Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
1
Lecture 1
Business Cycle Facts
Version 1.1
20/11/2011
Changes from version 1.0 are in red
These are the slides I am using in class. They are not self-contained, do not always constitute original material and do contain some “cut and paste” pieces from various
sources that I am not always explicitly referring to (not on purpose but because it takes time). Therefore, they are not intended to be used outside of the course or to be distributed.
Thank you for signalling me typos or mistakes at [email protected].
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
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•
2
Introduction
Macroeconomics is about the determination of aggregate vari-
ables, as measured by national accounts (output, consumption,
employment, inflation,...)
•
Economists makes a distinction (at least at first pass) between
the long run and the short run, between Growth and Business
Cycle
•
For the methodological part of that lecture, I will consider the
U.S.A. as an example.
3
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
Figure 1: US log Real GDP per capita
9.5
9
8.5
8
7.5
7
1950
1960
1970
1980
Quarters
1990
2000
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
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4
Burns and Mitchell “Measuring Business Cycles” (1946, Na-
tional Bureau of Economic Research):
“Business cycles are a type of fluctuation found in the ag-
gregate economic activity of nations that organize their
work mainly in business enterprises: a cycle consists of
expansions occurring at about the same time in many economic activities, followed by similarly general recessions,
contractions, and revivals which merge into the expansion
phase of the next cycle.”
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
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5
To identify cycles, B&M assume that they are no shorter than
6 quarters, and found a maximum length of 32 quarters.
adjusted figures of coke production in the United States from 1914
through 1933, a series chosen because it is relatively short and presents
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
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few of the complications we ordinarily encounter. These figures are
plotted on Chart 1, which shows also the turning points of business cycles
and of the specific cycles in coke production. The average monthly proFigure
Reproduced
Burns and
Mitchell
Measuring
Busiduction 2:
of coke
during thefrom
first complete
specific
cycle (November
1914
ness Cycles (1946)
CHART
I
Coke Production, United States, 1914 1933
Coo
,,riattens. Shaded ares, represent r,f.resc.
skite ares, represent
r.f.r.nc. .epanstoris. Mt,rieks tdeottty
arid trovjh.s of ripecific cycle.. 5.. tabl. 4.
Mjust.d
Logarithmic vertical usia
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
Figure 3: A Business Cycle
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Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
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Figure 4: U.S. Business Cycles, as identified by the NBER’s Business Cycle Dating Committee
US Business Cycle Expansions and Contractions ¹
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Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
Contractions (recessions) start at the peak of a business cycle and end at the trough.
Please also see:
Latest announcement from the NBER's Business Cycle Dating Committee, dated 9/20/10.
Press citations on NBER Business Cycles
Table 1: Recent U.S. Business Cycles, as identified by the NBER’s
Business Cycle Dating Committee
BUSINESS CYCLE
REFERENCE DATES
Peak
Trough
Quarterly dates
are in parentheses
DURATION IN MONTHS
Contraction
Expansion
Cycle
file:///C:/Documents and
Settings/ishapiro/Desktop/cyclesma
Peak
to
Trough
Previous
trough
to
this peak
Trough
from
Previous
Trough
Peak
from
Previous
Peak
10
-11
18
16
8
6
32
16
18
24
-106
30
36
22
58
46
12
18
34
-117
48
52
30
64
78
28
36
32
-116
-47
40
74
54
18
50
October 1873(III)
July 1990(III)
March 1882(I)
2001(I)
March
December
2007 (IV)
March
1887(II)
February 1961
December
1854(I)(IV)
November 1858
1970 (IV)
(IV)
December
March1861
1975(III)
(I)
June
July 1980 (III)
December
1867 (I)
November 1870
1982 (IV)
(IV)
December
March 1879 (I)
March 1991(I)
November
2001 (IV)
May
1885 (II)
June 1888
2009 (I)
(II)
April
65
8
8
38
18
13
34
92
120
36
73
22
99
100
128
74
91
35
52
108
128
101
81
60
July 1890(III)
January 1893(I)
May 1891 (II)
June 1894 (II)
10
17
27
20
37
37
40
30
April 1960(II)
December
1969(IV)
June
1857(II)
November
1973(IV)
October
1860(III)
January
1980(I)
April
1865(I)
July 1981(III)
June
1869(II)
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
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Table 2: Average Length of Expansions and Recessions for the
U.S. Business Cycles (from the NBER) (in month)
1854-2009
1854-1919
1919-1945
1945-2009
(33 cycles)
(16 cycles)
(6 cycles)
(11 cycles)
Contraction Expansion
Cycle
P to T
T to P T to T P to P
16
42
56
55
22
27
48
49
18
35
53
53
11
59
73
66
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
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•
How does the NBER establish this chronology?
•
Here is the “Statement of the NBER Business Cycle Dating
Committee on the Determination of the Dates of Turning Points
in the U.S. Economy”.
“The NBER’s Business Cycle Dating Committee maintains a chronology of the U.S. business cycle.
The chronology comprises alternating dates of peaks and troughs in economic activity. A recession
is a period between a peak and a trough, and an expansion is a period between a trough and a peak.
During a recession, a significant decline in economic activity spreads across the economy and
can last from a few months to more than a year. Similarly, during an expansion, economic activity
rises substantially, spreads across the economy, and usually lasts for several years.
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
In both recessions and expansions, brief reversals in economic activity may occur – a recession may
include a short period of expansion followed by further decline; an expansion may include a short
period of contraction followed by further growth. The Committee applies its judgment
based on the above definitions of recessions and expansions and has no fixed rule
to determine whether a contraction is only a short interruption of an expansion,
or an expansion is only a short interruption of a contraction . The most recent
example of such a judgment that was less than obvious was in 1980-1982, when the Committee
determined that the contraction that began in 1981 was not a continuation of the one that began
in 1980, but rather a separate full recession.
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Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
The Committee does not have a fixed definition of economic activity . It examines
and compares the behavior of various measures of broad activity: real GDP measured on the
product and income sides, economy-wide employment, and real income. The Committee also may
consider indicators that do not cover the entire economy, such as real sales and the Federal Reserve’s
index of industrial production (IP). The Committee’s use of these indicators in conjunction with the
broad measures recognizes the issue of double-counting of sectors included in both those indicators
and the broad measures. Still, a well-defined peak or trough in real sales or IP might help to
determine the overall peak or trough dates, particularly if the economy-wide indicators are in
conflict or do not have well-defined peaks or troughs.”
