π +  π The inflation rate would be π in the US before t 0 and π +  π after this time.  Suppose inflation is consistently 0% in Europe. The interest rate adjusts (jumps) according to the Fisher effect to reflect this higher inflation rate.

Copyright © 2006 Pearson Addison-Wesley. All rights reserved Monetary Approach to Exchange Rates (cont.)

Copyright © 2006 Pearson Addison-Wesley. All rights reserved Monetary Approach to Exchange Rates (cont.) Increase in interest rate decreases real money demand. To maintain equilibrium in the money market, prices must jump, i.e., P US = M s US /L (R $, Y US ). To maintain PPP, the exchange rate will then jump (the dollar will depreciate): E $/€ = P US /P EU  Dollar interest rate rises solely because people expect more rapid future inflation and dollar depreciation. As investors move into foreign deposits, which momentarily offer higher expected returns, the dollar depreciates sharply. Thereafter (after t 0 ), the money supply, prices, and exchange rate grow at rate π +  π.  Faster rate of growth than previous growth rate, π.

Copyright © 2006 Pearson Addison-Wesley. All rights reserved Monetary Approach to Exchange Rates (cont.)

Copyright © 2006 Pearson Addison-Wesley. All rights reserved Monetary Approach to Exchange Rates (cont.) Slope =  +  t0t0 M US, t 0 Slope =  (a) US money supply, M US Time Slope =  t0t0 Slope =  +  t0t0 t0t0 R $ 2 = R $ 1 +  R$1R$1 (d) exchange rate, E $/€ Time (b) dollar interest rate, R $ Time (c) US price level, P US Time

Copyright © 2006 Pearson Addison-Wesley. All rights reserved Comparison of different models Different assumptions about the speed of price adjustment lead to contrasting prediction between interest rate and exchange rate. If money supply level falls under sticky price, an interest rate rise is needed to preserve money market equilibrium.  An interest rate rise is associated with lower expected inflation and a long-run currency appreciations. In monetary approach (under flexible price & PPP) for a rise in money supply growth rate, interest rate rises associated with higher expected inflation.  Currency depreciation will immediately follow. We must carefully account for the factors causing interest rate rise, which simultaneously affect expected future exchange rate.  They ultimately have a decisive impact on the response of exchange rate to the interest rate change. (refer to Appendix).

Copyright © 2006 Pearson Addison-Wesley. All rights reserved How well does the PPP theory explain exchange rate determination in real world changes? Weak empirical support for PPP and the law of one price in recent data.  The prices of identical commodity baskets, when converted to a single currency, differ substantially across countries.  Relative PPP is sometimes a reasonable approximation to the data, but overall it also performs poorly. 4. Empirical Evidence on PPP and the Law of One Price

Copyright © 2006 Pearson Addison-Wesley. All rights reserved Shortcomings of PPP (cont.)