lecture 1 : business cycle facts and detrending...2017-2018 { deeqa { tse { advanced macroeconomics...

2017-2018 – DEEQA – TSE – Advanced Macroeconomics

Lecture 1 : Business Cycle Facts and Detrending

Franck [email protected]

Version 1.005/11/2017

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[email protected]

Disclaimer

These are the slides we are using in class. They are not self-contained, do not alwaysconstitute original material and do contain some “cut and paste” pieces from varioussources that we are not always explicitly referring to (not on purpose but because ittakes time). Therefore, they are not intended to be used outside of the course or to bedistributed. Thank you for signalime us typos or mistakes at [email protected].

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[email protected]

Introduction

I Macroeconomics is about the determination of aggregate variables, as measuredby national accounts (output, consumption, employment, inflation,...)

I Economists makes a distinction (at least at first pass) between the long run andthe short run, between Growth and Business Cycle

I For the methodological part of that lecture, I will consider the U.S.A. as anexample.

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Introduction

Figure 1 – US log Real GDP per capita

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Introduction

I Burns and Mitchell “Measuring Business Cycles” (1946, National Bureau ofEconomic Research) :

“Business cycles are a type of fluctuation found in the aggregate economic acti-vity of nations that organize their work mainly in business enterprises : a cycleconsists of expansions occurring at about the same time in many economicactivities, followed by similarly general recessions, contractions, and revivalswhich merge into the expansion phase of the next cycle.”

I To identify cycles, B&M assume that they are no shorter than 6 quarters, andfound a maximum length of 32 quarters.

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Introduction

Figure 2 – Reproduced from Burns and Mitchell Measuring Business 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

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Introduction

Figure 3 – A Business Cycle

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Introduction

Figure 4 – U.S. Business Cycles, as identified by the NBER’s Business Cycle DatingCommittee

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Introduction

Table 1 – Recent U.S. Business Cycles, as identified by the NBER’s Business Cycle DatingCommittee

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

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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

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Introduction

Table 2 – Average Length of Expansions and Recessions for the U.S. Business Cycles (fromthe 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

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Introduction

I How does the NBER establish this chronology ?

I Here is the “Statement of the NBER Business Cycle Dating Committee on theDetermination 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.”

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“In both recessions and expansions, brief reversals in economic activity may occur

– a recession may include a short period of expansion followed by further decline ;

an expansion may include a short period of contraction followed by further growth.

The Committee applies its judgment based on the above definitions of recessions

and expansions and has no fixed rule to determine whether a contraction is only a

short interruption of an expansion, or an expansion is only a short interruption of a

contraction . The most recent example of such a judgment that was less than obvious

was in 1980-1982, when the Committee determined that the contraction that began

in 1981 was not a continuation of the one that began in 1980, but rather a separate

full recession.”

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Introduction

I Is there a way to translate this into some statistical procedure ?

I What are the data that we shall use and how are they constructed ?

I What are the empirical regularities of BC ?

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1. A First Look at Some Methods To Extract the Cycle

I Any time series yt = logYt can be decomposed such that

yt = yTt + yCt

I Problem : How to define/identify each component ?

I Several ways of approaching the problem

I Actually : Infinite number of decomposition of a non-stationary process into acycle and a trend

I Let us see some “intuitive” definition of those decompositions

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1. A First Look at Some Methods To Extract the CycleGrowth Cycle

I Take the growth rate of the seriesI Expansion : Positive rate of growthI Note : the cycle is very volatile (almost iid) – a lot of medium run fluctuations are

eliminated

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

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1. A First Look at Some Methods To Extract the CycleTrend Cycle

I Deviation from linear trend

I The trend is obtained from linear regression

yt = α + βt + ut

I Cycle : yCt = yt − (α + βt)

I Expansion : Output above the trend

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1. A First Look at Some Methods To Extract the CycleTrend Cycle

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

I Note : the cycle can be large and very persistent - a lot of medium and long runfluctuations are not eliminated

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1. A First Look at Some Methods To Extract the CycleCycle = Output Gap

I Define the Output gap as

Actual output− Potential Output

I Expansion : Actual output > Potential output

I Actual output : easy to observe

I Note : How to identify potential output ? (full utilization ?, efficient ?)I Example :

1. estimate yt = α × ut + other controls + εt ,2. define potential output as yP

t = α × 0% + other controls + εt . (One might chooseu = un where un is the natural rate of unemployment (the Oecd chooses the NAIRU(Non Accelerating Inflation Rate of Unemployment))

I Cycle is then yt − yPt

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1. A First Look at Some Methods To Extract the CycleCycle = Output Gap

I This is an over simplified description of the method used by Oecd.