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Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
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Is there a way to translate this into some statistical procedure?
•
What are the data that we shall use and how are they con-
structed?
•
What are the empirical regularities of BC?
These are the questions we will answer in this first lecture.
2
•
A First Look at Some Methods To Extract the
Cycle
Any time series yt = log Yt can be decomposed such that
yt = ytT
+ ytC
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
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•
Problem: How to define/identify each component?
•
Several ways of approaching the problem
•
Actually: Infinite number of decomposition of a non-stationary
process into a cycle and a trend
•
Let us see some ”intuitive” definition of those decompositions
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
2.1
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Growth Cycle
•
Take the growth rate of the series
•
Expansion: Positive rate of growth
•
Note: the cycle is very volatile (almost iid) – a lot of medium
run fluctuations are eliminated
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Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
Figure 5: US Growth Cycles
Trend
Cycle
9.5
0.06
9
0.04
8.5
0.02
8
0
7.5
−0.02
7
−0.04
1950 1960 1970 1980 1990 2000
Quarters
1950 1960 1970 1980 1990 2000
Quarters
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
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Trend Cycle
•
Deviation from linear trend
•
The trend is obtained from linear regression
yt = α + βt + ut
•
bt)
Cycle: ytC = yt − (b
α+β
•
Expansion: Output above the trend
•
Note: the cycle can be large and very persistent - a lot of
medium and long run fluctuations are not eliminated
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Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
Figure 6: US Trend Cycles
Trend
Cycle
9.5
0.1
9
0.05
8.5
0
8
−0.05
7.5
−0.1
7
−0.15
1950 1960 1970 1980 1990 2000
Quarters
1950 1960 1970 1980 1990 2000
Quarters
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
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Cycle = Output Gap
Define the Output gap as
Actual output − Potential Output
•
Expansion: Actual output > Potential output
•
Actual output: easy to observe
•
Note: How to identify potential output? (full utilization?, effi-
cient?)
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
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Example:
(1) estimate yt = α × ut + other controls + εt,
(2) define potential output as ytP = α
b × 0% + other controls +
b
εt. (One might choose u = un where un is the natural rate of
unemployment (the Oecd chooses the NAIRU (Non Accelerating
Inflation Rate of Unemployment))
•
Cycle is then yt − ytP
•
This is an over simplified description of the method used by
Oecd.
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Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
Figure 7: US Output Gap and Potential Output
US Output Gap (Oecd)
US Potential Output (Oecd)
4
30.6
30.4
2
30.2
30
log of current $
%
0
−2
−4
29.8
29.6
29.4
29.2
−6
29
−8
1960
1970
1980
1990
2000
2010
2020
28.8
1960
1970
1980
1990
2000
2010
2020
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
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• One could describe many other methods to extract the Business
Cycle.
•
Ideally, we want to get rid of very short run and long run
movements of economic activity.
• The best way to understand this is to decompose economic time
series into the frequency domain and filter them.
•
For this, we need to understand how a time series can be rep-
resented in the frequency domain.
• Here I am giving the main intuitions, a more rigorous treatment
will be done in an econometrics course.
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Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
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Decomposing a time series into frequency domain
3.1
Typical periodic functions
•
Idea: A series can be seen as the sum of periodic functions.
•
A typical periodic function is cos(ωt), with period (the time it
takes to reproduce itself) 2π/ω.
•
Knowing that period of cos(t) is 2π, for a given t1, what is
the t2 such that cos(ωt2) = cos(ωt1)?
•
The solution is t2 − t1 = 2π/ω.
ω
• 2π
is the frequency of oscillation
(number of cycles per unit of time)
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Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
Figure 8: Cosine wave with ω=1
1
0.8
0.6
0.4
cos
0.2
0
−0.2
−0.4
−0.6
−0.8
−1
0
•
2
4
6
8
10
12
14
With ω = 1, the period is 2π = 6.28 and frequency is
1
2π
= 0.16.
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Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
Figure 9: Cosine waves with ω=1 or 1/2
1
0.8
0.6
0.4
cos
0.2
0
−0.2
−0.4
−0.6
cos(t)
cos(t/2)
−0.8
−1
0
•
2
4
6
8
10
12
14
With ω = 1/2, the period is 4π = 12.56 and frequency is
0.08.
1
4π
=
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Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
Figure 10: Cosine waves with ω=1 and different amplitudes
2
1.5
1
cos
0.5
0
−0.5
−1
cos(t)
2cos(t)
−1.5
−2
0
•
2
4
6
8
10
12
14
Here are plotted A cos(t) with A = 1 or A = 2.
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
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• sin(ωt) behaves the same way,
with same amplitude and period,
but with a phase shift
Figure 11: Cosine and Sine waves with ω=1
1
0.8
0.6
0.4
cos
sin
cos,sin
0.2
0
−0.2
−0.4
−0.6
−0.8
−1
0
2
4
6
8
10
12
14
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
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The idea of spectral decomposition is that with sin and cos, we
can span the all space of covariance stationary time series : the
typical periodic function is
a cos(ωt) + b sin(ωt)
(1)
whose period is 2π/ω but whose phase and amplitude depend on
(a, b)
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
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There is always a sum of type (??) periodic functions that
reproduces a given time series
• The spectral density or spectrum of a series indicates the weight
of each frequency (from low to high) in the total variance of the
series.
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Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
3.2
•
An approximation of the spectrum
Assume that we observe yt over T (even) periods, and that it is
centered.
•
Our goal is to decompose yt into T /2 periodic functions of fre-
quencies ω1, ω2, ..., ωT /2, with
ωj
=
2πj
T
,
j
= 1, ..., T /2
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
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Then, we want to write yt as
yt
=
+
+
+
a1 cos(ω1t) + b1 sin(ω1t)
a2 cos(ω2t) + b2 sin(ω2t)
···
aT /2 cos(ωT /2t) + bT /2 sin(ωT /2t)
(2)
for t=1,...,T.
• We can then find the T
parameters (ai, bi) under the assumption
that (??) is true, by running simple OLS.
