布兰查德宏观经济学第14章.ppt
Chapter 14:Expectations:The Basic ToolsNominal Versus RealInterest RatesInterest Rates expressed in terms of dollars(or,more generally,in units of the national currency)are called nominal interest ratesInterest rates expressed in terms of a basket of goods are called real interest rates.14-11Chapter 14:Expectations:The Basic ToolsNominal Versus RealInterest RatesDefinition and Derivation of the Real Interest Ratei it t=nominal interest rate for =nominal interest rate for year year t t.r rt t=real interest rate for year =real interest rate for year t t.(1+(1+i it t):Lending one dollar):Lending one dollar this year yields(1+this year yields(1+i it t)dollars)dollars next year.Alternatively,next year.Alternatively,borrowing one dollar this borrowing one dollar this year implies paying back(1+year implies paying back(1+i it t)dollars next year.)dollars next year.P Pt t=price this year.=price this year.P Pe et+1t+1=expected price next=expected price next year.year.Figure 14-12Chapter 14:Expectations:The Basic ToolsNominal Versus RealInterest Ratesthen,the expected rate of inflation equalsConsequently,Consequently,GivenGiven,and knowing that,and knowing thatIf the nominal interest rate and the expected rate If the nominal interest rate and the expected rate of inflation are not too large,a simpler expression of inflation are not too large,a simpler expression is:is:The real interest rate is(approximately)equal to the nominal interest rate minus the expected rate of inflation.3Chapter 14:Expectations:The Basic ToolsNominal Versus RealInterest RatesHere are some of the implications of the relation above:IfIfif4Chapter 14:Expectations:The Basic ToolsNominal and Real Interest Rates in the United States Since 1978Nominal and Real One-Year T-bill Rates in the United States since 1978Although the nominal interest rate has declined considerably since the early 1980s,the real interest rate was actually higher in 2001 than in 1981.Figure 14-25Chapter 14:Expectations:The Basic ToolsExpected PresentDiscounted ValuesComputing Present Discounted ValuesThe expected present discounted value of a sequence of future payments is the value today of this expected sequence of payments.14-2Figure 14-26Chapter 14:Expectations:The Basic ToolsComputing Expected Present Discounted Values(a)One dollar this year is worth 1+it dollars next year.(b)If you lend/borrow 1/(1+it)dollars this year,you will receive/repaydollar next year.(c)(c)One dollar is worth dollars two years from now.(d)(d)The present discounted value of a The present discounted value of a dollar two years from today is dollar two years from today is equal toequal to7Chapter 14:Expectations:The Basic ToolsComputing Expected Present Discounted ValuesThe word“discounted comes from the fact that the value next year is discounted,with(1+it)being the discount factor.(The 1-year nominal interest rate,it,is sometimes called the discount rate.8Chapter 14:Expectations:The Basic ToolsA General FormulaThe present discounted value of a sequence of payments,or value in todays 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.9Chapter 14:Expectations:The Basic ToolsUsing Present Values:ExamplesThis formula has these implications:Present value depends positively on todays actual payment and expected future payments.Present value depends negatively on current and expected future interest rates.10Chapter 14:Expectations:The Basic ToolsConstant Interest RatesTo 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:11Chapter 14:Expectations:The Basic ToolsConstant Interest Ratesand PaymentsWhen the sequence of payments is equalcalled them$z,the present value formula simplifies to:The terms in the expression in brackets represent a geometric series.Computing the sum of the series,we get:12Chapter 14:Expectations:The Basic ToolsConstant Interest Rates and Payments,ForeverAssuming 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:13Chapter 14:Expectations:The Basic ToolsZero Interest RatesIf 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.14Chapter 14:Expectations:The Basic ToolsNominal Versus Real Interest Rates,and Present ValuesReplacing nominal interest with real interest rates to obtain the present value of a sequence of real payments,we get:Which can be simplified to:15Chapter 14:Expectations:The Basic ToolsNominal and Real InterestRates,and the IS-LM ModelWhen 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 policythe one that enters the LM relationis the nominal interest rate,then:The real interest rate is:14-316Chapter 14:Expectations:The Basic ToolsNominal and Real InterestRates,and the IS-LM ModelNote 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.17Chapter 14:Expectations:The Basic ToolsMoney Growth,Inflation,Nominal and Real Interest RatesThis 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.14-418Chapter 14:Expectations:The Basic ToolsRevisiting the IS-LM ModelReducing the IS relation,LM relation and relation between the real and nominal interest rate gives us:ISLMThe 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.19Chapter 14:Expectations:The Basic ToolsRevisiting the IS-LM ModelEquilibrium Output and Interest RatesThe 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.Figure 14-420Chapter 14:Expectations:The Basic ToolsNominal and Real Interest Ratesin the Short RunThe Short-run Effects of an Increase in Money GrowthAn 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 a decrease in both the nominal and the real interest rate.Figure 14-521Chapter 14:Expectations:The Basic ToolsIn the medium run,the real interest rate equals the natural interest rate,rn,then:Finally,in the medium run,inflation is equal to money growth:Nominal and Real Interest Ratesin the Medium RunIn the medium run,then:The relation between the nominal interest rate and the real interest rate is:In the medium run,expected inflation is equal to actual inflation,so:22Chapter 14:Expectations:The Basic ToolsNominal and Real Interest Ratesin the Medium RunIn 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.23Chapter 14:Expectations:The Basic ToolsFrom the Short Run tothe Medium RunIn 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,24Chapter 14:Expectations:The Basic ToolsFrom the Short Run tothe Medium RunIn 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.25Chapter 14:Expectations:The Basic ToolsFrom the Short Run tothe Medium RunThe Adjustment of the Real and the Nominal Interest Rate to an Increase in Money GrowthAn increase in money growth leads initially to a decrease in both the real and the nominal interest rate.Over time,the real interest rate returns to its initial value.The nominal interest rate converges to a new higher value,equal to the initial value plus the increase in money growth.Figure 14-626Chapter 14:Expectations:The Basic ToolsEvidence on the Fisher HypothesisTo 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.27Chapter 14:Expectations:The Basic ToolsEvidence on the Fisher HypothesisThe 3-Month Treasury Bill Rate and Inflation since 1927The 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.Figure 14-728Chapter 14:Expectations:The Basic ToolsEvidence on the Fisher HypothesisFigure 14-7 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.29Chapter 14:Expectations:The Basic ToolsNominal Interest Rates and Inflation Across Latin America in the Early 1990sFigure 1Nominal Interest Rates and Inflation:Latin America,1992-199330Chapter 14:Expectations:The Basic ToolsKey Termsnominal interest ratereal interest rateexpected present valuediscount factordiscount ratepresent discounted valuepresent valueFisher effect,Fisher hypothesis31
