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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 fportier@cict.fr.
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 2
1 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.
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 3
Figure 1: US log Real GDP per capita
1950 1960 1970 1980 1990 20007
7.5
8
8.5
9
9.5
Quarters
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 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 eco-
nomic 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 5
• To identify cycles, B&M assume that they are no shorter than
6 quarters, and found a maximum length of 32 quarters.
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 6
Figure 2: Reproduced from Burns and Mitchell Measuring Busi-ness Cycles (1946)
REFERENCE AND SPECIFIC CYCLES 25
ureswe TABLE 4andard Coke Production, United States, 1914—1933
(Thousands of short tons)
Year Jan. Feb. Mar. Apr. May June July Aug. Sep. Oct. Nov. Dcc
1 1914 2973 3147 3476 3364 2940 2897 2991 2927 2797 2531 2193 2348cies 1915 2281 2555 2675 2897 2990 3410 3613 3873 3959 4320 4475 4553
1916 4381 4564 4554 4425 4581 4581 4392 4667 4684 4655 4593 4499usiness
1917 4664 4523 4672 4720 4693 4778 4731 4611 4693 4542 4577 4452
nsions, 1918 3855 3957 4415 4639 4801 4941 5228 5067 5033 5017 4844 47301919 4763 4126 3773 3335 2977 3173 3777 3987 3943 3157 3600 3624
we can 1920 4329 4261 4360 3885 4031 4299 4412 4536 4520 4496 4284 3971
e have 1921 3314 2886 2203 1855 1860 1679 1497 1637 1719 2076 2231 23381922 2391 2512 2658 2798 2979 3180 3038 2413 2927 3638 4145 43421923 4650 4695 4853 5174 5250 5216 5076 4901 4641 4362 4132 4107
peaks. 1924 4278 4493 4386 4199 3581 3108 2923 2936 3132 3466 3596 4182
for the 1925 4599 4458 4259 4204 3950 3900 3804 3838 4102 4333 4836 5087
and at192ô 5244 5280 4746 4719 4643 4635 4721 4606 4578 4604 4665 44951927 4471 4426 4521 4553 4389 4320 4219 4219 4112 4027 3887 3991
points 1928 4249 4348 4276 4365 4450 4413 4286 4344 4332 4524 4569 46881929 4822 4798 4889 5005 5250 5311 5361 5295 5000 4961 4761 4502
e more 1930 4441 4480 4387 4562 4460 4316 4041 3817 3579 3480 3280 3193re have
1931 3195 3193 3187 3266 3167 2870 2682 2522 2396 2403 2356 2277
those 19.32 2150 2174 2037 1948 1761 1619 1586 1522 1598 1741 1817 18461933 1853 1819 1664 1720 1948 2363 2928 3029 2803 2553 2443 2523
r than —Adjusted for seasonal variations. The original data come from the Bureau of Mines, Mineral Rosourc,s of :h.
United State; 1925, Part LI, p. 545, and later annual numbers (flow called Minerals Yearbook).
it into
the respect to the reference-cycle relatives, except that they show movementscessive during specific cycles.cycle' To exemplify these steps: Table 4 shows by months the seasonally
luring adjusted figures of coke production in the United States from 1914base; through 1933, a series chosen because it is relatively short and presents
cation few of the complications we ordinarily encounter. These figures areiCtiOfl plotted on Chart 1, which shows also the turning points of business cyclesrerage and of the specific cycles in coke production. The average monthly pro-corn- duction of coke during the first complete specific cycle (November 1914
uringCHART I
ation Coke Production, United States, 1914 1933
clicaldates
some
ecificiputeit theevery
tion of'ote theOn) t.hC Mjust.d 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. Logarithmic vertical usia
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 7
Figure 3: A Business Cycle
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 8
Figure 4: U.S. Business Cycles, as identified by the NBER’s Busi-ness Cycle Dating Committee
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 9
Table 1: Recent U.S. Business Cycles, as identified by the NBER’sBusiness Cycle Dating Committee
US Business Cycle Expansions and Contractions ¹
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
BUSINESS CYCLEREFERENCE DATES DURATION IN MONTHS
Peak Trough Contraction Expansion Cycle
Quarterly datesare in parentheses
Peakto
Trough
Previoustrough
tothis peak
Troughfrom
PreviousTrough
Peakfrom
PreviousPeak
June 1857(II)October 1860(III)April 1865(I)June 1869(II)October 1873(III)
March 1882(I)March 1887(II)July 1890(III)January 1893(I)December 1895(IV)
June 1899(III)September 1902(IV)May 1907(II)January 1910(I)January 1913(I)
August 1918(III)January 1920(I)May 1923(II)October 1926(III)August 1929(III)
May 1937(II)February 1945(I)November 1948(IV)July 1953(II)August 1957(III)
December 1854 (IV)December 1858 (IV)June 1861 (III)December 1867 (I)December 1870 (IV)March 1879 (I)
May 1885 (II)April 1888 (I)May 1891 (II)June 1894 (II)June 1897 (II)
December 1900 (IV)August 1904 (III)June 1908 (II)January 1912 (IV)December 1914 (IV)
March 1919 (I)July 1921 (III)July 1924 (III)November 1927 (IV)March 1933 (I)
June 1938 (II)October 1945 (IV)October 1949 (IV)May 1954 (II)April 1958 (II)
--188321865
3813101718
1823132423
718141343
13811108
--3022461834
3622272018
2421331912
4410222721
5080374539
--4830783699
7435373736
4244464335
5128364064
6388485547
----40545052
10160403035
4239563236
6717404134
9393455649
file:///C:/Documents and Settings/ishapiro/Desktop/cyclesmain.html
1 of 2 9/20/2010 4:47 PM
April 1960(II)December 1969(IV)November 1973(IV)January 1980(I)July 1981(III)
July 1990(III)March 2001(I)December 2007 (IV)
February 1961 (I)November 1970 (IV)March 1975 (I)July 1980 (III)November 1982 (IV)
March 1991(I)November 2001 (IV)June 2009 (II)
101116616
8818
24106365812
9212073
34117526428
10012891
32116477418
10812881
Average, all cycles:1854-2009 (33 cycles)1854-1919 (16 cycles)1919-1945 (6 cycles)1945-2009 (11 cycles)
16221811
42273559
56485373
55*
49**5366
* 32 cycles** 15 cycles
Source: NBER
file:///C:/Documents and Settings/ishapiro/Desktop/cyclesmain.html
2 of 2 9/20/2010 4:47 PM
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 10
Table 2: Average Length of Expansions and Recessions for theU.S. Business Cycles (from the NBER) (in month)
Contraction Expansion CycleP to T T to P T to T P to P
1854-2009 (33 cycles) 16 42 56 551854-1919 (16 cycles) 22 27 48 491919-1945 (6 cycles) 18 35 53 531945-2009 (11 cycles) 11 59 73 66
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 11
• 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 12
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.
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 13
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.”
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 14
• 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 theCycle
• Any time series yt = log Yt can be decomposed such that
yt = yTt + yCt
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 15
• 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 16
2.1 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
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 17
Figure 5: US Growth Cycles
1950 1960 1970 1980 1990 20007
7.5
8
8.5
9
9.5
Quarters
Trend
1950 1960 1970 1980 1990 2000−0.04
−0.02
0
0.02
0.04
0.06
Quarters
Cycle
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 18
2.2 Trend Cycle
• Deviation from linear trend
• The trend is obtained from linear regression
yt = α+ βt+ ut
• Cycle: yCt = yt − (α+ βt)
• 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
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 19
Figure 6: US Trend Cycles
1950 1960 1970 1980 1990 20007
7.5
8
8.5
9
9.5
Quarters
Trend
1950 1960 1970 1980 1990 2000−0.15
−0.1
−0.05
0
0.05
0.1
Quarters
Cycle
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 20
2.3 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 21
• Example:
(1) estimate yt = α × ut + other controls + εt,
(2) define potential output as yPt = α × 0% + other controls +
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 − yPt
• This is an over simplified description of the method used by
Oecd.