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)

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1. A First Look at Some Methods To Extract the Cycle

I One could describe many other methods to extract the Business Cycle.

I Ideally, we want to get rid of very short run and long run movements of economicactivity.

I The best way to understand this is to decompose economic time series into thefrequency domain and filter them.

I For this, we need to understand how a time series can be represented in thefrequency domain.

I Here I am giving the main intuitions, and will not be very rigourous. (see somestatics or econometrics courses)

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2. Decomposing a time series into frequency domainBackgroud

I A time series xt is a collection of random variables

I It is co-variance stationary if its expectation and autocovariance do not depend ontime

I A co-variance stationary process is therefore summarized by its auto-variancefunction

I Alternative representation : Moving average (link to impulse response)

I Wold theorem : Every co-stationary times series have a (possibly infinite)moving average representation

I Spectral representation is an alternative representation (that contains the sameinformation)

I We restrict to covariance stationary processes (it is constraining)

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2. Decomposing a time series into frequency domainTypical periodic functions

I Idea : A series can be seen as the sum of periodic functions.I 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 thatcos(ωt2) = cos(ωt1) ?

× The solution is t2 − t1 = 2π/ω.

I ω2π is the frequency of oscillation (number of cycles per unit of time)

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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

I With ω = 1, the period is 2π = 6.28 and frequency is 12π = 0.16.

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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)

I With ω = 1/2, the period is 4π = 12.56 and frequency is 14π = 0.08.

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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)

I Here are plotted A cos(t) with A = 1 or A = 2.

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I sin(ωt) behaves the same way, with same amplitude and period, but with a phaseshift

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

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I The idea of spectral decomposition is that with sin and cos, we can span thewhole 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)

I Here we want to treat a and b as mean zero random variables.

I There is always a sum of type (1) periodic functions that reproduces a given timeseries

I The spectral density or spectrum of a series indicates the weight of each frequency(from low to high) in the total variance of the series.

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2. Decomposing a time series into frequency domainAn approximation of the spectrum

I Assume that we observe yt over T (even) periods, and that it is centered.

I Our goal is to decompose yt into T/2 periodic functions of frequenciesω1, ω2, ..., ωT/2, with

ωj =2πj

T, j = 1, ...,T/2

I 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.

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I Find the T parameters (ai , bi ) in (2) by OLS.

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 =

y1y2......

yT−1yT

β =

a1b1......

aT/2bT/2

I If we assume Y = Xβ + u, we can compute the a and b. 29 / 97


I The a and b coefficients are computed as

β = (X ′X )−1X ′Y

I Given that we have T explanatory variables for T observations, the R2 is one andu = 0. Here we are just solving a representation problem, not an estimation one.

I Note that the last column of X is a column of 0. It is replaced by a column of 1to deal with non-centered series.

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I The coefficient are given by

aj =2

T

T∑

t=1

cos(ωj t)yt (3)

bj =2

T

T∑

t=1

sin(ωj t)yt (4)

for j ≤ T/2− 1, and

aT/2 =1

T

T∑

t=1

cos(ωT/2t)yt (5)

bT/2 =1

T

T∑

t=1

yt (6)

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I This is of course an approximation of the series.

I The spectral representation is :

yt =

∫ π

0(a(ω) cos(ωt) + b(ω) sin(ωt))dω (7)

I Any covariance stationary times series process can be represented in the form of(7).

I The function that gives the variance of a(ω) and b(ω), as a function of ω is thespectrum.

I Is y deterministic ? No, “as if” a(ω) and b(ω) were stochastic

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2. Decomposing a time series into frequency domainExtracting the business cycle (BC) component using the frequency domain representation

I A representation like (7) allow us to make precise the notion of extracting thebusiness cycle component of yt .

I Assume yt is observed on a quarterly basis, and that the BC is defined asfluctuations of periods between 6 and 32 quarters (1.5 to 8 years), i.e. forω ∈ [ω ω] = [2π32 ,

2π6 ].