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Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts


cos(ω1) sin(ω1) · · · · · · cos(ωT /2) sin(ωT /2)
 cos(2ω1) sin(2ω1) · · · · · · cos(2ωT /2) sin(2ωT /2) 


..
..
..
..
..

X=


..
..
..
..
..


cos(T ω1) sin(T ω1) · · · · · · cos(T ωT /2) sin(T ωT /2)




y1
y2




 .. 

Y =
 .. 


 yT −1 
yT
•
a1
b1




 .. 

β=
 .. 


 aT /2 
bT /2
If we assume Y = Xβ + u, we can compute the a and b.
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
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The a and b coefficients are computed as
β
•
= (X 0X )−1X 0Y
Given that we have T explanatory variables for T observations,
the R2 is one and u = 0. Here we are just solving a representation
problem, not an estimation one.
•
Note that the last column of X is a column of 0. It is replaced
by a column of 1 to deal with non-centered series.
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Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
•
The coefficient are given by
aj
bj
=
=
T
X
2
T
2
T
for j≤T /2 − 1, and
aT /2
bT /2
•
=
=
t=1
T
X
1
T
(3)
sin(ωj t)yt
(4)
cos(ωT /2t)yt
(5)
yt
(6)
t=1
T
X
1
T
cos(ωj t)yt
t=1
T
X
t=1
This is of course an approximation of the series, that can be
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
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represented as
yt =
Z
π
(a(ω) cos(ωt) + b(ω) sin(ωt))dω
(7)
0
•
Any covariance stationary times series process can be repre-
sented in the form of (??).
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
3.3
•
37
Extracting the business cycle (BC) component
using the frequency domain representation
A representation like (??) allow us to make precise the notion
of extracting the business cycle component of yt.
•
Assume yt is observed on a quarterly basis, and that the BC is
defined as fluctuations of periods between 6 and 32 quarters (1.5
2π ].
to 8 years), i.e. for ω ∈ [ω ω] = [ 2π
,
32 6
•
The the BC component of y, denoted yC , is
Z ω
ytC =
(a(ω) cos(ωt) + b(ω) sin(ωt))dω
ω
(8)
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
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38
It can be shown that this spectral representation has a time-
series equivalent, which is an infinite two-sided moving average
of yt:
ytC
with B0 =
•
= B0 + B1(yt−1 + yt+1) + B2(yt−2 + yt+2) + · · ·
ω−ω
π
and Bj =
(9)
sin(ωj)−sin(ωj)
πj
Why things are not as simple as they look? We have to make
an approximation of (??) because it requires an infinity of observations. Therefore, the MA is truncated according to some
distance criterium
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
3.4
•
39
Filters
We consider here univariate stationary processes.
Definition 1 The autocovariance of a series Yt is defined as
λτ
= cov(Yt, Yt−τ ) = E (YtYt−τ ) with the assumption E (Yt) = 0;.
Definition 2 For a sequence a0, a1, ..., aj , ..., the generating
P
function of this sequence is a(z ) = j aj z j .
•
Note: z needs not to have any interpretation
The generating function (or z-transform) of a process Yt is
P
t.
Y (z ) =
Y
z
t
t
•
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Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
Definition 3 Given a sequence of autocovariance λτ , the
P
autocovariance generating function is λ(z ) = τ λτ z τ .
Why is this notation useful? Consider a stationary process Y (t)
Pn
with E (Yt) = 0, then define Yn(z ) = t=1 Ytz t, then
X
Yn(z )Yn(z −1) =
YtYsz t−s
•
t,s
and
E [Yn(z )Yn(z −1)] =
n
X
τ =−1
(n − |τ |)λτ z τ
41
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
and therefore
λ(z ) =
•
1
lim E [Yn(z )Yn(z −1)]s
n→∞ n
With these notation, there is a simple correspondence between
spectrum and auto-covariogram:
•
Assume z = e−iω = cos ω−i sin ω and define
+∞
X
1
1
λ(z ) =
s (ω ) =
λτ e−iωτ
2π
2π
τ =−∞
•
Then one can show that
λτ
=
Z
π
−π
eiτ ω s(ω )dω
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Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
λ0 =
Z
π
s(ω )dω
−π
•
The sequence of {λτ } and {s(ω)} bring the same information.
s(ω)
• The function λ
0
has the property of a probability function over
R π s(ω)
−π ≤ ω ≤ π : s(ω ) ≥ 0 and −π λ dω = 1.
0
• s (ω )
(rescaled) is the spectral density.
• Next is an estimate of the spectral density, from Groth, Ghil,
Hallegatte and Dumas, “Evidence from Genuine Periodicity
and Deterministic Causes of US Business Cycles”, 2010.
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Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
Figure 12: A Estimate of US GDP Spectral Density (1954-2005,
annual)
(b) Power spectral density
values
Covariance function
0.3
0.04
0.25
0.02
PSD
0.2
0
0.15
−0.02
−20
0.1
0
20
Time lag in quarters
0.05
1.5
2
0
0
0.5
1
f in 1/year
1.5
2
44
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
Definition 4 Let Ybt =
version of Yt.
•
.
Pm
j=0 cj Yt−j
= C (L)Yt. Ybt is a filtered
One can show that the spectral density of Ybt is
syb(ω ) = C (e−iω )C (eiω )sy (ω ) = |C (eiω )|2sy (ω )
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
3.5
Band Pass Filter
• c0 = 1, c2 = −2, c4 = −1
and cj = 0 for other j .
bt = C (L)Yt = Yt − 2(Yt−2 + Yt+2) − (Yt−4 + Yt+4)
•Y
•
Then
|C (eiω )|2 = 4(1 − cos 2ω )2
45
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Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
Figure 13: A Band Pass Filter
16
14
12
|C(ei ω)|2
10
8
6
4
2
0
0
0.5
1
1.5
2
frequency
2.5
3
3.5
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
47
• Here is an example of the use of Band Pass filters from Roberto
Pancrazi, “Spectral Covariance Instability Test: An Application to the Great Moderation”, TSE 2010.