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 22
Figure 7: US Output Gap and Potential Output
1960 1970 1980 1990 2000 2010 2020−8
−6
−4
−2
0
2
4
%
US Output Gap (Oecd)
1960 1970 1980 1990 2000 2010 202028.8
29
29.2
29.4
29.6
29.8
30
30.2
30.4
30.6
log
of c
urre
nt $
US Potential Output (Oecd)
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 23
• 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.
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 24
3 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.
• ω2π is the frequency of oscillation (number of cycles per unit of time)
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 25
Figure 8: Cosine wave with ω=1
0 2 4 6 8 10 12 14−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
cos
• With ω = 1, the period is 2π = 6.28 and frequency is 12π = 0.16.
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 26
Figure 9: Cosine waves with ω=1 or 1/2
0 2 4 6 8 10 12 14−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
cos
cos(t)cos(t/2)
• With ω = 1/2, the period is 4π = 12.56 and frequency is 14π =
0.08.
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 27
Figure 10: Cosine waves with ω=1 and different amplitudes
0 2 4 6 8 10 12 14−2
−1.5
−1
−0.5
0
0.5
1
1.5
2
cos
cos(t)2cos(t)
• 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 28
• 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
0 2 4 6 8 10 12 14−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
cos,
sin
cossin
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 29
• 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 30
• 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.
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 31
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 =2πjT, j = 1, ..., T/2
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 32
• 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.
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 33
X =
cos(ω1) sin(ω1) · · · · · · cos(ωT/2) sin(ωT/2)cos(2ω1) sin(2ω1) · · · · · · cos(2ωT/2) sin(2ωT/2)
... ... ... ... ...
... ... ... ... ...cos(Tω1) sin(Tω1) · · · · · · cos(TωT/2) sin(TωT/2)
Y =
y1
y2......
yT−1
yT
β =
a1
b1......
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 34
The a and b coefficients are computed as
β = (X ′X)−1X ′Y
• 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.
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 35
• The coefficient are given by
aj =2T
T∑
t=1
cos(ωjt)yt (3)
bj =2T
T∑
t=1
sin(ωjt)yt (4)
for j≤T/2− 1, and
aT/2 =1T
T∑
t=1
cos(ωT/2t)yt (5)
bT/2 =1T
T∑
t=1
yt (6)
• 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 36
represented as
yt =
∫ π
0
(a(ω) cos(ωt) + b(ω) sin(ωt))dω (7)
• 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 37
3.3 Extracting the business cycle (BC) componentusing 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
to 8 years), i.e. for ω ∈ [ω ω] = [2π32 ,
2π6 ].
• The the BC component of y, denoted yC, is
yCt =
∫ ω
ω
(a(ω) cos(ωt) + b(ω) sin(ωt))dω (8)
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 38
• It can be shown that this spectral representation has a time-
series equivalent, which is an infinite two-sided moving average
of yt:
yCt = B0 +B1(yt−1 + yt+1) +B2(yt−2 + yt+2) + · · · (9)
with B0 = ω−ωπ and Bj = 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 ob-
servations. Therefore, the MA is truncated according to some
distance criterium
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 39
3.4 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
function of this sequence is a(z) =∑
j ajzj.
• Note: z needs not to have any interpretation
• The generating function (or z-transform) of a process Yt is
Y (z) =∑
t Ytzt.
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 40
Definition 3 Given a sequence of autocovariance λτ , the
autocovariance generating function is λ(z) =∑
τ λτzτ .
•Why is this notation useful? Consider a stationary process Y (t)
with E(Yt) = 0, then define Yn(z) =∑n
t=1 Ytzt, then
Yn(z)Yn(z−1) =∑
t,s
YtYszt−s
and
E[Yn(z)Yn(z−1)] =n∑
τ=−1
(n− |τ |)λτzτ
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 41
and therefore
λ(z) = limn→∞
1nE[Yn(z)Yn(z−1)]s
• With these notation, there is a simple correspondence between
spectrum and auto-covariogram:
• Assume z = e−iω = cosω−i sinω and define
s(ω) =12πλ(z) =
12π
+∞∑
τ=−∞
λτe−iωτ
• Then one can show that
λτ =
∫ π
−πeiτωs(ω)dω
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 42
λ0 =
∫ π
−πs(ω)dω
• The sequence of {λτ} and {s(ω)} bring the same information.
• The function s(ω)λ0
has the property of a probability function over
−π ≤ ω ≤ π: s(ω) ≥ 0 and∫ π−π
s(ω)λ0dω = 1.
• 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.
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 43
Figure 12: A Estimate of US GDP Spectral Density (1954-2005,annual)
8 A. GROTH, M. GHIL, S. HALLEGATTE AND P. DUMAS
0 0.5 1 1.5 20
0.05
0.1
0.15
0.2
(a) Spectrum of eigenvalues
f in 1/year
λ
0 0.5 1 1.5 20
0.05
0.1
0.15
0.2
0.25
0.3
f in 1/year
(b) Power spectral densityP
SD
−20 0 20−0.02
0
0.02
0.04Covariance function
Time lag in quarters
Figure 2.— Univariate spectral analysis of U.S. GDP. (a) Eigenvalue spec-trum of λk (circles) vs. dominant frequency of the associated eigenvector ρk,with window width M = 24 quarters; the error bars indicate the confidencelevel (cf. Sec. 2.1). (b) Power spectral density (PSD) estimate (solid lines) usingWelch’s averaged periodogram method, with a Hamming window of length 128quarters and 75% overlap (Priestley, 1991); the dashed lines indicate the signif-icance levels. Inset: Covariance estimates and significance levels. The upper andlower significance levels in both panels and in the inset are derived from the 2.5%and 97.5% percentiles of 1000 surrogate time series; see Sec. 2.1.
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 44
Definition 4 Let Yt =∑m
j=0 cjYt−j = C(L)Yt. Yt is a filtered
version of Yt.
• One can show that the spectral density of Yt is
sy(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 45
3.5 Band Pass Filter
• c0 = 1, c2 = −2, c4 = −1 and cj = 0 for other j.
• Yt = C(L)Yt = Yt − 2(Yt−2 + Yt+2)− (Yt−4 + Yt+4)
• Then
|C(eiω)|2 = 4(1− cos 2ω)2
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 46
Figure 13: A Band Pass Filter
0 0.5 1 1.5 2 2.5 3 3.50
2
4
6
8
10
12
14
16
frequency
|C(e
i ω)|2
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 Applica-
tion 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 14: US GDPFigure 1: GDP: Level and Trend
Note: GDP is de�ned in real per-capita terms from NIPA. The sample includes quarterly obser-
vation from 1947:1 to 2007:4 The cyclical components, which are the High-Frequencies (HF, solid
line), Medium-Frequencies (MF, dotted line), and High-to-Medium Frequencies (HM, dashed line)
are isolated using a band-pass �lter.
Figure 2: GDP: Cyclical Components
Note: The cyclical components, which are the High-Frequencies (HF, solid line), Medium-Frequencies
(MF, dotted line), and High-to-Medium Frequencies (HM, dashed line) are isolated using a band-
pass �lter.
30
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 49
Figure 15: Various Cycles
Figure 1: GDP: Level and Trend
Note: GDP is de�ned in real per-capita terms from NIPA. The sample includes quarterly obser-
vation from 1947:1 to 2007:4 The cyclical components, which are the High-Frequencies (HF, solid
line), Medium-Frequencies (MF, dotted line), and High-to-Medium Frequencies (HM, dashed line)
are isolated using a band-pass �lter.
Figure 2: GDP: Cyclical Components
Note: The cyclical components, which are the High-Frequencies (HF, solid line), Medium-Frequencies
(MF, dotted line), and High-to-Medium Frequencies (HM, dashed line) are isolated using a band-
pass �lter.