I The the BC component of y , denoted yC , is

yCt =

∫ ω

ω(a(ω) cos(ωt) + b(ω) sin(ωt))dω (8)

I It can be shown that this spectral representation has a time-series equivalent,which is an infinite two-sided moving average of yt :

yCt = B0yt + B1(yt−1 + yt+1) + B2(yt−2 + yt+2) + · · · (9)

with B0 = ω−ωπ and Bj = sin(ωj)−sin(ωj)

πj

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2. Decomposing a time series into frequency domainExtracting the business cycle (BC) component using the frequency domain representation

yCt =

∫ ω

ω(a(ω) cos(ωt) + b(ω) sin(ωt))dω (8)

yCt = B0yt + B1(yt−1 + yt+1) + B2(yt−2 + yt+2) + · · · (9)

I This is what we call a Band-Pass filter

I Why things are not as simple as they look ?

I We have to make an approximation of (9) because it requires an infinity ofobservations.

I Therefore, the MA is truncated according to some distance criterium

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2. Decomposing a time series into frequency domainz-transform

I 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 ) withthe assumption E (Yt) = 0 ;.

Definition 2

For a sequence a0, a1, ..., aj , ..., the generating function of this sequence isa(z) =

∑j ajz

j .

I Note : z needs not to have any interpretation

I The generating function (or z-transform) of a process Yt is Y (z) =∑

t Ytzt .

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2. Decomposing a time series into frequency domainSpectrum

I Correspondence between spectrum and auto-covariogram :I Assume z = e−iω = cosω − i sinω and define

s(ω) =1

2πλ(z) =

1

2π

+∞∑

τ=−∞λτe

−iωτ

I Then one can show that

λτ =

∫ π

−πe iτωs(ω)dω and λ0 =

∫ π

−πs(ω)dω

I The sequence of {λτ} and {s(ω)} bring the same information.

I The function s(ω)λ0

has the property of a probability function over −π ≤ ω ≤ π :

s(ω) ≥ 0 and∫ π−π

s(ω)λ0

dω = 1.I s(ω) (rescaled) is the spectral density.I Next is an estimate of the spectral density, from Groth, Ghil, Hallegatte

and Dumas, “Evidence from Genuine Periodicity and Deterministic Causes of USBusiness Cycles”, 2010. 36 / 97

2. Decomposing a time series into frequency domainFilters

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 density

PS

D

−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.

37 / 97

2. Decomposing a time series into frequency domainFilters

Definition 3

Let Yt =∑m

j=0 cjYt−j = C (L)Yt . Yt is a filtered version of Yt .

I One can show that the spectral density of Yt is

sy (ω) = C (e−iω)C (e iω)sy (ω) = |C (e iω)|2sy (ω)

.

I |C (e iω)|2 is the transfer function of the filter

38 / 97

2. Decomposing a time series into frequency domainExact Band Pass Filter

I Corresponds to a two-sided infinite filter.I |C (e iω)|2 = 1 if ω ∈ [ω ω] and 0 if not.

Figure 13 – Exact Band Pass Filter Transfer Function

0 0.5 1 1.5 2 2.5 3 3.5

frequency

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

|C(e

i )|

2

39 / 97

2. Decomposing a time series into frequency domainApproximate Band Pass Filter

I c0 = 1, c2 = −2, c4 = −1 and cj = 0 for other j .

I Yt = C (L)Yt = Yt − 2(Yt−2 + Yt+2)− (Yt−4 + Yt+4)I Then

|C (e iω)|2 = 4(1− cos 2ω)2

Figure 14 – Approximate Band Pass Filter Transfer Function

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

40 / 97

2. Decomposing a time series into frequency domainBand Pass Filter

I Here is an example of the use of Band Pass filters from Roberto Pancrazi,“Spectral Covariance Instability Test : An Application to the Great Moderation”,TSE 2010.