•
High Frequency : periodicity between 2 and 32 quarters
•
Medium Frequency : periodicity between 32 and 80 quarters
•
High to Medium Frequency : periodicity between 2 and 80
quarters
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
48
Figure
1: GDP:
Level
Trend
Figure
14:
USand
GDP
Note: GDP is de…ned in real per-capita terms from NIPA. The sample includes quarterly observation from 1947:1 to 2007:4 The cyclical components, which are the High-Frequencies (HF, solid
ne), Medium-Frequencies (MF, dotted line), and High-to-Medium Frequencies (HM, dashed lin
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
49
re isolated using a band-pass …lter.
Figure 2: GDP: Cyclical Components
Figure 15: Various Cycles
Note: The cyclical components, which are the High-Frequencies (HF, solid line), Medium-Frequen
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
3.6
et =
•Y
Low Pass Filter
Pm
j=0 Yt−j .
Then
|C (eiω )|2
1 − cos(m + 1)ω
=
1 − cos ω
50
51
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
Figure 16: A Low Pass Filter
40
35
30
|C(ei ω)|2
25
20
15
10
5
0
0
0.5
1
1.5
2
frequency
2.5
3
3.5
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
3.7
•
First Difference
First difference Yet = (1 − L)Yt. Then
|C (eiω )|2 = 2 − 2 cos ω
52
53
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
Figure 17: First Difference
4
3.5
3
|C(ei ω)|2
2.5
2
1.5
1
0.5
0
0
0.5
1
1.5
2
frequency
2.5
3
3.5
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
3.8
54
A High Pass Filter: The Hoddrick-Prescott
Filter
•
Very popular in the macro literature
•
In the time domain, the idea is to remove a trend which is
smooth, but not linear
•
The trend ytT is the Argmin of:
T
X
t=1
(yt − ytT )2 + λ
T
X
T − y T ) − (x − x
2
((yt+1
))
t
t−1
t
t=2
•
if λ = +∞, it is linear detrending.
•
T − 4y T + (6 +
The solution of this program solves yt/λ = yt+2
t+1
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
55
T − yT
λ)ytT − 4yt−1
t−2
•
The solution is a symmetric MA of order +∞:
∞
X
ytT =
a|j|yt+j
j=−∞
•
Then ytC = yt − ytT is a time invariant linear symmetric filter.
•
With λ = 1600 on quarterly data, it removes cycles of period
greater than 10 years.
•
The transfer function is
2(1 − cos ω )4
16
λ
|C (eiω )|2 =
(1 + 4λ(1 − cos ω)2)2
56
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
Figure 18: Hoddrick-Prescott Filter
1
0.9
0.8
λ=1600
λ=4
|C(ei ω)|2
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.5
1
1.5
2
frequency
2.5
3
3.5
57
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
3.9
The HP filter at work
Figure 19: US HP Trend
9.5
9
8.5
8
7.5
7
1950
1960
1970
1980
Quarters
1990
2000
58
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
Figure 20: US HP Cycle
Trend
Cycle
9.5
0.04
9
0.02
0
8.5
−0.02
8
−0.04
7.5
−0.06
7
−0.08
1950 1960 1970 1980 1990 2000
Quarters
1950 1960 1970 1980 1990 2000
Quarters
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
4
•
59
Quick Overview of National Accounts
Data: we mainly consider aggregate quantities of goods and
services and prices, labor market statistics and interest rates.
•
Aggregate quantities of goods and services and prices mostly
come from national accounts.
•
Decent level of harmonization across countries (System of Na-
tional Accounts (SNA) promoted by the United Nations)
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
•
60
from the UN Handbook of National Accounting:
“The System of National Accounts (SNA) helps economists to measure the level of economic
development and the rate of economic growth, the change in consumption, saving, investment,
debts and wealth (or net worth) for not only the total economy but also each of its institutional
sectors (such as government, public and private corporations, households and non-profit institutions
serving households)”
•
I present here the basic concepts
•
This is mainly about definitions and conventions (“accounting”)
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
4.1
•
61
Supply and Use
For an economy, the total supply of goods and services must
equal the total uses
total supply of goods and services = total uses of goods and services
•
Expanding each side:
output + imports = intermediate consumption + final consumption + gross capital formation
+ exports
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
62
Note 1: Intermediate consumption consists of the goods and
services consumed in the production process (excluding the consumption of fixed assets)
Note 2: Final consumption consists of the goods and services
provided to the benefit of final consumers.
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
•
63
We then define gross value added (leave for a moment the issue
of taxes and subsidies on goods and services aside)
gross value added = output - intermediate consumption = final consumption + gross capital formation + exports - imports
•
Final consumption and gross fixed capital formation are mea-
sured from the perspective of the consumer or purchaser. Their
values take into account the taxes and subsidies on goods and
services.
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
•
64
Output is measured from the perspective of producers in terms
of the receipts receivable by them, leaving all of the taxes on
goods and services aside while including subsidies on goods and
services.
•
Therefore, taxes on goods and services have to be added to
output and subsidies subtracted from output in order to arrive
at a uniform valuation of supply and uses.
output + taxes - subsidies - intermediate consumption = final consumption + gross capital formation + exports - imports
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
4.2
•
65
Gross domestic product
GDP can be measured by having the values for output and in-
termediate consumption aggregated across the various industries
of an economy. This is GDP by production approach:
GDP = output + taxes - subsidies - intermediate consumption = gross value added + taxes
- subsidies
•
Gross domestic product can also be viewed as the value of all
goods and services available for different domestic final uses or
for exports. This is GDP by expenditure approach:
66
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
GDP = final consumption + gross capital formation + exports - imports
• The production process creates incomes for not
only the owners
of the inputs used in production but also for owners of capital and
for the government. The value of those incomes is equal to gross
domestic product. Hence, GDP can also be calculated as the
sum of compensation of employees, taxes less subsidies and gross
operating surplus/mixed income. This is the GDP by income
approach:
GDP = compensation of employees + taxes - subsidies + gross operating surplus / mixed income
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
4.3
67
Gross national income
• Gross domestic product refers to production of all resident units
within the borders of a country, which is not exactly the same as
the production of all productive activities of residents:
GNI = GDP + compensation of employees and property income from the rest of the world
- compensation of employees and property income to the rest of the world
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
•
68
All GNI is not available for final uses domestically since some
of it is transferred to other countries without anything being received in exchange (for example remittances)
gross national disposable income = GNI + current transfers from the rest of the world current transfers to the rest of the world
•
Gross national disposable income is the income available for
consumption and saving:
gross national disposable income = final consumption expenditure + gross saving
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
4.4
•
69
Gross saving, gross capital formation and net
lending
Gross saving together with net capital transfers (capital trans-
fers receivable less capital transfers payable) from the rest of the
world provides the resources for investment in non-financial assets, which is called gross capital formation.