30
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 50
3.6 Low Pass Filter
• Yt =∑m
j=0 Yt−j. Then
|C(eiω)|2 =1− cos(m+ 1)ω
1− cosω
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 51
Figure 16: A Low Pass Filter
0 0.5 1 1.5 2 2.5 3 3.50
5
10
15
20
25
30
35
40
frequency
|C(e
i ω)|2
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 52
3.7 First Difference
• First difference Yt = (1− L)Yt. Then
|C(eiω)|2 = 2− 2 cosω
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 53
Figure 17: First Difference
0 0.5 1 1.5 2 2.5 3 3.50
0.5
1
1.5
2
2.5
3
3.5
4
frequency
|C(e
i ω)|2
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 54
3.8 A High Pass Filter: The Hoddrick-PrescottFilter
• 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∑
t=1
(yt − yTt )2 + λ
T∑
t=2
((yTt+1 − yTt )− (xt − xt−1))
2
• if λ = +∞, it is linear detrending.
• The solution of this program solves yt/λ = yTt+2 − 4yTt+1 + (6 +
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 55
λ)yTt − 4yTt−1 − yTt−2
• The solution is a symmetric MA of order +∞:
yTt =∞∑
j=−∞
a|j|yt+j
• Then yCt = 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
|C(eiω)|2 =16λ2(1− cosω)4
(1 + 4λ(1− cosω)2)2
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 56
Figure 18: Hoddrick-Prescott Filter
0 0.5 1 1.5 2 2.5 3 3.50
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
frequency
|C(e
i ω)|2
λ=1600λ=4
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 57
3.9 The HP filter at work
Figure 19: US HP Trend
1950 1960 1970 1980 1990 20007
7.5
8
8.5
9
9.5
Quarters
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 58
Figure 20: US HP Cycle
1950 1960 1970 1980 1990 20007
7.5
8
8.5
9
9.5
Quarters
Trend
1950 1960 1970 1980 1990 2000−0.08
−0.06
−0.04
−0.02
0
0.02
0.04
Quarters
Cycle
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 59
4 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 61
4.1 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 con-
sumption 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 capi-
tal 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 capi-
tal formation + exports - imports
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 65
4.2 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:
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 66
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 in-
come
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 67
4.3 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 re-
ceived 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 69
4.4 Gross saving, gross capital formation and netlending
• 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 as-
sets, which is called gross capital formation.
• Gross capital formation = the net acquisition of fixed assets,
such as residential and non-residential buildings, plants and equip-
ments, 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 cap-
ital formation
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 71
4.5 Net borrowing / net lending in financial ac-counts
• 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 72
4.6 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.
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 73
4.7 Summary
8
1.23. Changes in balance sheets due to changes in prices include holding gains or losses resulting from the revaluation of financial and non-financial assets.
1.24. For the sake of simplicity, other changes in the volume of assets and changes in the balance 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 Resources
Production account Output of goods and services 100Less Intermediate consumption 40Equals Gross value added/GDP 60
Primary distribution of income account Gross value added/GDP 60Plus Compensation of employees and property income receivable from the rest
of the world (ROW) 4
Less Compensation of employees and property income payable to ROW 1 Equals Gross national income 63
Secondary distribution of income account Gross national income 63Plus Current transfers receivable from ROW 1Less Less current transfers payable to ROW 2 Equals Gross disposable income 62
Use of income account Gross disposable income 62Less Final consumption 40Equals Gross saving 22
Uses Resources Capital account
Gross saving 22Less Gross capital formation 15Plus Capital transfers from ROW 1Less Capital transfers to ROW 1Equals Net lending to ROW 7
Financial account Changes in assets
Changes in liabilities
Net acquisition of financial assets Money 3Loans 4
Less Net incurrence of liabilities 0Equals Net lending to ROW 7
Changes in the balance sheet due to transactions Assets Liabilities Non-financial assets Gross capital formation 15Consumption of fixed capital -1
Less Financial assets/financial liabilities 7 0Equals Net worth 21
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 74
8
1.23. Changes in balance sheets due to changes in prices include holding gains or losses resulting from the revaluation of financial and non-financial assets.
1.24. For the sake of simplicity, other changes in the volume of assets and changes in the balance 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 Resources
Production account Output of goods and services 100Less Intermediate consumption 40Equals Gross value added/GDP 60
Primary distribution of income account Gross value added/GDP 60Plus Compensation of employees and property income receivable from the rest
of the world (ROW) 4
Less Compensation of employees and property income payable to ROW 1 Equals Gross national income 63
Secondary distribution of income account Gross national income 63Plus Current transfers receivable from ROW 1Less Less current transfers payable to ROW 2 Equals Gross disposable income 62
Use of income account Gross disposable income 62Less Final consumption 40Equals Gross saving 22
Uses Resources Capital account
Gross saving 22Less Gross capital formation 15Plus Capital transfers from ROW 1Less Capital transfers to ROW 1Equals Net lending to ROW 7
Financial account Changes in assets
Changes in liabilities
Net acquisition of financial assets Money 3Loans 4
Less Net incurrence of liabilities 0Equals Net lending to ROW 7
Changes in the balance sheet due to transactions Assets Liabilities Non-financial assets Gross capital formation 15Consumption of fixed capital -1
Less Financial assets/financial liabilities 7 0Equals Net worth 21
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 75
4.8 Definitions of Output, Consumption and Invest-ment
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 bro-
ken down into a) Final consumption expenditure of house-
holds; b) Final consumption expenditure of general govern-
ment; c) Final consumption expenditure of non-profit insti-
tutions 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, build-
ings, roads, artistic originals etc.) and improvements to non-
produced assets. Gross capital formation measures the addi-
tions to the capital stock of buildings, equipment and invento-
ries, 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 79
4.9 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
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 80
22
c) Consumption of fixed capital (which is the cost of produced fixed assets used in providing services);
d) Other taxes on production.
2.28. Figure F2.2 shows the relationship between basic price, producer price and purchasers’ price of a product in the market when it moves from the producer to the consumer at the end of the circulation process, either directly or through wholesale and retail channels. The basic price is the value of a product unit receivable by the producer, including subsidies on the product, but excluding the taxes paid on the product to be transferred to the government. The producer price is the price the producer charges at the time when it leaves the production unit (which includes taxes but less subsidies on the product). The purchasers’ price may go up as the product passes through many stages of circulation; each stage may incur taxes, subsidies, transport and trade margins. At each stage, a product has a different purchaser price from the point of view of the purchasers. Figure F2.3 illustrates the circulation of products from the producer to the consumer and the taxes and costs involved.
FIGURE F2.2. RELATIONSHIPS BETWEEN BASIC, PRODUCER AND PURCHASERS’ PRICES
Taxes less subsidies on products (including non-deductible value
added taxes) on consumers
Transport and trade margins
Taxes less subsidies on products
(including non-deductible value added taxes) on
producers
BASIC PRICE BASIC PRICE
PRODUCER PRICE
Basic price Producer price Purchasers’ price
FIGURE F2.3. PROCESS OF GOODS CIRCULATION ON THE MARKET
Producersof goods
Wholesalers and retailers
Consumers: other producers and final
users.Government
The payment of taxes, subsidies on products
Transport and trade margins added
Sphere where basic and producer pricesapply
Sphere where purchasers’ prices apply
• Output is recommended to be measured at production costs
when products have no market price.
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 81
4.10 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 82
computers or cars (improvement in quality).
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 83
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)
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 re-
spect 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 85
5.2 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
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 86
Output
1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005−0.2
−0.15
−0.1
−0.05
0
0.05
0.1
0.15
0.2
Quarters
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 87
Output – Consumption
1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005−0.2
−0.15
−0.1
−0.05
0
0.05
0.1
0.15
0.2
Quarters
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 88
Output – Consumption – Investment
1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005−0.2
−0.15
−0.1
−0.05
0
0.05
0.1
0.15
0.2
Quarters
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 89
Output – Hours worked
1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005−0.06
−0.05
−0.04
−0.03
−0.02
−0.01
0
0.01
0.02
0.03
0.04
Quarters
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 90
Output – Productivity
1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005−0.06
−0.05
−0.04
−0.03
−0.02
−0.01
0
0.01
0.02
0.03
0.04
Quarters
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 91
Productivity – Hours worked
1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005−0.06
−0.05
−0.04
−0.03
−0.02
−0.01
0
0.01
0.02
0.03
0.04
Quarters
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 92
5.3 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
Ch. 1: Business Cycle Fluctuations in US Macroeconomic Time Series 15
be percentage changes at an 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:I- 1996: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.
co i r i i i i i i i i / ~ ~¢ i [ i i i i i i r i
: 'd . . . . ] ] [ I I I ] I I
ol ',1' , i i ',,, ,,, . . . . . . , , , , , , , ,
I I I I I I
, . 1 f~ ~ \ E / f v . . . . I ] , l t " . . . . I . . . .
