© The McGraw-Hill Companies, 2005 EXPLAINING BUSINESS CYCLES Chapter 19 Advanced Macroeconomics

©The McGraw-Hill Companies, 2005

EXPLAINING BUSINESS

CYCLES

Chapter 19Advanced Macroeconomics


Themes of the chapter

• Explaining business cycles by means of the AS-AD model.

The Frisch-Slutzky paradigm: Impulse and propagation.

The deterministic versus the stochastic AS-AD model.

Supply versus demand shocks. Permanent versus temporary shocks. The theory of real business cycles.


-5

-4

-3

-2

-1

0

1

2

3

4

5

1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998

US GDP US InflationPercent

The cyclical components of real GDP and inflation in the United States


-2

-1

0

1

2

3

4

1996 1997 1998 1999 2000 2001 2002 2003

percent

USA

Germany

Japan

Growth in real per capita GDP in the USA, Germany and Japan


The Frisch-Slutzky Paradigm The impulses (demand and supply shocks) initiating business cyclesmay be unsystematic

The propagation of the impulses may generate systematic fluctuations due to the structure of the economy

Basic questions

Why do movements in economic activity display persistence?

Why do these movements tend to follow a cyclical pattern?


Restating the AS-AD model 1 2t t t ty y g g r r v (1)

1e

t t tr i (2)

1e *

t t t ti r h b y y (3)

et t t ty y s (4)

1et t (5)


The AS-AD Model in compact form

12

2 2

1 1

t t t

t tt

y y * z ,

v g gh, zb b

1SRAS: t t t ty y s

(7)

(8)

Inserting (2), (3) and (5) into (1), we get

which may be rearranged to give the aggregate demand curve:

1AD: *

t t ty y z

Substituting (5) into (4), we obtain the short-run aggregate supply curve:

(6)


A short-run macroeconomic equilibrium with cyclical unemployment

y

LRAS

AD

0

y

SRAS

y0

E0

©The McGraw-Hill Companies, 2005The adjustment to long-run equilibrium

y

LRAS

AD

0

1

23

*

y0 y1 y2 y3 y

SRAS0

SRAS ( = )1 0 e

SRAS ( = )2 1 e

SRAS ( = )3 e


How long is the Long Run?Defining

21 1

2

1ˆ ˆAD: ,

1t t

hy

b

(10)1 1ˆ ˆ ˆSRAS: t t ty

(9)

ˆ t ty y y (output gap)

*ˆt t (inflation gap)

Inserting (9) into (10), we find

and assuming st = zt = 0, we may rewrite (7) and (8) as


How long is the Long Run?

1

1ˆ ˆ ,

1t ty y

(11)

1ˆ ˆt t (12)

The solutions to these linear first-order difference equations are

0ˆ ˆ , 0,1,2,.....tty y t

0ˆ ˆ , 0,1,2,.....tt t

Note that the long-run equilibrium is stable, since 0 < β < 1.

(13)

(14)


The speed of convergencenumber of periods before half the adjustment to long-run

equilibrium has been completedht

0 0

1 1 1ˆ ˆ ˆ ln ln

2 2 2h ht t h

ty y y t

(15)ln 2 0.693

ln lnht

According to equation (12) in Chapter 17 we have


Calibrating the model (one time period = one quarter)

2

2

20 0

1

1 1

1

(1 ) 1 (1 )

0.05 0.2 0.8 3.6 0.5

ln 2From this it follows that 0.958

r r

y y

y

h

h

b

D D

Y D D Y

D h b

t

16 4 yearsln

©The McGraw-Hill Companies, 2005Effects of a temporary negative supply shock

y

LRAS

E

E 2

E 1

yy 1 y 2

SRA S 0

SRA S 1

AD

SRA S 2

s 1

©The McGraw-Hill Companies, 2005Effects of a temporary negative demand shock

y

LRAS

E

E 2

E 1

yy 1 y 2

SRA S 0

SRA S 2

AD 0 = AD 2

AD 1


-1

-0,8

-0,6

-0,4

-0,2

0

0,2

0,4

0,6

0,8

1

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29Year

Percent y - y - π π*

The adjustment to a temporary negative supply shock (s1=1)


-1

-0,8

-0,6

-0,4

-0,2

0

0,2

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29Year

Percent y - y π - π*

The adjustment to a temporary negative demand shock (z1= -1)


Permanent ShocksWhen analyzing permanent shocks, we must account for the fact that suchshocks will change the long-run equilibrium real interest rate (the ’natural’interest rate). Denoting the initial values of natural output and the naturalinterest rate by zero subscripts, we may write our AS-AD model as

0 2 0 1 t t t t t ty y v r r , v v g g

1 0t t t ty y s

(21)

(22)

