34
Notes to the Instructor Chapter Summary This chapter extends the analysis of short-run fluctuations to consider the response over time of key macroeconomic variables. The chapter does this by constructing a dynamic model of aggregate demand and aggregate supply in which the time dimension is explicitly considered. A feature of the model is that it incorporates the response of monetary policy to economic conditions, thereby providing a more realistic setting for understanding the interaction of policy and economic outcomes. Comments The material presented in this chapter is more difficult than the AD–AS, IS–LM models analyzed in earlier chapters. But because many of the building blocks of this model have already been discussed, instructors should have a relatively easy time motivating the approach, and students should readily see the connections to what they have already learned. The model consists of five equations—a relatively large number for undergraduates to work with—but the discussion surrounding the model requires only basic algebra. Dynamic solution of the model is done through simulation exercises, with figures illustrating the time paths of different variables. Faculty who don’t feel comfortable with going through the algebra of the model’s details can still use the chapter effectively by relying on the simulation figures to discuss how various shocks and changes in policy affect the economy over time. Use of the Dismal Scientist Web Site Go to the Dismal Scientist Web site and download annual data on the federal funds rate, real GDP, and the GDP price index over the past 30 years. Compute the trend level of real GDP over time by graphing it and choosing as endpoints 1979 and 2006 (cyclical peaks). Now construct a GDP gap series by subtracting your trend GDP from actual GDP. Compute the inflation rate using the GDP price index. Using the specification of Taylor’s Rule discussed in Chapter 14, compute predictions for the federal funds rate over this time period. Now compare your predictions with the actual federal funds rate. When are they similar and when are they different? Does the rule fit better after the shift in 1984 to interest-rate targeting and away from monetary-aggregate targeting by the Federal Reserve? Assess whether your findings suggest that monetary policy may have been too expansionary in the early to mid-2000s, during the time when real estate prices began to rise sharply. Chapter Supplements This chapter includes the following supplements: 14-1 How a Real Business Cycle Model Is Constructed 14-2 The Microeconomics of Labor Supply 337 CHAPTER A Dynamic Model of Aggregate Demand and Aggregate Supply 14

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Page 1: Mankiw IM Ch 14

Notes to the Instructor

Chapter SummaryThis chapter extends the analysis of short-run fluctuations to consider the response overtime of key macroeconomic variables. The chapter does this by constructing a dynamic modelof aggregate demand and aggregate supply in which the time dimension is explicitlyconsidered. A feature of the model is that it incorporates the response of monetary policy toeconomic conditions, thereby providing a more realistic setting for understanding theinteraction of policy and economic outcomes.

CommentsThe material presented in this chapter is more difficult than the AD–AS, IS–LM modelsanalyzed in earlier chapters. But because many of the building blocks of this model havealready been discussed, instructors should have a relatively easy time motivating theapproach, and students should readily see the connections to what they have alreadylearned. The model consists of five equations—a relatively large number for undergraduatesto work with—but the discussion surrounding the model requires only basic algebra.Dynamic solution of the model is done through simulation exercises, with figures illustratingthe time paths of different variables. Faculty who don’t feel comfortable with going throughthe algebra of the model’s details can still use the chapter effectively by relying on thesimulation figures to discuss how various shocks and changes in policy affect the economyover time.

Use of the Dismal Scientist Web SiteGo to the Dismal Scientist Web site and download annual data on the federal funds rate,real GDP, and the GDP price index over the past 30 years. Compute the trend level of realGDP over time by graphing it and choosing as endpoints 1979 and 2006 (cyclical peaks). Nowconstruct a GDP gap series by subtracting your trend GDP from actual GDP. Compute theinflation rate using the GDP price index. Using the specification of Taylor’s Rule discussedin Chapter 14, compute predictions for the federal funds rate over this time period. Nowcompare your predictions with the actual federal funds rate. When are they similar andwhen are they different? Does the rule fit better after the shift in 1984 to interest-ratetargeting and away from monetary-aggregate targeting by the Federal Reserve? Assesswhether your findings suggest that monetary policy may have been too expansionary in theearly to mid-2000s, during the time when real estate prices began to rise sharply.

Chapter SupplementsThis chapter includes the following supplements:

14-1 How a Real Business Cycle Model Is Constructed

14-2 The Microeconomics of Labor Supply

337

C H A P T E R

A D y n a m i c M o d e l o f A g g r e g a t eD e m a n d a n d A g g r e g a t e S u p p l y

14

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14-3 Quits and Layoffs

14-4 Involuntary Unemployment and Overqualification

14-5 Why Technology Shocks Are So Important in Real Business Cycle Models

14-6 Real Business Cycles and Random Walks

14-7 Inflation Inertia

14-8 Volatility and Growth

14-9 How Long Is the Long Run? Part Four

14-10 Additional Readings

338 CHAPTER 14 A Dynamic Model of Aggregate Demand and Aggregate Supply

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Lecture Notes

IntroductionThe chapter builds on the earlier development of the AD–AS, IS–LM models bydeveloping a dynamic model of aggregate demand and aggregate supply. This modelis another way to study short-run business-cycle fluctuations and the effects offiscal and monetary policies. The model is simplified version of the sorts of modelsused by policymakers in formulating macroeconomic policy.

14-1 Elements of the ModelMany of the variables in the model are familiar from previous chapters, but now wewill use a “t” subscript to denote the time period. Thus, total output and nationalincome in period “t” will be given as Yt and, similarly, in period “t – 1” it is given asYt – 1. The model is composed of five equations, which we describe below.

Output: The Demand for Goods and ServicesThe demand for goods and services in the economy is determined by:

Yt � Y—

t – � (rt – �) � �t,

where Yt is the total output of goods and services, Y—

t is the economy’s natural levelof output, rt is the real interest rate, �t is a random demand shock, and � and � areparameters greater than zero. This equation is similar to the IS equation fromChapter 10. An increase in the real interest rate lowers demand through areduction in both investment spending by business firms and consumptionspending by households, with the response depending on the size of the parameter� (a higher interest rate might also appreciate the real exchange rate, dampeningnet exports). The demand for goods and services grows with the natural level ofoutput. This feature allows us to consider long-run economic growth in this model.Finally, the demand shock represents exogenous shifts in spending that includeshifts in fiscal policy. The parameter � is the natural rate of interest, which is thevalue of the real interest rate when the demand for goods and services equals thenatural level of output.

The Real Interest Rate: The Fisher EquationWe define the real interest as equal to the nominal rate minus expected inflation:

rt � it – Et�t � 1

which is similar to the Fisher equation presented in Chapter 4. The variable Et�t � 1represents the period t expectation of inflation for period t � 1. Notation and timingreflect the convention of dating variables by when they are known. Accordingly, theex ante real interest rate rt and the nominal interest rate it are known at time t andrepresent returns between period t and t � 1, and the inflation rate �t � 1, which isa function of prices in period t and t � 1, is known at t � 1. The expectation ofinflation in period t is, therefore, known in period t.

Inflation: The Phillips CurveThe model uses a standard Phillips curve, similar to the one derived in Chapter 13:

�t � Et – 1�t � �(Yt – Y—

t) � �t.

Lecture Notes 339

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As in Chapter 13, inflation depends on expected inflation, the gap between outputand its natural level, and a supply shock �t. The parameter � determines howresponsive inflation is to changes in the output gap.

Expected Inflation: Adaptive ExpectationsExpectations of inflation are formed adaptively, so that last period’s inflation rate isused as the expectation for inflation in the current period:

Et – 1�t � �t – 1.

As discussed in Chapter 13, this assumption about expectations ignores thepossibility that people are forward-looking and use all available information to formtheir expectations. An alternative approach, known as rational expectations,assumes forward-looking behavior but is more complicated mathematically (and itsempirical validity is open to question). Using adaptive expectations simplifies theanalysis of the model while maintaining its key implications.

The Nominal Interest Rate: The Monetary Policy RuleThe last equation of the model is a rule for monetary policy in which the centralbank sets a target for the nominal interest rate based on inflation and output:

it � �t � � � �(�t – �t*) � Y(Yt – Y—

t).