I 47 52 57 62 67 72 77 82 87 92
Date
Fig. 3.1. Contract and construction employment.
~'¢ I I [ I I I I [ [ [ I [ I [
i° I ~ I/I i~/ I Bl/I n l ~ / / ~ I X ~ / i \~ ~ rT ] \ \ l / / V i ~ ~ -
• l @ 7 I ~ E } / I I J , i V , , i V , , o I I v i i I i i r J I i I r l I i i i
r 47 52 57 62 67 72 77 82 87 92 Date
Fig. 3.2. Manufacturing employment.
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 9316 JH. Stock and M.W. Watson
/ I [ I I I I [ I I I I I I I I
~ I I I I I I I I [ I / I
~,,r t , ' ~ ~/ U , V - ' ~ , ~ , / , ~ / 2 4 ~ ~ ~ v . ~ | / I / , Y I V i i i i i V ' ' V
e / , 4 i i i i i i i i i [ i i i
147 5'2 5'7 6'2 6'7 7'2 7'7 8'2 8'7 g'2 g7 Dole
Fig. 3.3. Finance, insurance and real estate employment.
to
I [ [ [ I I I [ [ I [ I I I
'~03 I f [ [ I I I [ I I I I I I c t / ~ [ I I I I E I I I I I I I
/ i V I m, , I I I I I i i v ~ I v ~ ! I I n / I I I I i i I j I I I I I I I v I I [ 47 52 57 62 67 72 77 82 87 92 ']7
D0le
Fig. 3.4. Mining employment.
I [ I I I I ~ 1 [ I I I I [ I [
[ I I I I I f I [
I [ 5.7[ J J [ I . I I I I [ I I I 52 82 67 72 77 82 8'] 92 97
Dole
Fig. 3.5. Government employment.
I I I I I [ I I I [ I I I ] I I ~ 1 I I I [ [ I I I [ [ I I ] I
~ ~"¢" " ~ ~ '¢ " \ "¢~"~~ ' \ ' N ' F ' I " Y '~'l'x~ " " " " ~ " ' ~ I ~, ~, , I , , ~ , T , , , , , ~ I ~l~kY :~ ' , v , , , , v , , , ,oL I ~ I [ [ I I [ I I I I I [ I . ]
'47 -~ 7 -~ ~ "~ ~ -~ "g" -~ 97 Dole
Fig. 3.6. Service employment.
el I I I I I I / / ~ I I
I I I I [ - - I I I I I
I I [ [ I I I [ I [ I I I I I I
7 52 57 62 67 72 77 82 87 f12 Dote
Fig. 3.7. Wholesale and retail trade employment.
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 94Ch. 1: Business Cycle Fluctuations in US Macroeconomic Time Series
N I I I I I I I I
,,,,,,,// ,llll tk// ,V ~ ,k<v" , XW<I ,,,~VI - - ' ~ :~ I ~1 'tt'// ..,~s ,~ ,, , , , v" ,, ~ ,,
0 I I I I I I I I I I I I I I I I
47 52 §7 82 07 72 77 ~2 87 02 07
17
Dole
Fig. 3.8. Transportation and public utility employment.
/t I I I I I I I I I I I I I I I I I ~ ° ~ i I I [ I I I I I I [ I I I I I
I I I I I V ] I I [ I ~ / I
, \p , y ~t/ , , , , , Y ' ' t j ,~
'°1 " ~ , , , , , , I , I ! ' , ' , ' . . . . . . . . ~! . . . . . 47 ' ' ' 52 57 02 67 72 77 82 87 92 97
Dole
Fig. 3.9. Consumption (total).
~ I . . . . I i 1 1 I I " I i x ' k l i . . . . I ] I I . . . . . . . . I I . . . . . e~ ~ 1 I I I ] J , I I / t ~ ii : / k \ I I I I I II
• 1 "7 ,4 "J ,~7 ,DT/ i ~ ~ W \ k , / / ,,,'~k7/ , ~ J ] ~'1 V ',7 ',V ,~ : v ,:,,,,,V ,'
c°l I [ , I I , [ , , I 1 , 1 , I . . . . I . . . . / I 47 52 57 02 67 72 77 82 87 02 97
O~te
Fig. 3.10. Consumption (nondurables).
I I I I [ I I I I I I I ~ 1 I I I I I I [ I I I I I I I
o I I I I I I x / I T I I I I I I
17 ~ ',tT,, ,, , v , , t 7 , 1 co ~ i I I [ [ I I I I I I I I I I I /
4 7 ' ' 5'2 ' ' §'7 . . . . 0'2 . . . . 6'7 ' ' ' 7'7 7'7 8'7 8'7 9'2 97
Date
Fig. 3.11. Consumption (services).
~ I I I I I I I I I I I [ I I [ [
I I I I ~ s I T I i I I I I I
[ :/7 :~ t / , , ,, , v , ',V ,, ©1 I ~ f , I I I I I I I I [ [ I I I I I I
'47 s7 ~'7 ' ' 6 7 ' ' ' o ' 7 ' ' 72 D '8'2 ' 8 7 ' ' ' 9 7 ' ' ' ~ 7 Dole
Fig. 3.12. Consumption (nondurables + services).
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 9518 J.H. Stock and M.W. Watson
to I ^ ~ [ I I I I [ I [ I I I II I I II , , , ,
c~O I / / ~ . . . ~ , / . ~ [ [ I I I [ I I I I I ~ [ II I I II
i! . . . . . I 147 52 57 62 67 72 77 82 87 92 97
Date
Fig. 3 .13 . C o n s u m p t i o n (durables ) .
2 i i i i i i l i ' i i i ' i l l r . . . . l l
:F:V ,v " v' V 47 52 57 62 67 12 77 82 87 92
Dote
Fig. 3 .14 . I n v e s t m e n t ( total f ixed) .
2 ~ ' A ~ ' ' " " "
'V . . . . ,V/ I [ I I I V
147 52 57 62 67 72 77 82 87 92 97 Dote
Fig. 3 .15 . I n v e s t m e n t ( e q u i p m e n t ) .
147
I I I I I I I I I I I i I / ~
I [ I
, ', , ;', , ,~ U :V ~ ' , 57 62 67 72 17 82 87 92 97
Date
Fig. 3 .16 . I n v e s t m e n t ( n o n r e s i d e n t i a l s tructures) .
o I [ I I I I I I I I I [ I I I J ~ I [ I I I I I I I I / ~ I I I I I
l ] i I I I I [ [ I Y i [ ~ / I I o ,~ll II II , I I I . . . . . . . . . . J , . . . . . . . . . . . 147 52 57 62 67 72 ] / 82 87 92
Dote
Fig. 3 .17 . I n v e s t m e n t ( res ident ia l s tructures) .
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 96Ch. 1." Business Cycle Fluctuations in US Macroeconomic Time Series
N I I [ I I I I [ I [ [ I I I I I
[ [ I I I I [ I [ [ I I I I I ©l ] H [ [ I , , I 47 52 57 62 67 72 77 82 87 02 97
19
Date
Fig. 3.18. Change in business inventories (relative to trend GDP).
to . . . . .
