Presentation on theme: "Price Levels and the Exchange Rate in the Long Run"— Presentation transcript:
1 Price Levels and the Exchange Rate in the Long Run Chapter 16International EconomicsUdayan Roy
2 Overview Long-run analysis Flexible exchange rates Real variables Nominal variablesFlexible exchange ratesWe will study fixed exchange rates in Chapter 18
3 The Real Exchange Rate We discussed exchange rates in Chapter 14 Example: €1 = $1.50Those exchange rates are nominal exchange ratesNow we’ll discuss real exchange rates
4 The Real Exchange RateLet us consider the price of an iPhone in US and Europe:In US, it is PUS = $200In Europe, it is PE = €150The value of the euro is E = 2 dollars per euroSo, Europe’s price in dollars is E × PE = $300So, each iPhone in Europe costs as much as 1.5 iPhones in USE × PE / PUS = 1.5This is the real dollar/euro Exchange Rate for iPhones
5 The Real Exchange RateIn general, the real exchange rate is a broad summary measure of the prices of one country’s goods and services relative to another’s.The real dollar/euro exchange rate is the number of US reference commodity baskets—not just iPhones—that one European reference commodity basket is worthEquation (16-6) in KOM9eE$/€ is the nominal exchange rate, the price of one euro in dollarsPE is the overall price level in Europe, such as the consumer price indexPUS is the overall price level in the United States
7 The Real Exchange RateExample: If the European reference commodity basket costs €100, the U.S. basket costs $120, and the nominal exchange rate is $1.20 per euro, then the real dollar/euro exchange rate (q$/€) is 1 U.S. basket per European basket.
8 Real Depreciation and Appreciation Real depreciation of the dollar against the euroA rise in the real dollar/euro exchange rate (q$/€↑)is a fall in the purchasing power of a dollar within Europe’s borders relative to its purchasing power within the United StatesOr alternatively, a fall in the purchasing power of America’s products in general over Europe’s.Real appreciation of the dollar against the euro is the opposite of a real depreciation: a fall in q$/€.
9 Absolute PPPA very simple theory of the real exchange rate is called Absolute Purchasing Power ParityIt says that:q = 1Why?
10 Law of One PriceGoing back for a second to the iPhone example, one can argue that PUS, the dollar price in the US, ought to be equal to E × PE, the dollar price in Europe. That is,E × PE = PUS.In general, E$/€ x PE = PUS.Therefore, q$/€ = (E$/€ x PE)/PUS = 1.This is the Law of One Price or Absolute Purchasing Power Parity.Immediately after this slide, I should skip to the empirical relevance of APPP. And immediately after that, I should develop the Y = D(q) equation of chapter 16, and then derive the long run value q by imposing Y = Yf. The long run effect of Ms on E and Ee can then be derived. This will also allow the discussion of the long run effects of fiscal policy.
11 Absolute and Relative PPP Chapter 16 of the textbook (KOM9e) uses Absolute PPP in the first part of the chapter and Relative PPP in the second partAbsolute PPP: q = 1Relative PPP: q = a constant, not necessarily 1Although the results in the following slides have been proved for APPP, they are also true under RPPP
12 Prices and the Exchange Rate Absolute PPP says: 𝑞= 𝐸∙ 𝑃 ∗ 𝑃 =1Therefore, 𝐸= 𝑃 𝑃 ∗Therefore, the faster domestic prices (P) grow, the faster the foreign currency’s exchange value (E) will growAnd, the faster foreign prices (P*) grow, the slower the foreign currency’s exchange value (E) will grow
13 Prices and the Exchange Rate Equation (16-2) of the textbook, KOM9eIn general, 𝐸 𝑔 =𝜋− 𝜋 ∗where Eg is the growth rate of E. This is the appreciation rate of the foreign currencyπ* is the foreign inflation rate, andπ is the domestic inflation rateExample: If US inflation is 3% a year and Canadian inflation is 1% a year, then the exchange value of the Canadian dollar, measured in US dollars, will increase 2% a year
14 The Interest RateWe have seen in Chapter 15 that the interest parity equation is 𝑅= 𝑅 ∗ + 𝐸 𝑒 −𝐸 𝐸The second term on the right-hand side is the expected appreciation rate of the foreign currencyAssumption: The expected appreciation rate is assumed to be equal to the actual appreciation rate (Eg), in the long run
15 Equation (16-5) of the textbook, KOM9e The Interest RateTherefore, 𝑅= 𝑅 ∗ + 𝐸 𝑒 −𝐸 𝐸 = 𝑅 ∗ + 𝐸 𝑔We saw two slides earlier that 𝐸 𝑔 =𝜋− 𝜋 ∗Therefore, 𝑅= 𝑅 ∗ +𝜋− 𝜋 ∗Assumption: The foreign interest rate (R*) and the foreign inflation rate (π*) will be assumed to be exogenous constantsEquation (16-5) of the textbook, KOM9e
16 The Interest Rate: Fisher Effect 𝑅= 𝑅 ∗ +𝜋− 𝜋 ∗As the foreign interest rate (R*) and the foreign inflation rate (π*) are assumed to be exogenous constants, any change in the domestic inflation rate will cause an equal change (both in magnitude and direction) in the domestic nominal interest rateThis is called the Fisher Effect
17 The Interest Rate 𝑅= 𝑅 ∗ +𝜋− 𝜋 ∗ implies 𝑅−𝜋= 𝑅 ∗ − 𝜋 ∗ R is the nominal interest rate.It tells you how fast the dollar value of your wealth is increasingR – π is the real (or, inflation-adjusted) interest rate.It tells you how fast the purchasing power of your wealth is increasingWe now see that in the long run equilibrium, real interest rates must be equal in all countries
18 The Interest RateAssumption: The domestic inflation rate (π) is constant in the long run equilibriumThen 𝑅= 𝑅 ∗ +𝜋− 𝜋 ∗ must also be constant in the long run equilibriumWe will now use this constancy of R to get a theory of long run inflation
19 OutputThe real GNP produced when all resources are fully utilized is known by various names:Long-run GNPNatural GNPFull-employment GNPPotential GNP(Yp)Assumption: In the long run, the economy makes full use of all its resourcesTherefore, in long-run equilibrium, Y = Yp.