The policy rule assumes that the central bank responds to deviations ininflation from its target inflation rate �t* and to deviations in output relative to itsnatural level Y

—t. Policy parameters, � and Y, determine how much the central

bank responds to these deviations. In the absence of deviations from targetinflation (�t � �t*) and from the natural level of output (Yt � Y

—t), the central bank

sets the real interest rate, it – �t, equal to the natural rate of interest �. (Recall thatrt � it – Et�t � 1 � it – �t under adaptive expectations.) Thus, when inflation exceedsits target (�t �t*) or output is above its natural level (Yt Y

—t), the real interest

rate rises. And when inflation is below its target or output is below it natural level,the real interest rate falls.

Unlike earlier chapters that focused on changes in the money supply as thepolicy instrument for the central bank, here the policy instrument is the interestrate. The implicit assumption here is that the central bank adjusts the moneysupply as necessary to achieve its target for the interest rate. Choosing the interestrate as the policy instrument is more realistic as it closely matches the practice ofcentral banks around the world.

Case Study: The Taylor RuleThe Fed chooses a target for federal funds rate using two general guidelines: Wheninflation rises, the federal funds rate should rise, and when economic activity slowsdown, the federal funds rate should fall. Economist John Taylor has proposed asimple rule for the federal funds rate following these guidelines:

Nominal Federal Funds Rate �Inflation � 2.0 � 0.5(Inflation – 2.0) – 0.5(GDP gap).

The federal funds rate responds to both inflation and the GDP gap when using thisrule. For each percentage point by which inflation rises above 2 percent, the realfederal funds rate rises by 0.5 percent. For each percentage point by which realGDP falls below its natural rate, the real federal funds rate falls by 0.5 percent. Ifinstead inflation falls below 2 percent or GDP rises above its natural rate, thefederal funds rate rises or falls accordingly. John Taylor’s monetary rule may be therule that the Federal Reserve follows in setting policy.

340 CHAPTER 14 A Dynamic Model of Aggregate Demand and Aggregate Supply

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14-2 Solving the ModelThe five equations presented above determine the paths of the model’s fiveendogenous variables: output Yt, the real interest rate rt, inflation �t, expectedinflation Et – 1�t, and the nominal interest rate it. Before using the model to analyzethe economy’s response to economic shocks, we first describe the model’s long-runequilibrium.

Figure 1 The Federal Funds Rate: Actual and Suggested

1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007

Percent

Year

Actual

Taylor’s rule

10

8

3

2

1

5

6

9

7

4

Table 14-1 The Variables and Parameters in the Dynamic AD-As Model

Endogenous VariablesYt Output�t Inflation�t Real interest rateit Nominal interest rateEt�t � 1 Expected inflation

Exogenous VariablesY—

t Natural level of output�t* Central Bank’s target fro inflation�t Shock to the demand for goods and services�t Shock to the Phillips curve (supply shock)

Predetermined Variable�t-1 Previous period’s inflation

Parameters� The responsiveness of the demand for goods and services to the real interest rate� The natural rate of interest� The responsiveness of inflation to output in the Phillips curve� The responsiveness of the nominal interest rate to inflation in the monetary-

policy ruleY The responsiveness of the nominal interest rate to output in the monetary-

policy rule

Source: Federal Reserve Board, U.S. Department of Commerce, U.S. Department of Labor, and author’scalculations. To implement the Taylor rule, the inflation rate is measured as the percentage change in theGDP deflator over the previous four quarters, and the GDP gap is measured as negative two times thedeviation of the unemployment rate from its natural rate (as shown in Figure 6-1).

341

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The Long-Run EquilibriumLong-run equilibrium for the model is the situation where there are no shocks andinflation is constant over time. Applying this to the five equations of the modelgives output and the real interest rate equal to their natural values, inflation andexpected inflation equal to the target rate of inflation, and the nominal interest rateequal to the natural rate of interest plus target inflation (Yt �Y

—t, rt � �, �t � �t*,

Et�t � 1 � �t*, it � � � �t*). The long-run equilibrium reflects the classicaldichotomy whereby real variables are determined separately from nominal ones,and it reflects monetary neutrality in that monetary policy does not influence realvariables.

The Dynamic Aggregate-Supply CurveTo analyze the economy in the short run, we need to derive two equations that arethe analogues of the AD and AS equations of Chapter 13. The dynamic aggregate-supply equation is the Phillips curve, with lagged inflation substituted for expectedinflation:

�t � �t – 1 � �(Yt – Y—

t) � �t. (DAS)

This equation gives rise to an upward-sloping schedule called the dynamicaggregate-supply curve when plotted with inflation on the y-axis and output plottedon the x-axis. Its slope reflects the Phillips curve whereby high levels of economicactivity give rise to high inflation. The curve is drawn for given values of laggedinflation, the natural level of output, and the supply shock. If these variableschange, DAS will shift.

342 CHAPTER 14 A Dynamic Model of Aggregate Demand and Aggregate Supply

Income, Output, Y

Inflation, �

Dynamic aggregatesupply, DASt

The Dynamic Aggregate Supply CurveFigure 2

The Dynamic Aggregate-Demand CurveTo derive the dynamic aggregate-demand curve, start with the demand for goodsservices equation and substitute for the real interest rate using the Fisherequation. Next, eliminate the nominal interest rate by using the monetary policyequation and substitute for expected inflation using the equation for inflationexpectations. Finally, cancel terms and rearrange the equation to yield:

Yt � Y—

t – [��/(1� �Y)](�t – �t*) � [1/(1� �Y)] �t. (DAD)

This equation is represented as a downward-sloping schedule called the dynamicaggregate-demand curve when plotted with inflation on the y-axis and outputplotted on the x-axis. Its slope reflects the response of the central bank to inflation,whereby an increase in inflation leads to an increase in the nominal interest rate by

Page 7: Mankiw IM Ch 14

more than the rise in inflation, so that the real interest rate also increases, therebyreducing the quantity of goods and services demanded. The curve is drawn forgiven values of the natural level of output, the inflation target, and the demandshock. If these variables change, DAD will shift.

The Short-Run EquilibriumThe intersection of the dynamic aggregate-demand curve and the dynamicaggregate-supply curve determines the economy’s short-run equilibrium. These tworelationships determine two endogenous variables (inflation and output in period t),given the five other exogenous (or predetermined) variables. These are the naturallevel of output, the target inflation rate, the demand shock, the supply shock, andthe previous period’s inflation rate. The short-run equilibrium level of output canbe less than, equal to, or greater than its natural level. In the long run, it will equalits natural level.

Note that the short-run equilibrium rate of inflation becomes next period’slagged inflation rate and so will influence the position of the dynamic aggregatesupply curve in period t � 1. This link between periods is responsible for thedynamic patterns of adjustment of the economy in response to shocks or changes inpolicy. In other words, expectations of inflation in period t � 1, which determine theposition of the dynamic aggregate-supply curve in period t � 1, depend on theoutcome of inflation in period t, providing a link between time periods. This

Lecture Notes 343

Income, Output, Y

Inflation, �

Dynamic aggregatedemand, DADt

The Dynamic Aggregate Demand CurveFigure 3

Natural level of output, YtIncome, Output, Y

Inflation, �

DADt

DASt

The Short-Run EquilibriumFigure 4

Short-runequilibrium

Yt

Yt

Page 8: Mankiw IM Ch 14

continues into the future, with inflation in period t � 1 in turn determiningexpected inflation in period t � 2, etc.

14-3 Using the ModelWe can use the model to assess the effects of change in the exogenous variables. Tosimplify the analysis, the economy is assumed to initially be at its long-runequilibrium.

Long-Run GrowthAs discussed in Chapters 7 and 8, increases over time in the natural level of output,Y—

t, may occur due to population growth, capital accumulation, and technologicalprogress. Both the DAD and DAS curves shift to the right by an amount equal tothe increase in the natural level of output. Output increases by the same amountand inflation is unchanged.

344 CHAPTER 14 A Dynamic Model of Aggregate Demand and Aggregate Supply

An Increase in the Natural Level of OutputFigure 5

4. … leading togrowth in output …

5. … andstable inflation.

