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).

~o~.

&[

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

~vl t/,// ,~// ~ / ~ , ~ :/~ ~' ,, ,/\/ , ~ l '/\l// r ,~ , , r~" I I r r ' v r, I \ y , , [ I f f t I I f I I I I I [ ~( I I

~ 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

l :iV , , , , , v , , ,y , , ~h I H ~ J [ I I I I I I I I I I r I I I

25

j q I

O_l [

I ' ' 5'? '

[)ale

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