Fluctuations and facts

Chapter 2

R. Lucas (1977) «Understanding Business Cycles»

“…[understanding] business cycles means constructing a model in the most literal sense: a fully articulated artificial economy which behaves through time as to imitate closely the time series behavior of actual economies.”

King and Rebelo (1999)“Resuscitating RBC”

"Business cycles research studies the causes and consequences of the recurrent expansions and contractions in aggregate economic activity"

Burns and Mitchell [1946]“Measuring business cycles”, NBER

“Business cycles are a type of fluctuation found in the aggregate economic activity of nations that organize their work mainly in business enterprises: a cycle consists of expansions occurring at the same time in many economic activities, followed by similarly general recessions, contractions and revivals which merge into the expansion phase of the next cycle; this sequence of changes is recurrent but not periodic; in duration, business cycles vary from more than one year to ten or twelve years; they are not divisible into shorter cycles of similar character with amplitudes approximating their own.”

BUSINESS CYCLE DURATION IN MONTHSREFERENCE DATESPeak Trough Contraction Expansion CycleQuarterly dates Peak Previous trough Trough from Peak fromare in parentheses to to Previous Previous

Trough this peak Trough Peak

December 1854 (IV) -- -- -- --June 1857(II) December 1858 (IV) 18 30 48 --October 1860(III) June 1861 (III) 8 22 30 40April 1865(I) December 1867 (I) 32 46 78 54June 1869(II) December 1870 (IV) 18 18 36 50October 1873(III) March 1879 (I) 65 34 99 52

March 1882(I) May 1885 (II) 38 36 74 101March 1887(II) April 1888 (I) 13 22 35 60July 1890(III) May 1891 (II) 10 27 37 40January 1893(I) June 1894 (II) 17 20 37 30December 1895(IV) June 1897 (II) 18 18 36 35

June 1899(III) December 1900 (IV) 18 24 42 42September 1902(IV) August 1904 (III) 23 21 44 39May 1907(II) June 1908 (II) 13 33 46 56January 1910(I) January 1912 (IV) 24 19 43 32January 1913(I) December 1914 (IV) 23 12 35 36

August 1918(III) March 1919 (I) 7 44 51 67January 1920(I) July 1921 (III) 18 10 28 17May 1923(II) July 1924 (III) 14 22 36 40October 1926(III) November 1927 (IV) 13 27 40 41August 1929(III) March 1933 (I) 43 21 64 34

Source: Public Information Office National Bureau of Economic Research, Inc.

Business Cycles expansionsand contractions

May 1937(II) June 1938 (II) 13 50 63 93February 1945(I) October 1945 (IV) 8 80 88 93November 1948(IV) October 1949 (IV) 11 37 48 45July 1953(II) May 1954 (II) 10 45 55 56August 1957(III) April 1958 (II) 8 39 47 49

April 1960(II) February 1961 (I) 10 24 34 32December 1969(IV) November 1970 (IV) 11 106 117 116November 1973(IV) March 1975 (I) 16 36 52 47January 1980(I) July 1980 (III) 6 58 64 74July 1981(III) November 1982 (IV) 16 12 28 18

July 1990(III) March 1991(I) 8 92 100 108March 2001(I) November 2001 (IV) 8 120 128 128

Average, all cycles:1854-2001 (32 cycles) 17 38 55 56*1854-1919 (16 cycles) 22 27 48 49**1919-1945 (6 cycles) 18 35 53 531945-2001 (10 cycles) 10 57 67 67Average, peacetime cycles:1854-2001 (27 cycles) 18 33 51 52***1854-1919 (14 cycles) 22 24 46 47****1919-1945 (5 cycles) 20 26 46 451945-2001 (8 cycles) 10 52 63 63* 31 cycles** 15 cycles*** 26 cycles**** 13 cycles

Source: Public Information Office National Bureau of Economic Research, Inc.

Business Cycles expansions and contractions (f’d)

Cycles in the US (1876 – 1986) Sachs et Larrain (1990)Macroeconomics

Cycles in the US (1876 – 1986) Sachs et Larrain (1990)Macroeconomics (f’d)

Cycles in the US (1876 – 1986) Sachs et Larrain (1990)Macroeconomics (f'd)

Estimated instantaneous standard deviation of 4-quarter growth of GDP per capita

Source : Stock and Watson 2003

Estimated instantaneous standard deviation of 4-quarter growth of GDP per capita (f’ed)

Stock and Watson (1988)« Variable trends in Economic Time Series »

O. Blanchard and S. Fischer [1989] Lectures on macroeconomics

“the picture that emerge is […] that of an economy on which both types of shocks play an important role. Transitory shocks matter and have a hump-shaped effect on output before their effects die out.

But the path of output would be far from smooth even in the absence of those transitory shocks.

What emerges is a more complex image of fluctuations, with temporary shocks moving output around a stochastic trend that itself contributes significantly to the movements in the real GNP”

Linear filter 1: HP filter

: cycle component

: trend component

: controls the properties of the trend component generated by the filter

1

2

2

11

1

2

..

min1

tTTTT

tT

x

xxxxts

xxtT

Tx

J

Jjjj

T xaxxxx ˆ

x

King and Rebelo (1999)

King and Rebelo (1993)

linear

King and Rebelo (1993)

Stock and Watson (1998)

Linear filter 2: BP-filter (Baxter and King, 1999)

The ideal band-pass filter has the following 2-sided infinite moving average representation: :

L : lag operator. Symmetry ( ) is imposed.

For stationary time-series:

: random periodic components

hthth

BPt xLaxax )(

kk aa

dxt )(

)(

BP filter (f’d)

Then :

Frequency-response function :

with , and

One can then show that :

dx BPt )()(

otherwise0

if1)(

21

3/,16/ 21 P/2 326 P

,...2,1/)sin(/)sin(/ 12120 hforhhhhaanda h

K

KhtKhth

BKt xLaxax )(

M. Baxter and R. King (1999)« Measuring BC: Approximate Band-Pass Filters for Economic Time Series »

Goods’market

Inputs

Labor market

Source: Stock and Watson (1998)

All variables (except r) are in logaritms and have been detrended using HP filter

Stylized facts for Europe

y c i h p x 2.38 1.68 9.41 1.37 1.57 yx ˆˆ / 1 0.71 3.93 0.58 0.66

)ˆ,ˆ( yxCorr 1 0.67 0.89 0.78 0.84

y c i h p x 1.56 1.42 4.59 1.10 1.19 yx ˆˆ / 1 0.91 2.94 0.71 0.76

)ˆ,ˆ( yxCorr 1 0.66 0.79 0.65 0.71

y c i h p x 1.73 1.99 3.42 1.11 1.55 yx ˆˆ / 1 1.15 1.98 0.64 0.89

)ˆ,ˆ( yxCorr 1 0.66 0.71 0.48 0.77

y c i h p x 0.91 0.81 3.64 0.83 0.65 yx ˆˆ / 1 0.9 4.01 0.92 0.72

)ˆ,ˆ( yxCorr 1 0.63 0.80 0.71 0.45

Switzerland 1967:1-1984:2 Germany 1967:1-1984:2

UK 1967:1-1984:2 France 1970:1-1990:2