3. … as doesthe dynamicAD curve, …

1. When the naturallevel of output increases, …

2. … the dynamic AScurve shifts to the right, …

Income, Output, Y

Inflation, �

DASt + 1

DADt + 1

DASt

DADt

Yt

Yt

Yt + 1

Yt + 1

A B

A Shock to Aggregate SupplySuppose that the aggregate supply shock variable �t increases to 1 percent for oneperiod of time and then returns to zero. The DAS curve will shift to the left inperiod t by exactly the amount of the shock. The DAD curve will remain unchanged.Inflation rises and output falls in period t. These effects reflect in part the responseof the central bank through its policy rule that leads to higher nominal and realinterest rates, which in turn reduces demand for goods and services and pushesoutput below its natural level. Lower output dampens inflationary pressure, soinflation does not rise by the full extent of the supply shock.

In periods following the shock, expected inflation is higher (since it depends onthe previous period’s inflation), so the DAS curve does not return immediately to itsinitial position. Instead, adjustment occurs gradually with inflation declining andoutput rising, as the DAS curve gradually shifts to the right. Simulation analysisthat uses realistic parameter values (see the FYI box) helps to illustrate theadjustment path for the economy over time in response to a supply shock, includingpaths for the nominal and real interest rates. The simulation analysis shows thephenomenon known as stagflation.

➤ Supplement 14-1,“How a RealBusiness CycleModel IsConstructed”

➤ Supplement 14-2,“TheMicroeconomics ofLabor Supply”

➤ Supplement 14-3,“Quits and Layoffs”

➤ Supplement 14-4,“InvoluntaryUnemployment andOverqualification”

➤ Supplement 14-5,“Why TechnologyShocks Are SoImportant in RealBusiness CycleModels”

➤ Supplement 14-6,“Real BusinessCycles and RandomWalks”

Page 9: Mankiw IM Ch 14

Lecture Notes 345

B

C

A

�t

�t + 1

�t - 1

Inflation, �

2. … causinginflation torise …

3. … and output to fall.

1. An adverse supplyshocks shifts the DAScurve upward, …

Income, Output, YYtYt + 1

Yt - 1 = Yall

DADall

DASt

DASt + 1

DASt - 1

A Supply ShockFigure 6

Yall

Figure 7The Dynamic Response to a Supply Shock

(a) Supply Shock

vt

-2.0t-2 t t+2 t+4 t+6 t+8 t+10 t+12

-1.5-1.0-0.50.00.51.01.52.0

Time

(e) Nominal Interest Rate

it

2.0t-2 t t+2 t+4 t+6 t+8 t+10 t+12

2.53.03.54.04.55.05.5

6.0%

Time

(d) Inflation

�t

t-2 t t+2 t+4 t+6 t+8 t+10 t+120.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5%

Time

(b) Output

Yt

99.0

99.5

100.0

100.5

t-2 t t+2 t+4 t+6 t+8 t+10 t+12

101.0

Time

(c) Real Interest Rate

Yt

t-2 t t+2 t+4 t+6 t+8 t+10 t+12

3.0%2.82.62.42.22.01.81.61.41.21.0

Time

Page 10: Mankiw IM Ch 14

A Shock to Aggregate DemandSuppose that the aggregate demand shock variable equals one for five periods andthen returns to its normal value of zero. This positive shock might reflect a warthat increases government purchases or a stock-market boom that raises wealthand consumption. More generally, a demand shock could represent any event thatchanges the demand for goods and services at given values of the natural level ofoutput and the real interest rate. In period t, the DAD curve will shift to the right.The DAS curve remains unchanged in period t. Output and inflation both increase.As in the analysis of the supply shock, the effects work partly through the centralbank’s policy rule. In response to higher output and inflation, the central bankraises nominal and real interest rates, thereby partly dampening the expansionaryeffect of the demand shock.

346 CHAPTER 14 A Dynamic Model of Aggregate Demand and Aggregate Supply

FYI: The Numerical Calibrationand Simulation

The textbook uses simulation analysis to explore the adjustment of theeconomy to various shocks and changes in policies. Each period is bestthought of as one year in length. The model is calibrated using numericalvalues for the parameters of the model and some of the exogenousvariables. These are taken to approximate the actual U.S. economy andthe policy rule proposed by John Taylor, which broadly captures thebehavior of the Federal Reserve. Graphs of the time paths of theendogenous variables after a shock are known as impulse responsefunctions.

C

B

DE

FG

A

�t + 5

�t - 1

�t

Inflation, �

3. … andinflationto rise.

4. In subsequentperiods, higher expected inflationshifts the DAScurve upward.

1. A positive shockto demand …

2. … causes outputto increase …

5. When the demandshock disappears, output falls, andthe economy beginsits return to itsinitial equilibrium

Income, Output, YYtYt + 5

DASt + 1

DASt + 2

DASt + 3

DASt + 4

DASt + 5

DASt - 1, t

DADt…t + 4 DADt - 1, t + 5…

A Demand ShockFigure 8

Yall

Yall

In subsequent periods, expected inflation is higher, and so the DAS curve shiftsupward continually, reducing output and increasing inflation. When the demandshock disappears in period t � 5, the DAS curve returns to its original position. Butthe DAS curve remains higher than its original level since expected inflation

Page 11: Mankiw IM Ch 14

remains above its original value. As a result, the decline in demand pushes outputbelow its natural level. The economy then gradually adjusts to its original positionas inflation is slowly reduced and output expands.

A Shift in Monetary PolicySuppose that the central bank lowers its target for inflation from 2 percent to 1percent and keeps it at the lower value from then on. This will cause the DAD curveto shift to the left (and, to be exact, downward by one percentage point). Since thetarget for inflation does not enter the dynamic aggregate-supply equation, the DAScurve does not shift initially. Output and inflation initially fall. Once again, theresponse of monetary policy is behind this outcome: A lower inflation target impliesthat actual inflation is now above target, so the central bank raises real andnominal interest rates. The higher real interest rate reduces the demand for goodsand services, thereby lowering output below its natural level and lowering inflationalong the initial DAS curve.

Lecture Notes 347

Figure 9The Dynamic Response to a Demand Shock

(a) Demand Shock

et

-2.0t-2 t t+2 t+4 t+6 t+8 t+10 t+12

-1.5-1.0-0.50.00.51.01.52.0

Time

(e) Nominal Interest Rate

it

2.0t-2 t t+2 t+4 t+6 t+8 t+10 t+12

2.53.03.54.04.55.05.5

6.0%

Time

(d) Inflation

�t

t-2 t t+2 t+4 t+6 t+8 t+10 t+120.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5%

Time

(b) Output

Yt

99.0

99.5

100.0

100.5

t-2 t t+2 t+4 t+6 t+8 t+10 t+12

101.0

Time

(c) Real Interest Rate

Yt

t-2 t t+2 t+4 t+6 t+8 t+10 t+12

3.0%2.82.62.42.22.01.81.61.41.21.0

Time

Page 12: Mankiw IM Ch 14

348

C

BA

Z

�t - 1 = 2%

�final = 1%

�t

Inflation, �

2. … causingoutput to fall …

3. … andinflation tofall as well.

4. In subsequentperiods, lower expected inflationshifts the DAScurve downward.

1. A reduction in target inflation shiftsthe DAD curve downward, …

5. Eventually, the economyapproaches a final equilibrium, withoutput at its natural level andinflation at its new, lower target.

Income, Output, YYt

Yt - 1 =Yfinal =

DASt + 1

DASt - 1, t

DASfinal

DADt - 1 DADt, t +1

A Reduction in Target InflationFigure 10

Yall =

Yall

Figure 11The Dynamic Response to a Reduction in Target Inflation

(a) Inflation Target

et

0.0t-2 t t+2 t+4 t+6 t+8 t+10 t+12

0.5

1.0

1.5

2.0

2.5

3.0

Time

(e) Nominal Interest Rate

it

2.0t-2 t t+2 t+4 t+6 t+8 t+10 t+12

2.53.03.54.04.55.05.5

6.0%

Time

(d) Inflation

�t

t-2 t t+2 t+4 t+6 t+8 t+10 t+120.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5%

Time

(b) Output

Yt

99.0

99.5

100.0

100.5

t-2 t t+2 t+4 t+6 t+8 t+10 t+12

101.0

Time

(c) Real Interest Rate

Yt

t-2 t t+2 t+4 t+6 t+8 t+10 t+12

3.0%2.82.62.42.22.01.81.61.41.21.0

Time

Page 13: Mankiw IM Ch 14

With inflation lower, expected inflation falls as well, causing the DAS curve toshift downward. Over time, the process continues with output rising and inflationfalling until the economy reaches long-run equilibrium with output at its naturallevel and inflation at the new target rate of 1 percent.