20 InflationWe have seen in Chapter 15 that equilibrium in the money market implies 𝑀 𝑠 = 𝑀 𝑑Moreover, 𝑀 𝑑 =𝑃∙𝐿(𝑅,𝑌)Simplifying a bit, 𝑀 𝑑 = 𝑃∙ 𝐿 0 ∙𝑌 𝑅Therefore, in equilibrium, 𝑀 𝑠 = 𝑃∙ 𝐿 0 ∙𝑌 𝑅Therefore, 𝑃= 𝑀 𝑠 ∙𝑅 𝐿 0 ∙𝑌
21 InflationTherefore, in the long-run, 𝑃= 𝑀 𝑠 ∙𝑅 𝐿 0 ∙𝑌 = 𝑀 𝑠 ∙𝑅 𝐿 0 ∙ 𝑌 𝑝We saw three slides back that R is constant in the long run equilibrium. Moreover, L0 is an exogenous constantTherefore, the faster the money supply (Ms) grows, the faster the price level (P) will growAnd, the faster potential GDP (Yp) grows, the slower the price level (P) will grow
22 Inflation In general, 𝜋= 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔 For example, if the Federal Reserve expands US money supply at the rate of 5% a year and if the US economy’s potential GDP increases at the rate of 3% a year, then, in the long run, the US inflation rate will be 2% a year.
23 The Interest Rate, again So far, we have 𝑅= 𝑅 ∗ +𝜋− 𝜋 ∗ and 𝜋= 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔Therefore, the domestic nominal interest rate in the long run is 𝑅= 𝑅 ∗ + 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔 − 𝜋 ∗ , a constant
24 The Price LevelA few slides back, we saw that in the long run the domestic price level is 𝑃= 𝑀 𝑠 ∙𝑅 𝐿 0 ∙ 𝑌 𝑝Moreover, we just saw that 𝑅= 𝑅 ∗ + 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔 − 𝜋 ∗Therefore, in the long run, the domestic price level is 𝑃= 𝑀 𝑠 ∙ 𝑅 ∗ + 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔 − 𝜋 ∗ 𝐿 0 ∙ 𝑌 𝑝
25 Appreciation Rate of the Foreign Currency We saw earlier that the foreign currency appreciates at the rate 𝐸 𝑔 =𝜋− 𝜋 ∗As the inflation rate is 𝜋= 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔 , we can now write 𝐸 𝑔 = 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔 − 𝜋 ∗
26 The Exchange Rate: APPP version Recall that under absolute purchasing power parity, we have 𝑞= 𝐸∙ 𝑃 ∗ 𝑃 =1, which implies 𝐸= 𝑞∙𝑃 𝑃 ∗ = 𝑃 𝑃 ∗We have also seen two slides back that 𝑃= 𝑀 𝑠 ∙ 𝑅 ∗ + 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔 − 𝜋 ∗ 𝐿 0 ∙ 𝑌 𝑝Therefore, 𝐸= 𝑀 𝑠 ∙ 𝑅 ∗ + 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔 − 𝜋 ∗ 𝐿 0 ∙ 𝑌 𝑝 ∙ 𝑃 ∗
27 Summary: Long-Run, Flexible Exchange Rates q = 1, absolute PPPY = Yp𝜋= 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔𝑅= 𝑅 ∗ + 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔 − 𝜋 ∗𝑃= 𝑀 𝑠 ∙ 𝑅 ∗ + 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔 − 𝜋 ∗ 𝐿 0 ∙ 𝑌 𝑝𝐸 𝑔 = 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔 − 𝜋 ∗𝐸= 𝑀 𝑠 ∙ 𝑅 ∗ + 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔 − 𝜋 ∗ 𝐿 0 ∙ 𝑌 𝑝 ∙ 𝑃 ∗The crucial point to note about these expressions is that the variables on the right-hand sides of these equations are all exogenous. As exogenous variables are ‘mystery variables’ about which our theory has nothing to say, the equations on this slide say all that our theory can say about the endogenous variables on the left-hand sides of these equations.