J O I I I [ I I [ I [ I I I I
i°[ ' l ' l~V' l \ V / ,~/ I , Y ' X 7 - - " ~ q W I J ~"~x, . / II I\kL// M . . J l l ~ - . / - - ~ I v I / . . w I V I I [ ~%./ , [ [ I I ~ ' ' / I I
I i ~ / I I I I I [ I I [ [ I I I I 01 L I.V . . . . [ . i i . , . . . . . . . . / . I . . . ] . I . . . . I . . . . . . . . . I . . . . . I 47 52 57 62 67 72 77 82 87 92
Date
Fig. 3.19. Exports.
to
co I [ I [ I I I [ I ] I [ I I I ~ [ / I ~ F ~ I I I I ] I [ I I I I
& l - - J ~ ~ ' ' ' J - - - -
t I V ~ i I ~ l r l I \ / r l I v ~ l i [ I r I i F r I I r..,' I l l I
I 47 52 57 62 67 72 77 82 87 92 97
Date
Fig. 3.20. Imports,
I [ ] [ [ I I I I I I I I I ] ~1 I [ I [ F I I [ I [ [ I I I I I
L [ - \,Y-", \, 7 "---',T ,\, ~l [ ] [ [ [ I ~ J ] 1- ] I I I I ]
© / I H [ I I I I I I / [ ] I ]
Date
Fig. 3.21. Trade balance (relative to trend GDP).
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&[
o 147 52 57 82 87 92 97
I I
I ]
[ I
I1 I I I I I ]
62 67 72 77
Date
Fig. 3.22. Government purchases.
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 97
D a l e
JH. Stock and M. W. Watson
147 52 57 62 67 72 77 82 87 92 97
20
Fig. 3.23. Government purchases (defense).
i ~ ~ / ~ , + ~ . ~ , ~ ~ . ° :i II Ii ii :i :II: ii
I 47 52 57 62 67 7'2 7'7 8'2 8'7 9'2 97 Dole
Fig. 3.24. Government purchases (non-defense).
'~[ r i I I J l F i I ~ 1 " I I I [ I I I I
u I ii I II I i I'~ I I ~ J
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~ 1 , I , ~ , , , I , [ , [ I I I , , , [, h r I I , I 1 , 1 , I, , ,1 ' . . . . . ' 47 52 57 62 67 72 77 82 87 92 97
DoLe
Fig. 3.25. Employment (total employees).
N I I I I I I I I i I I [ I J I I I . ~ [ -2 -TM,~ ' ,A , A A , ~ , / ~ , ~ p , ~ o l I J l ~ I r l I T I I
° F ' I : / I : V , ,, , v F ~'~l I l l / I '(,/ [ M ~ " I I ~ , / I ~ [ I i I I I I I I I [ [ L'v . . . . . . . . ~0 I J I I I I I ] I I I [ I
I 47 52 57 62 67 72 77 82 87 92 D a t e
Fig. 3.26. Employment (total hours).
I I I I J I I I [ I J I I
~ I [ [ I I I I I [ f I I I I I I
~ b4 '~ ~ W ~/~ - ~'~J Y'U ~'~-~/ "~ "~-~ ~ 1 I I I I I x / [ T I I I [ I I I
l0 H I I I I I I I I I I [ I I [ J , , , , , , , , ,
I 47 52 57 62 67 72 77 82 87 92 97 DaLe
Fig. 3.27. Employment (average weekly hours).
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 98Ch. 1: Business Cycle Fluctuations in US Macroeconomic Time Series
I I I I I I I I I I I I I I I I I J t i I I I I I i i I LI
,~h " ~ _ i i ~ i i i i i i [ i i i i
142 " ~ ~ " " ~ " ~ " ~ ~ " ~ ~ " ~ 97
21
Date
Fig. 3.28. Unemployment rate.
,,v,~w v'~/ i I ' ,V I V ',:1~v~ "Y tL ,/Y/ V / , ~ 7 ~ - ,,W/ , Y Y , , ,Vq - ,~--./
i 47 52 57 62 67 72 77 82 87 92 97
Date
Fig. 3.29. Vacancies (Help Wanted index).
o I I I t I i i i I I I I I I I I • I t
~o : : ',' ',', " ' " " "
: ° t ' v ~ - / ~ i ' v ~ / " ~ V X/W\ ,/, x . . j , , ~ - % , , ' ' , ,_ . / , , , , . H , O11 ~ V ' ,' : , ] . . . . . . V ' ', 1 ~ ' r i , ~[1' ' ' . . . . I 47 52 57 62 67 72 77 82 87 02 97
Dote
Fig. 3.30. New unemployment claims.
oo . . . . . . . . . . . . . . . . . . . .
~'~ i I i I I I i I i i i i I I I [ , , / : ~ , A , / ' / A / ~ , , ,.,i , A . _ . ~ , A
i ° l ~ - - , r v ,V/# ~,1 ; t , / " ~ : " v , , ~4 , ~ i / ~ , v , ~ , f " ,~" \~--.----~ 'J'~l I \ J LiYI I ~ / ik[J i ' l l / I ~ / / [ i i % , / i i v
~'1 U ,v ,V ,, ,v , k/ , , , ' , ; ' ,, ~l V i i I i i ~ i i i i~ El i i i i
1 47 52 57 62 67 72 77 82 87 92 97
Dab
Fig. 3.31. Capacity utilization.
eel i i
E47' ' ' 5'2 '
I I ¸ l i I r / # ~ I . . . . I ] I I . . . . . . I I . . . .
5'7 6'2 . . . . 6'7 . . . . 7 ' 2 ' ' " 7'7 ' ' 8'2 8'7 ' ' 9 ' 2 ' 97 Dole
Fig. 3.32. Total factor productivity.
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 992 2 JH. Stock and M.W. Watson
] I I I I I I I I I I [ I I I I I ~ 1 i I I I I I I I I [ [ I I I I I
i4"N]/ - ' VY ' \ k / / ' z % / / - - ' V / J IOl I I W T I I I I I I I
, I 't7 ,v ,v :: ,, , v , , ' , v ,, ~) I ] i l I I I I I I I I r I i f
I " . . . . . . . . . I I 47 52 57 62 67 72 77 82 87 92 97
Date
Fig. 3.33. Average labor productivity.
~t I [ [ I I I I I I [ [ I I I I I I [ [ I l i I I I [ I [
C~I j I I J I ] I
° , " , , , , ,
{~ I ~ I I I I I [ [ I I I I [ / I I , . . . . . . . ,
I 47 52 57 62 67 72 77 82 87 92 97
Dote
Fig. 3.34. Consumer price index (level).
I I I I • I " O I . . . . . . . . J J I I " II I " I . . . . . . . . IE . . . . . t 0 / ~ l / ~ i A J I I I I I / / ~ j / ' ~ J I I I I
~ Z ~ l ~ / / ~ 1 I J I I I I I ~ 1 ~ ~ 1 , 1 ~ I
~i I, l~r/ l r v r w r '~ /F v ~ it k V k / i I I f ~ / r r = i k / i i i I tl
~°i I" , , P . . . . . I, I, , , I . . . . . r l , ] , P . . . . . . . . 11 . . . . 47 52 57 62 67 72 77 82 87 92 97
Date
Fig. 3.35. Producer price index (level).
0 I I I I I I I r I I I I I
~ o I I I I I I I
I I I I ] I I , I, I, , , i , I , i J i
I I I I I I I
- - h
I I [ II [ I II II I J
I I I I [I I V t l I I ] I II I II
I 47 52 57 62 67 72 77 82 87 92 97 Date
Fig. 3.36. Oil prices.
[ I I J l I I I I I I I I , I I
o l II I[ r l I J ~ ~ _.d..~[ E II I I
I ] J/ / I ~ / I I I I I I I I
tO I H I I I I I I I I I I [ I I I I I / . . . . . . . . . l I 47 52 57 82 D7 72 77 82 87 92 g7
Dote
Fig. 3.37. GDP price deflator (level).
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 100Ch. 1." Business Cycle Fluctuations in US Macroeconomic Time Series 23
I .. I I
, , , , , , , . . . . . . . . . I 47 52 57 62 67 72 77 82 87 g2 97
Date
Fig. 3.38. Commodity price index (level).
