曼昆宏观经济学第14章

1、S E V E N T H E D I T I O Nhow to incorporate dynamics into the AD-AS model we previously studiedhow to use the dynamic AD-AS model to illustrate long-run economic growthhow to use the dynamic AD-AS model to trace out the effects over time of various shocks and policy changes on output, inflation, a

2、nd other endogenous variables2CHAPTER 14 Dynamic AD-AS ModelIntroductionThe dynamic model of aggregate demand and aggregate supply gives us more insight into how the economy works in the short run. It is a simplified version of a DSGE model, used in cutting-edge macroeconomic research. (DSGE = Dynam

3、ic, Stochastic, General Equilibrium)3CHAPTER 14 Dynamic AD-AS ModelIntroductionThe dynamic model of aggregate demand and aggregate supply is built from familiar concepts, such as:the IS curve, which negatively relates the real interest rate and demand for goods & servicesthe Phillips curve, whic

4、h relates inflation to the gap between output and its natural level, expected inflation, and supply shocksadaptive expectations, a simple model of inflation expectations4CHAPTER 14 Dynamic AD-AS ModelHow the dynamic AD-AS model is different from the standard modelInstead of fixing the money supply,

5、the central bank follows a monetary policy rule that adjusts interest rates when output or inflation change. The vertical axis of the DAD-DAS diagram measures the inflation rate, not the price level.Subsequent time periods are linked together:Changes in inflation in one period alter expectations of

6、future inflation, which changes aggregate supply in future periods, which further alters inflation and inflation expectations.5CHAPTER 14 Dynamic AD-AS ModelKeeping track of timeThe subscript “t ” denotes the time period, e.g.Yt = real GDP in period t Yt -1 = real GDP in period t 1Yt +1 = real GDP i

7、n period t + 1We can think of time periods as years. E.g., if t = 2008, then Yt = Y2008 = real GDP in 2008Yt -1 = Y2007 = real GDP in 2007Yt +1 = Y2009 = real GDP in 20096CHAPTER 14 Dynamic AD-AS ModelThe models elementsThe model has five equations and five endogenous variables: output, inflation, t

8、he real interest rate, the nominal interest rate, and expected inflation. The equations may use different notation, but they are conceptually similar to things youve already learned. The first equation is for output7CHAPTER 14 Dynamic AD-AS ModelOutput: The Demand for Goods and Services()ttttYYr0,0o

9、utputnatural level of outputreal interest rateNegative relation between output and interest rate, same intuition as IS curve.8CHAPTER 14 Dynamic AD-AS ModelOutput: The Demand for Goods and Services()ttttYYrdemand shock, random and zero on averagemeasures the interest-rate sensitivity of demand“natur

10、al rate of interest” in absence of demand shocks, ttYYwhentr9CHAPTER 14 Dynamic AD-AS ModelThe Real Interest Rate: The Fisher Equation1ttttriEnominal interest rateexpected inflation rateex ante (i.e. expected) real interest rateincrease in price level from period t to t +1, not known in period texpe

11、ctation, formed in period t, of inflation from t to t +11t1ttE10CHAPTER 14 Dynamic AD-AS ModelInflation: The Phillips Curve1()ttttttEYYpreviously expected inflationcurrent inflationsupply shock, random and zero on average indicates how much inflation responds when output fluctuates around its natura

12、l level011CHAPTER 14 Dynamic AD-AS ModelExpected Inflation: Adaptive Expectations1tttEFor simplicity, we assume people expect prices to continue rising at the current inflation rate.12CHAPTER 14 Dynamic AD-AS ModelThe Nominal Interest Rate: The Monetary-Policy Rule*()()ttttYttiYYnominal interest rat

13、e, set each period by the central banknatural rate of interestcentral banks inflation target0,0Y13CHAPTER 14 Dynamic AD-AS ModelThe Nominal Interest Rate: The Monetary-Policy Rule*()()ttttYttiYYmeasures how much the central bank adjusts the interest rate when inflation deviates from its targetmeasur

14、es how much the central bank adjusts the interest rate when output deviates from its natural rate14CHAPTER 14 Dynamic AD-AS ModelCASE STUDYThe Taylor RuleEconomist John Taylor proposed a monetary policy rule very similar to ours:iff = + 2 + 0.5 ( 2) 0.5 (GDP gap)whereiff = nominal federal funds rate

15、 targetGDP gap = 100 x = percent by which real GDP is below its natural rateThe Taylor Rule matches Fed policy fairly well.YYYCASE STUDYThe Taylor Rule012345678910198719891991199319951997199920012003200520072009PercentTaylors ruleactual Federal Funds rate16CHAPTER 14 Dynamic AD-AS ModelThe models va

16、riables and parametersEndogenous variables:tY tr t1ttEti OutputInflationReal interest rateNominal interest rateExpected inflation17CHAPTER 14 Dynamic AD-AS ModelThe models variables and parametersExogenous variables:Predetermined variable:tY *ttt1tNatural level of outputCentral banks target inflatio

