ADEMU Research Project Overview at the presented at the Kick-Off Conference in Cambridge

1. Is the Macroeconomy Locally Unstable and Why
Should We Care?
Paul Beaudry, Dana Galizia & Franck Portier
ADEMU 1st Conference
Cambridge, October 2015
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2. Is the Macroeconomy Locally Unstable and Why
Should We Care?
Watching The Dancing Bear
Paul Beaudry, Dana Galizia & Franck Portier
ADEMU 1st Conference
Cambridge, October 2015
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3. 0. Introduction
Big Questions
What moves the economy?
What are the pros and cons of stabilization policy?
Two (obviously) interrelated questions
3 / 94

4. 0. Introduction
Common view in Macro
A majority of modern business cycle models have the
following structure:
× There is a unique (relevant) steady state for labor market
variables (ex: hours per capital, unemployment, job finding
rates..)
× The dynamic system is stable, that is, in the absence of shocks
the labor market outcomes will converge to this steady state
× Business cycle fluctuations for these variables are interpreted
as reflecting the dynamics induced by shocks compounded by
transitional dynamics.
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5. 0. Introduction
Common Way of Looking at the Data
Some of the evidence for this view is based on the following
× The business cycle movement in labor market variables is well
captured by a low order AR or ARMA process
× In particular, dynamic simulation of the resulting estimated AR
process maps closely to the data
× The implied convergence rate is quite quick
Let’s look at this
(US data unless explicitly mentionned)
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6. 0. Introduction
Common Way of Looking at the Data
Figure 1: Total Hours
1940 1950 1960 1970 1980 1990 2000 2010 2020
-7.25
-7.2
-7.15
-7.1
-7.05
-7
-6.95
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7. 0. Introduction
Common Way of Looking at the Data
Figure 2: Total Hours and Trend (High-pass filter, 80 quarters)
1940 1950 1960 1970 1980 1990 2000 2010 2020
-7.25
-7.2
-7.15
-7.1
-7.05
-7
-6.95
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8. 0. Introduction
Common Way of Looking at the Data
Figure 3: Cyclical Component of Total Hours
1960 1970 1980 1990 2000 2010 2020
-6
-4
-2
0
2
4
6
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9. 0. Introduction
Common Way of Looking at the Data
Fit an AR(2) (standard AIC-BIC criteria)
Ordinary Least-squares Estimates
Dependent Variable = x
R-squared = 0.9362
Durbin-Watson = 2.2217
Nobs, Nvars = 220, 3
***************************************************************
Variable Coefficient t-statistic t-probability
constant -0.000712 -0.017705 0.985891
x(-1) 1.418969 23.746422 0.000000
x(-2) -0.481165 -8.054144 0.000000
Max Eigenvalue Modulus
AR :0.85849 [0.85849]
Autocor : .95
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10. 0. Introduction
Common Way of Looking at the Data
xt = α0 + α1xt−1 + α2xt−2 + εt
Dynamic simulation :
x1 = x1
x2 = x2
xt = α0 + α1xt−1 + α2xt−2
Simulation as of date T0:
xS
1 = x1
xS
2 = x2
xS
t = α0 + α1xS
t−1 + α2xS
t−2
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11. 0. Introduction
Common Way of Looking at the Data
Figure 4: Dynamic Simulation, AR(2) Model
1960 1970 1980 1990 2000 2010 2020
-6
-4
-2
0
2
4
6
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12. 0. Introduction
Common Way of Looking at the Data
Figure 5: Forecasting as of 1961, Linear Model
1960 1970 1980 1990 2000 2010 2020
-6
-4
-2
0
2
4
6
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13. 0. Introduction
Our (alternative) view
The steady state may be locally unstable, but globally stable
limit cycles (or chaos)
Macroeconomy might be the outcome of a limit cycle
perturbed by shocks
Think of stabilization policies as affecting both reactions to
shocks and behaviors that generates the endogenous cycle
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14. 0. Introduction
Support for this view
Theory? Complementarity + dynamics:
Beaudry-Galizia-Portier 2014 and 2015
Quantitative plausibility with structural econometrics?
Beaudry-Galizia-Portier 2015
Looking at the data from a non-structural time-series
perspective : this paper and this talk
Stabilization policies
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15. 0. Introduction
Support for this view
Theory? Complementarity + dynamics:
Beaudry-Galizia-Portier 2014 and 2015
Quantitative plausibility with structural econometrics?
Beaudry-Galizia-Portier 2015
Looking at the data from a non-structural time-series
perspective : this paper and this talk
Stabilization policies: ... see you again in 2017...
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16. 0. Introduction
Question
How to explore possibility local instability when shocks are
present?
× Know that this conjecture is not possible in linear models
× Idea: estimate a reduced form dynamics allowing for
non-linearities
× Shut down the stochastic elements and look at implied
dynamics
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17. 0. Introduction
Challenge
“There is only one way to be linear, but millions to be
non-linear”
We will start exploring in the direction pointed by our
theoretical analysis.
As a first pass, we limit ourselves to uni-variate representations
17 / 94