•
Gross capital formation = the net acquisition of fixed assets,
such as residential and non-residential buildings, plants and equipments, the net acquisition of valuables and/or the increase in
inventories.
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
•
70
The difference between gross saving plus net capital transfers
and gross capital formation is net borrowing or net lending from
the rest of the world, depending whether uses exceed resources
or vice versa.
gross saving = gross national disposable income - final consumption
and
net lending (+) / net borrowing (-) = gross saving + net capital transfers - gross capital formation
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
4.5
•
71
Net borrowing / net lending in financial accounts
Net borrowing / net lending is also reflected in transactions in
financial assets and liabilities with the rest of the world. It is
equal to the difference between net acquisition of financial assets
and net incurrence of liabilities (foreign exchange, bonds, loans
etc.):
net lending (+) / net borrowing (-) = net acquisition of financial assets - net incurrence
of liabilities
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
4.6
•
72
Changes in net worth
Net worth is the difference between the total value of non-
financial and financial assets and the total value of liabilities of
an economy. It is a measure of the net wealth of a nation. Change
in net worth measures the change in wealth of a nation.
•
Net capital transfers from abroad are equal to gross capital
formation less consumption of fixed capital and plus net lending
(+)/net borrowing (-) from the rest of the world.
in balance
sheets
due toCycle
changes
Franck Portier – TSE 1.23.
– Macro IChanges
& II – 2011-2012
– Lecture
1 – Business
Facts
in prices include holding gains or losses
from the revaluation of financial and non-financial assets.
4.7
resulting
1.24. For the sake of simplicity, other changes in the volume of assets and changes in the balance
Summary
sheets due to changes in prices are not included in the sequence of accounts provided in table T 1.1.
TABLE T1.1. SIMPLIFIED SEQUENCE OF ACCOUNTS OF THE DOMESTIC ECONOMY
Uses
Less
Equals
Plus
Less
Equals
Plus
Less
Equals
Less
Equals
Production account
Output of goods and services
Intermediate consumption
Gross value added/GDP
Primary distribution of income account
Gross value added/GDP
Compensation of employees and property income receivable from the rest
of the world (ROW)
Compensation of employees and property income payable to ROW
Gross national income
Secondary distribution of income account
Gross national income
Current transfers receivable from ROW
Less current transfers payable to ROW
Gross disposable income
Use of income account
Gross disposable income
Final consumption
Gross saving
100
40
60
60
4
1
63
63
1
2
62
62
40
22
Uses
Less
Plus
Less
Equals
Capital account
Gross saving
Gross capital formation
Capital transfers from ROW
Capital transfers to ROW
Net lending to ROW
Financial account
Resources
Resources
22
15
1
1
7
Changes in
assets
Changes in
liabilities
73
Less
Gross capital formation
Plus
Capital transfers from ROW
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
Less
Capital transfers to ROW
Equals Net lending to ROW
Financial account
Net acquisition of financial assets
Money
Loans
Less Net incurrence of liabilities
Equals Net lending to ROW
Changes in the balance sheet due to transactions
Non-financial assets
Gross capital formation
Consumption of fixed capital
Less Financial assets/financial liabilities
Equals Net worth
15
1
1
7
Changes in
assets
Changes in
liabilities
3
4
0
7
Assets
15
-1
7
Liabilities
0
21
8
74
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
4.8
75
Definitions of Output, Consumption and Investment
Definition 5 Output is the value of the goods and services
which are produced by an establishment in the economy that
become available for use outside that establishment
Definition 6 Intermediate consumption includes goods and
services which are entirely used up by producers in the course
of production to produce output of goods and services during
the accounting period.
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
76
Definition 7 Final consumption includes goods and services
which are used by households or the community to satisfy
their individual wants and social needs. Consumption is broken down into a) Final consumption expenditure of households; b) Final consumption expenditure of general government; c) Final consumption expenditure of non-profit institutions serving households.
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
•
77
For households, all consumed goods, whether durable (cars, re-
frigerators, air-conditioners etc.) or non-durable (food, clothes),
are part of final consumption, with the exception of purchases for
own-construction or improvements of residential housing, which
are treated as part of gross capital formation.
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
78
Definition 8 Gross capital formation in SNA is the same
as the concept of investment in capital goods used by economists.
It includes only produced capital goods (machinery, buildings, roads, artistic originals etc.) and improvements to nonproduced assets. Gross capital formation measures the additions to the capital stock of buildings, equipment and inventories, i.e., the additions to the capacity to produce more goods
and income in the future.
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
4.9
•
79
Prices
Outputs, whether or not sold, are valued at market or “equiva-
lent market prices”.
•
There are three types of market prices of the same good due to
taxes and subsidies.
•
Basic price is the amount receivable by the producer from the
purchasers for a unit of output.
•
Then Producer price and Purchasers price are defined
FIGURE
F2.2.I &RELATIONSHIPS
BETWEEN
Franck Portier
– TSE – Macro
II – 2011-2012 – Lecture 1 – Business
Cycle FactsBASIC,
PRODUCER AND PURCHASERS’
80
PRICES
Taxes less subsidies
on products (including
non-deductible value
added taxes) on
consumers
Transport and trade
margins
Taxes less subsidies
on products
(including nondeductible value
added taxes) on
producers
BASIC PRICE
BASIC PRICE
Basic price
Producer price
PRODUCER PRICE
Purchasers’ price
FIGURE F2.3. PROCESS OF GOODS CIRCULATION ON THE MARKET
•
Output is recommended to be measured at production costs
Sphere where basic
and producer prices
when products haveTransport
no market
price.
and trade margins added
Sphere where
purchasers’ prices apply
apply
Producers
of goods
Wholesalers
and retailers
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
4.10
•
81
Nominal and Real Quantities
To compare quantities of two different years, one needs to ad-
just for changes in prices, to deflate nominal (current dollars)
measures in order to obtain real (constant dollars) quantities.