I High Frequency : periodicity between 2 and 32 quarters

I Medium Frequency : periodicity between 32 and 80 quarters

I High to Medium Frequency : periodicity between 2 and 80 quarters

41 / 97


Figure 15 – 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

42 / 97


Figure 16 – 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

43 / 97

2. Decomposing a time series into frequency domainLow Pass Filter

I Yt =∑m

j=0 Yt−j . Then

|C (e iω)|2 =1− cos(m + 1)ω

1− cosω

Figure 17 – A Low Pass Filter Transfer Function

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

44 / 97

2. Decomposing a time series into frequency domainFirst Difference

I First difference Yt = (1− L)Yt . Then

|C (e iω)|2 = 2− 2 cosω

Figure 18 – First Difference Transfer Function

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

45 / 97

2. Decomposing a time series into frequency domainA High Pass Filter : The Hoddrick-Prescott Transfer Function

I Very popular in the macro literatureI In the time domain, the idea is to remove a trend which is smooth, but not linearI The trend yTt is the Argmin of :

T∑

t=1

(yt − yTt )2 + λ

T∑

t=2

((yTt+1 − yTt )− (yTt − yTt−1))2

I if λ = +∞, it is linear detrending.I The solution of this program solves

yt/λ = yTt+2 − 4yTt+1 + (6 + λ)yTt − 4yTt−1 − yTt−2I The solution is a symmetric MA of order +∞ :

yTt =∞∑

j=−∞a|j |yt+j

I Then yCt = yt − yTt is a time invariant linear symmetric filter.

46 / 97

2. Decomposing a time series into frequency domainA High Pass Filter : The Hoddrick-Prescott Filter

I With λ = 1600 on quarterly data, it removes cycles of period greater than 10years.

I The transfer function is |C (e iω)|2 = 16λ2(1−cosω)4(1+4λ(1−cosω)2)2

Figure 19 – 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

47 / 97

2. Decomposing a time series into frequency domainThe HP filter at work

Figure 20 – US HP Trend

1950 1960 1970 1980 1990 20007

7.5

8

8.5

9

9.5

Quarters

48 / 97

2. Decomposing a time series into frequency domainThe HP filter at work

Figure 21 – 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

49 / 97

4. U.S. Business CyclesBusiness Cycles = Comovements

I Lucas’ definition :“Recurrent fluctuations of macroeconomic aggregates around trend”

I Want to find regularities (Stylized facts)

I Business Cycles are characterized by a set of statistics :

× Volatilities of time series (standard deviations)× Comovements of time series (correlations, serial correlations)

I Why only looking at the US ?

“Though there is absolutely no theoretical reason to anticipate it, one is ledby the facts to conclude that, with respect to the qualitative behavior of co-movements among series, business cycles are all alike.” (Lucas 1977)

50 / 97

4. U.S. Business CyclesMain Real Aggregates

I Consumption (C ) : Nondurables + Services

I Investment (I ) : Durables + Fixed Investment + Changes in inventories

I Government spending (G )

I Output : C + I + G

I Labor : hours worked

I Labor Productivity : Output / Labor

51 / 97


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

52 / 97


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

53 / 97


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

54 / 97


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

55 / 97


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

56 / 97


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

57 / 97

4. U.S. Business CyclesMore (Much More) Data

I Those figures are taken from Stock and Watson, “Business Cycle Fluctuationsin US Macroeconomics Time Series”, chapter 1 of the Handbook ofMacroeconomics, 1999

I Quarterly US data, 1947-1997

58 / 97


16 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.


/ 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. 59 / 97

4. U.S. Business CyclesMore (Much More) DataCh. 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).

Ch. 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). 60 / 97

4. U.S. Business CyclesMore (Much More) Data18 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) .

18 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) .

61 / 97

4. U.S. Business CyclesMore (Much More) DataCh. 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.

Ch. 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.

62 / 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).

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).

63 / 97

4. U.S. Business CyclesMore (Much More) DataCh. 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.

Ch. 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.

64 / 97

4. U.S. Business CyclesMore (Much More) Data2 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).

2 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).

65 / 97

4. U.S. Business CyclesMore (Much More) DataCh. 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).

Ch. 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).

66 / 97



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.


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.

67 / 97


Ch. 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.

Ch. 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.

68 / 97

4. U.S. Business CyclesMore (Much More) Data26 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).

26 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).

69 / 97

4. U.S. Business CyclesMore (Much More) Data2 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.

2 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.

70 / 97



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.


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.