18. 0. Introduction
Results
We obtain intriguing evidence of limit cycle type of dynamics
This happens with a small amount of non-linearities and local
explosiveness
Monte-Carlo simulations tend to convince us that those
results are not artifacts
18 / 94

19. Roadmap
1. Reduced Form Model
2. Total Hours and Other Labor Market Variables
3. Robustness and Monte Carlo Analysis
4. Quantity Variables
5. What’s next
19 / 94

20. Roadmap
1. Reduced Form Model
2. Total Hours and Other Labor Market Variables
3. Robustness and Monte Carlo Analysis
4. Quantity Variables
5. What’s next
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21. 1. Reduced Form Model
Model
Micro-founded in BGP (2014, 2015)
Xit = (1 − δ)Xit−1 + Yit
Yit = α0 + α1Yit−1 − α2Xit−1 + α3Et−1F (ht) + εt
ht = γ 1
N
N
i=1 Yit
α1, α2 ∈ ]0, 1[
Key: complementarities + dynamics
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22. 1. Reduced Form Model
BGP (2015) results
Write in h
Hit = (1 − δ)hit−1 + hit
hit = α0 + α1hit−1 − α2Hit−1 + α3Et−1F
γ
N
N
i=1
hit + εt
Results in BGP (2015)
× α3 = 0 unique symmetric SS that is globally stable
× When strong enough complementarities at the SS, i.e.
F (Y SS
) positive and large enough (but < 1):
Hopf bifurcation as long as “ α2 large enough and δ not too
large”
meaning eigenvalues of the difference equation become
complex and bigger than one in modulus
We then have limit cycles
× The limit cycle is attractive if F is S-shaped.
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23. 1. Reduced Form Model
Adding Trend and Hours
Because of technological trend in Y , we start working with
the equation in h
ht = α0 + α1ht−1 − α2 Ht−1
+∞
τ=1(1−δ)τ ht−τ−1
+α3Et−1F (ht) + εt
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24. 1. Reduced Form Model
Towards estimation
ht = α0 + α1ht−1 − α2 Ht−1
+∞
τ=1(1−δ)τ ht−τ−1
+α3Et−1F (ht) + εt
In our model, ht represents the cyclical component of hours
In practice, observed ht is affected by demographic, social and
cultural trends
Identification assumption in this paper: data are the sum of a
trend component and a business cycle one filter data with
a high-pass filter
What to do with Et−1? : use a projection on ht−1 and Ht−1
What to do with F?
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25. 1. Reduced Form Model
Simple specification
ht = α0 + α1ht−1 − α2 Ht−1
+∞
τ=1(1−δ)τ ht−τ−1
+α3Et−1F (ht) + εt
Theory has suggested that an S-shaped F is generating
attractive limit cycles
The simplest S-shaped function is −x3
Use two lags of h (AR(2))
Define H = (1 − δ)H−1 + h
ht = α0 + α1ht−1 + α2ht−2 + α3Ht−1 + α4h3
t−1 + εt
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26. 1. Reduced Form Model
Simple specification
We will estimated the (super simple) following equation