•
This is done (basically) by choosing a base year (year N ). The
real quantities of year N + 1 are then multiplied by their price in
year N to compute constant dollar measures (in dollars of year
N ).
•
This is easy for potatoes (always the same good), not so for
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
computers or cars (improvement in quality).
82
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
5
U.S. Business Cycles
5.1
•
Business Cycles = Comovements
Lucas’ definition:
“Recurrent fluctuations of macroeconomic aggregates
around trend”
•
Want to find regularities (Stylized facts)
83
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
•
•
84
Business Cycles are characterized by a set of statistics:
•
Volatilities of time series (standard deviations)
•
Comovements of time series (correlations, serial correlations)
Why only looking at the US?
“Though there is absolutely no theoretical reason to antic-
ipate it, one is led by the facts to conclude that, with respect to the qualitative behavior of co-movements among
series, business cycles are all alike.” (Lucas 1977)
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
5.2
85
Main Real Aggregates
•
Consumption (C ): Nondurables + Services
•
Investment (I ): Durables + Fixed Investment + Changes in
inventories
•
Government spending (G)
•
Output: C + I + G
•
Labor: hours worked
•
Labor Productivity: Output / Labor
86
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
Output
0.2
0.15
0.1
0.05
0
−0.05
−0.1
−0.15
−0.2
1950
1955
1960
1965
1970
1975 1980
Quarters
1985
1990
1995
2000
2005
87
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
Output – Consumption
0.2
0.15
0.1
0.05
0
−0.05
−0.1
−0.15
−0.2
1950
1955
1960
1965
1970
1975 1980
Quarters
1985
1990
1995
2000
2005
88
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
Output – Consumption – Investment
0.2
0.15
0.1
0.05
0
−0.05
−0.1
−0.15
−0.2
1950
1955
1960
1965
1970
1975 1980
Quarters
1985
1990
1995
2000
2005
89
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
Output – Hours worked
0.04
0.03
0.02
0.01
0
−0.01
−0.02
−0.03
−0.04
−0.05
−0.06
1950
1955
1960
1965
1970
1975 1980
Quarters
1985
1990
1995
2000
2005
90
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
Output – Productivity
0.04
0.03
0.02
0.01
0
−0.01
−0.02
−0.03
−0.04
−0.05
−0.06
1950
1955
1960
1965
1970
1975 1980
Quarters
1985
1990
1995
2000
2005
91
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
Productivity – Hours worked
0.04
0.03
0.02
0.01
0
−0.01
−0.02
−0.03
−0.04
−0.05
−0.06
1950
1955
1960
1965
1970
1975 1980
Quarters
1985
1990
1995
2000
2005
Ch. 1:
15
Business Cycle Fluctuations in US Macroeconomic Time Series
Franck Portier – TSE – Macro I & II – 2011-2012
Lecture 1 changes
– Business
Facts
be –percentage
at anCycle
annual
rate). Interest rates, spreads, capacity utilization,
and the unemployment rate are used without further transformation.
The graphical presentations in this section cover the period 1947:I-1996:IV The
early years of this period were dominated by some special features such as the
peacetime conversion following World War II and the Korean war and the associated
price controls. Our statistical analysis therefore is restricted to the period 1953:I1996:IV
Three sets of empirical evidence are presented for each of the three series. This
evidence examines comovements between each series and real GDR Although the
business cycle technically is defined by comovements across many sectors and series,
fluctuations in aggregate output are at the core of the business cycle so the cyclical
component of real GDP is a useful proxy for the overall business cycle and is thus a
useful benchmark for comparisons across series.
First, the cyclical component of each series (obtained using the bandpass filter)
is plotted, along with the cyclical component of output, for the period t947-1996.
For series in logarithms, the business cycle components have been multiplied by 100,
so that they can be interpreted as percent deviation from long run trend. No further
transformations have been applied to series already expressed in percentage points
(inflation rates, interest rates, etc.). These plots appear in Figures 3.1-3.70. Note that
the vertical scales of the plots differ. The thick line in each figure is the cyclical
component of the series described in the figure caption, and the thin line is the cyclical
component of real GDR Relative amplitudes can be seen by comparing the series to
aggregate output.
5.3
•
92
More (Much More) Data
Those figures are taken from Stock and Watson, “Business
Cycle Fluctuations in US Macroeconomics Time Series”, chapter
1 of the Handbook of Macroeconomics, 1999
•
Quarterly US data, 1947-1997
co
~¢
i r
i [
ii
i i
ii
i i
ii
i i
i i
r i
/~
II
I
I
II
:'d . . . .
ol
',1'
I 47
]]
[I
, ii
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52
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,,, ......
57
62
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67
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77
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82
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92
....
87
Fig. 3.1. Contract and constructionemployment.
~'¢
I I
II
II
i° I
~ I/I
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n l ~ / / ~
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i \~ ~
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52
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62
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77
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i ~
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I i
82
Date
Fig. 3.2. Manufacturingemployment.
,,
ii
87
92
~-
93
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
16
JH. Stock and M.W. Watson
[ I
~
~,,r
~ |
e/
/I
I I
[ I
I
I
~/
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ii
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Fig. 3.3. Finance, insurance and real estate employment.
to
I
'~03
I
c t/~[
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[
f
[
[
i V
I I
n/
[I
[I
II
[ 47
I
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II
II
IE
I I
ii
I
I
57
52
62
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[
I
[
I
I
I
j
I
I
67
I
I
I
[
I
I
i
I
iv
I
72
II
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II
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I
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77
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Fig. 3.4. Mining employment.
I
~1
[I
I
[
I [
5.7[ J
I
I
I
[
J
I
[
I
I
52
82
67
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.
I
I
I
I
72
If
II
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77
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II
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82
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Fig. 3.5. Government employment.
~1
I I
I I
I I
I
~
~"¢" " ~
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-~
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Fig. 3.6. Service employment.
el
I
I
II
7
52
[ [
57
I I
I I
62
67
I
I
I
I
I
I
[
[ - I [
72
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I / / ~
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II
II
77
I
I
I
II
II
I
82
Fig. 3.7. Wholesale and retail trade employment.
I
.]