~ 0 / i ~ l i i J l ~ i , i i i I i i I I / ~ [ I I I ] 1 I I ~ ~ L I I I L I I I
o / ' x ~ , , ' , ~ " / : X ~ ' k , , , , , , , ~ , ~ . , . , ~ , , . , z X T ~ ~ _ J E ~ / - - ~ " " , 2 / - :,2 , . . . . . . . . ~ 41\ ,Y ,, w I .
o_' \ L / ~ I V , , , , - , Y rl I ~ T / I oOl ~.4 [ I I I I I I I I [ I I I I
1'47 52 5'7 6'2 6'7 7'2 7'7 82 8'7 92 9'7 DoLe
Fig. 3.39. Consumer price index (inflation rate).
~ o I [ l i [ I I I I I J I I L I
~! ~ , ~ tr-4~Y" r ~ 7 - ' , ~ ' ~ v f ~ l , ~ , " J i , k . Z g / ' ~ l - ~ i ~ t ~ ' "
[ l ~ [ I I I I I I I I I I I I I I I
147 52 57 62 67 72 77 82 87 92 97 Dote
Fig. 3.40. Producer price index (inflation rate).
1 ~0 I I I I I I I I I I I I [ I I i [ |
] I I I I I I I I I I [ [I I I I
~ 1 i \ ~ " ' Y I I I I I Y I I I V 11 1 I I [ [ i I I I I I I I F I
~L '~ . . . . . . . . . J i 47 52 57 62 67 72 77 82 87 92 97
Date
Fig. 3.41. GDP price deflator (inflation rate).
I [ I I I ] I I I I I I I I ] I I I cO I [ I I i l ] I I I I I I I I I I
I I I I I I ] I I I I i [ I I I I
, v ,,,~.w,.v ~ , ~ , v v v ,
~ I , " , l . . . . . . . . ~ , , , , , T , [ I I , ] ~ i l , ,
147 52 57 62 67 72 77 82 87 92 DQte
Fig. 3.42. Commodity price index (inflation rate).
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 10124 JH. Stock and M.W. Watson
I [ I I [ I I I I I I [ I I I I I
~{~ [ [ [ I I I I I I [ I I
~.r ~\I ,\,~,} ~,i ,\r/~ ,\,5c~4, 9--",Y ,\,/~ ~ k/,~/-~-~ ~I I II I I l"g 1 1 II [ I II
co/ ' 4 I I I I I I I I I I I I I I I I
147 5'2 5'7 6'2 6'7 72 7'7 8'2 8'7 9'2 97 Dale
Fig. 3.43. Nominal wage rate (level).
I I II II II F r I II I I II
(I I [ I [ I I I [ I [ II I 1 II c , ,,s-,.,,~,A ..
°o° ? f l "~ ,,, ~ T V ,, k7 ~ / ,,~, : ~ ~ ~ , " ~ i ' l /,/ , " w , , , , , v , , y ,
to I I I I I I I I I I I I I I I I '4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
I 47 52 57 62 67 72 77 12 17 92 97 Date
Fig. 3.44. Real wage rate (level).
I I A i " d l " "1"1 I I . . . . . . . . I" I" I I " IJ I I I I " I I / / ~ 1 I I I I I I I I [ I I I
, v r v ~ ~ ,~ - ,T, , V ,T ~ ti l/ ~ ~Y ~ ~ ,I,'7-" ,, ,\VE V ,~ w~ I l t l v I V " ' ' ' v '~ J\V - -
d.~,., i.i .,211 .... i.i...i.i .... II.',.D.~' .......... 1 I 47 52 57 62 67 72 77 82 87 92 97
Date
Fig. 3.45. Nominal wage rate (rate of change).
I I I I I I I I I I I I I I I
~ ~ 1 I I I I I I I I I I I I I , M
i.,J~"v'v ~,~,A/V/ ~r; ¥ / ' ~ - "~r ' j \ , /~," j v - , x \ / v V \ / ' ~ - / ~ t I l l I [ I I I I x J I I [ I P I I I
~ / 1'4 i i i i i r i r i i r , iJ I 147'-- g "~ g "~ 77 ~ "~ ~" "~ ~97
Dale
Fig. 3.46. Real wage rate (rate of change).
I I
I I - t i l l I [
& I [ I [
1 47 5'2
I I I I [ I I [ I I I I I [ I I I I [ I I I I I
I F I I I I I I I I I I I I [
57 62 67 72 77 82 87 92 07 Date
Fig. 3.47. Federal funds rate.
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 102Ch. 1." Business Cycle Fluctuations in US Macroeconomic 7~me Series
I [ l i r I L I I I I I I I I I
( / I [ ] [ L I L I I I I I I
!/ ~ T , ~ N ,~"rYv/~ '-" ,\<k/ , /,b+--' ,, , iV ~ ,k~ , ' ikl I I I " V I T I ~1 I I [ I I I
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25
j q I
O_l [
I ' ' 5'? '
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Fig. 3.48. Treasm'y Bill rate (3 month).
I I I I I I I I I [ I I I I i [ I I I I I [ I I I i l
'iv/ v i [ I i I I [ I I ',~ i? ', , , , ,v : ' , ' , V ,,
52 57 62 67 72 77 82 87 92 97 D~J[e
Fig. 3.49. Treasury Bond rate (10 year).
to i i . . . . I I I i I I . . . . . . i i i I " i i i i I I
I I I [ I I I I I I I I I I I I I
[~1 A J ( / '\'/ "'1'7 ' \7 ~ / ' " ~ ' \ ' _ / " ' ~ ' F ~ " , , - J ' \ ' Y - V_/-" ~ k / " ~ - ' ~ I W r I I [Y I I I i I [ II I M/ I
©I , Ii,~ v . . . . . Ir . . . . . . I, I , I I r , If,l,' . . . . . . ' ..... 1 I
I 47 52 57 62 67 72 77 82 87 92 97 DGte
Fig. 3.50. Real Treasury Bill rate (3 month).
~o t
Lq I I
I I I I I I I [ I I I I I i [ I [ L I I I [ I I I I I
I v i\l] i i r r ~ / Ii r \ l / iI I I I V I I I [ [ I I I [ w I I
52 57 62 67 72 77 82 87 92 97
~o b 0.
1 4 7
Dole
Fig. 3.51. Yield curve spread (long-short).
I [ I I L I I I I I I
-,\,7%/~- ~V-7--,\,~-2~ ~Y~\,'~--~ -i~--/-~ ,,~ ,~ ,Ill ,, I \ , / ll,., ii i, i v rl I\7 II I I I I I i [I I </ II
52 57 62 67 72 77 82 87 92 97 Dale
Fig. 3.52. Commercial paper/Treasury Bill spread.
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 10326 JH. Stock and M. W. Watson
7~ ' O ' r " - -
V , , V v iT ~I , ' ' i , ' G , 1 i r , r , ; . . . . . . . . 'l I i ~ 'It v . . . . [[ : ' , , ' V . . . . . . . " ; . . . . . t I 47 52 57 62 67 72 77 82 87 92 97
Dote
Fig. 3.53. Stock prices.
7 ~
~ ° 7 . . . . 5'2 . . . . 5'
I I I I t ~ X [ ~ , . ~ r l I I I
i J _ /~x .. , ~ v ~\,# ,\/,/J " ~ / "~ - , ~ / % ' ¢ E ~ / ~ ' ~ I I F i I [ 1 % / i i l ' V i ~ '[J I 1 ~ / I I
i I I [ - i i i l [ i I I
57 62 67 72 77 82 87 92 97
Dole
Fig. 3.54. Money stock (M2, nominal level).
v I i i I I I I i i • i i l i i ¸ I . . . . t l , t [ I I I I I I [ I I I I [ I I I
, ,
& i [ i ] I [ [ i [ [ i [ i I I
I 47 52 57 62 67 72 77 82 87 92 97
Dote
Fig. 3.55. Monetary base (nominal level).
:I 1 4 7 ' ' ' 5'2 ' '
] I J I I I I I d I J I I I I I [ I I I I I I
W \~# ,\\, Y \~\t/ ,~'%,~j " J\Y '\V " ~(F ,r / I I I "~] I "t J I I i I ]1 /
, , , , , , , . . . . , . . . . , . . . . . . . . , , / 57 62 67 72 77 82 87 92 97
[)Die
Fig. 3.56. Money stock (M2, real level).