xt = α0 + α1xt−1 + α2xt−2 + α3Xt−1 + α4x3
t−1 + εt
Xt = N
j=0(1 − δ)j xt−j
This specification is driven by our previous theoretical results
We make the following choices:
× Filter: High-pass 80
× Truncation N : 40 quarters
× “Depreciation” δ : .05
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27. 1. Reduced Form Model
Extended specification
At some point, we will explore with a more flexible
specification :
xt = α0 + α1xt−1 + α2xt−2 + α3Xt−1 + εt
+α4x3
t−1 + α5x3
t−2
+α6X3
t−1 + α7X3
t−2
+α8x2
t−1Xt−1 + α9xt−1X2
t−1
27 / 94

28. Roadmap
1. Reduced Form Model
2. Total Hours and Other Labor Market Variables
3. Robustness and Monte Carlo Analysis
4. Quantity Variables
5. What’s next
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29. 2. Total Hours and Other Labor Market Variables
Full equation



xt = α0 + α1xt−1 + α2xt−2 + α3Xt−1 + α4x3
t−1 + εt
Xt = N
j=0(1 − δ)j xt−j
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30. 2. Total Hours and Other Labor Market Variables
Total Hours
Ordinary Least-squares Estimates
Dependent Variable = x
R-squared = 0.9424
Durbin-Watson = 2.1163
Nobs, Nvars = 220, 5
***************************************************************
Variable Coefficient t-statistic t-probability
constant -0.020394 -0.526499 0.599084
x(-1) 1.391289 19.728102 0.000000
x(-2) -0.342470 -5.121542 0.000001
X(-1) -0.013430 -4.377008 0.000019
x(-1)^3 -0.006238 -2.386330 0.017884
Max Eigenvalue Modulus
Full :1.0178 [1.01+0.12547i]
AR :0.85849 [0.85849]
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31. 2. Total Hours and Other Labor Market Variables
Total Hours
Figure 6: The Limit Cycle - Simulation as of T0 = 1961
-3
20
-2
-1
10
0
xt
1
0
2
Xt−1
3
-10
3
2
xt−1
-20 1
0
-1
-2-30
-3
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32. 2. Total Hours and Other Labor Market Variables
Total Hours
Figure 7: The Limit Cycle
-3
-2
30
-1
0
20
1
2
xt
3
10
4
Xt−1
5
6
0
654
xt−1
-10 3210-1-20 -2-3
32 / 94

33. 2. Total Hours and Other Labor Market Variables
Total Hours
Figure 8: The Limit Cycle
-3
-2
30
-1
0
20
1
2
xt
3
10
4
Xt−1
5
6
0
654
xt−1
-10 3210-1-20 -2-3
33 / 94

34. 2. Total Hours and Other Labor Market Variables
Total Hours
Figure 9: The Limit Cycle
-3
-2
30
-1
0
20
1
2
xt
3
10
4
Xt−1
5
6
0
654
xt−1
-10 3210-1-20 -2-3
34 / 94

