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CHAPTER 14 Expectations: The Basic Tools Expectations: The Basic Tools CHAPTER 14 Prepared by: Fernando Quijano and Yvonn Quijano Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard

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Chapter 14: Expectations: The Basic Tools Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 2 of 32 Interest Rates expressed in terms of dollars (or, more generally, in units of the national currency) are called nominal interest rates. Interest rates expressed in terms of a basket of goods are called real interest rates. 14-1 Nominal versus Real Interest Rates

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Chapter 14: Expectations: The Basic Tools Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 3 of 32 14-1 Nominal versus Real Interest Rates Definition and Derivation of the Real Interest Rate Figure 14 - 1 i t = nominal interest rate for year t. r t = real interest rate for year t. (1+ i t ): Lending one dollar this year yields (1+ i t ) dollars next year. Alternatively, borrowing one dollar this year implies paying back (1+ i t ) dollars next year. P t = price this year. P e t+1 = expected price next year.

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Chapter 14: Expectations: The Basic Tools Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 4 of 32 then, the expected rate of inflation equals Consequently, Given,, and knowing that If the nominal interest rate and the expected rate of inflation are not too large, a simpler expression is: The real interest rate is (approximately) equal to the nominal interest rate minus the expected rate of inflation. 14-1 Nominal versus Real Interest Rates

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Chapter 14: Expectations: The Basic Tools Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 5 of 32 Here are some of the implications of the relation above: If if 14-1 Nominal versus Real Interest Rates

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Chapter 14: Expectations: The Basic Tools Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 6 of 32 Nominal and Real Interest Rates in the United States since 1978 14-1 Nominal versus Real Interest Rates Although the nominal interest rate has declined considerably since the early 1980s, the real interest rate was actually higher in 2006 than in 1981. Nominal and Real One- Year T-bill Rates in the United States since 1978 Figure 14 - 2

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Chapter 14: Expectations: The Basic Tools Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 7 of 32 When deciding how much investment to undertake, firms care about real interest rates. Then, the IS relation must read: The interest rate directly affected by monetary policy— the one that enters the LM relation—is the nominal interest rate, then: The real interest rate is: 14-2 Nominal and Real Interest Rates and the IS–LM Model

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Chapter 14: Expectations: The Basic Tools Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 8 of 32 Note an immediate implication of these three relations: The interest rate directly affected by monetary policy is the nominal interest rate. The interest rate that affects spending and output is the real interest rate. So, the effects of monetary policy on output depend on how movements in the nominal interest rate translate into movements in the real interest rate. 14-2 Nominal and Real Interest Rates and the IS–LM Model

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Chapter 14: Expectations: The Basic Tools Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 9 of 32 This section focuses on the following assertions: Higher money growth leads to lower nominal interest rates in the short run, but to higher nominal interest rates in the medium run. Higher money growth leads to lower real interest rates in the short run, but has no effect on real interest rates in the medium run. 14-3 Money Growth, Inflation, and Nominal and Real Interest Rates

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Chapter 14: Expectations: The Basic Tools Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 10 of 32 Reducing the IS relation, LM relation and relation between the real and nominal interest rate gives us: IS LM The IS curve is still downward sloping. The LM curve is upward sloping. The equilibrium is at the intersection of the IS curve and the LM curve. 14-3 Money Growth, Inflation, and Nominal and Real Interest Rates Revisiting the IS–LM Model

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Chapter 14: Expectations: The Basic Tools Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 11 of 32 14-3 Money Growth, Inflation, and Nominal and Real Interest Rates Revisiting the IS–LM Model The equilibrium level of output and the equilibrium nominal interest rate are given by the intersection of the IS curve and the LM curve. The real interest rate equals the nominal interest rate minus expected inflation. Equilibrium Output and Interest Rates Figure 14 - 3

