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Money Supplement

Money Supplement. Adjusting for Inflation/Converting Current Price Series into Constant Price Series. One may have a time series of a nominal aggregate, N t , (in current prices) without the microeconomic data necessary to construct a corresponding real aggregate.

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Money Supplement

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  1. Money Supplement

  2. 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 year, R, (the reference year may or may not be the base year). • Series measured in reference year dollars is

  3. Catch Me If You Can • Frank Abagnale Jr. cashed bad checks in 1965 worth US$2.5 million. How much would that be worth in terms of today’s goods? • US Base year, 1996, P1965= .23474 • Convert nominal amount (2.5 Mil) into real amount in 1996 dollars • Convert nominal amount into 2002 dollars using P2000 = 1.11945.

  4. 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. it≡ Net Nominal Interest Rate at time t. Liquidity demand is a negative function of the nominal interest rate. Example: Economists often assume that liquidity demand is written as a constant e ≈2.72 raised to the power of some negative function of i. In this example, for each increase in the interest rate of .01, liquidity demand will decrease by l%. Nominal Interest Rate

  5. 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.

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

  7. Example • On February 13, 2003, the yield on a 1 year US Treasury bond as 1.27% and the yield on a 2 year Treasure bond was 1.57% • If Expectations theory holds true, the expected interest rate on a 1 year bond next year is

  8. Bond Investment • An Indian investor decided to invest Rp.1,000,000 in Indian bonds in 1970. The strategy will be to buy bonds in 1970 and roll over all payments of principal and interest back into a bond fund. • The balance in the bond fund after 1 year would be • After reinvesting this balance into bonds for another year, the balance would be: • After 20 years, the balance on the bonds was

  9. Average Returns • If we want to calculate the average return on an investment strategy, we calculate an artificial investment strategy that offers a constant return (1+i) in every year of the T years of the investment strategy but has the same final balance as the actual investment strategy. • Example: An artificial Indian investor who had initially invested Rp. 1 Mill. in a bond that paid approximately 6.1% would have the same final balance as the actual Indian investor.

  10. Real Returns • India’s price index (base year 1980) in 1990 was P1990 = 1.99. The price index in 1970 was .3806. Prices have more than quadrupled. • We could calculate the average Indian inflation rate as a constant growth rate of prices π that generates an equal change in the price level over T (in this case T = 20) periods. • The average Indian inflation rate during this period was 8.6%. • The average ex post real return, r, was the average nominal return divided by the inflation rate. The real return is negative! • Convert the final balance of the bond investment strategy into 1970 dollars. Thus, in 1990, the pay-off of the savers bond investment would only buy the same amount of goods as Rp.$622,346 would have bought in 1970. • Investing in Indian bonds has cut the purchasing power of savings nearly in half!

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