35. 2. Total Hours and Other Labor Market Variables
Total Hours
Figure 10: The Limit Cycle - Simulation as of T0 = 1961
-3 -2 -1 0 1 2 3
xt
-25
-20
-15
-10
-5
0
5
10
15
20
Xt
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36. 2. Total Hours and Other Labor Market Variables
Total Hours
Figure 11: Dynamic Simulation, Non Linear Model
1960 1970 1980 1990 2000 2010 2020
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
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37. 2. Total Hours and Other Labor Market Variables
Total Hours
Figure 12: Dynamic Simulation, Full Model
1960 1970 1980 1990 2000 2010 2020
-6
-4
-2
0
2
4
6
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38. 2. Total Hours and Other Labor Market Variables
Total Hours
Figure 13: Forecasting as of 1961, Full Model
1960 1970 1980 1990 2000 2010 2020
-6
-4
-2
0
2
4
6
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39. 2. Total Hours and Other Labor Market Variables
Total Hours
Figure 14: Forecasting as of 1961, AR(2) and Full Model
1960 1970 1980 1990 2000 2010 2020
-6
-4
-2
0
2
4
6
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40. 2. Total Hours and Other Labor Market Variables
Total Hours
Figure 15: Visual Inspection of Non Linearities
xt = α0 + α1xt−1 + α2xt−2 + α3Xt−1 + α4x3
t−1 + εt
-8 -6 -4 -2 0 2 4 6 8
α1xt−1 + α4x3
t−1
-8
-6
-4
-2
0
2
4
6
8
xt
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41. 2. Total Hours and Other Labor Market Variables
Other variables
Now let’s look at some other labor market variables
× Non Farm Business Hours
× Unemployment
× Shimer’s (2012) job finding probability for unemployed workers
We find a similar pattern
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42. 2. Total Hours and Other Labor Market Variables
NFB Hours
Figure 16: Cyclical Component
1960 1970 1980 1990 2000 2010 2020
-8
-6
-4
-2
0
2
4
6
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43. 2. Total Hours and Other Labor Market Variables
NFB Hours
Figure 17: The Limit Cycle - Simulation as of T0 = 1961
-3 -2 -1 0 1 2 3
xt
-25
-20
-15
-10
-5
0
5
10
15
Xt
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44. 2. Total Hours and Other Labor Market Variables
NFB Hours
Figure 18: Forecasting as of 1961
1960 1970 1980 1990 2000 2010 2020
-8
-6
-4
-2
0
2
4
6
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45. 2. Total Hours and Other Labor Market Variables
Unemployment Rate
Figure 19: Cyclical Component
1960 1970 1980 1990 2000 2010 2020
-3
-2
-1
0
1
2
3
4
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46. 2. Total Hours and Other Labor Market Variables
Unemployment Rate
Figure 20: The Limit Cycle - Simulation as of T0 = 1961
-1.5 -1 -0.5 0 0.5 1 1.5 2
xt
-10
-5
0
5
10
15
Xt
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47. 2. Total Hours and Other Labor Market Variables
Unemployment Rate
Figure 21: Forecasting as of 1961
1960 1970 1980 1990 2000 2010 2020
-3
-2
-1
0
1
2
3
4
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48. 2. Total Hours and Other Labor Market Variables
Job Finding Probability
Figure 22: Cyclical Component
1960 1970 1980 1990 2000 2010
-15
-10
-5
0
5
10
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49. 2. Total Hours and Other Labor Market Variables
Job Finding Probability
Figure 23: The Limit Cycle - Simulation as of T0 = 1961
-6 -4 -2 0 2 4 6
xt
-50
-40
-30
-20
-10
0
10
20
30
40
Xt
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50. 2. Total Hours and Other Labor Market Variables
Job Finding Probability
Figure 24: Forecasting as of 1961
1960 1970 1980 1990 2000 2010
-15
-10
-5
0
5
10
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51. 2. Total Hours and Other Labor Market Variables
Other variables
Is the limit cycle an artifact of the data treatment and model
estimation?
Let’s consider Shimer’s (2012) employment exit probability,
that we know is not cyclical
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52. 2. Total Hours and Other Labor Market Variables
Employment Exit Probability
Figure 25: Cyclical Component
1960 1970 1980 1990 2000 2010
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
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53. 2. Total Hours and Other Labor Market Variables
Employment Exit Probability
Figure 26: The (absence of) Limit Cycle - Simulation as of T0 = 1961
-0.1 0 0.1 0.2 0.3 0.4 0.5 0.6
xt
-1
-0.5
0
0.5
1
1.5
Xt
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54. 2. Total Hours and Other Labor Market Variables
Employment Exit Probability
Figure 27: Forecasting as of 1961
1960 1970 1980 1990 2000 2010
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
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55. 2. Total Hours and Other Labor Market Variables
Recap
xt = α0 + α1xt−1 + α2xt−2 + α3Xt−1 + α4x3
t−1 + εt
Variable α4 p-val Max eig. Limit Cycle
Total H .001% 1.0178
[1.01+0.12547i]
NFB Hours .04% 1.006
[0.99677+0.13566i]
Unemp .8% 1.0094
[1.0007+0.13244i]
Job Finding Prob. 1% 1.0206
[1.0123+0.13016i]
Unemp. Exit Prob. 84% 0.95126 X
[0.94351+0.12119i]
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56. 2. Total Hours and Other Labor Market Variables
Unemployment in Other Countries
We take a bunch of unemployment series for other developed
countries
We use that simple specification and various samples
Country Limit Cycle
Australia X
Austria
Canada X
France X
Germany
Great-Britain X
Japan X
Netherlands
Switzerland X
Sweden
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57. 2. Total Hours and Other Labor Market Variables
Unemployment, Canada
Figure 28: Forecasting as of 1961
1960 1970 1980 1990 2000 2010 2020
-3
-2
-1
0
1
2
3
4
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58. 2. Total Hours and Other Labor Market Variables
Unemployment, Netherlands
Figure 29: Forecasting as of 1961
1975 1980 1985 1990 1995 2000 2005 2010 2015
-3
-2
-1
0
1
2
3
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59. Roadmap
1. Reduced Form Model
2. Total Hours and Other Labor Market Variables
3. Robustness and Monte Carlo Analysis
4. Quantity Variables
5. What’s next
59 / 94

