The Monetary Approach to the Exchange Rate

1. The Monetary Approach to the Exchange Rate Antu Panini Murshid

2. Today’s Agenda • The law of one price and purchasing power parity • The monetary approach to the exchange rate • Implications of the model • Real interest rate and the Fisher effect • Impact of an expansionary monetary policy

3. Law of One Price • The law of one price states that as long as there are no barriers to trade or transportation costs, identical goods in two countries must sell for the same price, when their prices are expressed in the same currency • Thus Pi = e * Pif for any two countries and any good i Why? Arbitrage once again

4. Purchasing Power Parity • Purchasing power parity is the law of one price applied to a fixed basket of commodities • The law of one price implies that e=P/Pf, where P is the price of a basket of commodities in the home country and Pf is the price of that same basket of commodities abroad

5. Implications of Purchasing Power Parity • PPP states that the exchange rate between two currencies is in equilibrium when their purchasing power is the same in each country, i.e. the exchange rate between two countries should equal the ratio of the two countries' price levels • Thus when one country’s price level is increasing (decreasing) its exchange rate must also be depreciating (appreciating) • PPP implies that the real exchange rate should be equal to one

6. Relative PPP vs. Absolute PPP • Absolute PPP was described in the previous slides • Relative PPP refers to rates of changes of price levels, that is, inflation rates. This proposition states that the rate of appreciation of a currency is equal to the difference in inflation rates between the foreign and the home country: %De = p - pf

7. Example • If the US inflation rate is 10% and the UK inflation rate is 5%, the dollar will depreciate against the pound by 5% • Relative PPP is a useful concept when we are trying to conceptualize the impact of changes in rates of monetary growth (or prices) as opposed to one off changes

8. Monetary Approach to the Exchange Rate • In its simplest form, the monetary approach to the exchange rate is simply a restatement of PPP • Hence according to the monetary approach to the exchange rate, the exchange rate should be equal to the ratio of the domestic and foreign price levels, i.e. e = P/Pf • Alternatively the rate of depreciation of one currency relative to another should be equal to the difference in their rates of inflation, i.e. %∆e = p-pf

9. Price Level: Key to Understanding the Exchange Rate • According to the monetary approach, the key variable to understanding the long-run behavior of the exchange rate is the price level and the rate of change of the price level • This differs from the asset market approach which emphasized the interest rate

10. A Long-Run Theory • The monetary approach to the exchange rate is a theory on the long-run behavior of the exchange rate, since it assumes that prices are flexible. In the short run prices could very well be rigid and PPP need not apply • This contrasts with the asset market approach, which is a theory of the short-run behavior of the exchange rate

11. Money Supply and Money Demand • Given the role of prices, a theory of the determinants of the exchange rate must hope to explain movements in the price level • The monetary approach to the exchange rate focuses on the supply and demand for money as the key determinants of the price level

12. Basic Model • Md=P*L(y,i): Liquidity preference • Ms=Md:Money market equilibrium • e=P/Pf:PPP • There is a little bit more to it than this. The money supply is normally written as the sum of domestic credit and foreign exchange reserves (we will study this in greater detail later)

13. Basic Model • Equations (1) and (2) ⇒ P=Ms/L(y,i)Hence by PPP: • Recognizing that the foreign price level is simply the ratio of foreign money supply to money demand we have:

14. Implications of the Model • Let us ignore developments in the foreign country and focus on the implications of developments at home, i.e. take the foreign price level, Pf, as given then: • An increase in US money supply implies P↑, dollar depreciates (e↑) • An increase in interest rates implies L(i,y)↓, P↑, dollar depreciates (e↑) • An increase in output implies L(i,y)↑, P↓, dollar appreciates (e↓)

15. Graphical Illustration • It will be useful to illustrate these implications of the model graphically, but in order to that first we need to introduce a new diagram for analyzing money market developments that emphasizes the price level, not the interest rate, as the adjustment mechanism

16. Consider the following money market diagram drawn with nominal money balances on the horizontal axis and the price level on the vertical axis The Money Market in the Long-Run Ms Price level Md(i,y) e P1 nominal money balances

17. Since we are interested in the long-run, it makes sense to draw the money market with the price level as opposed to the interest rate on the vertical axis The Money Market in the Long-Run Ms Price level Md(i,y) e P1 nominal money balances

18. Note that since an increase in income will raise the demand for nominal money balances the money demand curve will rotate clockwise The Money Market in the Long-Run Ms Price level Md(i,y) Md(i,y2) e P1 P2 e2 nominal money balances