Consider an initial equilibrium where 0t tv s and suppose that st permanently changes from zero to some s ≠ 0. The new long-run equilibriumlevel of output may then be found from (22) by inserting

1 t t t t, y y , s s to get


A permanent supply shockThe effect of a permanent supply shock on natural output

0

sy y

(23)

The new equilibrium real interest rate is found from (21) by setting

0 to gett t

sy y y , r r

The effect of a permanent supply shock on the equilibrium real interest rate

02

sr r

(24)


A permanent demand shockA permanent demand shock does not affect natural output. Hence the effect onthe equilibrium real interest rate may be found from (21) by setting

0 , and to get t t ty y v v r r

The effect of a permanent demand shock on the equilibrium real interest rate

02

vr r

(25)

To keep inflation close to its target rate and to avoid large deviations of outputfrom trend, the central bank must revise the estimates of natural output and of theequilibrium real interest rate entering the Taylor rule when the economy is hit bypermanent shocks. The adjustment of the economy to the new long-run equilibriumwill depend on how long it takes the central bank to realize the permanency of theshock. Exercise 19.2 invites you to study these issues further.


The Stochastic AS-AD modelThe deterministic AS-AD model considered above can explain the persistence in macroeconomic time series, but it cannot explain the recurrent cyclical fluctuations observed in the real world. To generate such fluctuations, we now assume:

Stochastic demand and supply shocks

1 1 0 1 , t t tz z x (27)

2(0, ) . . .t x tx N x i i d ,

1 1 , 0 1t t ts s c (28)

2(0, ) . . .t c tc N c i i d ,

Our goal is to calibrate a stochastic AS-AD simulation model which can reproducethe stylized business cycle facts summarized in Table 19.1.


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-1

0

1

2

3

4

5

1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998

US GDP US Inflation

Percent

Year

Cyclical components of real GDP and inflation in the USA, 1974-98


1 Φ = 0, σc = 0, σ

x = 1, δ = 0.75, ω = 0

1955:I-2001:IV4

The U.S economy,

of demand and supply shocks3

expectations and a combination

AS-AD model with adaptive

expectations and no demand shocks2

AS-AD model with static

expectations and no supply shocks1

AS-AD model with static

1,66

1,66

1,67

1,62

Output

0,29

0,30

1,90

0,52

Inflation

0,10

0,15

-1,00

0,08

output and inflation

Correlation between

0,86

0,82

0,92

0,81

t-1

0,65

0,68

0,86

0,66

t-2

0,41

0,50

0,79

0,47

t-3

0,18

0,38

0,73

0,37

t-4

0,50

0,47

0,92

0,99

t-1

0,29

0,33

0,86

0,96

t-2

0,24

0,24

0,79

0,91

t-3

0,17

0,32

0,73

0,85

t-4

Standard deviation (%) Autocorrelation in output Autocorrelation in inflation

Table 19.1: The stochastic AS-AD model and the stylized business cycle facts

Common parameter values in all AS-AD simulations: γ = 0.05, τ = 0.2, DY = 0.8, η = 3.6, h = b = 0.5

2 Φ = 0, σc = 0.75, σ

x = 0, δ = 0, ω = 0 3 Φ = 0.92, σ

c = 0.25, σ

x = 1, δ = 0.75, ω = 0.25

4 The cyclical components of output and inflation have been estimated via detrending of quarterly data using the HP-filter with λ = 1600.


-5-4-3-2-1012345

1 11 21 31 41 51 61 71 81 91

y-y Percent

Quarter

Simulation of the stochastic AS-AD model with static expectations and nosupply shocks


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0

2

4

6

8

10

12

14

1981-III 1984-III 1987-III 1990-III 1993-III 1996-III 1999-III 2002-III

Expected inflation rate for the current quarter Actual inflation rate during the previous quarter

(πt )(πt-1)

e

Expected current inflation and lagged actual inflation in the United States


The Stochastic AS-AD model with static expectations

The model with demand shocks can reproduce the stylized facts regarding output, but it generates far too much persistence of inflation

The model with supply shocks is unable to reproduce the stylized facts of output as well as inflation

To solve these problems we will now allow for simultaneous demand and supply shocks as well as adaptive expectations.

Problems

● The assumption of static expectations implies greater fluctuations in theexpected inflation rate than what we observe in practice (see Figure 19.12)


Adaptive expectationsrevision of expected last period's inflation inflation rate forecast error

1 1 1(1 ) ( ) , 0 1e e et t t t

Eq. (29) may be rewritten as

1

1

(1 )e nt t n

n

For 0 we get static expectations.