60. 3. Robustness and Monte Carlo Analysis
Robustness
We have made several choices in the specification:
× Xt =
N
j=0(1 − δ)j
xt−j
N
δ
× Filter
× Sample
How robust is the detection of the limit cycle?
Here we show results with Unemployment U and Job Finding
rate F
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61. 3. Robustness and Monte Carlo Analysis
Robustness to N
N Limit Cycle with F Limit Cycle with U
N = 20
N = 30
N = 40
N = 50
N = 60
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62. 3. Robustness and Monte Carlo Analysis
Robustness to δ
δ Limit Cycle with F Limit Cycle with U
δ = .01
δ = .05
δ = .1
δ = .2 X X
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63. 3. Robustness and Monte Carlo Analysis
Robustness to Filter
Filter Limit Cycle with F Limit Cycle with U
High-pass 40 X
High-pass 60 X
High-pass 70
High-pass 80
High-pass 90
High-pass 100 X
High-pass 120 X
HP 1600 X
t5 X
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64. 3. Robustness and Monte Carlo Analysis
Robustness to sample
Note that F is available up to 2007:1
Sample Limit Cycle with F Limit Cycle with U
1960:1-2014:4
1970:1-2014:4 X
1980:1-2014:4
1960:1-2006:4
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65. 2. Total Hours and Other Labor Market Variables
65 / 94

66. 3. Robustness and Monte Carlo Analysis
Monte Carlo Analysis
Is there anything mechanical in our procedure that “creates”
spurious limit cycles?
We answer that question by performing two Monte Carlo tests
66 / 94