17、n rateDemand shockSupply shockPrevious periods inflation18CHAPTER 14 Dynamic AD-AS ModelThe models variables and parametersParameters:YResponsiveness of demand to the real interest rateNatural rate of interestResponsiveness of inflation to output in the Phillips CurveResponsiveness of i to inflation

18、 in the monetary-policy ruleResponsiveness of i to output in the monetary-policy rule19CHAPTER 14 Dynamic AD-AS ModelThe models long-run equilibriumThe normal state around which the economy fluctuates. Two conditions required for long-run equilibrium:There are no shocks:Inflation is constant:0tt1tt2

19、0CHAPTER 14 Dynamic AD-AS ModelThe models long-run equilibriumPlugging the preceding conditions into the models five equations and using algebra yields these long-run values:ttYYtr*tt*1tttE*tti21CHAPTER 14 Dynamic AD-AS ModelThe Dynamic Aggregate Supply CurveThe DAS curve shows a relation between ou

20、tput and inflation that comes from the Phillips Curve and Adaptive Expectations:1()tttttYY(DAS)22CHAPTER 14 Dynamic AD-AS ModelThe Dynamic Aggregate Supply CurveDAS slopes upward: high levels of output are associated with high inflation. Y DASt1()tttttYYDAS shifts in response to changes in the natur

21、al level of output, previous inflation, and supply shocks. 23CHAPTER 14 Dynamic AD-AS ModelThe Dynamic Aggregate Demand CurveTo derive the DAD curve, we will combine four equations and then eliminate all the endogenous variables other than output and inflation.Start with the demand for goods and ser

22、vices:()ttttYYr1()ttttttYYiEusing the Fisher eqn24CHAPTER 14 Dynamic AD-AS ModelThe Dynamic Aggregate Demand Curve1()ttttttYYiEresult from previous slide()tttttYYiusing the expectations eqn*()()tttttYttttYYYY using monetary policy rule*()()ttttYtttYYYY 25CHAPTER 14 Dynamic AD-AS ModelThe Dynamic Agg

23、regate Demand Curveresult from previous slidecombine like terms, solve for Y*()()ttttYtttYYYY 1A0,B011YY*A()B,tttttYYwhere(DAD)26CHAPTER 14 Dynamic AD-AS ModelThe Dynamic Aggregate Demand CurveDAD slopes downward:When inflation rises, the central bank raises the real interest rate, reducing the dema

24、nd for goods & services. Y DAD shifts in response to changes in the natural level of output, the inflation target, and demand shocks. DADt*A()BtttttYY27CHAPTER 14 Dynamic AD-AS ModelYt The short-run equilibriumIn each period, the intersection of DAD and DAS determines the short-run eqm values of

25、 inflation and output.tYtY DADtDAStAIn the eqm shown here at A, output is below its natural level. 28CHAPTER 14 Dynamic AD-AS ModelLong-run growthPeriod t:initial eqm at AY DAStYtDADtAYttPeriod t + 1 :Long-run growth increases the natural rate of output.Yt +1DASt +1DADt +1Bt + 1t=DAS shifts because

26、economy can produce more g&sDAD shifts because higher income raises demand for g&sNew eqm at B, income grows but inflation remains stable.Yt +129CHAPTER 14 Dynamic AD-AS ModelA shock to aggregate supplyPeriod t 1:initial eqm at At 1Yt 1Period t:Supply shock ( 0) shifts DAS upward; inflation

27、rises, central bank responds by raising real interest rate, output falls. Period t + 1 :Supply shock is over ( = 0) but DAS does not return to its initial position due to higher inflation expectations.Period t + 2:As inflation falls, inflation expectations fall, DAS moves downward, output rises. Y D

28、ASt -1YDADADAStYtBtDASt +1CDASt +2DYt + 2t + 2This process continues until output returns to its natural rate. LR eqm at A. 30CHAPTER 14 Dynamic AD-AS ModelThus, we can interpret as the percentage deviation of output from its natural level.Yt YtParameter values for simulations100tY*2.0t1.02.00.250.5

29、0.5YCentral banks inflation target is 2 percent.A 1-percentage-point increase in the real interest rate reduces output demand by 1 percent of its natural level.The natural rate of interest is 2 percent. When output is 1 percent above its natural level, inflation rises by 0.25 percentage point.These

30、values are from the Taylor Rule, which approximates the actual behavior of the Federal Reserve. The following graphs are called impulse response functions. They show the “response” of the endogenous variables to the “impulse,” i.e. the shock. The dynamic response to a supply shocktYtA one-period sup

31、ply shock affects output for many periods.The dynamic response to a supply shockttBecause inflation expect-ations adjust slowly, actual inflation remains high for many periods. The dynamic response to a supply shocktrtThe real interest rate takes many periods to return to its natural rate.The dynami