The adjustment of the economy to this change in monetary policy assumesthat expectations are formed adaptively. But if the central bank’s announcement ofthe change in its target inflation rate is credible, then people may lower theirexpectation about inflation immediately. In this case, where expectations areformed rationally based on all available information, the DAS curve will shiftdownward by the same amount and at the same time that the policy change shiftsthe DAD curve, and the economy will instantly reach its new long-run equilibrium.

14-4 Two Applications: Lessons for Monetary PolicyThe model developed in the previous sections can be used to motivate a discussionabout the design of monetary policy. In particular, we can consider how the valuesof the parameters of the monetary policy rule influence the effectiveness ofmonetary policy.

Lecture Notes 349

BA

Inflation, �

Figure 12

Large changein ouput

Small changein inflation

Income, Output, YYt Yt - 1

DASt

DASt - 1

DADt - 1, t

Two Possible Responses to a Supply Shock

A?

B?

�t - 1

�t - 1

�t

�t

Inflation, �

Small changein ouput

Large changein inflation

Income, Output, YYt Yt - 1

DASt

DASt - 1

DADt - 1, t

➤ Supplement 14-7,“Inflation Inertia”

Page 14: Mankiw IM Ch 14

The Tradeoff Between Output Variability and InflationVariabilityConsider the effect of a supply shock on the economy. As shown earlier, the initialresponse is for output to fall below its natural level and inflation to rise above thecentral bank’s target. But the extent to which output declines or inflation risesdepends importantly on the slope of the DAD curve. When the slope is steep,inflation rises relatively more and output declines relatively less, whereas when theslope is flat, inflation rises relatively less and output declines relatively more.

Because the slope of the DAD curve depends on the parameters of themonetary policy rule, the central bank can affect the slope by choosing whether torespond more or less strongly to deviations from target inflation or the naturallevel of output. In particular, when � is large compared to Y, the DAD curve isrelatively flat and the central bank responds strongly to deviations from itsinflation target by raising interest rates a lot to keep inflation contained andresponds only weakly to deviations of output from the natural level. In this case,a supply shock has a relatively small effect on inflation and a relatively largeeffect on output. Alternatively, when the central bank responds weakly todeviations from its inflation target and strongly to deviations of output from itsnatural level, the DAD curve is relatively steep and a supply shock has arelatively large effect on inflation and a relatively small effect on output. Thecentral bank thus faces a tradeoff between the variability of output and thevariability of inflation.

As discussed earlier, the central bank does not face a tradeoff between thelevel of output and the rate of inflation in the long run—since the classicaldichotomy holds. But it does face a tradeoff between the variability of output andthe variability of inflation.

Case Study: The Fed Versus the European Central BankThe legislation that created the Federal Reserve gave it the dual mandate ofstabilizing both employment and prices, whereas the European Central Bank(ECB) is charged with the primary objective of maintaining price stability, definedas inflation close to 2 percent over the medium term. These differences in mandatescan be interpreted in our model as being reflected in different parameters in themonetary policy rule. For the ECB compared to the Federal Reserve, more weight isgiven to inflation stability and less to output stability. The events of 2008, when oilprices rose sharply and the world economy headed into recession, support thisinterpretation: The Federal Reserve lowered interest rates from 5 percent to arange of 0 to 0.25 percent, while the ECB cut interest rates by much less.Apparently, the ECB was less concerned about recession and more concerned aboutkeeping inflation contained, whereas the Federal Reserve was more concernedabout limiting the recession. Over time, one might expect the ECB’s monetarypolicy to result in more variable output and more stable inflation in Europecompared to the United States. Assessing this prediction is difficult, however,because the ECB has only been in existence for about a decade, not long enough tohave sufficient data to determine the long-term results of its policy. Also, Europeand the United States differ in other ways besides the policy mandates of theircentral banks, and these other differences may influence output and inflationindependently from monetary policy.

The Taylor PrincipleSuppose that the central bank responded to a rise in inflation above its target bycutting the real interest rate. From the monetary policy equation, this would implythat the parameter � is less than zero:

it � �t � � � �(�t – �t*) � Y(Yt – Y—

t).

350 CHAPTER 14 A Dynamic Model of Aggregate Demand and Aggregate Supply

➤ Supplement 14-8,“Volatility andGrowth”

Page 15: Mankiw IM Ch 14

In other words, the central bank would increase the nominal interest rate by lessthan the rise in inflation. This policy response will produce a positively sloped DADcurve. Now consider a one-period demand shock. This will shift the DAD curve tothe right and initially lead to a rise in inflation and an increase in output. Higherinflation will lead to an increase in expected inflation for next period, which willshift the DAS curve upward. But with a positively sloped DAD curve, output risesfurther and remains above its natural level because the central bank lowers thereal interest rate in response to higher inflation. Inflation becomes unstable, risingcontinually to higher levels.

To prevent inflation getting out of control, the central bank must increase thenominal interest by more than the rise in inflation (� must be greater than zero),so that the DAD curve is negatively sloped. The requirement that the central bankrespond to inflation by raising the nominal interest more than one-for-one issometimes called the Taylor Principle, after economist John Taylor, whohighlighted it as a key consideration in the design of monetary policy.

Case Study: What Caused the Great Inflation?Inflation during the 1970s in the United States reached high levels. Paul Volcker,who was appointed chairman of the Federal Reserve in 1978, instituted a change inmonetary policy beginning in 1979 that eventually brought inflation under control.Volcker and his successor, Alan Greenspan, subsequently oversaw low and stableinflation for the next 25 years. Estimates of the monetary policy rule show that theparameter � was 0.72 during the Volcker-Greenspan regime after 1979, but –0.14during the pre-Volcker era from 1960 to 1978. This suggests that monetary policydid not conform to the Taylor Principle in the earlier period, possibly explainingwhy inflation got out of control.

14-5 Conclusion: Toward DSGE ModelsAdvanced courses in macroeconomics develop a class of models known as dynamic,stochastic, general equilibrium (DSGE) models. The dynamic AD–AS modeldiscussed in this chapter is a simpler version of these more advanced DSGE

Lecture Notes 351

C

AB

D�t + 2

�t + 1

�t - 1

�t

Inflation, �

Spirallinginflation

Income, Output, Y

DASt + 2

DASt + 1

DASt, t - 1

Yt + 1

Yt + 2 Yt

DADt - 1, t + 1…

Figure 13The Importance of the Taylor Principle

Yt - 1 = Yall

Yall

DADt

Page 16: Mankiw IM Ch 14

models. This model illustrates how the key macroeconomic variables (output,inflation, and real and nominal interest rates) respond to shocks, interact with eachother, and adjust over time. The model also provides insight into the design ofmonetary policy, highlighting the tradeoff that central banks face betweenvariability in output and variability in inflation. And it suggests the importantadvice that central banks need to respond strongly to inflation so that it does notget out of hand.

352 CHAPTER 14 A Dynamic Model of Aggregate Demand and Aggregate Supply

➤ Supplement 14-9,“How Long Is theLong Run? PartFour”

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353

L E C T U R E S U P P L E M E N T

14-1 How a Real Business Cycle Model Is ConstructedThe dynamic AD–AS model developed in Chapter 14 can be used to analyze economic growthby considering how an increase in the natural level of output affects the economy. While thisfeature can be interpreted as incorporating a long-run growth path for the economy into amodel of short-run fluctuations, it can also be interpreted as allowing for elements of the realbusiness cycle approach (discussed in the appendix to Chapter 8) to play a role in short-runbusiness cycle analysis. In this sense, the model of Chapter 14 can be viewed as a hybridmodel that includes both Keynesian features that allow money to have short-run real effectsand real business cycle elements that influence short-run fluctuations. The more advanceddynamic, stochastic, general equilibrium (DSGE) models mentioned in the text also exhibitthese hybrid characteristics. This supplement and the several to follow discuss how realbusiness cycle models are constructed and tested.

Real business cycle models emphasize the role of technology shocks in driving short-runeconomic fluctuations. These models generally differ from other macroeconomic models, notonly in their theoretical explanation of economic fluctuations, but also in the way they aretested with economic data. Typically, economists test a theory by ascertaining an implicationof that theory for economic data and then applying statistical and econometric techniques tosee whether or not the data are consistent with the theory. The approach of real businesscycle theorists, however, has usually been to simulate the outcomes of their models and tocompare those simulations with actual data.