(29)

(33)

The AS-AD model with adaptive expectations

AD: *t t ty y z

SRAS: et t t ty y s

1 1Expectations: 1e et t t

(34)

(35)

(36)


The AS-AD model with adaptive expectations

1 1 1ˆ ˆ ( )t t t t t ty ay z z s s

1 1 1ˆ ˆ

1 11 1

1 1

t t t t t ta z z s s

a

The model (34) through (36) may be condensed to:

(41)

(42)

The third row in Table 19.1 shows that this model reproduces the U.S. businesscycle reasonably well, given its simplicity.


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y-y

Percent

-0

Quarters

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0

1

2

3

4

5

1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998

US GDP US Inflation

Percent

Year

The AS-AD model with adaptive expectations (top diagram) versus the actual U.S. business cycle (bottom diagram)


The theory of real business cycles

Our AS-AD model of the business cycle emphasizes the role of expectational errors and sluggish wage and price adjustment, and the microfoundation for the SRAS curve implies that business fluctuations are associated with fluctuations in involuntary unemployment. The model also assigns an important role to demand shocks. A very different theory is:

Real business cycle theory (basic version)

● The business cycle is mainly driven by fluctuations in the rate ofproductivity growth

● The employment fluctuations observed during business cycles reflectvoluntary movements along individual labour supply curves (intertemporalsubstitution in labour supply, no involuntary unemployment)

● Economic growth and business cycles can and should be explained within aunified model framework. To explain business cycles, there is no need topostulate nominal and/or real rigidities.


A simple RBC model: technology

1Production function: 0 1t t t tY K AL , (44)

21 1

Actual productivity: ln

0 <1, 0

t t

t t t t c

A gt s ,

s s c , c N ,

(45)

Trend productivity: ln tA gt

1 1Capital accumulation: 1t t tK K S

(46)

(47)

For simplicity, we will assume that δ = 1.


A simple RBC model: economic behaviour

Saving: 0 1t tS s Y , s (48)

Labour supply: 0s tt

t

wL ,

w

(49)

Profit maximization: 1t tt

t t t

Y Kw

L A L

(50)

Trend real wage: 1 *t tw cA , c k

(51)

Labour market clearing: st tL L (52)


A simple RBC modelAs shown on pp. 585-86 in the text, the model (44) through (52) may be reduced to

1

1 1

1 1 1 1 1t t tˆ ˆy y s ,

t tˆ ˆL y

(59)

(60)

Propagation mechanism in the model: A positive productivity shock raises current income which in turn raises saving and capital accumulation. This leads to a higher capital stock in the next period, which in turn raises next period’s income and saving, and so on. In this way a temporary productivity shock generates persistence in output and employment. Indeed, we see from Table 19.3 that the calibrated version of the model generates too much persistence compared to the persistence observed in the U.S. data.


Table 19.3: The RBC model versus the U.S. economy

Standard deviation of Autocorrelation Autocorrelation

Standard deviation (%) output relative to standard in output in hours worked

Output Hours worked deviation of hours worked t-1 t-2 t-3 t-1 t-2 t-3

RBC model1 3.42 2.84 0.83 0.75 0.50 0.23 0.75 0.50 0.23

The U.S economy2 3.47 2.88 0.83 0.76 0.38 0.08 0.73 0.29 0.06

1 α = 0.33, η = 0.83, ω = 0.1, σc = 0.015

2 Annual data for the business sector.

Note: The cyclical components of output and employment have been estimated via linear OLS detrending of annual data.

Source: Economic Outlook Database, OECD.


Some problems with basic RBC theory

• The virtue of the basic RBC model is that it is simple and fully integrates the theory of business cycles with the theory of economic growth. However, critics object to the theory by raising the following questions:

• Is technological progress really so uneven as postulated in the RBC model?

• Is it really plausible that recessions are periods of technological regress? (Alternative hypothesis: the observed fluctuations in productivity reflect fluctuations in capacity utilization caused by demand shocks).


Some problems with basic RBC theory

• Are the observed fluctuations in employment really a reflection of intertemporal substitution in labour supply? To reproduce the observed volatility of employment relative to the volatility of output, the wage elasticity of labour supply in our simple RBC model (ε) has to be set at 4.9 which is much higher than the elasticity estimated by labour economists. More generally: Is all recorded unemployment really voluntary?

• The RBC model predicts that the real wage is procyclical. This is in line with U.S. data, but it is not consistent with European data.


The lasting contribution of real business cycle theory

In response to these criticisms, real business cycle theorists have recently tried to make their models more realistic by allowing for various frictions and rigidities, including (in some cases) nominal rigidities.

At the methodological level RBC theorists have made a lasting contribution by pointing out that supply shocks may play an important part in the explanation of business cycles, and by insisting that a satisfactory theory of the business cycle should consist of a dynamic stochastic general equilibrium model which is able to reproduce the most important stylized facts of the business cycle reasonably well.

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© The McGraw-Hill Companies, 2005 EXPLAINING BUSINESS CYCLES Chapter 19 Advanced Macroeconomics