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Chapter 14: Expectations: The Basic Tools Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 12 of 32 14-3 Money Growth, Inflation, and Nominal and Real Interest Rates Nominal and Real Interest Rates in the Short Run An increase in money growth increases the real money stock in the short run. This increase in real money leads to an increase in output and decreases in both the nominal and real interest rates. The Short-Run Effects of an Increase in Money Growth Figure 14 - 4

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Chapter 14: Expectations: The Basic Tools Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 13 of 32 14-3 Money Growth, Inflation, and Nominal and Real Interest Rates Nominal and Real Interest Rates in the Medium Run In the medium run, the rate of inflation is equal to the rate of money growth minus the rate of growth of output. In the medium run, output returns to the natural level of output,.

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Chapter 14: Expectations: The Basic Tools Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 14 of 32 In the medium run, the nominal interest rate increases one for one with inflation. This result is known as the Fisher effect, or the Fisher Hypothesis. For example, an increase in nominal money growth of 10% is eventually reflected by a 10% increase in the rate of inflation, a 10% increase in the nominal interest rate, and no change in the real interest rate. 14-3 Money Growth, Inflation, and Nominal and Real Interest Rates Nominal and Real Interest Rates in the Medium Run

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Chapter 14: Expectations: The Basic Tools Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 15 of 32 In the short run, lower nominal interest rates lead to higher output and inflation. In the medium run, this situation changes. In the short run, Over time, In the medium run, 14-3 Money Growth, Inflation, and Nominal and Real Interest Rates From the Short Run to the Medium Run

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Chapter 14: Expectations: The Basic Tools Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 16 of 32 In words: So long as the real interest rate is below the natural real interest rate, output is higher than the natural level of output, and unemployment is below its natural rate. From the Phillips curve relation, we know that as long as unemployment is below the natural rate of unemployment, inflation increases. As inflation increases, it becomes higher than nominal money growth, leading to negative real money growth. In the medium run, the real interest rate increases back to it initial value. 14-3 Money Growth, Inflation, and Nominal and Real Interest Rates From the Short Run to the Medium Run

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Chapter 14: Expectations: The Basic Tools Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 17 of 32 14-3 Money Growth, Inflation, and Nominal and Real Interest Rates From the Short Run to the Medium Run An increase in money growth leads initially to decreases in both the real and the nominal interest rates. Over time, however, the real interest rate returns to its initial value, and the nominal interest rate converges to a new higher value, equal to the initial value plus the increase in money growth. The Adjustment of the Real and the Nominal Interest Rates to an Increase in Money Growth Figure 14 - 5

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Chapter 14: Expectations: The Basic Tools Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 18 of 32 To see if increases in inflation lead to one-for-one increases in nominal interest rates, economists look at: Nominal interest rates and inflation across countries. The evidence of the early 1990s finds substantial support for the Fisher hypothesis. Swings in inflation, which should eventually be reflected in similar swings in the nominal interest rate. Again, the data appears to fit the hypothesis quite well. 14-3 Money Growth, Inflation, and Nominal and Real Interest Rates Evidence on the Fisher Hypothesis

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Chapter 14: Expectations: The Basic Tools Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 19 of 32 Nominal Interest Rates and Inflation across Latin America in the Early 1990s Figure 1 Nominal Interest Rates and Inflation in Latin America, 1992 to 1993

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Chapter 14: Expectations: The Basic Tools Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 20 of 32 14-3 Money Growth, Inflation, and Nominal and Real Interest Rates Evidence on the Fisher Hypothesis The increase in inflation from the early 1960s to the early 1980s was associated with an increase in the nominal interest rate. The decrease in inflation since the mid-1980s has been associated with a decrease in the nominal interest rate. The Three-Month Treasury Bill Rate and Inflation since 1927 Figure 14 - 6