,¢ I I I I [ [ I I I I I I I I [ IJ
E [ J I ~ I I I/~ I I _ (~0 I [ I
~I , r v ~r ,~, # . . . . . Lr, , , ~ , , , !,,i,, ..... ,! ..... I 1 47 52 57 ~2 67 72 77 82 87 92 97
Dote
Fig. 3.57. Monetary base (real level).
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 104Ch. 1." Business Cycle Fluctuations in US Macroeconomic Time Series 27
~ 7
I I I I I I I I I I I I
w v k, /V ,, ,"t:k" I I ~1/I I P " ' l I I I ] I I [ ' t i l l I [ r l I I I
52 57 62 67 72 77 82 87 92 07 Date
Fig. 3.58. Money stock (M2, nominal rate of change).
I I I I [ I I I I I [ [ I I I E ~,~ I I ~ 1 1 f I I I I I I I I I I I
7~ vklr / I ~ ' ~ ~ ~ ~ ~ , 7 " , ~ ' , i X,J E~'m ~ ~1 iI~/ I I [ [ I I [ I I [ [ I I I II
I I I [ I I I [ I I [ [ i I I I [ . . . . ;, ,~ I I , , [ I , ,I I [ I ] I ! 1 , [ I I [
I 47 52 57 62 07 72 77 82 87 92 97 Date
Fig. 3.59. Monetary base (Nominal rate of change).
I I i i J J I I I I • i i i 1 1 I i i - -
to ~ ~ . 1 1 I l i I I i I I I I I I I / ~
[ ' 1 l i l i - l i I i i I V i i I \ 1 i i \ m | I I , r , I , , , I , I , ,I I . k , /
I 47 52 57 62 67 72 77 82 87 92 g7 Dote
Fig. 3.60. Consumer credit.
I I I [ I I I I I I [ I I I I I I I
, V , , , , , --, ,, ,.,
, I, I .... ID, , ,II , ,I I i, L , , I, I , II i, ~ II ..... i 47 52 57 62 67 72 77 82 87 92 97
Dote
Fig. 3.61. Consumer expectations.
i f I I " o I
uO F ~n r & r
r
i47 52 57 62 67 72 77 82 87 92 Date
Fig. 3.62. Building permits.
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 1052 8 J.H. Stock and M.W. Watson
t ' ' ~ r' "A~ r f' " ' ' A ' '~ / ' ' , r 0 I [ [ / J J I I I [ I I I I I I
~ o l ~ # ~ ? - ~ - , r \ , ~ i,¢",--W "A ? ' -~ -~7-~- ' rw ~ ~','x>'-- "-,-" ~ - " ',71 ~,I \ I ' v q " ~ v, v , v ' I ' I ~ ' ' ~'
[ [ I I I I I I I I ] i I I
I 47 52 57 52 67 72 77 82 87 92 97 Dale
Fig. 3.63. Vendor performance.
o I ~ ] I I I I [ " I I I " I " " I I [ I I I I I I
~ , ~ I I I [ I [ I F I
0~ ° , ~ ~ , f ~ ' ~ - , ~ , - . . . . . . . . . . . . I . . . . , r r y , I 7 ' ! , ' r . . . . . . . . . . .
147 52 57 62 67 72 77 82 87 92 97 Dote
Fig. 3.64. Manufacturers' unfilled orders, durable goods industry.
i i i
tq I J ~ I I
147
i E i i • i i • i [ i ¸ I • ii I I I [ I £ [ ~ [ ~ 1 1 I ~ Jl
[ [ I i I I [ I
' ' - y / v ' W / I r ] I I I I ~ " { I ~ / / I I I N J I [
52 57 62 67 72 77 82 87 92 97 Date
Fig. 3.65. Manufacturers' new orders, non-defense capital goods.
147
1 1 I I r I " / ~ [ I[ I ¸ ~ Ji
" " " I " ' II A _
[ i f I I [ ir i I[
57 62 67 72 77 82 87 92 97 Date
Fig. 3.66. Industrial production, Canada.
'r ~o ' ' AI' " [ I I / ~ ¢ ~ [ I I ] J I I I I I
, \ / " I~V,r \ / I r i Y I II I L v r v I ~ ,~ I I I I I I u [ [ I I [ I I I I I I I [ [ I I I ] ] J~] I I I I I I
147 52 57 62 67 72 77 82 87 92 Date
Fig. 3.67. Industrial production, France.
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 106Ch. 1." Business Cycle Fluctuations in US Macroeconomic Time Series
to ] ' } a ' " " " I [ I I I I I I
~ ° l / X d - , W / , V / , ' ¢ V - ' ~ / ~ , ~ f " " ,, , V ~ / , ,~w,. ,2~/ I t l i l l v i ~ / i~ ~ - " i ~ / i~ i i i i 1
21 , ' , ' . . . . ' , ' , , , ' , ~ , , ' J . . . . . . ', ', , , ' , ~ ' . . . . l ' , ' , ' . . . . . . . . ' ! . . . . . /
2 9
147 52 57 62 67 72 77 82 87 92 97 Dote
Fig. 3.68. Industrial production, Japan.
© I I I f I I I I I I I I I I I I I
v i, w cO I I I i t I I I I I I I I I
I "47 5'2 5'7 6'2 6'7 7'2 7'7 8'2 8'7 9'2 ! Oate
Fig. 3.69. Industrial production, UK.
to
I I I [ I I I I I I I I I I I I I I I f ~ l l I I I I I I I I I
/ ' , , ' , ' ,!! " . . . . . " , ' ' , " ' , ' . . . . . ' I , , 147 52 57 62 67 72 77 82 87 92 97
Dote
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 107
5.4 Moments
• We want to characterize fluctuations ; amplitude and move-
ments
• Amplitude: volatilities ; standard deviations
• Comovements: correlations
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 108
Variable σ(·) σ(·)/σ(y) ρ(·, y) ρ(·, h) Auto(1)Output 1.70 – – – 0.84Consumption 0.80 0.47 0.78 – 0.83Services 1.11 0.66 0.72 – 0.80Non Durables 0.72 0.42 0.71 – 0.77Investment 6.49 3.83 0.84 – 0.81Fixed investment 5.08 3.00 0.80 – 0.88Durables 5.23 3.09 0.58 – 0.72Changes in inventories 22.48 13.26 0.48 – 0.40Hours worked 1.69 1.00 0.86 – 0.89Labor productivity 0.90 0.53 0.41 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 to-
gether.
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 re-
sources have lower than average conformity.
4. Business profits show high conformity and much greater am-
plitude 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 113
5.5 Some Other Countries
• From Fiorito and Kollintzas, “Stylized facts of business
cycles in the G7 from a real business cycles perspective”, Euro-
pean Economic Review, 1994.