87
f12
97
94
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
Ch. 1:
17
Business Cycle Fluctuations in US Macroeconomic Time Series
N
I
I
'tt'//
47
I I
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,llll tk// ,V ~
,,,,,,,//
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Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
25
Ch. 1." Business Cycle Fluctuations in US Macroeconomic 7~me Series
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87
92
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103
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
26
JH. Stock and M. W. Watson
7~
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104
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
27
Ch. 1." Business Cycle Fluctuations in US Macroeconomic Time Series
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97
105
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
J.H. Stock and M.W. Watson
28
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106
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
Ch. 1." Business Cycle Fluctuations in US Macroeconomic Time Series
29
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Fig. 3.70. Industrial production, Germany.
Second, the comovements evident in these figures are quantified in Table 2, which
reports the cross-correlation of the cyclical component of each series with the cyclical
component of real GDR Specifically, this is the correlation between xt and Y~+k, where
x¢ is the bandpass filtered (transformed) series listed in the first column and Yt+k is
the k-quarter lead of the filtered logarithm of real GDE A large positive correlation
at k = 0 indicates procyclical behavior of the series; a large negative correlation at
k = 0 indicates countercyclical behavior; and a maximum correlation at, for example,
k = - i indicates that the cyclical component of the series tends to lag the aggregate
business cycle by one quarter. Also reported in Table 2 is the standard deviation of
the cyclical component of each of the series. These standard deviations are comparable
across series only when the series have the same units. For the series that appear in
logarithms, the units correspond to percentage deviations from trend growth paths.
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
5.4
•
107
Moments
We want to characterize fluctuations ; amplitude and movements
•
Amplitude: volatilities ; standard deviations
•
Comovements: correlations
108
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
Variable
Output
Consumption
Services
Non Durables
Investment
Fixed investment
Durables
Changes in inventories
Hours worked
Labor productivity
σ (·) σ (·)/σ (y ) ρ(·, y ) ρ(·, h)
1.70
0.80
1.11
0.72
6.49
5.08
5.23
22.48
1.69
0.90
–
0.47
0.66
0.42
3.83
3.00
3.09
13.26
1.00
0.53
–
0.78
0.72
0.71
0.84
0.80
0.58
0.48
0.86
0.41
Auto(1)
–
0.84
–
0.83
–
0.80
–
0.77
–
0.81
–
0.88
–
0.72
–
0.40
–
0.89
0.09 0.69
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
109
Summary
1. Consumption (of non-durables) is less volatile than output
2. Investment is more volatile than output
3. Hours worked are as volatile as output
4. Capital is much less volatile than output
5. Labor productivity is less volatile than output
6. Real wage is much less volatile than output
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
110
7. All those variables are persistent and procyclical except Labor
productivity that is acyclical
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
•
111
Quoting Lucas 1977 “Understanding Business Cycles”
1. Output movements across broadly defined sectors move together.
2. Production of producer and consumer durables exhibits much
greater amplitude than does the production of nondurables
3. Production and prices of agricultural goods and natural resources have lower than average conformity.
4. Business profits show high conformity and much greater amplitude than other series.
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
112
5. Prices generally are procyclical.
6. Short-term interest rates are procyclical; long-term rates slightly
so.
7. Monetary aggregates and velocity measures are procyclical.
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
5.5
•
113
Some Other Countries
From Fiorito and Kollintzas, “Stylized facts of business
cycles in the G7 from a real business cycles perspective”, European Economic Review, 1994.
•
Quarterly data 1960-1989
114
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
Table
Cross correlations
Variable
______-
Vol.
(I) Real GNP/GDP
I .74
irkA
I .39
Canada
I.53
Japan
1.69
Germany
0.90
France
1.54
UK
1.70
Italy
(2) Consumption
us
Canada
Japan
Germany
France
UK
kdy
of real GNP/GDP
X,_,
.
I
with the components
of spending,
income.
-
_
0.01
-0.12
0.02
-0.02
-0.06
-0.02
-0.21
expenditure
1.29
0.32
1.27
-0.08
1.33
-0.10
I.53
0.1 I
0.86
-0.27
I .67
0.03
1.1’) -0. IS
0.2 I
0.04
0.19
0.23
0.10
0.07
-0.04
0.48
0.16
0.08
0.26
0.42
0. I 3
0.07
and outout
in levels. a.b
X ,+2
X ,+3
X ,+4
X *+5
0.41
0.27
0.38
0.35
0.30
0.20
0.22
0.65