19. An increase in interest rates will have the opposite effect by lowering the demand for nominal money balances The Money Market in the Long-Run Ms Price level Md(i,y3) Md(i,y) e3 P3 e P1 nominal money balances

20. Implications of Monetary Model for the Exchange Rate Price level Ms This diagram shows that for a given value of Pf there is a unique equilibrium exchange rate that corresponds to any given P e=P/Pf Md(i,y) P1 e1 exchange rate nominal money balances

21. Implications of Monetary Model for the Exchange Rate Price level Ms Ms2 Increases in money supply will raise the price level, which will correspond to higher values of e e=P/Pf Md(i,y) P2 P1 e2 e1 exchange rate nominal money balances

22. Implications of Monetary Model for the Exchange Rate Price level Ms Increases in interest rates will also raise the price level, which will correspond to higher values of e Md(i2,y) e=P/Pf Md(i,y) P2 P1 e2 e1 exchange rate nominal money balances

23. Implications of Monetary Model for the Exchange Rate Price level Ms Increases in income by contrast will cause the price level to fall, which will correspond to lower values of e Md(i2,y) e=P/Pf Md(i,y) P1 P2 e1 e2 exchange rate nominal money balances

24. Do the Model Predictions Make Sense? • The first implication that an increase in money supply raises the price level and causes the exchange rate to depreciate is uncontroversial • Similarly the implication that an increase in output will cause the exchange rate to appreciate is reasonable, since increases output would apply downward pressure on prices (think of a rightward shift in the aggregate supply curve) • However why should an increase in interest rates cause the exchange rate to depreciate?

25. The Implications of a Rise in Interest Rates • There are two problems with how the model links interest rates to the exchange rate • First in the long-run the price level adjusts to remove money market disequilibria, so what is causing the interest rate to change? • Second, the prediction that an increase in interest rates will ultimately lead to a depreciation of the currency seems inconsistent with our discussion on the short-run behavior of the exchange rate

26. Understanding Why the Interest Rate Changes • In fact the implication that an exchange rate depreciation will follow an interest rate increase is quite reasonable. The key is to understand why the interest rate changes • It turns out that increases in the interest rate follow from expansionary monetary policies that raise the rate of inflation, which is consistent with an exchange rate depreciation • To see why this is the case, we will need to introduce the notion of the real interest rate

27. The Real Interest Rate • The ex ante real interest rate is defined as: r = i - pe, where pe is the expected inflation rate • The ex post or realized real interest rate is defined as: r = i - p, where p is the realized inflation rate

28. What Determines the Real Interest Rate? • The real interest rate is determined in the market for loanable funds • The supply of loanable funds comes from savers • The demand for loanable funds comes from those who wish to borrow to make investments

29. Determinants of the Demand for Loanable Funds • The most important factor that determines the demand for loanable funds is the cost of obtaining a loan—the real interest rate. Since borrowers do not know the inflation rate before hand the demand for loanable funds is influenced by the ex ante real interest rate • A higher expected (real) cost of borrowing implies a lower demand for loanable funds • A lower expected (real) cost of borrowing implies a higher demand for loanable funds

30. Demand Schedule for Loanable Funds Technological changes, which affect the MPK, as well as factors influencing the risk characteristics of investments will shift the demand for loanable funds schedule real interest rate 2…the quantity of loanable funds demanded increases 5% 4% 1. As the real interest rate falls… I, demand 1,000 1,500 loanable funds

31. Determinants of the Supply of Loanable Funds • The supply of loanable funds could also respond to the ex ante real interest rate, however the evidence suggests that this relationship is weak • More important determinants are demographic shifts that alter private savings behavior and changes in fiscal expenditure patterns of governments

32. Supply Schedule for Loanable Funds An increase in real interest rates might create greater incentives for savers to save. However this effect is weak SN, supply real interest rate 5% Changes in government expenditure and demographic shifts will cause the savings schedule to shift 4% 900 1,000 loanable funds

33. Market for Loanable Funds SN, supply real interest rate Equilibrium 5% I, demand 1,000 loanable funds

34. Fisher Effect • Clearly long-run factors that shift the demand for and supply of loanable funds will affect the real interest rate, however Irving Fisher noted that in general the long-run real interest rate can be regarded as roughly constant or at least exhibiting only weak trends • The Fisher effect implies that there is a one-to-one relationship between the inflation rate and the nominal interest rate It is interesting that he argued this, since at the time of writing this was definitely not the case