• Quarterly data 1960-1989
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 114
Table I
Cross correlations of real GNP/GDP with the components of spending, income. and outout in levels. a.b -
Variable Vol. X,_, X ,+2 X ,+3 X ,+4 X *+5 . _ ______- (I) Real GNP/GDP irkA I .74 0.01 Canada I .39 -0.12 Japan I.53 0.02 Germany 1.69 -0.02 France 0.90 -0.06 UK 1.54 -0.02 Italy 1.70 -0.21
(2) Consumption expenditure us 1.29 0.32 Canada 1.27 -0.08 Japan 1.33 -0.10 Germany I.53 0.1 I France 0.86 -0.27 UK I .67 0.03 kdy 1.1’) -0. IS (3) I:ixed invcslment US 5.51 0.14 Canada 4.60 -0.43 Japan 4.57 -0.11
0.2 I 0.41 0.65 0.85 1.0 0.85 0.65 0.41 0.21 0.0 I 0.04 0.27 0.51 0.78 I.0 0.78 0.51 0.27 0.04 -0.12 0.19 0.38 0.59 0.78 I.0 0.78 0.59 0.38 0.19 0.02 0.23 0.35 0.46 0.67 1.0 0.67 0.46 0.35 0.23 -0.02 0.10 0.30 0.54 0.77 I.0 0.77 0.54 0.30 0.10 -0.06 0.07 0.20 0.37 0.55 I.0 0.55 0.37 0.20 0.07 -0.02
-0.04 0.22 0.52 0.80 I.0 0.80 0.52 0.22 -0.04 -0.21
0.48 0.59 0.72 0.79 0.16 0.40 0.57 0.72 0.08 0.28 0.42 0.56 0.26 0.37 0.46 0.58 0.42 -0.63 0.73 0.72 0. I 3 0.30 0.30 0.46 0.07 0.34 0.5’) 0.74
0.80 0.63 0.43 0.22 0.00 -0.17 0.79 0.65 0.44 0.21 0.06 -0.03 0.72 0.54 0.40 0.22 0.01 -0.11 0.69 0.55 0.49 0.38 0.32 0.21 0.62 0.30 0.10 -0.14 0.25 -0.32 0.67 0.42 0.3x 0.26 0. IO 0.08 0.78 0.69 0.50 0.25 0.03 - 0. I 5
0.30 0.47 0.67 0.83 0.90 0.78 0.59 0.35 0.12 -0.09 -0.29 -0.07 0. I 8 0.40 0.53 0.52 0.41 0.32 0.21 0.14
0.04 0.23 0.45 0.64 0.83 0.78 0.69 0.51 0.29 0.05
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 115
Germany 4.90 0.04 0.26 France 2.70 -0.11 0.06 UK 3.57 -0.11 -0.04 Italy 4.88 -0.16 -0.00
(5) Equipment investment US 6.28 -0.13 0.02 Canada 7.13 -0.49 -0.35 Japan 5.96 -0.09 0.02 Germany 6.09 0.12 0.36 France 3.90 0.08 -0.23 UK 4.88 -0.12 -0.07 Italy 7.92 -0.15 0.01
(6) Construction investment us 6.26 0.31 0.45 Canada 3.83 -0.23 -0.12 Japan 5.58 -0.04 0.09 Germany 5.56 0.00 0.15
_ France 2.49 -0.25 -0.11 UK 3.90 0.15 0.19 Italy 3.57 -0.11 0.00
(7) Inventory changes us 18.2 -0.01 0.08 Canada 35.4 0.07 0.15 Japan 45.4 -0.05 -0.03 Germany 49.2 0.07 0.19 France 30.1 -0.15 -0.09 UK 26.6 0.03 0.12 Wy 66.X - 0.07 0. IO
(8) Government tiniil consumption US 1.98 -0.07 -0.04 Canada 1.46 -0.18 -0.20 Japan 2.89 0.25 0.33 Germany 1.47 -0.19 -0.11 France 0.70 0.46 0.6 I UK 1.43 -0.09 -0.03 Italy 0.60 0.30 0.18
0.37 0.42 0.60 0.84 0.54 0.42 0.37 0.29 0.12 0.26 0.46 0.66 0.78 0.69 0.57 0.41 0.25 0.13 0.08 0.23 0.33 0.60 0.53 0.38 0.31 0.23 0.05 0.23 0.47 0.70 0.88 0.81 0.67 0.47 0.25 0.05
0.21 0.46 0.68 0.86 0.87 0.77 0.59 0.38 0.18 -0.18 0.03 0.27 0.43 0.51 0.53 0.50 0.34 0.25
0.17 0.38 0.58 0.74 0.73 0.69 0.54 0.34 0.14 0.48 0.52 0.61 0.73 0.58 0.49 0.39 0.23 0.09 0.39 0.58 0.70 0.74 0.53 0.31 0.12 -0.06 -0.17 0.05 0.21 0.38 0.56 0.51 0.47 0.44 0.32 0.25 0.25 0.48 0.69 0.85 0.74 0.57 0.38 0.14 -0.05
0.57 0.70 0.80 0.78 0.58 0.35 0.10 0.34 0.50 0.55 0.41 0.18 0.23 0.31 0.32 0.43 0.35 0.18 0.22 0.27 0.47 0.72 0.40 0.28 0.08 0.25 0.48 0.65 0.65 0.65 0.28 0.26 0.21 0.38 0.27 0.08 0.18 0.36 0.57 0.74 0.74 0.65
0.11 -0.10 -0.27 0.06 0.01 -0.04 0.07 -0.05 -0.18 0.27 0.25 0.10 0.54 0.45 0.33
-0.00 -0.08 -0.24 0.50 0.36 0.20
0.22 0.35 0.49 0.64 0.48 0.26 0.03 -0.14 -0.30 0.25 0.43 0.60 0.68 0.53 0.33 0.06 -0.18 -0.32 0.07 0.23 0.38 0.38 0.38 0.25 0.20 0.20 0.10 0.31 0.32 0.33 0.35 0.29 0.14 0.02 -0.13 -0.27
- 0.04 0.05 0.22 0.47 0.44 0.25 0.16 -0.05 -0.27 0. I6 0.26 0.42 0.55 0.38 0. I9 O.ofl - 0.08 -- 0. I7 0.2 I 0.39 0.51 0.56 0.32 o.txl - 0.24 - 0.4 1 - 0.4x
0.00 0.06 0.1 I 0.19 0.24 0.27 0.30 0.35 0.37 -0.24 -0.23 -0.20 -0.12 -0.09 -0.08 0.05 0.14 0.18
0.30 0.28 0.30 0.32 0.04 -0.05 -0.08 -0.05 -0.06 -0.13 -0.10 - 0.06 0.05 0.06 0.16 0.23 0.36 0.4 I
0.56 0.46 0.32 0.18 -0.07 -0.23 -0.31 -0.30 -0.24 - 0.07 -0.06 0.02 0.04 -0.05 -0.01 - 0.07 -0.05 0.04
0.05 -0.14 -0.30 -0.39 -0.43 -0.41 -0.33 -0.21 -0.04
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 116
5.6 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?”, Jour-
nal of Monetary Economics, 2004.
Franck Portier – TSE – Macro I & II – 2011-2012 – Lecture 1 – Business Cycle Facts 118
effort.6 In addition to the negative cross-correlation of output, investment and hoursworked and strongly positive cross-correlation of consumption the followingstatements summarize the main implications of the baseline model:
ry;ynprc;cn;
ry;ynprz;zn;
ARTICLE IN PRESS
Table 1
Average cross-correlations
Averages from 190 cross-correlations From BKK (1995)
Variable Full sample Europe-U.S. Baseline model
1960:1–2000:4 1973:1–2000:4 1973:1–1990:4 1970:1–1990:2
Output 0.22 0.28 0.30 0.66 �0.21(0.03) (0.03) (0.03)
0.00 0.00 0.00
Consumption 0.14 0.15 0.14 0.51 0.88
(0.02) (0.03) (0.03)
0.00 0.00 0.00
Investment 0.18 0.22 0.22 0.53 �0.31(0.04) (0.04) (0.03)
0.00 0.00 0.00
Employment 0.20 0.22 0.21 0.33 �0.31(0.03) (0.03) (0.04)
0.00 0.00 0.00
Total hours 0.26 0.29 0.26
(0.04) (0.04) (0.03)
0.00 0.00 0.00
Employmenta 0.25 0.26 0.25
(0.04) (0.04) (0.05)
0.00 0.00 0.00
Productivity 0.16 0.21 0.24 0.56 0.25
(from y and n only) (0.02) (0.02) (0.03)
0.00 0.00 0.00
Productivity 0.09 0.11 0.13
(best available)b (0.02) (0.02) (0.02)
0.00 0.00 0.00
First line: average correlation. Second line: standard deviation of average correlation. Third line: marginal
significance level of average correlation.aCountries for which total hours are measured.bCapital stock and hours when available, otherwise y and n only.
6There is also a wealth effect that reduces their labor supply if leisure is a normal good.
S. Ambler et al. / Journal of Monetary Economics 51 (2004) 257–276260