Money and Prices

1. Money and Prices Chapter 12

2. The Bond Market Chapter 22

3. Objective • Calculate price indexes and inflation rates. • Calculate a discount bond yields using discount bond prices. • Calculate Bond Returns using interest rates. • Use the Expectations Theory of the Term Structure to deconstruct the yield curve. • Calculate the demand for money balances using nominal GDP and interest rates.

4. Money • Money is a tool for conducting transactions and, like all tools, is subject to technological advance. • Barter was replaced by commodity money, precious metal with intrinsic value. • Problems (Issues) with commodity money • Commodities used as money can’t be used for other purposes. • Supply of money determined by availability of resources. • Government must share the revenues from the creation of money (Perhaps only a problem from governments point of view).

5. Fiat Money • Fiat money is intrinsically valueless commodity (typically paper) widely accepted as payment rendered (by government command. • First paper money circulated in Szechwan province during the Northern Sung dynasty. Szechwan had iron coins which are heavy and rusty. Banks issued receipts for the coins called chiao-tzu which circulated as the origins of paper money. • In 1161, under the Southern Sung dynasty, the government developed a paper called hui-tzu which eventually developed into first nationwide paper money.

6. Decade-by-Decade History of Hui-tzu Observations • For many years, inflation lags money growth rate. • Money growth rate accelerates near turn of the century. • During final years of dynasty, inflation is faster than money growth. Why? (Cite: F. Lui, JPE 1983)

7. What is Inflation? • Define Inflation as the growth rate of prices. • The Greek letter π is often used as a symbol of inflation

8. Aggregate Prices • We also might want a measure of average prices. • Aggregate price measures are weighted averages of the prices of a set of goods n = 1..N relative to their price in a base year B. • Two main types of measures • Price Indices • Price Deflators

9. Price Indices • Most commonly used price index is the Consumer Price Index (CPI) • In constructing the CPI, statisticians calculate the total expenditure of the average household during a benchmark year. • The weight on good n in the CPI is the share of expenditure in the base year that was on good n.

10. Another type of price aggregate is the deflator which is calculated simultaneously with a real quantity aggregate. The deflator uses weights which change over time. The weight for good n in the GDP deflator is the ratio of the quantity of that good relative to real GDP. The GDP deflator is also the ratio of nominal GDP to real GDP. Deflators can be constructed for any sub-category of GDP. Price Deflator

11. HK Price Aggregates(Base Year 2000)

12. Adjusting for Inflation/Converting Current Price Series into Constant Price Series • One may have a time series of a nominal aggregate, Nt, (in current prices) without the microeconomic data necessary to construct a corresponding real aggregate. • We can use some price index to “adjust for inflation” effectively converting into a real variable. • Select a reference or base year. • Series measured in base year dollars is

13. Role of Money • Money has 3 roles • Medium of Exchange – Money is a technology for engaging in transactions. • Unit of Account – Value of most goods and assets is measured in money. • Store of Value – Money is an asset. It can be exchanged for goods in the future.

14. Monetary Aggregates • Real world Different assets have different levels of usefulness in transactions. • Money is measured in sums of these assets. • M2 & M3 include less liquid assets and are called broad money. • M1 is the most liquid type of money.

15. Monetary Aggregates in HK(Nov. 2002)

16. Velocity/Liquidity • Define the ratio of transactions to the supply of money as ‘Velocity’, the speed with which money circulates. • The value of transactions is nominal GDP. • The inverse of velocity is the willingness to hold money between transactions or the willingness to hold a liquid position, L

17. Rules of Thumb • If Z = X×Y, then gZ = growth rate of z gZ ≈ gX + gY • Example: Z = Nominal GDP = P×Y gZ ≈ gP + gY = π + gY Growth rate of Nominal GDP is approximately equal to inflation plus growth rate of real GDP. • If Z = Y/X, then gZ ≈ gY - gX • Example: Z = Per Capita Real GDP = Y/POP gZ ≈ gY - gPOP Growth rate of per capita real GDP is growth rate of real GDP minus the growth rate of population.

18. Quantity Theory & Inflation • Using the definition of velocity, we can say gY + π ≈ gM + gV = gM - gL • This gives us an equation for inflation. • π ≈ (gM - gY ) + gV • π ≈ (gM - gY ) - gL • Inflation (the growth rate of prices {money per good}) is equal to the growth rate of money minus growth rate of goods unless there are significant changes in the willingness to hold money.