67. 3. Robustness and Monte Carlo Analysis
Monte Carlo Analysis
Test A:
× Take an AR(2) as the DGP
× Simulate (sample size) and add the hours trend (t5
)
× Filter with High-pass 80
× Estimate our simple non-linear equation
× Do we find limit cycles (α4 significant at 10%, negative and
maximum eigenvalue > 1)
Test B:
× Take a simple model with limit cycle as the DGP
× Simulate (sample size) and add the hours trend (t5
)
× Filter with High-pass 80
× Estimate our simple non-linear equation
× Do we find limit cycles (α4 significant at 10%, negative and
maximum eigenvalue > 1)
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68. 3. Robustness and Monte Carlo Analysis
Monte Carlo Analysis
Test A
% of λmax > 1 .9
% of signif. LC .9
Our procedure does not create spurious limit cycles
68 / 94

69. 3. Robustness and Monte Carlo Analysis
Monte Carlo Analysis
Test B
% of λmax > 1 47.2
% of signif. LC 46.5
With our procedure, limit cycles are quite hard to detect
Explains why results are mixed for other countries
On top of that, our model is VERY restrictive in terms of non
linearity and error term structure
69 / 94

70. Roadmap
1. Reduced Form Model
2. Total Hours and Other Labor Market Variables
3. Robustness and Monte Carlo Analysis
4. Quantity Variables
5. What’s next
70 / 94

71. 5. What’s next
We think we have convincing evidence for limit cycle being
part of the story for business cycle (together with shocks)
The macroeconomy looks locally unstable
Implication for stabilization
× Are limit cycles a case for stabilization?
× Destabilizing effect of some macro policies?
× Stabilizing high frequencies fluctuations at the cost of
destabilizing low frequencies? (monetary policy, the great
moderation and the great recession)
71 / 94

72. 72 / 94

73. Roadmap
1. Reduced Form Model
2. Total Hours and Other Labor Market Variables
3. Robustness and Monte Carlo Analysis
4. Quantity Variables
5. What’s next
73 / 94

74. 4. Quantity Variables
Simple model
xt = α0 + α1xt−1 + α2xt−2 + α3Xt−1 + α4x3
t−1 + εt
Variable Limit Cycle
y X
y NFB X
Fixed i X
Struct.
Dur. X
Resid. X
Equip. X
c X
Util.
74 / 94

75. 4. Quantity Variables
Simple model
It is not a surprise that it is harder to detect limit cycles (if
there are) with quantities.
Yt = θtht
The high frequencies in θ enters in a very on linear way, and
are hard to get rid of
This is confirmed by the following Monte Carlo exercice
75 / 94

76. 4. Quantity Variables
Monte Carlo
Take the simple limit cycle equation as the DGP for hours
Simulate 10000 times and add the Hours trend (t5) and
Average labor productivity Y /h
Filter with High-pass 80
Estimate our simple non-linear equation
Do we find limit cycles (α4 significant at 10%, negative and
maximum eigenvalue > 1)?
76 / 94

77. 4. Quantity Variables
Monte Carlo
% of λmax > 1 17.4
% of signif. LC 15.5
77 / 94

78. 4. Quantity Variables
Monte Carlo
Figure 30: Distribution of λmax
0.94 0.96 0.98 1 1.02 1.04 1.06
λmax
0
5
10
15
20
25
30
35
%
78 / 94

79. 4. Quantity Variables
Extended model
xt = α0 + α1xt−1 + α2xt−2 + α3Xt−1 + εt
+α4x3
t−1 + α5x3
t−2 + α6X3
t−1 + α7X3
t−2 + α8x2
t−1Xt−1 + α9xt−1X2
t−1
Variable Limit Cycle p-value
α4 to α9
y X 8%
y NFB 5%
Fixed i X 5%
Struct. .6%
Dur. 2.5%
Resid. X 49%
Equip. X 9%
c .2%
Util. 2%
79 / 94

