chapter 13. some b usiness cycle facts econ320 prof mike kennedy
TRANSCRIPT
Chapter 13. Some business cycle facts
ECON320Prof Mike Kennedy
Overview
• We want to examine the business cycle facts as this will help us to:– Understand the driving forces in the determination of
the business cycle– This in turn tells us where to look
• Any theory that we develop must be able to explain the business cycle facts
• We will need to understand some basic statistical concepts as this will help us to better quantify things
Characteristics of business cycles: What will have to be explained
• Aggregate economic activity: Cycles are characterised by co-movements in a large number of activities that affects the aggregate output
• Organisation in business enterprises: They occur in decentralised market economies
• Expansions and contractions: They are characterised by period of positive and negative (or slow) growth, with expansions generally lasting longer than contractions, especially after WWII
• Duration of more than a year: A full cycle will last more than one year
• Recurrent but not periodic: While repetitive they are not regular or periodic – there is no fixed period for a cycle to arrive
Dating the Canadian business cycle: Typically defined from the peak to the trough
What a business cycle looks like at the aggregate level in theory
Actual business cycles in some major OECD economies
19851986
19871988
19891990
19911992
19931994
19951996
19971998
19992000
20012002
20032004
20052006
20072008
20092010
20112012
20132014
20152016
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8Great recession Canada
Japan United Kingdom
United States Euro area (15 countries)
OECD - Total
Source: OECD Economic Outlook database and IMF (for UK)
Business cycles in the euro area
19851986
19871988
19891990
19911992
19931994
19951996
19971998
19992000
20012002
20032004
20052006
20072008
20092010
20112012
20132014
20152016
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8 Great recession Austria Belgium Denmark
Finland France Germany Italy
Netherlands Portugal Spain
Source: OECD Economic Outlook database
Quantifying the business cycle: De-trending time series
• We want to separate the trend from the cycle in any times series in which we are interested. Suppose that GDP (Y) is:
Where the superscripts – g and c – represent the growth and cyclical components of Yt, respectively.
• Letting yt = ln(Yt) then:
• We could measure the trend by a simple regression of GDP on time but this wouldn’t capture changes in potential growth.
• We know from growth theory – either neo-classical or endogenous – the underlying or potential growth will change over time.
€
Yt =Ytg ×Yt
c
€
yt = ytg + yt
c
The properties of the Hodrick-Prescott filter• A well known and used technique for estimating the yt
g component in a times series – like GDP – is the Hodrick-Prescott filter, which can capture changes in potential growth.
• The growth component of the series is determined by minimizing:
• The first term (yt – gt) measure the cycle while the second captures change in the growth rate.
• If λ is set equal to 0 then yt = gt implying that output was always at potential.• If we set λ = ∞ then we would get a straight line for potential output implying
that potential growth never changed.• The compromise is somewhere in the middle. For quarterly series the
convention is to set λ = 1600 (ie, 402) and 100 (102) for annual data.
€
HP = (ytt=1
T
∑ − gt )2 +λ [(gt+1
t=2
T−1
∑ − gt ) − (gt − gt−1)]2
Criteria for identifying a business cycle
1. A trough must be followed by a peak and vice versa
2. The expansion and contraction phases must last a minimum of 2 quarters – we need a minimum degree of persistence
3. The cycle must span a minimum of 5 quarters – this is a convention
Real GDP vs. Trend (using an HP filter: λ = 1600)
Q1-1981
Q1-1982
Q1-1983
Q1-1984
Q1-1985
Q1-1986
Q1-1987
Q1-1988
Q1-1989
Q1-1990
Q1-1991
Q1-1992
Q1-1993
Q1-1994
Q1-1995
Q1-1996
Q1-1997
Q1-1998
Q1-1999
Q1-2000
Q1-2001
Q1-2002
Q1-2003
Q1-2004
Q1-2005
Q1-2006
Q1-2007
Q1-2008
Q1-2009
Q1-2010
Q1-2011
Q1-2012
Q1-201313.2
13.4
13.6
13.8
14
14.2
14.4
14.6
14.8
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
Recessions
Cycle GDP
Trend GDP
LnGDP
Standard deviation = 1.104%
Volatility
• We want to study the statistical components of the of each series (consumption, investment, government spending, exports and imports)
• We can measure volatility by calculating the standard deviation of the cyclical component.