A simple illustration has been provided by the economist Charles Plosser.1 Heconsidered the problem of a representative individual who has to make two decisions at anypoint in time.2 First, the individual must decide how to divide her time between leisure andworking; and, second, she must decide how to divide her output between consumption andinvestment to increase future consumption. The individual makes these choices in order tomaximize her expected utility (happiness), which depends upon her consumption and leisurenow and at all times in the future.3 Plosser assumes that the individual also has access to aCobb–Douglas production function:

Here, At represents the possibility of random technology shocks.The first step in this model is calibration, or choosing values for the parameters of the

model. In this case, Plosser has to choose values for capital’s share of output (α) and thedepreciation rate of capital, as well as for parameters reflecting the individual’s preferences.These parameters are chosen on the basis of other information that we have about theeconomy.4 Next, Plosser solves the choice problems of the agent—in essence deriving aconsumption function and a labor supply function. Finally, Plosser uses the Solow residualas a measure of technology shocks.

Plosser then simulates the model. This means that he works out how this economywould behave under the assumption that the representative agent sees technology shocks asunpredictable and permanent. Plosser can then find the implied series for GDP,consumption, investment, employment, and real wages. Figures 1 to 5 show how Plosser’ssimulations compare with the actual behavior of the U.S. economy.

1C. Plosser, “Understanding Real Business Cycles,” Journal of Economic Perspectives 3, no. 3 (Summer 1989): 51–77.2If the economy is competitive (as Plosser assumes), then markets will allocate resources efficiently and we are not badly misled by simply imaginingthat the economy consists of a single individual.

3Technically, Plosser assumes that the agent maximizes the following utility function:∞

U = ∑ β t[log(Ct) + η log(1 – Lt)].t = 0

He thus assumes that the agent has one unit of time, so that 1 – Lt corresponds to leisure. The parameter β measures how much the agent values thepresent relative to the future, and the parameter η measures how much the agent values leisure relative to consumption.

4Specifically, Plosser chooses α = 0.42, β = 0.95, the depreciation rate = 0.1, and the parameter η such that Lt = 0.2 at all times.

Y A K Lt t t t= −� �1 .

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354 CHAPTER 14 A Dynamic Model of Aggregate Demand and Aggregate Supply

±4

±6

±2

0

2

4

6

1955 1960 1965 1970 1975 1980 1985

Perc

ent

ActualPredicted

Annual Growth Rate of Real Output

Figure 1

±4

±6

6

4

2

0

±2

1955 1960 1965 1970 1975 1980 1985

Perc

ent

Annual Growth Rate of Real Consumption

Figure 2

Predicted

Actual

Source: Figures 1 to 5 from C. Plosser, “Understanding Real Business Cycles,” Journal of Economic Perspectives 3, no. 3 (Summer 1989): 51–77.

Page 19: Mankiw IM Ch 14

5

10

0

10

5

1955 1960 1965 1970 1975 1980 1985

Predicted

Perc

ent

Actual

Annual Growth Rate of Real Investment

Figure 3

Source: C. Plosser, Understanding Real Business Cycles, Journal of Economic Perspectives, Summer 1989.

Source: C. Plosser, Understanding Real Business Cycles, Journal of Economic Perspectives, Summer 1989.

6

4

2

0

2

4

6

1955 1960 1965 1970 1975 1980 1985

Perc

ent

Annual Growth Rate of Hours Worked

Figure 4

Predicted

Actual

Chapter Supplements 355

Page 20: Mankiw IM Ch 14

356 CHAPTER 14 A Dynamic Model of Aggregate Demand and Aggregate Supply

Interpreting these figures is not easy, but they are quite striking. In particular,Plosser’s simulations for output and consumption seem to match up very well with theactual data, although the fit is worse for investment and labor market variables. Thesepictures indicate that a competitive economy hit by technology shocks can exhibitfluctuations that broadly resemble those experienced by the U.S. economy.

A problem with this line of research is that there has been insufficient formal statisticalanalysis of what constitutes a good match between simulated results and actual data. Plosser’ssimulations look as if they correspond to the U.S. data, but we cannot tell from inspectionwhether or not there is a good fit in a more formal statistical sense. Also, as discussed in Chap-ter 19 of the textbook, the Solow residual may not be a good measure of technological change.

The methodology followed by Plosser is essentially that pursued by most real businesscycle theorists, except that they do not usually assume a specific series (such as the Solowresidual) for technical change. Instead, they simply suppose that there are random shocks tothe technology drawn from some statistical distribution. Rather than running just onesimulation, real business cycle theorists simulate their models many times over. By doingthis often enough, they can discover the broad patterns that their models imply for the data(for example, the correlation between output and consumption). They then compare thesepatterns with those observed in actual data.5 Much modern research in macroeconomicsexamines refinements of this basic model in an attempt to improve the match between themodels and the data. Some researchers are pursuing versions of the model that include thesort of imperfections emphasized by new Keynesian economists. As a result, manyeconomists are hopeful that a synthesis of real business theory and new Keynesianeconomics is starting to emerge through the development of DSGE models in which moneyhas effects on real variables in the short run alongside the effects of technology shocks.

5See also Supplement 7-3, “Does the Solow Model Really Explain Japanese Growth?” for another use of a real business cycle model. That supplementdiscusses Christiano’s simulation of a neoclassical growth model to investigate the hypothesis that Japanese saving behavior is explained bypost–World War II reconstruction.

6

4

2

0

2

4

6

Perc

ent

1955 1960 1965 1970 1975 1980 1985

Annual Growth Rate of Real Wage Rate

Figure 5

Actual

Predicted

Source: C. Plosser, Understanding Real Business Cycles, Journal of Economic Perspectives, Summer 1989.

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357

L E C T U R E S U P P L E M E N T

14-2 The Microeconomics of Labor SupplyMany economists are unconvinced that real business cycle theory can adequately explainfluctuations in employment. To pursue this further, we start from two features of thistheory: first, prices are assumed to be flexible; and, second, shocks to technology are thedriving force behind economic fluctuations.

Since prices are flexible, it follows that the labor market is always in equilibrium, solabor demand always equals labor supply. Technology shocks affect the marginal product oflabor and so cause the demand for labor to shift. Looking at the effects of shifts in labordemand in Figures 1A and 1B, we see that steep labor supply implies little variation inemployment and large variation in the real wage; whereas if labor supply is flat, then realwages would be relatively stable and employment would vary substantially. The data exhibitmuch employment fluctuation and little real-wage variation. It follows that, to explain thedata, real business cycle theories need either a relatively flat labor supply curve or anexplanation of why technology shocks might also shift labor supply. We consider each in turn.

Neither theory nor the data provide a great deal of support for a flat labor supply curve.An individual’s labor supply decision is based on the choice between leisure and goods.Individuals have a certain amount of time at their disposal, which they can either take asleisure or else can use for working in order to earn income with which to buy goods. The realwage, w, is the relative price of leisure in terms of goods. The higher the real wage, the moregoods must be forgone for an extra hour of leisure. We illustrate this in the standardmicroeconomic manner in Figure 2.

w w

L(A)

L(B)

Ls

L d

L s

L d

24w

24w

^

Goo

ds

Leisure

24Ls

A

B

Figure 2

Figure 1

Page 22: Mankiw IM Ch 14

We suppose that the individual has 24 hours to allocate between working and leisure.At one extreme, she could not work at all and take all her time as leisure. At the otherextreme, the worker could work all 24 hours, have no leisure time, and consume 24w worthof goods. The line connecting these two points is the budget line; any point on this line is afeasible combination of leisure and goods. The optimal combination of goods and leisure isfound where the indifference curve is tangent to the budget line.

Now suppose that the real wage rises to w. We can see from Figure 2 that althoughleisure has now become more expensive, the individual may increase (case A) or decrease(case B) her supply of labor. The reason is that changes in the real wage generate incomeand substitution effects that act in opposite directions. The substitution effect encouragespeople to work more (that is, consume less leisure) when the wage goes up. A rise in the realwage, however, increases the income from working, allowing the individual to consume moreleisure. Thus, the effect of an increase in the real wage on labor supply is theoreticallyambiguous. It is perhaps not surprising that the data show that changes in the real wage donot have strong effects on labor supply. In terms of our original diagrams, therefore, thelabor supply curve is steep. Contrary to the data, we would expect to see large changes in thereal wage and small changes in employment if the economy is competitive and characterizedby changes in labor demand.