80. 4. Quantity Variables
y NFB
Ordinary Least-squares Estimates
Dependent Variable = x
R-squared = 0.9098
Durbin-Watson = 2.0121
Nobs, Nvars = 220, 10
***************************************************************
Variable Coefficient t-statistic t-probability
constant -0.054752 -0.777016 0.438024
x(-1) 1.147607 11.836131 0.000000
x(-2) -0.102091 -1.096783 0.273993
X2(-1) -0.008816 -0.969247 0.333537
x(-1)^3 -0.000605 -0.320916 0.748593
x(-2)^3 -0.003949 -2.046696 0.041934
X2(-1)^3 -0.000047 -0.453589 0.650593
X2(-2)^3 0.000032 0.363689 0.716456
x(-1)^2*X2(-1) 0.000636 1.050411 0.294737
X2(-1)^2*x(-1) 0.000110 0.334494 0.738341
p-value full vs AR (%) :0.092564
p-value full vs linear (%) :5.4029
Max Eigenvalue Modulus : Full :1.0027 [0.99859+0.090455i]
: AR :0.86919 [0.86919] 80 / 94

81. 4. Quantity Variables
y NFB
Figure 31: Cyclical Component
1960 1970 1980 1990 2000 2010 2020
-10
-8
-6
-4
-2
0
2
4
6
8
81 / 94

82. 4. Quantity Variables
y NFB
Figure 32: The Limit Cycle - Simulation as of T0 = 1961
-8 -6 -4 -2 0 2 4
xt
-40
-30
-20
-10
0
10
20
30
Xt
82 / 94

83. 4. Quantity Variables
y NFB
Figure 33: Forecasting as of 1961
1960 1970 1980 1990 2000 2010 2020
-10
-8
-6
-4
-2
0
2
4
6
8
83 / 94

84. 4. Quantity Variables
c
Figure 34: Cyclical Component
1960 1970 1980 1990 2000 2010 2020
-6
-4
-2
0
2
4
6
84 / 94

85. 4. Quantity Variables
c
Figure 35: The Limit Cycle - Simulation as of T0 = 1961
-4 -3 -2 -1 0 1 2 3
xt
-30
-20
-10
0
10
20
30
Xt
85 / 94

86. 4. Quantity Variables
c
Figure 36: Forecasting as of 1961
1960 1970 1980 1990 2000 2010 2020
-6
-4
-2
0
2
4
6
86 / 94

87. 4. Quantity Variables
Structures
Figure 37: Cyclical Component
1960 1970 1980 1990 2000 2010 2020
-30
-20
-10
0
10
20
30
87 / 94

88. 4. Quantity Variables
Structures
Figure 38: The Limit Cycle - Simulation as of T0 = 1961
-15 -10 -5 0 5 10 15
xt
-100
-50
0
50
100
Xt
88 / 94

89. 4. Quantity Variables
Structures
Figure 39: Forecasting as of 1961
1960 1970 1980 1990 2000 2010 2020
-30
-20
-10
0
10
20
30
89 / 94

90. Roadmap
1. Reduced Form Model
2. Total Hours and Other Labor Market Variables
3. Robustness and Monte Carlo Analysis
4. Quantity Variables
5. What’s next
90 / 94

91. 5. What’s next
We think we have convincing evidence for limit cycle being
part of the story for business cycle (together with shocks)
The macroeconomy looks locally unstable
Implication for stabilization
× Are limit cycles a case for stabilization?
× Destabilizing effect of some macro policies?
× Stabilizing high frequencies fluctuations at the cost of
destabilizing low frequencies? (monetary policy, the great
moderation and the great recession)
91 / 94

92. Roadmap
1. Reduced Form Model
2. Total Hours and Other Labor Market Variables
3. Robustness and Monte Carlo Analysis
4. Quantity Variables
5. What’s next
92 / 94

93. 5. What’s next
We think we have convincing evidence for limit cycle being
part of the story for business cycle (together with shocks)
The macroeconomy looks locally unstable
Implication for stabilization
× Are limit cycles a case for stabilization?
× Destabilizing effect of some macro policies?
× Stabilizing high frequencies fluctuations at the cost of
destabilizing low frequencies? (monetary policy, the great
moderation and the great recession)
93 / 94

94. 94 / 94