1. Advanced Macroeconomics
Chapter 19
EXPLAINING BUSINESS CYCLES

2. 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.

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

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

5. The Frisch-Slutzky Paradigm
The impulses (demand and supply shocks) initiating business cycles
may 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?

6. Restating the AS-AD model
(1)
(2)
(3)
(4)
(5)

7. The AS-AD Model in compact form
Inserting (2), (3) and (5) into (1), we get
(6)
which may be rearranged to give the aggregate demand curve:
(7)
Substituting (5) into (4), we obtain the short-run aggregate supply curve:
(8)

8. A short-run macroeconomic equilibrium with cyclical unemployment

9. The adjustment to long-run equilibrium

10. How long is the Long Run? Defining (output gap) (inflation gap)
and assuming st = zt = 0, we may rewrite (7) and (8) as
(9)
(10)
Inserting (9) into (10), we find

11. How long is the Long Run? (11) (12)
The solutions to these linear first-order difference equations are
(13)
(14)
Note that the long-run equilibrium is stable, since 0 < β < 1.

12. The speed of convergence
(15)
According to equation (12) in Chapter 17 we have

13. Calibrating the model (one time period = one quarter)

14. Effects of a temporary negative supply shock

15. Effects of a temporary negative demand shock

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

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

18. Permanent Shocks
When analyzing permanent shocks, we must account for the fact that such
shocks will change the long-run equilibrium real interest rate (the ’natural’
interest rate). Denoting the initial values of natural output and the natural
interest rate by zero subscripts, we may write our AS-AD model as
(21)
(22)
Consider an initial equilibrium where
and suppose that st
permanently changes from zero to some s ≠ 0. The new long-run equilibrium
level of output may then be found from (22) by inserting
to get

19. A permanent supply shock
The effect of a permanent supply shock on natural output
(23)
The new equilibrium real interest rate is found from (21) by setting
The effect of a permanent supply shock on the equilibrium real interest rate
(24)

20. A permanent demand shock
A permanent demand shock does not affect natural output. Hence the effect on
the equilibrium real interest rate may be found from (21) by setting
The effect of a permanent demand shock on the equilibrium real interest rate
(25)
To keep inflation close to its target rate and to avoid large deviations of output
from trend, the central bank must revise the estimates of natural output and of the
equilibrium real interest rate entering the Taylor rule when the economy is hit by
permanent shocks. The adjustment of the economy to the new long-run equilibrium
will depend on how long it takes the central bank to realize the permanency of the
shock. Exercise 19.2 invites you to study these issues further.

21. The Stochastic AS-AD model
The 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
(27)
(28)
Our goal is to calibrate a stochastic AS-AD simulation model which can reproduce
the stylized business cycle facts summarized in Table 19.1.

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

24. Simulation of the stochastic AS-AD model with static expectations and no
supply shocks

25. Expected current inflation and lagged actual inflation in the United States

26. The Stochastic AS-AD model with static expectations
Problems
 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
● The assumption of static expectations implies greater fluctuations in the
expected inflation rate than what we observe in practice (see Figure 19.12)
To solve these problems we will now allow for simultaneous demand and supply shocks as well as adaptive expectations.

27. Adaptive expectations
(29)
Eq. (29) may be rewritten as
(33)
The AS-AD model with adaptive expectations
(34)
(35)
(36)

28. The AS-AD model with adaptive expectations
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. business
cycle reasonably well, given its simplicity.

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

30. 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 of
productivity growth
● The employment fluctuations observed during business cycles reflect
voluntary movements along individual labour supply curves (intertemporal
substitution in labour supply, no involuntary unemployment)
● Economic growth and business cycles can and should be explained within a
unified model framework. To explain business cycles, there is no need to
postulate nominal and/or real rigidities.

31. A simple RBC model: technology
(44)
(45)
(46)
(47)
For simplicity, we will assume that δ = 1.

32. A simple RBC model: economic behaviour
(48)
(49)
(50)
(51)
(52)

33. A simple RBC model
As shown on pp in the text, the model (44) through (52) may be reduced to
(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.

34. Table 19.3: The RBC model versus the U.S. economy
Standard deviation of
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
RBC model1
3.42
2.84
0.83
0.75
0.50
0.23
The U.S economy2
3.47
2.88
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.
Table 19.3: The RBC model versus the U.S. economy

35. 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).

36. 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.

37. 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.