€
sx =1
T −1(xt
t=1
T
∑ − x )2
Real Consumption vs. Trend (using an HP filter)
12.6
12.8
13
13.2
13.4
13.6
13.8
14
14.2
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
Recessions
Cycle CON
Trend CON
LnCON
Standard deviation = 1.106%
Real Investment vs. Trend (using an HP filter)
Q1-1981
Q1-1982
Q1-1983
Q1-1984
Q1-1985
Q1-1986
Q1-1987
Q1-1988
Q1-1989
Q1-1990
Q1-1991
Q1-1992
Q1-1993
Q1-1994
Q1-1995
Q1-1996
Q1-1997
Q1-1998
Q1-1999
Q1-2000
Q1-2001
Q1-2002
Q1-2003
Q1-2004
Q1-2005
Q1-2006
Q1-2007
Q1-2008
Q1-2009
Q1-2010
Q1-2011
Q1-2012
Q1-201311.6
11.8
12
12.2
12.4
12.6
12.8
13
13.2
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2Recessions
Cycle INV
Trend INV
LnINV
Standard deviation = 5.528%
Real Government Spending vs. Trend (using an HP filter)
Q1-1981
Q1-1982
Q1-1983
Q1-1984
Q1-1985
Q1-1986
Q1-1987
Q1-1988
Q1-1989
Q1-1990
Q1-1991
Q1-1992
Q1-1993
Q1-1994
Q1-1995
Q1-1996
Q1-1997
Q1-1998
Q1-1999
Q1-2000
Q1-2001
Q1-2002
Q1-2003
Q1-2004
Q1-2005
Q1-2006
Q1-2007
Q1-2008
Q1-2009
Q1-2010
Q1-2011
Q1-2012
Q1-201311.6
11.8
12
12.2
12.4
12.6
12.8
13
13.2
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2Recessions
Cycle GOV
Trend GOV
LnGOV
Standard deviation = 0.959%
Real Exports vs. Trend (using an HP filter)
Q1-1981 Q2-1983 Q3-1985 Q4-1987 Q1-1990 Q2-1992 Q3-1994 Q4-1996 Q1-1999 Q2-2001 Q3-2003 Q4-2005 Q1-2008 Q2-2010 Q3-201211.6
11.8
12
12.2
12.4
12.6
12.8
13
13.2
13.4
13.6
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2Recessions
Cycle EXP
Trend EXP
LnEXPScale different
Standard deviation = 3.761%
Real Imports vs. Trend (using an HP filter)
Q2-1981 Q3-1983 Q4-1985 Q1-1988 Q2-1990 Q3-1992 Q4-1994 Q1-1997 Q2-1999 Q3-2001 Q4-2003 Q1-2006 Q2-2008 Q3-2010 Q4-201211.4
11.6
11.8
12
12.2
12.4
12.6
12.8
13
13.2
13.4
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2Cycle IMPRecessionsTrend IMPLnIMP
Scale different
Standard deviation = 4.980%
Employment vs. Trend (using an HP filter)
Q1-1981
Q1-1982
Q1-1983
Q1-1984
Q1-1985
Q1-1986
Q1-1987
Q1-1988
Q1-1989
Q1-1990
Q1-1991
Q1-1992
Q1-1993
Q1-1994
Q1-1995
Q1-1996
Q1-1997
Q1-1998
Q1-1999
Q1-2000
Q1-2001
Q1-2002
Q1-2003
Q1-2004
Q1-2005
Q1-2006
Q1-2007
Q1-2008
Q1-2009
Q1-2010
Q1-2011
Q1-2012
Q1-20132.3
2.4
2.5
2.6
2.7
2.8
2.9
-0.20
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
0.20Cycle EmplRecessionsTrend emplLnEmpl
Standard deviation = 1.06%
Summing up volatilityThe table below shows three stylised business cycle facts:
1. Investment is much more volatile than GDP2. Foreign trade is also more volatile3. Employment is typically less volatile as is consumption and
government spending
Correlations and leads and lags• We also want to know how the various variables (cycles) we examined
move in relationship to GDP – how do they co-vary?• We can calculate the covariance between say cyclical consumption and
cyclical GDP which will give the degree to which they move together
• To be independent of the units choose we normalise the deviations by their respective standard deviations which gets us the coefficient of correlation€
sxc =1
T −1(xt
t=1
T
∑ − x )2 (ct −c )2
€
ρ(xt , xt−n ) =sxc
sxsc
=
(xtt=1
T
∑ − x )2 (xt−n − x ' )2
(xtt=1
T
∑ − x )2 × (xt−n − x ' )2
t=1
T
∑
Correlations and leads and lags, con’t
• If ct represents the cyclical component of GDP then any variable xt is procyclical if ρ(xt, ct) is greater than zero and vice versa
Correlations and leads and lags, con’t
The stylised business cycle facts that emerge from this are:
4. Consumption, investment and imports are strongly pro-cyclical
5. Employment (unemployment) is procyclical with GDP and more so than real wages and productivity (not shown)
6. Inflation is procyclical but not that strong7. Employment, inflation and nominal interest rates are
lagging indicators (not shown, see text)
Persistence
• We can measure persistence by calculating the correlation between its current and lagged values.