35. Empirical Evidence It would appear that over the past 40-years, the Fisher effect worked fairly well

36. Expansionary Monetary Policy and the Interest Rate • According to the Fisher effect an expansionary monetary policy, which raises the rate of inflation, i.e. an increase in the rate of growth of money, will also cause the nominal interest rate to rise

37. Expansionary Monetary Policy in the Market for Loanable Funds 3…This is excess demand is eliminated when i rises SN, supply real interest rate 5% 2…creating an excess demand for loanable funds 4% 1. A rise in p causes the real interest rate to fall I, demand 1,000 1,500 loanable funds

38. When pincreases, for any given i, r must fall The Fisher effect implies that i must rise The resulting disequilibrium is cleared by the rising price level Expansionary Monetary Policy in the Money Market M1s/P2 Money supply M1s/P Interest rate i1=15% Equilibrium interest rate i1=10% Money demand L(i,y) real money balances

39. Why Does the Price Level Rise? • Why exactly does the price level rise? • There are two ways to think about this depending on how you want to attribute causality • First the price level rises as a consequence of the rise in the nominal interest rate • Second the price level rises because of an excess demand for loanable funds, which in turn causes the interest rate to increase

40. Inflationary Expectations and Financial Assets • The increase in the rate of growth of money raises inflationary expectations • Investors anticipate a rise in interest rates, which leads to a shift out of bonds an into money • The price of bonds falls and the interest rate rises • The excess demand for money causes the price of money to fall and the price level to rise • In this case the rise in interest rate induces the price level to rise

41. Rise in Investment Demand • The initial inflationary spurt causes r to fall which creates an excess demand for loanable funds • Consequently aggregate demand rises (investment is a component of aggregate demand) • This puts upward pressure on P, lowering real money supply and raising i • In this case the rise in the price level induces the rise in nominal interest rates

42. Summarizing • To summarize the interest rate rises in the long-run because of increased inflationary pressures. This can result from a change in the rate of growth of money supply, but not from one-off changes in money, which have no effect on the interest rate

43. Real Interest Rate Parity • We can now bring together what we have learned about the Fisher effect, interest rate parity and PPP • Interest rate parity: i - if = E(%∆e) • PPP: %∆e = p – pf • Real interest rate parity: i - if = E(p – pf) • Note that real interest rate parity is just another way of stating the Fisher effect

44. Impact of an Expansionary Monetary Policy • First consider the effects of a one-off 10% increase in US money supply? • In the short-run: • ↑ Ms⇒ ↓ i⇒ ↑ e > 10% (overshooting) • In the long-run: • ↑ P ⇒ ↑ i to initial level, and ↓ e such that overall increase in e is 10%

45. Impact of an Expansionary Monetary Policy • Now consider the implications of an increase in the rate of growth of money from p to p+Dp • The increase in money growth rate is illustrated in the diagram as a rise in the slope of M(t) US money supply M(t) Slope = p+Dp M(t0) Slope = p t0 time

46. Impact of an Expansionary Monetary Policy • As a consequence of the rise in the rate of money expansion, the expected rate of inflation rises from p to p+Dp • To preserve real interest rate parity the nominal interest rate must rise by Dp Nominal interest rate i1+Dp i1 t0 time

47. Impact of an Expansionary Monetary Policy • The rise in i creates a disequilibrium in the money market, which is cleared by a jump in the price level • Moreover from t0 onward the price level is increasing at a faster rate Price level Slope = p+Dp Slope = p t0 time

48. Impact of an Expansionary Monetary Policy • Finally note that by PPP the exchange rate jumps at t0 • And continues rise thereafter at a faster tate Exchange rate Slope = p+Dp Slope = p t0 time

49. The Short-Run and the Long-Run • In the short run an increase in Ms produces a fall in the interest rate to equilibrate the money market, as prices are rigid ⇒ the only way to maintain interest parity is to expect an exchange rate appreciation • In the long run, when prices adjust, an increase in rate of growth of MSleads to an increase in expected inflation and the interest rate (Fisher effect). This in turn leads to an exchange rate depreciation (PPP)

50. The Short-Run and the Long-Run • The key difference between the short-run and the long-run is the speed of adjustment in prices • In the short-run prices are sticky and the interest rate adjusts to bring the money market to an equilibrium • In the long-run prices are flexible and interest rates are insensitive to one-off changes in money but do respond to changes in money growth rates and inflationary expectations