We observe a larger change in employment and a smaller change in the real wage iftechnology shocks affect both labor demand and labor supply in the same direction. This canoccur if the interest rate changes or if there is a temporary change in the real wage. Forexample, if the real wage is high in the present but expected to be low in the future, workersmight prefer to work very hard when the wage is high and take much leisure time when thewage is lower. To put the same point a slightly different way, labor supply might be veryresponsive to short-run fluctuations in the real wage, even if it is not responsive to long-runchanges. Similarly, if the interest rate is higher, working today looks relatively attractive.

We can illustrate this in terms of the labor market by putting the current real wage onthe axis and noting that changes in the expected future real wage or the interest rate shiftthe labor supply curve, as in Figures 3A and 3B.

An increase in the future real wage (wt + 1) makes the current supply of labor lessattractive and so causes the labor supply curve to shift inward. An increase in the interestrate is like a decrease in the future real wage and so shifts the labor supply curve outward.

Now, consider a temporary shock to labor demand (caused perhaps by a temporaryshock to the technology). This shock does not affect the future real wage and so leads to arelatively large change in employment. Such a shock is unlikely to have a large effect on the

358 CHAPTER 14 A Dynamic Model of Aggregate Demand and Aggregate Supply

(A) (B)

Lt

Ld'Ld

L s(wt+1

, r)w

tw

tL s(w

t+1, r)

Ld Ld'

Lt

Ls'

Figure 3

Page 23: Mankiw IM Ch 14

Lecture Notes 359

interest rate. On the other hand, a permanent (positive) shock to labor demand leads toexpectations of higher real wages in the future, causing the labor supply curve to shift in.This results in a relatively small change in employment.

A focus on temporary changes in the real wage thus allows real business cycle theory toexplain fluctuations in employment while recognizing that labor supply need not be verysensitive to real wages in the long run. Microeconomic analyses of individual labor supply,however, are still not very supportive of strong intertemporal substitution effects of thiskind—that is, they do not indicate that labor supply is very responsive to temporary realwage changes or to changes in the interest rate.

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L E C T U R E S U P P L E M E N T

14-3 Quits and LayoffsJob separations can occur either because workers voluntarily quit their jobs or because theyare laid off (or fired with cause). We can thus write

s = q + l,

where s is the separation rate (see Chapter 6), q is the quit rate, and l is the layoff rate.Theories of intertemporal substitution argue that employment is lower in recessions becausethe real wage (or the interest rate) falls and workers are unwilling to work at this lowerwage. Such an explanation suggests that quits should be an important component of flowsfrom employment to unemployment, and also that quits should be higher in recessions.

The data reveal, however, that layoffs are much more important than quits inexplaining flows into unemployment. Data suggest that less than 15 percent of the unem-ployed become unemployed as a result of quitting their job. For example, unemployment in2005 was 7.6 million. Of these, 3.7 million (48 percent) were unemployed as a result oflayoffs, and 0.7 million (9 percent) were new entrants into the labor force. Of the remainder,2.4 million (31 percent) had been previously employed and were reentering the labor forceafter a spell of nonparticipation. Only 0.9 million (12 percent) were job leavers—that is,individuals who quit their jobs voluntarily.1 Finally, the data indicate that quits areprocyclical and layoffs are countercyclical. These data do not support the belief thatemployment fluctuations over the business cycle are the result of voluntary shifting of labor.

360

1U.S. Department of Labor, Bureau of Labor Statistics.

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L E C T U R E S U P P L E M E N T

14-4 Involuntary Unemployment and OverqualificationSome economists distinguish between two types of unemployment: voluntary andinvoluntary. According to the usual definition, someone is voluntarily unemployed if, at theexisting wage, she does not think it worthwhile to work. A person who is involuntarilyunemployed would like to work at existing wages but cannot obtain a job.

Other economists argue that the idea of involuntary unemployment makes no sense.After all, they suggest, an unemployed investment banker or neurosurgeon could always geta job flipping hamburgers or waiting tables. So how can we distinguish between involuntaryand voluntary unemployment? Robert Lucas expands on this argument as follows:1

Nor is there any evident reason why one would want to draw this distinction. Certainly the moreone thinks about the decision problem facing individual workers and firms the less sense thisdistinction makes. The worker who loses a good job in prosperous times does not volunteer to bein this situation; he has suffered a capital loss. . . . Nevertheless the unemployed worker at anytime can always find some job at once. . . . Thus there is an involuntary element in allunemployment, in the sense that no one chooses bad luck over good; there is also a voluntaryelement in all unemployment, in the sense that however miserable one’s current work options,one can always choose to accept them.

Truman Bewley, an economist at Yale University, interviewed a large number ofbusinesspeople in order to learn more about their decisions about hiring workers. Hisfindings suggest that it may not be quite so easy for unemployed workers to find jobs, evenat lower wages2:

Cannot workers find jobs immediately simply by accepting sufficiently low pay? Perhaps theclearest regularity of the survey was that large classes of unemployed workers find it very difficultto obtain work paying substantially less than what they earned before, unless they take temporaryjobs or low-paying jobs in the secondary labor market. Most employers offering good permanent jobsshun workers who earned significantly more previously, significantly meaning 20–30 percent more.Employers label such workers as overqualified and fear that they will be discontent, be a threat totheir supervisors, and above all, will leave as soon as they find better jobs.

Note that Bewley’s findings do not completely contradict Lucas’s argument. They suggestthat the unemployed investment banker could indeed get a job flipping hamburgers. But theyalso suggest that this unfortunate investment banker probably cannot do much better.

361

1R. Lucas, “Unemployment Policy,” American Economic Review, Papers and Proceedings 68 (May 1978): 354.2T. Bewley, “A Depressed Labor Market as Explained by Participants,” American Economic Review, Papers and Proceeding 85, no. 2 (May 1995): 253.

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A D V A N C E D T O P I C

14-5 Why Technology Shocks Are So Importantin Real Business Cycle Models

In any competitive flexible-price model, such as those espoused by real business cycletheorists, labor market clearing implies that the real wage must equal the marginal productof labor. As explained in Chapter 3, the marginal product of labor gives the firm’s demandfor labor and depends upon the amount of capital and labor that firms possess. In particular,we expect to see diminishing marginal product: the marginal product of labor will be lowerwhen employment is higher, other things being equal. We write

MPL(K, L) = W/P.

We know that employment is procyclical—not surprisingly, employment is higher inbooms and lower in recessions. Other things being equal, we would expect to see themarginal product of labor falling in booms, and hence, if the economy is competitive, wewould expect to see the real wage also being lower in booms. But we also know from CaseStudy 13-1 that the real wage is actually mildly procyclical—real wages are higher in boomsand lower in recessions.1

It follows that if we are to reconcile a procyclical real wage with diminishing marginalproduct of labor in a competitive model, other things are not equal. Something must happenin booms to raise the marginal product of labor even though employment is higher. Since thecapital stock changes only slowly and does not vary in any significant way over the businesscycle, the only possibility is that the marginal product of labor is higher in booms because oftechnological improvements. This is why technology shocks are an essential ingredient ofreal business cycle models.

If the economy is not competitive, these issues need not arise. First of all, the demandfor labor may depend upon other factors. For example, when prices are sticky, firms maydemand less labor in recessions because they cannot sell all their output (whereas in acompetitive model with flexible prices, firms can always sell as much as they want at themarket price).

As another example, suppose that the economy is not perfectly competitive but insteadexhibits imperfect competition. We can rewrite the earlier equation as

P = W/MPL.

This says that, in a competitive economy, the price of output equals the marginal cost ofproduction (since the wage is the cost of a unit of labor and the marginal product of laborgives the amount of output contributed by the last unit of labor). Under imperfectcompetition, however, firms set prices as a markup (m) over marginal cost:

P = m × (W/MPL)

⇒ MPL/m = (W/P).

In this case, the real wage can be procyclical even if the marginal product of labor iscountercyclical, provided that the markup is also countercyclical. That is, if markups arehigher in recessions, then MPL/m will be lower, and so the real wage may be lower.