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Chapter 14: Expectations: The Basic Tools Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 21 of 32 Figure 14-6 has at least three interesting features: The steady increase in inflation from the early 1960s to the early 1980s was associated with a roughly parallel increase in the nominal interest rate. The nominal interest rate lagged behind the increase in inflation in the 1970s, while the disinflation of the early 1980s was associated with an initial increase in the nominal interest rate. The other episode of inflation underscores the importance of the “medium-run” qualifier in the Fisher hypothesis. 14-3 Money Growth, Inflation, and Nominal and Real Interest Rates Evidence on the Fisher Hypothesis

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Chapter 14: Expectations: The Basic Tools Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 22 of 32 The expected present discounted value of a sequence of future payments is the value today of this expected sequence of payments. 14-4 Expected Present Discounted Values Interest Rates Computing Expected Present Discounted Values Computing Present Discounted Values Figure 14 - 7

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Chapter 14: Expectations: The Basic Tools Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 23 of 32 (a) One dollar this year is worth 1+i t dollars next year. (b)If you lend/borrow 1/(1+i t ) dollars this year, you will receive/repay dollar next year. (c)One dollar is worth dollars two years from now. (d)The present discounted value of a dollar two years from today is equal to. 14-4 Expected Present Discounted Values Interest Rates Computing Expected Present Discounted Values

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Chapter 14: Expectations: The Basic Tools Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 24 of 32 The word “discounted” comes from the fact that the value next year is discounted, with (1+i t ) being the discount factor. The 1-year nominal interest rate, i t, is sometimes called the discount rate. 14-4 Expected Present Discounted Values Interest Rates Computing Expected Present Discounted Values

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Chapter 14: Expectations: The Basic Tools Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 25 of 32 The present discounted value of a sequence of payments, or value in today’s dollars equals: When future payments or interest rates are uncertain, then: Present discounted value, or present value are another way of saying “”expected present discounted value.” 14-4 Expected Present Discounted Values Interest Rates Computing Expected Present Discounted Values The General Formula

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Chapter 14: Expectations: The Basic Tools Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 26 of 32 This formula has these implications: Present value depends positively on today’s actual payment and expected future payments. Present value depends negatively on current and expected future interest rates. 14-4 Expected Present Discounted Values Interest Rates Using Present Values: Examples

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Chapter 14: Expectations: The Basic Tools Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 27 of 32 To focus on the effects of the sequence of payments on the present value, assume that interest rates are expected to be constant over time, then: 14-4 Expected Present Discounted Values Interest Rates Using Present Values: Examples Constant Interest Rates Constant Interest Rates and Payments When the sequence of payments is equal—called them $z, the present value formula simplifies to:

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Chapter 14: Expectations: The Basic Tools Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 28 of 32 The terms in the expression in brackets represent a geometric series. Computing the sum of the series, we get: 14-4 Expected Present Discounted Values Interest Rates Using Present Values: Examples Constant Interest Rates and Payments

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Chapter 14: Expectations: The Basic Tools Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 29 of 32 Assuming that payments start next year and go on forever, then: Using the property of geometric sums, the present value formula above is: Which simplifies to: 14-4 Expected Present Discounted Values Interest Rates Using Present Values: Examples Constant Interest Rates and Payments, Forever

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Chapter 14: Expectations: The Basic Tools Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 30 of 32 If i = 0, then 1/(1+i) equals one, and so does (1/(1+i) n ) for any power n. For that reason, the present discounted value of a sequence of expected payments is just the sum of those expected payments. 14-4 Expected Present Discounted Values Interest Rates Using Present Values: Examples Zero Interest Rates

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Chapter 14: Expectations: The Basic Tools Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 31 of 32 Replacing nominal interest with real interest rates to obtain the present value of a sequence of real payments, we get: Which can be simplified to: 14-4 Expected Present Discounted Values Interest Rates Nominal versus Real Interest Rates and Present Values

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Chapter 14: Expectations: The Basic Tools Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics, 5/e Olivier Blanchard 32 of 32 Key Terms nominal interest rate real interest rate Fisher effect, Fisher hypothesis, expected present value discount factor discount rate present discounted value present value

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