19. Sung Dynasty • In the early years of the introduction of hui-tzu, there was likely an increasing willingness to hold new form of money, gL > 0 → π < (gM - gY ) • In the final years of the Sung Dynasty, there was a reduced willingness to hold Sung money, gL > 0 → π > (gM - gY )

20. Ordinary Determinants of Velocity • What determines the willingness of people to hold money or conversely what determines the speed with which they spend money. • Money is an asset that does not pay interest. When you hold money, opportunity cost is lost interest. The higher is the interest rate, the greater is the opportunity cost. • Some forms of money, (e.g. savings and time deposits) pay interest, however, they are lower than the interest rate on bonds.

21. The nominal interest rate is the ratio of money you get in the future relative to the money you give up today, i.e. the time value of money. If you give the bank $1, they will give you $1+i after one period. i ≡ Net Nominal Interest Rate Liquidity demand is a negative function of the nominal interest rate. L(i-) Nominal Interest Rate

22. Money Demand Curve • Write the Quantity Equation as a money demand curve MD = L(i)∙PY • Given the level of nominal GDP, the nominal interest rate will determine the demand for money. • We write this as a downward sloping relationship between MD and i.

23. i MD M

24. Q: Why does the money demand curve slope down? A: The greater is the nominal interest rate, the greater is the opportunity cost of holding money. Q: What shifts the money demand curve? A: An increase in the nominal GDP will increase the need for money for transactions. This will shift the demand curve out. A reduction in nominal GDP will shift the demand curve in. Money Demand

25. Money Supply • Central banks in large economies (the US, Euroland) typically set an interest rate target though they directly control the money supply. • Relationship between interest rates and money demand give them tools to control interest rate. • Set money supply as straight line indicating central bank control. • Given nominal GDP, interest rate will set money supply equal to money demand.

26. MS i iEQ MD M

27. Reaching Equilibrium • If i > iEQ, then money demand will be less than money supply. People will buy bonds which will reduce the interest rates that borrowers must offer. • If i<iEQ, then money demand will be greater than money supply. People will sell bonds to get money. This will increase the interest rate that bond issuers must sell.

28. Open Market Operations • The government authority controlling the money supply is the central bank. In Hong Kong, this is Hong Kong Monetary Authority (HKMA) • Central banks typically (though not in HK) change the money supply through open market operation (OMO). An OMO is the purchase or sale of government bonds by the central bank. • In an open market purchase, the central bank prints new money and uses it to buy bonds. This increases the supply of money in the short run. • In an open market sale, the central bank sells some of its stock of bonds and receives existing money in exchange. This reduces the supply of money in the short run.

29. Interest Targets • When the central bank selects an interest rate target, they will instruct their bond department to conduct OMO’s to keep interest rate in some market (typically interbank lending market) inside some target zone. • If money demand increases, the bond dept. will do an open market purchase. • If money demand falls, the dept. will do an open market sale.

30. MS • Increase in money demand • due to increase in GDP i iEQ 2. Open Market Purchase increases money supply MD’ MD M

31. Liquidity Effect • In the very short run (less than 3 months or so), open market operations can be thought of as having little effect on nominal GDP. • An unexpected increase in the money supply growth will increase the available liquidity. This will lead to increased demand for bonds and reduced interest rates. • An unexpected decrease in the money supply will reduce available liquidity, causing sales of bonds and upward pressure on interest rates. • The negative short-run relationship between money supply and interest rate is called the liquidity effect.

32. MS MS’ 1. Open Market Purchase increases money supply i iEQ Excess Liquidity causes interest rates to fall iEQ’ MD M

33. Long-run Neutrality of Money • Hypothesis: In the long run, real production and relative prices of different goods do not depend on the level or growth rate of money. • Reason: Money is of intrinsically no value. Money prices are just an arbitrarily chosen value. In short run, money may matter due to market imperfections, but cannot matter in long run.

34. Real Interest Rate • The price level of goods is Pt and the interest rate is it. • If you buy $1 worth of bonds you will give up opportunity to by 1/Pt goods. • You will get $1+i in the future which will allow you to buy 1+i/Pt+1 goods in the future. • The payoff of future goods relative to foregone current goods is the goods interest rate or the real interest rate.