1Procyclical real wages are also a necessary ingredient of real business cycle theory. If high employment in booms and low employment in recessionsarise from voluntary shifting of labor, it follows that workers are choosing to consume less leisure in booms and more leisure in recessions. But whywould they choose to consume less leisure and more consumption goods at the same time? The answer has to be that leisure is relatively moreexpensive in booms—that is, real wages must be higher.

362

Page 27: Mankiw IM Ch 14

Chapter Supplements 363

There are reasons for believing that markups may indeed be countercyclical. Onereason why markups may fall in booms is that higher profits when the economy is boomingcause more firms to enter an industry. The more firms in the industry, the closer it is tobeing competitive, and so the lower is the markup. Another possibility is that imperfectcompetition reflects collusion among firms, and firms maintain such collusion by a threat toincrease output if other firms cheat. In a boom, demand is high, so the potential gain fromcheating is greater and firms can sustain less collusion.2

Mark Bils investigated the behavior of marginal cost and price over the course of thebusiness cycle. He found that marginal costs are strongly procyclical but prices do not varymuch over the business cycle. His evidence suggests that the markup—the differencebetween price and marginal cost—is countercyclical.3

Julio Rotemberg and Michael Woodford investigated a real business cycle model withsome imperfect competition and countercyclical markups. They carried out simulations andargue that they were better able to match the U.S. data by their inclusion of imperfectcompetition.4 This may be an encouraging route for synthesis between real business cycleand new Keynesian theories. Once we introduce imperfect competition, however, there is nolonger a presumption that fluctuations are efficient and there may be a case for governmentintervention to stabilize the economy.

2For theoretical exposition of these ideas, see S. Chatterjee and R. Cooper, “Multiplicity of Equilibria and Fluctuations in Dynamic ImperfectlyCompetitive Economies,” American Economic Review, Papers and Proceedings 79 (May 1989): 353–57; and J. Rotemberg and G. Saloner, “ASupergame-Theoretic Model of Price Wars During Booms,” American Economic Review 76 (June 1986): 390–407.

3Mark Bils, “The Cyclical Behavior of Marginal Cost and Price,” American Economic Review 77 (December 1987): 838–55.4J. Rotemberg and M. Woodford, “Oligopolistic Pricing and the Effects of Aggregate Demand on Economic Activity,” mimeo (November 1989).

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A D V A N C E D T O P I C

14-6 Real Business Cycles and Random WalksReal business cycle theory provides a challenge to the traditional explanation of macro-economic fluctuations. One reason why this theory has been so influential is the work of twoeconomists, Charles Nelson and Charles Plosser.

In an important article published in 1982, Nelson and Plosser argued that there isevidence to suggest that U.S. GDP may follow a random walk.1 That is, they suggested thatthe behavior of real GDP over time could be described by the equation

Yt = Yt – 1 + ut , (1)

where ut is a random shock that is zero on average. This equation states that the bestprediction of GDP this year is whatever value it had last year.

The conventional view of macroeconomic fluctuations is that the behavior of GDP overtime can be decomposed into a long-run natural-rate or trend component and a short-runcyclical component. This approach underlies the models used in the textbook: the Solow growthmodel explains the long-run behavior of the economy and the aggregate demand–aggregatesupply model explains short-run fluctuations. In this view, shocks to the economy will push itaway from the natural rate only temporarily; the economy always has a tendency to revert tothe natural rate. But the Nelson–Plosser finding challenges this characterization. If GDP doesfollow a random walk, then shocks to output have permanent effects.

To see this, suppose that at some time (t = 0), GDP is at the value Y0, and that at t = 1there is a one-unit shock to GDP (u1 = 1). Suppose also that there are no further shocks (u2 =u3 = . . . = 0). Then

Y1 = Y0 + 1.

Now

Y2 = Y1 + u2

= Y1

= Y0 + 1.

Similarly,

Y3 = Y0 + 1,

and so on. The shock to GDP in period 1 persists forever. Following this shock, our bestprediction about GDP is that it will forever be one unit higher (Figure 1).

The observed fluctuations in GDP, according to this theory, are then fluctuations in thenatural rate of output, not cyclical fluctuations of output around the natural rate. Whereasthe traditional theory suggests that technological progress is a relatively smooth andgradual process, real business cycle theory suggests that technological progress is irregularand a source of fluctuations. Indeed, if this real business cycle characterization of the data isaccurate, then the traditional decomposition of output into cycle and trend does not reallymake sense.

If GDP does not follow a random walk, then the conclusion is very different. Suppose,for example, that the behavior of GDP can be described by the equation

Yt = 0.9Yt – 1 + ut. (2)

364

1C. Nelson and C. Plosser, “Trends and Random Walks in Macroeconomic Time Series: Some Evidence and Implications,” Journal of MonetaryEconomics 10 (September 1982): 139–67.

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Lecture Notes 365

Then, if we carry out the same experiment, we find that the shock raises output by 1 at timet = 1, as before. Next period, however, output is 0.9 higher as a result of the shock. In period3, output is only 0.81 (= 0.92) units higher, and so on. In other words, the impact of the shockon GDP gradually dies out. In this representation, shocks to the economy are temporary, notpermanent, and output does tend to return to the natural rate following a shock (Figure 2).

So, if the Nelson–Plosser result is right, and GDP can be well described by a randomwalk, we need to think in terms of models where shocks have permanent effects. In terms ofstandard aggregate demand–aggregate supply models, this suggests that real or supplyshocks, such as to technology, govern the behavior of GDP; aggregate demand shocks do nothave permanent effects on output in such models. Demand shocks may, however, havepermanent effects on GDP in other models such as the hysteresis models discussed inChapter 13. Steve Durlauf, however, points out that if GDP follows a random walk, it is alsoconsistent with a world in which coordination failures are important. In this case, demandshocks might push the economy from one equilibrium to another.2

Unfortunately, it is very hard to distinguish in the data between equations (1) and (2),and so we simply are not sure whether the random-walk characterization is accurate. Verydifferent theories will generate very similar predictions for the behavior of GDP. Forexample, a world with demand shocks and very sticky prices is one in which shocks wouldexhibit a great deal of persistence, so GDP might appear close to a random walk. On thebasis of GDP data alone, it is nearly impossible to distinguish between this economy and aneconomy governed by real shocks.

Modern macroeconomics is making progress toward a synthesis in which it is recognizedthat both demand and supply shocks have important effects on output.3 In this view, the nat-ural rate of output grows irregularly, as suggested by real business cycle theory, rather thanexhibiting the smooth change of the Solow growth model. Nevertheless, demand shocks maystill cause the actual level of GDP to differ from the natural rate and so may be an additionalsource of variability in GDP. In principle, in such a world, there is still room for stabilizationpolicy in order to eliminate inefficient cyclical fluctuations. Eliminating all fluctuations is nolonger desirable, however, since some variation in GDP is an efficient response to technologyshocks. Although many economists doubt that real business cycle theory completely explainseconomic fluctuations, most might agree that it teaches the important lesson that some varia-tion in GDP is to be expected and is indeed desirable in a well-functioning economy.

2S. Durlauf, “Output Persistence, Economic Structure and the Choice of Stabilization Policy,” Brookings Papers on Economic Activity 2 (1989): 69–136.3See, for example, O. Blanchard and D. Quah, “The Dynamic Effects of Aggregate Demand and Supply Disturbances,” American Economic Review 79(September 1989): 655–73.

Y

Figure 1

1 Time

Figure 2

1

Y Y

Time

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14-7 Inflation InertiaThe Phillips curve used in the dynamic AD–AS model of Chapter 14 can be derived underthe assumption that all firms have the ability to set prices and some of those firms set theirprices one period in advance. As shown in Chapter 13, this assumption implies a Phillipscurve that relates period t inflation to the period t – 1 expectation of period t inflation andthe gap between actual and the natural level of output. Introducing adaptive expectationsthen allows derivation of the DAS curve, which relates period t inflation to period t – 1inflation and the deviation in output from its natural level. The effect of lagged inflation inthe DAS curve is responsible in the model for the gradual adjustment of inflation in responseto shocks.