32、c response to a supply shocktitThe behavior of the nominal interest rate depends on that of the inflation and real interest rates.35CHAPTER 14 Dynamic AD-AS ModelA shock to aggregate demandPeriod t 1:initial eqm at At 1Y DASt -1,tYDADt ,t+1,t+4DADt -1, t+5DASt +5Yt 1ADASt + 1CDASt +2DDASt +3EDASt +4

33、FYtBtYt + 5Gt + 5Period t:Positive demand shock ( 0) shifts AD to the right; output and inflation rise. Period t + 1 :Higher inflation in t raised inflation expectations for t + 1, shifting DAS up.Inflation rises more, output falls.Periods t + 2 to t + 4 :Higher inflation in previous period raises i

34、nflation expectations, shifts DAS up.Inflation rises, output falls.Period t + 5:DAS is higher due to higher inflation in preceding period, but demand shock ends and DAD returns to its initial position. Eqm at G. Periods t + 6 and higher:DAS gradually shifts down as inflation and inflation expectatio

35、ns fall, economy gradually recovers until reaching LR eqm at A.The dynamic response to a demand shocktYtThe demand shock raises output for five periods. When the shock ends, output falls below its natural level, and recovers gradually.The dynamic response to a demand shockttThe demand shock causes i

36、nflation to rise. When the shock ends, inflation gradually falls toward its initial level.The dynamic response to a demand shocktrtThe demand shock raises the real interest rate. After the shock ends, the real interest rate falls and approaches its initial level.The dynamic response to a demand shoc

37、ktitThe behavior of the nominal interest rate depends on that of the inflation and real interest rates.40CHAPTER 14 Dynamic AD-AS ModelA shift in monetary policyPeriod t 1:target inflation rate * = 2%, initial eqm at At 1 = 2%Yt 1Period t:Central bank lowers target to * = 1%, raises real interest ra

38、te, shifts DAD leftward. Output and inflation fall.Period t + 1 :The fall in treduced inflation expectationsfor t + 1, shifting DAS downward. Output rises, inflation falls.Y DASt -1, tYDADt 1ADADt, t + 1,DASfinalYttBDASt +1CSubsequent periods:This process continues until output returns to its natura

39、l rate and inflation reaches its new target. Zfinal = 1% , YfinalThe dynamic response to a reduction in target inflationtY*tReducing the target inflation rate causes output to fall below its natural level for a while. Output recovers gradually.The dynamic response to a reduction in target inflationt

40、*tBecause expect-ations adjust slowly, it takes many periods for inflation to reach the new target.The dynamic response to a reduction in target inflationtr*tTo reduce inflation, the central bank raises the real interest rate to reduce aggregate demand.The real interest rate gradually returns to its

41、 natural rate.The dynamic response to a reduction in target inflationti*tThe initial increase in the real interest rate raises the nominal interest rate. As the inflation and real interest rates fall, the nominal rate falls.45CHAPTER 14 Dynamic AD-AS ModelAPPLICATION:Output variability vs. inflation

42、 variabilityA supply shock reduces output (bad) and raises inflation (also bad). The central bank faces a tradeoff between these “bads” it can reduce the effect on output, but only by tolerating an increase in the effect on inflation. 46CHAPTER 14 Dynamic AD-AS ModelAPPLICATION:Output variability vs

43、. inflation variabilityCASE 1: is large, Y is smallY DADt 1, tDAStDASt 1Yt 1t 1YttA supply shock shifts DAS up.In this case, a small change in inflation has a large effect on output, so DAD is relatively flat. The shock has a large effect on output, but a small effect on inflation. 47CHAPTER 14 Dyna

44、mic AD-AS ModelAPPLICATION:Output variability vs. inflation variabilityCASE 2: is small, Y is largeY DADt 1, tDAStDASt 1Yt 1t 1YttIn this case, a large change in inflation has only a small effect on output, so DAD is relatively steep. Now, the shock has only a small effect on output, but a big effec

45、t on inflation. 48CHAPTER 14 Dynamic AD-AS ModelAPPLICATION:The Taylor PrincipleThe Taylor Principle (named after John Taylor):The proposition that a central bank should respond to an increase in inflation with an even greater increase in the nominal interest rate (so that the real interest rate ris

46、es).I.e., central bank should set 0. Otherwise, DAD will slope upward, economy may be unstable, and inflation may spiral out of control.49CHAPTER 14 Dynamic AD-AS ModelAPPLICATION:The Taylor PrincipleIf 0:When inflation rises, the central bank increases the nominal interest rate even more, which inc

47、reases the real interest rate and reduces the demand for goods & services. DAD has a negative slope. *1()11tttttYYYY(DAD)*()()ttttYttiYY(MP rule)50CHAPTER 14 Dynamic AD-AS ModelAPPLICATION:The Taylor PrincipleIf 0:When inflation rises, the central bank increases the nominal interest rate by a smaller amount. The real interest rate falls, which increases the demand for goods & services. DAD has a positive slope. *1()11tttttYYYY(DAD)*()()ttttYttiYY(MP rule)51CHAPTER 14 Dynamic AD-AS ModelAPPLICATION:The Taylor PrincipleIf D