28 Summary: Long-Run, Flexible Exchange Rates q = 1, absolute PPPY = Yp𝜋= 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔𝑅= 𝑅 ∗ + 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔 − 𝜋 ∗𝑃= 𝑀 𝑠 ∙ 𝑅 ∗ + 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔 − 𝜋 ∗ 𝐿 0 ∙ 𝑌 𝑝𝐸 𝑔 = 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔 − 𝜋 ∗𝐸= 𝑀 𝑠 ∙ 𝑅 ∗ + 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔 − 𝜋 ∗ 𝐿 0 ∙ 𝑌 𝑝 ∙ 𝑃 ∗Keep in mind that we are talking about the long run here. So, these equations show us the long run effects of permanent changes in the exogenous variables on the equations’ right-hand sides.
29 Summary: Long-Run, Flexible Exchange Rates q = 1, absolute PPPY = Yp𝜋= 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔𝑅= 𝑅 ∗ + 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔 − 𝜋 ∗𝑃= 𝑀 𝑠 ∙ 𝑅 ∗ + 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔 − 𝜋 ∗ 𝐿 0 ∙ 𝑌 𝑝𝐸 𝑔 = 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔 − 𝜋 ∗𝐸= 𝑀 𝑠 ∙ 𝑅 ∗ + 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔 − 𝜋 ∗ 𝐿 0 ∙ 𝑌 𝑝 ∙ 𝑃 ∗The first two variables are real variables: they can be measured even in barter (or, non-monetary) economies. The remaining variables are nominal variables: they make sense only on monetary economies.Note that the money supply (Ms) has no effect on real variables. This is an instance of monetary neutrality in the long run.
30 Summary: Long-Run, Flexible Exchange Rates q = 1, absolute PPPY = Yp𝜋= 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔𝑅= 𝑅 ∗ + 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔 − 𝜋 ∗𝑃= 𝑀 𝑠 ∙ 𝑅 ∗ + 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔 − 𝜋 ∗ 𝐿 0 ∙ 𝑌 𝑝𝐸 𝑔 = 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔 − 𝜋 ∗𝐸= 𝑀 𝑠 ∙ 𝑅 ∗ + 𝑀 𝑠 𝑔 − 𝑌 𝑝 𝑔 − 𝜋 ∗ 𝐿 0 ∙ 𝑌 𝑝 ∙ 𝑃 ∗Flashback to Ch. 15 of the textbook (KOM9e):“A change in the supply of money has no effect on the long-run values of the interest rate or real output.” (p. 369)“A permanent increase in the money supply causes a proportional increasein the price level’s long-run value. In particular, if the economy is initially at full employment, a permanent increase in the money supply eventually will be followed by a proportional increase in the price level.” (p. 370)
31 Absolute PPP: logical but not factual Despite the logical appeal of Absolute Purchasing Power Parity, available data suggests that it is not trueWe need to look for another theory of the real exchange rate, q.
33 Bonus Topic: The Current Account We will return to this after discussing Chapter 17The balance on a country’s current account (CA) is roughly its net exportsWhat does CA depend on in the long run?Bonus Topic: The Current Account
34 The Current AccountRecall the goods market equilibrium equation: 𝑌=𝐶 𝑌−𝑇 +𝐼+𝐺+𝐶𝐴Therefore, 𝐶𝐴=𝑌−𝐶 𝑌−𝑇 −𝐼−𝐺Recall that 𝑌= 𝑌 𝑝 in the long runTherefore, 𝐶𝐴= 𝑌 𝑝 −𝐶 𝑌 𝑝 −𝑇 −𝐼−𝐺
35 The Current Account 𝐶𝐴= 𝑌 𝑝 −𝐶 𝑌 𝑝 −𝑇 −𝐼−𝐺 𝐶𝐴= 𝑌 𝑝 −𝐶 𝑌 𝑝 −𝑇 −𝐼−𝐺If Yp increases by, say, $100, then, in the long run, income (Y) will increase by $100 and consumption (C) will increase, but by less than $100Therefore, CA will increaseTherefore, in the long run, Yp and CA move in the same direction
36 The Current Account 𝐶𝐴= 𝑌 𝑝 −𝐶 𝑌 𝑝 −𝑇 −𝐼−𝐺 YCAYp+TI, G−𝐶𝐴= 𝑌 𝑝 −𝐶 𝑌 𝑝 −𝑇 −𝐼−𝐺It is also straightforward to check thatWhen taxes (T) change, CA moves in the same direction, andWhen I and G change, CA moves in the opposite directionFiscal austerity (T↑ or G↓) is a way to raise CAA fall in consumer wealth—caused by, say, a real estate crash or a stock market crash—has the same effect as a tax increase. So, CA will increase!
37 The Long RunThe macroeconomic analysis of the long run is characterized by the concept of monetary neutralityThat is, monetary arrangements and monetary policy have no effect on the behavior of real variablesTherefore, the predictions summarized by the table on this and the previous slide are true for both the flexible exchange rate system of this chapter and the fixed exchange rate system of Chapter 18YCAYp+TI, G−