A more sophisticated approach, known as staggered price setting, assumes that firmsall set prices in advance for two periods, with half of the firms setting prices in any givenperiod. Staggered price setting makes the overall level of prices adjust gradually, even whenindividual prices adjust frequently. In other words, the price level will adjust fully to anincrease (decrease) in aggregate demand only after a period of time during which outputexceeds (falls short of) its natural rate. But a surprising implication of these New Keynesianmodels of staggered price setting under rational expectations is that inflation—the percentchange in prices—does not exhibit inertia. Instead, inflation is expected to decline whenoutput is above its natural rate and vice versa.1

The reason for this result is that when price-setters fix a price for the current andfuture periods, they consider not only today’s overall price level, but also the price levelexpected to prevail in the future. The resulting Phillips curve expresses inflation as afunction of next period’s inflation and the current output gap. Accordingly, a declining pathfor inflation is associated with output above its natural rate.

Evidence for the United States and many other countries contradicts this implicationand supports the view that inflation is highly persistent. Periods of disinflation acrosscountries are overwhelmingly periods when output is below normal.2 And estimates of theinflation process for the United States find that lagged inflation helps explain currentinflation.3

Various ways of reconciling New Keynesian models of price dynamics with evidence ofinflation inertia have been proposed. These include adding delays in price adjustment,incorporating some backward-looking price-setters, indexing fixed prices to overall inflationbetween adjustments, and introducing more complex dynamics in costs or markups.

Greg Mankiw and Ricardo Reis have suggested changing the basic framework from onewith “sticky prices” to one with “sticky information.”4 Instead of assuming full informationwith staggered price setting, Mankiw and Reis assume firms can always adjust prices butare limited by the cost of obtaining and processing information. As a result, firms maychoose a path for their prices that is set until the next time they update their information.The result leads to a Phillips curve in which past inflation affects current inflation and inwhich disinflations are associated with below-normal output.

One drawback of the Mankiw-Reis approach is that it does not allow a role for fixedprices, despite evidence of their importance in the economy. In addition, the sort of

1 This supplement draws on the discussion in Chapter 6 of David Romer, Advanced Macroeconomics, third edition, (New York: McGraw-Hill/Irwin,2006).

2 See Laurence Ball, “What Determines the Sacrifice Ratio?” in N.Gregory Mankiw, ed., Monetary Policy, (Chicago: University of Chicago Press, 1994):155-183.

3 See Jeffrey Fuhrer, “The (Un)Importance of Forward-Looking Behavior in Price Specifications,” Journal of Money, Credit, and Banking, 29 (August1997): 338-350.

4 N. Gregory Mankiw and Ricardo Reis, “Sticky Information versus Sticky Prices: A Proposal to Replace the New Keynesian Phillips Curve,” QuarterlyJournal of Economics, 117 (November 2002): 1295-1398.

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predetermined paths that firms choose in their model do not appear to be widespread in theeconomy. Furthermore, fixed prices appear essential for explaining why shifts in aggregatedemand have smaller and shorter-lasting effects in high-inflation economies, and why theannouncement in advance of disinflation policies doesn’t measurably affect the output costsof disinflation. Most likely, a complete framework for explaining inflation dynamics willrequire both fixed prices and predetermined price paths.

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14-8 Volatility and GrowthGarey Ramey and Valerie Ramey investigated the connection between the growth and thevolatility of GDP in a number of different countries.1 They wished to find out if long-rungrowth and short-run volatility were related. As a matter of theory, growth and volatilitycould be directly or inversely related. For example, large fluctuations in output might makefirms reluctant to commit to irreversible investment, implying that growth would be lower incountries with highly variable output. Conversely, consumers in a relatively uncertain worldmight save a lot, which could lead to higher growth.

Figure 1 shows the relationship between volatility and growth in OECD countries,measured over the period 1952–1988.2 There is a strong negative relationship: countrieswith highly variable output tend to be countries that grow more slowly, and conversely. Oneimplication of Ramey and Ramey’s findings is that the benefit of reducing business cyclefluctuations might therefore be larger than is commonly supposed: stabilization of theeconomy in the short run might help promote growth in the long run.

Figure 1

CANITAL

USAAUT

NLD

GBR

BELPAT

DEU GRC CHE

ISL

LUX

ESP

FINDNK

NZL

IRL

TUR

3.82Standard deviation of output growth

2.03

2.02

AUSSWE

JPN

FRA

NOR

4.07

Mea

n ou

tput

gro

wth

Source: G. Ramey and V. Ramey, “Cross-Country Evidence on the Link Between Volatility and Growth,” American EconomicReview 85, no. 5 (December 1995): 1143.

1G. Ramey and V. Ramey, “Cross-Country Evidence on the Link Between Volatility and Growth,” American Economic Review 85, no. 5 (December1995): 1138–51.

2In constructing this figure, Ramey and Ramey controlled for a number of factors that could cause differences in growth rates, including initial realGDP, initial human capital, average investment rates, and population growth rates.

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14-9 How Long Is the Long Run? Part FourMacroeconomists traditionally decompose the overall behavior of GDP through time into itslong-run growth (or trend) and its short-run fluctuations (or cycle). That is the approachfollowed in the textbook. Chapters 3 to 8 explain the determination of the natural level ofoutput at a point in time and show how the natural level of output grows through time asthe economy’s resources and technology change. Chapters 9 to 13 explain how actual GDPmay differ from the natural level in the short run because of shocks to aggregate demandcombined with an upward-sloping aggregate supply curve (as a result of price stickiness orinformation imperfections). Thus, Chapters 3 to 8 explain the trend growth of GDP, whereasChapters 9 to 13 explain the business cycle.

The simple dynamic model presented in Chapter 14 incorporates elements of bothshort-run business cycle fluctuations and long-run economic growth into a unifiedframework. It does so by allowing for growth over time in the natural level of output withina model that has sticky prices in the short run. Economists have developed much moresophisticated models, known as stochastic, dynamic, general equilibrium models, in whichthis traditional decomposition between trend and cycle can be misleading. Both the “short-run” fluctuations in output and the “long-run” growth of output are, according to this view,in part manifestations of the same phenomenon—the response of the economy to technologyshocks. To put it another way, output sometimes fluctuates because the natural level ofoutput fluctuates. But it may also fluctuate because of shifts in aggregate demand arisingfrom changes in the money supply when prices are sticky. Hence, DSGE models are hybridsthat combine both Keynesian elements and real business cycle elements into a singleapproach.

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14-10 Additional ReadingsThe Summer 1989 issue of the Journal of Economic Perspectives 3, no. 3, contains twoarticles on real business cycle theory: one by Charles Plosser, a proponent of the theory,“Understanding Real Business Cycles,” pages 51–77; and one by Greg Mankiw, who is moreskeptical, “Real Business Cycles: A Keynesian Perspective,” pages 79–90. A useful, but moretechnical, survey is B. McCallum, “Real Business Cycle Models,” in R. Barro (ed.), ModernBusiness Cycle Theory (Cambridge, Mass.: Harvard University Press, 1989).

The Fall 1986 issue of the Federal Reserve Bank of Minneapolis Quarterly Review 10,no. 4, contains a debate on the topic between Edward Prescott and Lawrence Summers.Rodolfo Manuelli’s introduction is also very useful.

Much work on real business cycles has focused on the labor market. For a survey, seeG. Hansen and R. Wright, “The Labor Market in Real Business Cycle Theory,” FederalReserve Bank of Minneapolis Quarterly Review 16, no. 2 (Spring 1992).

There are a number of good surveys of the current state of macroeconomics, includingRobert Gordon, “What Is New-Keynesian Economics?” Journal of Economic Literature 28(September 1990); Bennett McCallum, “Post-War Developments in Business Cycle Theory: AModerately Classical Perspective,” Journal of Money, Credit, and Banking 20 (August 1988);Greg Mankiw, “A Quick Refresher Course in Macroeconomics,” Journal of EconomicLiterature 28 (December 1990): 1645–60; Greg Mankiw and D. Romer, “Introduction,” in G.Mankiw and D. Romer, eds., New Keynesian Economics (Cambridge, Mass.: MIT Press,1991). The Mankiw and Romer volumes also contain many of the important papers on newKeynesian economics.

The Journal of Economic Perspectives 7, no. 1 (Winter 1993), contains a symposium on“Keynesian Economics Today” that includes articles by avowed new Keynesians DavidRomer, Bruce Greenwald, and Nobel Prize winner Joseph Stiglitz; self-described oldKeynesian and Nobel Prize winner James Tobin; and Robert King, who is skeptical of thenew Keynesian approach.

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