71 / 97

4. U.S. Business CyclesMoments

I We want to characterize fluctuations amplitude and movementsI Amplitude : volatilities standard deviationsI Comovements : correlations

Variable σ(·) σ(·)/σ(y) ρ(·, y) ρ(·, h) Serial(1)

Output 1.70 – – – 0.84

Consumption 0.80 0.47 0.78 – 0.83

Services 1.11 0.66 0.72 – 0.80Non Durables 0.72 0.42 0.71 – 0.77

Investment 6.49 3.83 0.84 – 0.81

Fixed 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 – 0.40

Hours worked 1.69 1.00 0.86 – 0.89

Labor productivity 0.90 0.53 0.41 0.09 0.6972 / 97

4. U.S. Business CyclesSummary

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

7. All those variables are persistent and procyclical except Labor productivity that isacyclical

73 / 97

4. U.S. Business CyclesLucas

I Quoting Lucas 1977 “Understanding Business Cycles”

1. Output movements across broadly defined sectors move together.2. Production of producer and consumer durables exhibits much greater amplitude than

does the production of nondurables3. Production and prices of agricultural goods and natural resources have lower than

average conformity.4. Business profits show high conformity and much greater amplitude than other series.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.

74 / 97

5. International Business CyclesWithin countries

I From Fiorito and Kollintzas, “Stylized facts of business cycles in the G7from a real business cycles perspective”, European Economic Review, 1994.

I Quarterly data 1960-1989

75 / 97


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 76 / 97


Table I




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

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

77 / 97


Table I




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

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

78 / 97

5. International Business CyclesBetween countries

I The cross-correlations of output are high

I The cross-correlations of output are higher than the one of productivity

I The cross-correlations of productivity are higher than the cross-correlations ofconsumption.

I The cross-correlations of output, investment and employment are generallypositive.

I See Ambler, Cardia and Zimmermann, “International business cycles : Whatare the facts ?”, Journal of Monetary Economics, 2004.

79 / 97


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 1Average cross-correlations

Averages from 190 cross-correlations From BKK (1995)

Variable Full sample Europe-U.S. Baseline model1960:1–2000:4 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: marginalsignificance 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


ry;ynprc;cn;

ry;ynprz;zn;

ARTICLE IN PRESS




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


0.00 0.00 0.00


0.00 0.00 0.00





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ry;ynprc;cn;

ry;ynprz;zn;

ARTICLE IN PRESS




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


0.00 0.00 0.00


0.00 0.00 0.00






ry;ynprc;cn;

ry;ynprz;zn;

ARTICLE IN PRESS




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


0.00 0.00 0.00


0.00 0.00 0.00





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3. Quick Overview of National Accounts

I Data : we mainly consider aggregate quantities of goods and services and prices,labor market statistics and interest rates.

I Aggregate quantities of goods and services and prices mostly come from nationalaccounts.

I Decent level of harmonization across countries (System of National Accounts(SNA) promoted by the United Nations)

I 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 I present here the basic concepts – mainly about definitions and conventions(“accounting”)

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3. Quick Overview of National AccountsSupply and Use

I For an economy, the total supply of goods and services must equal the total usestotal supply of goods and services = total uses of goods and services

I Expanding each side :output + imports = intermediate consumption + final consumption + gross

capital formation + exports

I Note 1 : Intermediate consumption consists of the goods and services consumedin the production process (excluding the consumption of fixed assets)

I Note 2 : Final consumption consists of the goods and services provided to thebenefit of final consumers.

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I Gross value added (leave for a moment the issue of taxes and subsidies on goodsand services aside)

gross value added = output - intermediate consumption = final

consumption + gross capital formation + exports - imports

I Final consumption and gross fixed capital formation are measured from theperspective of the consumer or purchaser. Their values take into account thetaxes and subsidies on goods and services.

I Output is measured from the perspective of producers in terms of the receiptsreceivable by them, leaving all of the taxes on goods and services aside whileincluding subsidies on goods and services.

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I Therefore, taxes on goods and services have to be added to output and subsidiessubtracted from output in order to arrive at a uniform valuation of supply anduses.

output + taxes - subsidies - intermediate consumption = final

consumption + gross capital formation + exports - imports

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3. Quick Overview of National AccountsGross domestic product

I GDP can be measured by having the values for output and intermediateconsumption aggregated across the various industries of an economy. This is GDPby production approach :

GDP = output + taxes - subsidies - intermediate consumption = gross

value added + taxes - subsidies

I Gross domestic product can also be viewed as the value of all goods and servicesavailable for different domestic final uses or for exports. This is GDP byexpenditure approach :

GDP = final consumption + gross capital formation + exports - imports

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3. Quick Overview of National AccountsGross domestic product

