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Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin

I. Nominal Versus Real Rates of Interest

Real Interest Rate: the equilibrium rate r at which claims to future consumption are traded for current consumption.

where Qi is the quantity from period i.

Nominal Interest Rate:the nominal interest rate R incorporates both the real rate of interest and the effect of price changes (inflation).

The Behavior of Nominal Interest Rates

r

Q1 Q0

Q0

Q1

Q0

1

where Pi is the price level from period i.

R

Q1P1 Q0P0

Q0P0

Q1P1

Q0P0

1

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Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin

One-period inflation rate:

Combining expressions:

Solving for the real rate:

P1 P0

P0

P1

P0

1

R Q1

Q0

P1

P0

1

1 r 1 1

r r

r

1R1

1R 1

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Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin

II. Expected Inflation and Nominal Interest Rates

• Fisher reasoned that in competitive markets, rational individuals would want to maintain purchasing power by demanding rates of interest that incorporate anticipated price increases.

• Expected rates are before-the-fact (ex ante) predictions of future rates.

• Actual rates reflect after-the-fact (ex post) calculations.

• Fisher’s nominal interest rate:

or an approximation,

R re e ree

R re e

Nominal interest rate = Anticipated real interest rate

+ Expected inflation rate

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Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin

Problems with the nominal theory of interest rates:• real interest rates and inflation are not observable and must

therefore be predicted

• how should inflation be determined

• very difficult to test

• not based upon theoretical models

Mundell Effect:• Inflation reduces wealth. Attempts at saving to restore wealth

cause a downward pressure on interest rates. This results in a less than one-to-one adjustment in nominal rates for changes in expected inflation.

Darby Effect:• Taxes on nominal returns result in a demand to be compensated.

This causes a greater than one-to-one adjustment in nominal rates for changes in expected inflation.

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Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin

III. Empirical Evidence Regarding Inflation and Nominal Interest RatesInsert 4.1

Expected Real Rate and Inflation Proxies• Past inflation rates as predictors• Survey data on inflationary expectations• Long vs. short-term interest rates• Inflation indexed bonds• Commodity-linked bonds

Extracting Estimates from Theoretical Models• Macroeconomic models• Aggregate money supply and demand models

Other Problems in Testing• Which inflation rate?• Logical tautologies

• Non constant real rate of interest

IV. Evidence From Several CountriesInsert 4.2 & 4.3

• The positive relationship between nominal interest rates and inflationary expectations.

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Copyright © 2001 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin

V. Index Bonds as a Solution to Fisher’s Problem• What are they?• How do they work?

VI. Where Does This Lead Us?• The effect of inflation on nominal interest rates seems clear but

imprecise. What is the implication of this for investors?

Question: Suppose you were planning for retirement at some distant point in the future. What are your choices; what are your expectations; and what are the risks?

VII. Summary

• The distinction between nominal and real interest rates was developed.

• Financial investments generally carry nominal rates of return

• Changes in nominal interest rates may not keep pace with changes in expected inflation because of forecasting errors, wealth effects, and tax repercussions.