0.51
0.59
0.46
0.54
0.37
0.52
0.85
0.78
0.78
0.67
0.77
0.55
0.80
1.0
I.0
I.0
1.0
I.0
I.0
I.0
0.85
0.78
0.78
0.67
0.77
0.55
0.80
0.65
0.51
0.59
0.46
0.54
0.37
0.52
0.41
0.27
0.38
0.35
0.30
0.20
0.22
0.21
0.04
0.19
0.23
0.10
0.07
-0.04
0.0 I
-0.12
0.02
-0.02
-0.06
-0.02
-0.21
0.59
0.40
0.28
0.37
-0.63
0.34
0.72
0.57
0.42
0.46
0.73
0.30
0.5’)
0.79
0.72
0.56
0.58
0.72
0.46
0.74
0.80
0.79
0.72
0.69
0.62
0.67
0.78
0.63
0.65
0.54
0.55
0.30
0.42
0.69
0.43
0.44
0.40
0.49
0.10
0.3x
0.50
0.22
0.21
0.22
0.38
-0.14
0.26
0.25
0.00
0.06
0.01
0.32
0.25
0. IO
0.03
-0.17
-0.03
-0.11
0.21
-0.32
0.08
- 0. I 5
0.47
-0.07
0.23
0.67
0. I 8
0.45
0.83
0.40
0.64
0.90
0.53
0.83
0.78
0.52
0.78
0.59
0.41
0.69
0.35
0.32
0.51
0.12
0.21
0.29
-0.09
0.14
0.05
0.30
(3) I:ixed invcslment
US
Canada
Japan
5.51
4.60
4.57
0.14
-0.43
-0.11
0.30
-0.29
0.04
115
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
Germany
France
UK
Italy
(5) Equipment
US
Canada
Japan
Germany
France
UK
Italy
(6) Construction
us
Canada
Japan
Germany
France _
UK
Italy
(7) Inventory
us
Canada
Japan
Germany
France
UK
Wy
(8) Government
US
Canada
Japan
Germany
France
UK
Italy
4.90
2.70
3.57
4.88
0.04
-0.11
-0.11
-0.16
0.26
0.06
-0.04
-0.00
0.37
0.26
0.08
0.23
0.42
0.46
0.23
0.47
0.60
0.66
0.33
0.70
0.84
0.78
0.60
0.88
0.54
0.69
0.53
0.81
0.42
0.57
0.38
0.67
0.37
0.41
0.31
0.47
0.29
0.25
0.23
0.25
0.12
0.13
0.05
0.05
investment
6.28
7.13
5.96
6.09
3.90
4.88
7.92
-0.13
-0.49
-0.09
0.12
0.08
-0.12
-0.15
0.02
-0.35
0.02
0.36
-0.23
-0.07
0.01
0.21
-0.18
0.17
0.48
0.39
0.05
0.25
0.46
0.03
0.38
0.52
0.58
0.21
0.48
0.68
0.27
0.58
0.61
0.70
0.38
0.69
0.86
0.43
0.74
0.73
0.74
0.56
0.85
0.87
0.51
0.73
0.58
0.53
0.51
0.74
0.77
0.53
0.69
0.49
0.31
0.47
0.57
0.59
0.50
0.54
0.39
0.12
0.44
0.38
0.38
0.34
0.34
0.23
-0.06
0.32
0.14
0.18
0.25
0.14
0.09
-0.17
0.25
-0.05
investment
6.26
0.31
3.83
-0.23
5.58
-0.04
5.56
0.00
2.49
-0.25
3.90
0.15
3.57
-0.11
0.45
-0.12
0.09
0.15
-0.11
0.19
0.00
0.57
0.10
0.23
0.22
0.08
0.28
0.18
0.70
0.34
0.31
0.27
0.25
0.26
0.36
0.80
0.50
0.32
0.47
0.48
0.21
0.57
0.78
0.55
0.43
0.72
0.65
0.38
0.74
0.58
0.41
0.35
0.40
0.65
0.27
0.74
0.35
0.18
0.18
0.28
0.65
0.08
0.65
0.11
0.06
0.07
0.27
0.54
-0.00
0.50
-0.10
0.01
-0.05
0.25
0.45
-0.08
0.36
-0.27
-0.04
-0.18
0.10
0.33
-0.24
0.20
0.08
0.15
-0.03
0.19
-0.09
0.12
0. IO
0.22
0.25
0.07
0.31
- 0.04
0. I6
0.2 I
0.35
0.43
0.23
0.32
0.05
0.26
0.39
0.49
0.60
0.38
0.33
0.22
0.42
0.51
0.64
0.68
0.38
0.35
0.47
0.55
0.56
0.48
0.53
0.38
0.29
0.44
0.38
0.32
0.26
0.33
0.25
0.14
0.25
0. I9
o.txl
0.03
0.06
0.20
0.02
0.16
O.ofl
- 0.24
-0.14
-0.18
0.20
-0.13
-0.05
- 0.08
- 0.4 1
-0.30
-0.32
0.10
-0.27
-0.27
-- 0. I7
- 0.4x
-0.04
-0.20
0.33
-0.11
0.6 I
-0.03
0.18
0.00
-0.24
0.30
-0.13
0.56
- 0.07
0.05
0.06
-0.23
0.28
-0.10
0.46
-0.06
-0.14
0.1 I
-0.20
0.30
- 0.06
0.32
0.02
-0.30
0.19
-0.12
0.32
0.05
0.18
0.04
-0.39
0.24
-0.09
0.04
0.06
-0.07
-0.05
-0.43
0.27
-0.08
-0.05
0.16
-0.23
-0.01
-0.41
0.30
0.05
-0.08
0.23
-0.31
- 0.07
-0.33
0.35
0.14
-0.05
0.36
-0.30
-0.05
-0.21
0.37
0.18
-0.06
0.4 I
-0.24
0.04
-0.04
changes
18.2
35.4
45.4
49.2
30.1
26.6
66.X
-0.01
0.07
-0.05
0.07
-0.15
0.03
- 0.07
tiniil consumption
1.98
-0.07
1.46
-0.18
2.89
0.25
1.47
-0.19
0.70
0.46
1.43
-0.09
0.60
0.30
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
5.6
116
International Business Cycles
•
The cross-correlations of output are high
•
The cross-correlations of output are higher than the one of
productivity
• The cross-correlations of productivity are higher than the cross-
correlations of consumption.
•
The cross-correlations of output, investment and employment
are generally positive.
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts
•
117
See the following table from Ambler, Cardia and Zimmer-
mann, “International business cycles: What are the facts?”, Journal of Monetary Economics, 2004.
ARTICLE IN PRESS
118
260
S. Ambler et al. / Journal of Monetary Economics 51 (2004) 257–276
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture
1 – Business
Cycle Facts
Table 1
Average cross-correlations
Averages from 190 cross-correlations
From BKK (1995)
Full sample
1960:1–2000:4
1973:1–1990:4
Europe-U.S.
1970:1–1990:2
Baseline model
1973:1–2000:4
Output
0.22
(0.03)
0.00
0.28
(0.03)
0.00
0.30
(0.03)
0.00
0.66
0.21
Consumption
0.14
(0.02)
0.00
0.15
(0.03)
0.00
0.14
(0.03)
0.00
0.51
0.88
Investment
0.18
(0.04)
0.00
0.22
(0.04)
0.00
0.22
(0.03)
0.00
0.53
0.31
Employment
0.20
(0.03)
0.00
0.22
(0.03)
0.00
0.21
(0.04)
0.00
0.33
0.31
Total hours
0.26
(0.04)
0.00
0.29
(0.04)
0.00
0.26
(0.03)
0.00
Employmenta
0.25
(0.04)
0.00
0.26
(0.04)
0.00
0.25
(0.05)
0.00
Productivity
(from y and n only)
0.16
(0.02)
0.00
0.21
(0.02)
0.00
0.24
(0.03)
0.00
0.56
0.25
Productivity
(best available)b
0.09
(0.02)
0.00
0.11
(0.02)
0.00
0.13
(0.02)
0.00
Variable
First line: average correlation. Second line: standard deviation of average correlation. Third line: marginal
significance level of average correlation.
a
Countries for which total hours are measured.
b
Capital stock and hours when available, otherwise y and n only.
6