I The production process creates incomes for not only the owners of the inputs usedin production but also for owners of capital and for the government. The value ofthose incomes is equal to gross domestic product. Hence, GDP can also becalculated as the sum of compensation of employees, taxes less subsidies andgross operating surplus/mixed income. This is the GDP by income approach :

GDP = compensation of employees + taxes - subsidies + gross operating

surplus / mixed income

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3. Quick Overview of National AccountsGross national income

I Gross domestic product refers to production of all resident units within theborders of a country, which is not exactly the same as the production of allproductive 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

I All GNI is not available for final uses domestically since some of it is transferred toother countries without anything being received in exchange (for exampleremittances)gross national disposable income = GNI + current transfers from the

rest of the world - current transfers to the rest of the world

I Gross national disposable income is the income available for consumption andsaving :gross national disposable income = final consumption expenditure +

gross saving 88 / 97

3. Quick Overview of National AccountsGross saving, gross capital formation and net lending

I Gross saving together with net capital transfers (capital transfers receivable lesscapital transfers payable) from the rest of the world provides the resources forinvestment in non-financial assets, which is called gross capital formation.

I Gross capital formation = the net acquisition of fixed assets, such as residentialand non-residential buildings, plants and equipments, the net acquisition ofvaluables and/or the increase in inventories.

I The difference between gross saving plus net capital transfers and gross capitalformation is net borrowing or net lending from the rest of the world, dependingwhether uses exceed resources or vice versa.gross saving = gross national disposable income - final consumption

andnet lending (+) / net borrowing (-) = gross saving + net capital

transfers - gross capital formation

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3. Quick Overview of National AccountsNet borrowing / net lending in financial accounts

I Net borrowing / net lending is also reflected in transactions in financial assets andliabilities with the rest of the world. It is equal to the difference between netacquisition 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

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3. Quick Overview of National AccountsChanges in net worth

I Net worth is the difference between the total value of non-financial and financialassets and the total value of liabilities of an economy. It is a measure of the netwealth of a nation. Change in net worth measures the change in wealth of anation.

I Net capital transfers from abroad are equal to gross capital formation lessconsumption of fixed capital and plus net lending (+)/net borrowing (-) from therest of the world.

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3. Quick Overview of National AccountsSummary

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

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

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Definition 4

Output is the value of the goods and services which are produced by an establishmentin the economy that become available for use outside that establishment

Definition 5

Intermediate consumption includes goods and services which are entirely used up byproducers in the course of production to produce output of goods and services duringthe accounting period.

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3. Quick Overview of National AccountsDefinitions of Output, Consumption and Investment

Definition 6

Final consumption includes goods and services which are used by households or thecommunity to satisfy their individual wants and social needs. Consumption is brokendown into a) Final consumption expenditure of households ; b) Final consumptionexpenditure of general government ; c) Final consumption expenditure of non-profitinstitutions serving households.

I For households, all consumed goods, whether durable (cars, refrigerators,air-conditioners etc.) or non-durable (food, clothes), are part of final consumption,with the exception of purchases for own-construction or improvements ofresidential housing, which are treated as part of gross capital formation.

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3. Quick Overview of National AccountsDefinitions of Output, Consumption and Investment

Definition 7

Gross capital formation in SNA is the same as the concept of investment in capitalgoods used by economists. It includes only produced capital goods (machinery,buildings, roads, artistic originals etc.) and improvements to non-produced assets.Gross capital formation measures the additions to the capital stock of buildings,equipment and inventories, i.e., the additions to the capacity to produce more goodsand income in the future.

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3. Quick Overview of National AccountsPrices

I Outputs, whether or not sold, are valued at market or “equivalent market prices”.I 3 types of market prices of the same good due to taxes and subsidies.I 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

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

I Output is recommended to be measured at production costs when products haveno market price.

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3. Quick Overview of National AccountsNominal and Real Quantities

I To compare quantities of two different years, one needs to adjust for changes inprices, to deflate nominal (current dollars) measures in order to obtain real(constant dollars) quantities.

I This is done (basically) by choosing a base year (year N). The real quantities ofyear N + 1 are then multiplied by their price in year N to compute constant dollarmeasures (in dollars of year N).

I This is easy for potatoes (always the same good), not so for computers or cars(improvement in quality).

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