35. Ex Ante vs. Ex Post Real Interest Rates • The future inflation rate, πt+1, is not known at the time a bond is purchased. • Ex Ante Real Interest Rate is the interest rate less the expected inflation rate, πEt+1. rAt = it - πEt+1 • Ex Post Real Interest Rate is the interest rate less the actual realized inflation rate rPt = it - πt+1

36. HK Interest Rates

37. Fisher Effect • In the long run, the money growth rate does not affect the real interest rate. • Money growth affects the interest rate through its affect on inflation. • The higher is future inflation, the higher is the interest rate.

38. Long Run Inflation and Interest Rate • Assume there is a long run money growth rate, gM , and long run output growth rate, gY. Also assume there is a stable real interest rate, r. • If there is a stable long run inflation rate, then there is a stable nominal interest rate. • If there is a stable nominal interest rate, then velocity is stable, gV = 0. • If velocity is stable, then π = gM – gY • If there is a stable inflation rate, then nominal interest rate is i=r+ gM – gY. • An increase in the money growth rate will increase inflation in the long run. Given a target real interest rate, this will increase the nominal interest rate demanded by lenders.

39. Money and Interest Rates • In short run, there is a negative relationship between interest rates and an increase in money growth. • In the long run, there is a positive relationship between an increase in money growth and the long run interest rate. • This dichotomy is often manifested in the yield curve, the difference between a long-term interest rate and a short-term interest rate.

40. Deflation • Deflation is defined simply as negative inflation or falling prices over time. • Nominal Interest Rate has a lower bound. Since money pays 0% rate, bonds that pay less than 0% cannot be sold. Thus, the lower bound of the nominal interest rate is 0% • When interest rate reaches lower bound (as in HK now) deflation pushes up real interest rate.

41. Long-term Interest Rates • Bonds are sold with different maturities. For example, there are Hong Kong government bonds with maturities as long as 10 years. • An expansion in money growth will have different effects on interest rates on long-term bonds and short-term bonds

42. Consider two strategies which should have the same expected pay-off. Starting with $1. • Buy a two year discount bond and hold it for two years. Payoff: • Buy a 1 year bond. After 1 year, invest pay-off in another 1 year bond. Payoff: • Equal pay-offs imply that yield on a two year bond is equal to the expected average yield of 1 year bonds over the next two years.

43. In general, if the pay-off for investing in an n period bond should be the same as the pay-off from rolling over 1 year bonds for n periods: • Then a n period bond yield is (approximately) equal to the average expected yield on 1 period bonds between today and date n.

44. On average, longer term bonds have higher interest rates than short-term bonds.

45. Discount Bonds • There are many types of bonds. The simplest type of bond is a discount bond. The issuer of a discount bond makes a single payment (called the face value) at some designated time T periods from now. • The standard unit of bonds are in $100 of face value. So if a bond price is quoted at PB, this is the price per $100 worth of face value. • Ex. If a bond had a face value of $10,000 and you were quoted a price of 90, you would have to pay $9000 for this bond.

46. What is a Bond • Bonds are a promise to repay certain amounts of money at specific dates in future. • Most bonds specify specific amounts of currency units that will be repaid (unlike stocks which entitle owner to a share of profits). • Bonds unlike bank loans can be traded on securities markets. • Since governments cannot issue equity, they rely on bonds for financing. Government bonds are a large share of world bond market.

47. HK Dollar Bond Market

48. Bond Prices and Interest Rates • The interest rate quoted on a discount bond of maturity date T is calculated as • If you put PB into a bank account that offered and interest rate of it,T for T years, you would have a final balance of 100. • This interest rate is the average return you will get on your bond if you hold it for T periods which is referred to as the yield to maturity or the yield. • Holding interest rates constant, the price of a discount bond gets closer to 100 as the bond matures.

49. Implications • There is an inverse relationship between the price of a bond and the interest yield on the bond. • When a bond is relatively cheap, an investor can earn a high return by buying it and holding it until maturity. • When interest rates rise, bond prices fall.

50. Long-term bond prices are more sensitive to a persistent increase in interest rates because they are held for many periods. The percentage change in discount bond prices are approximately equal to the negative maturity level. Example: Interest rates at all maturities change from 2% to 3%: Δi=.01 The % change in a two year bond price will be approximately -2%. The % change in a 3 year bond price will be approximately -3% The % change in a 10 year bond price will be approximately -10%. Implications