Transcript Politique environmentale

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 Cycles expansions
and contractions
BUSINESS CYCLE
REFERENCE DATES
Peak
Quarterly dates
are in parentheses
DURATION IN MONTHS
Trough
Contraction
Peak
to
Trough
Expansion
Previous trough
to
this peak
Cycle
Trough from Peak from
Previous
Previous
Trough
Peak
--
--
June 1857(II)
October 1860(III)
April 1865(I)
June 1869(II)
October 1873(III)
December 1854 (IV) -December 1858 (IV)
June 1861 (III)
December 1867 (I)
December 1870 (IV)
March 1879 (I)
18
8
32
18
65
30
22
46
18
34
-48 -30
78
36
99
March 1882(I)
March 1887(II)
July 1890(III)
January 1893(I)
December 1895(IV)
May 1885 (II)
April 1888 (I)
May 1891 (II)
June 1894 (II)
June 1897 (II)
38
13
10
17
18
36
22
27
20
18
74
35
37
37
36
101
60
40
30
35
June 1899(III)
September 1902(IV)
May 1907(II)
January 1910(I)
January 1913(I)
December 1900 (IV)
August 1904 (III)
June 1908 (II)
January 1912 (IV)
December 1914 (IV)
18
23
13
24
23
24
21
33
19
12
42
44
46
43
35
42
39
56
32
36
August 1918(III)
January 1920(I)
May 1923(II)
October 1926(III)
August 1929(III)
March 1919 (I)
July 1921 (III)
July 1924 (III)
November 1927 (IV)
March 1933 (I)
7
18
14
13
43
44
10
22
27
21
51
28
36
40
64
67
17
40
41
34
Source: Public Information Office National Bureau of Economic Research, Inc.
40
54
50
52
Business Cycles expansions
and contractions (f’d)
May 1937(II)
February 1945(I)
November 1948(IV)
July 1953(II)
August 1957(III)
June 1938 (II)
October 1945 (IV)
October 1949 (IV)
May 1954 (II)
April 1958 (II)
13
8
11
10
8
50
80
37
45
39
63
88
48
55
47
93
93
45
56
49
April 1960(II)
December 1969(IV)
November 1973(IV)
January 1980(I)
July 1981(III)
February 1961 (I)
November 1970 (IV)
March 1975 (I)
July 1980 (III)
November 1982 (IV)
10
11
16
6
16
24
106
36
58
12
34
117
52
64
28
32
116
47
74
18
July 1990(III)
March 2001(I)
March 1991(I)
November 2001 (IV)
8
8
92
120
100
128
108
128
17
22
18
10
38
27
35
57
55 56*
48 49**
53
67
18
22
20
10
33
24
26
52
51
46
46
63
Average, all cycles:
1854-2001 (32 cycles)
1854-1919 (16 cycles)
1919-1945 (6 cycles)
1945-2001 (10 cycles)
Average, peacetime cycles:
1854-2001 (27 cycles)
1854-1919 (14 cycles)
1919-1945 (5 cycles)
1945-2001 (8 cycles)
* 31 cycles
** 15 cycles
*** 26 cycles
**** 13 cycles
Source: Public Information Office National Bureau of Economic Research, Inc.
53
67
52***
47****
45
63
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
xˆ  x  xT  x 
J
a
j  J
x
j j
xˆ : cycle component
x T : trend component
min  x
t
x 
T t
1
t 1
 1


 xT

2
 
s.t. xT1  xT  xT  xT1
 2

2

 : controls the properties of the trend component generated by the filter
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: :
x
BP
t


a
h
xt  h  a ( L) xt
h  
L : lag operator.
Symmetry ( ak  ak ) is imposed.
For stationary time-series:

xt    ( ) d

 ( ) : random periodic components
BP filter (f’d)
Then :

x
BP
t
   ( ) ( )d


1 if 1     2
Frequency-response function :  ( )  

0 otherwise
with 1   / 16,  2   / 3 ,   2 / P and 6  P  32
One can then show that :
a0  2  1  /  and ah  sin(h2 ) / h  sin(h1 ) / h for h  1,2,...
x
BK
t

K
a
h K
h
x t  h  a K ( L) x t
M. Baxter and R. King (1999)
« Measuring BC: Approximate Band-Pass
Filters for Economic Time Series »
Goods’market
Inputs
Labor market
All variables (except r) are in logaritms and have been detrended using HP filter
Source: Stock and Watson (1998)
Stylized facts for Europe
Germany 1967:1-1984:2
Switzerland 1967:1-1984:2
 xˆ
 xˆ /  yˆ
Corr ( xˆ, yˆ )
yˆ
cˆ
iˆ
hˆ
pˆ
2.38
1
1
1.68
0.71
0.67
9.41
3.93
0.89
1.37
0.58
0.78
1.57
0.66
0.84
UK 1967:1-1984:2
 xˆ
 xˆ /  yˆ
Corr ( xˆ, yˆ )
 xˆ
 xˆ /  yˆ
Corr ( xˆ, yˆ )
yˆ
cˆ
iˆ
hˆ
pˆ
1.56
1
1
1.42
0.91
0.66
4.59
2.94
0.79
1.10
0.71
0.65
1.19
0.76
0.71
France 1970:1-1990:2
yˆ
cˆ
iˆ
hˆ
pˆ
1.73
1
1
1.99
1.15
0.66
3.42
1.98
0.71
1.11
0.64
0.48
1.55
0.89
0.77
 xˆ
 xˆ /  yˆ
Corr ( xˆ, yˆ )
yˆ
cˆ
iˆ
hˆ
pˆ
0.91
1
1
0.81
0.9
0.63
3.64
4.01
0.80
0.83
0.92
0.71
0.65
0.72
0.45