• For this we need the coefficient of autocorrelation
• Note that the variable ( ) is the mean of the lagged series€
ρ(xt ,xt −n ) =sxc
sxsc
=(xt
t =1
T
∑ − x )2(xt −n − x ')2
(xtt =1
T
∑ − x )2 × (xt −n − x ')2
t =1
T
∑
€
x '
Persistence, con’t
The stylised business cycle facts that emerge from this analysis are:8. There is considerable persistence in GDP and about the
same in consumption9. Employment tends to be more persistent than GDP
Measuring and decomposing the output gap: The production function approach
€
Yt = BtK tα Lt
1−α , 0 < α <1
€
Lt = (1 − ut )N tH t
€
Yt = BtK tα [(1 − ut )N tH t ]
1−α
€
ln Bt = lnYt −α ln K t + (1 −α )ln Lt€
Y t = B tK tα [(1−u t )N tH t ]
1−α
€
yt − y t = ln Bt − ln B t +(1−α )[(ln N t − ln N t ) + (ln H t − ln H t ) − (ut −u t )]
Real GDP vs. Trend Annual Data (using an HP filter: λ = 100)
19851986
19871988
19891990
19911992
19931994
19951996
19971998
19992000
20012002
20032004
20052006
20072008
20092010
20112012
20132014
20152016
6.7
6.8
6.9
7
7.1
7.2
7.3
7.4
7.5
7.6
-0.20
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
0.20
Cyclical output production function Recessions
Potential output production function GDP
Real GDP vs. Potential Annual Data(Using a production function)
19851986
19871988
19891990
19911992
19931994
19951996
19971998
19992000
20012002
20032004
20052006
20072008
20092010
20112012
20132014
20152016
6.7
6.8
6.9
7
7.1
7.2
7.3
7.4
7.5
7.6
-0.20
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
0.20
Cyclical output HP filter
Recessions
GDP
Potential output HP filter
Comparing the two methods of estimating the output gap
19851986
19871988
19891990
19911992
19931994
19951996
19971998
19992000
20012002
20032004
20052006
20072008
20092010
20112012
20132014
20152016
-0.05
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
0.04
0.05RecessionsCyclical output production functionCyclical output HP filter
The output gap and the contribution of labour (L)
19851986
19871988
19891990
19911992
19931994
19951996
19971998
19992000
20012002
20032004
20052006
20072008
20092010
20112012
20132014
20152016
-0.05
-0.04
-0.03
-0.02
-0.01
0.00
0.01
0.02
0.03
0.04
Cyclical output production function
(1-α)(lnL-lnL*)
The output gap and the contribution of productivity shocks (B)
19851986
19871988
19891990
19911992
19931994
19951996
19971998
19992000
20012002
20032004
20052006
20072008
20092010
20112012
20132014
20152016
-0.05
-0.04
-0.03
-0.02
-0.01
0.00
0.01
0.02
0.03
0.04Cyclical output production function
ln(B)-ln(B*)
The contribution of labour vs. productivity: Productivity looks to be very important
19851986
19871988
19891990
19911992
19931994
19951996
19971998
19992000
20012002
20032004
20052006
20072008
20092010
20112012
20132014
20152016
-0.05
-0.04
-0.03
-0.02
-0.01
0.00
0.01
0.02
0.03
0.04
0.05 ln(B)-ln(B*)
(1-α)(lnL-lnL*)
Cyclical output production function
The output gap and the contribution of unemployment rate (u)
19851986
19871988
19891990
19911992
19931994
19951996
19971998
19992000
20012002
20032004
20052006
20072008
20092010
20112012
20132014
20152016
-0.050
-0.040
-0.030
-0.020
-0.010
0.000
0.010
0.020
0.030
0.040
0.050
Cyclical output production function
(1-α)(u*-u)
The output gap and the contribution of hours worked (H)
19851986
19871988
19891990
19911992
19931994
19951996
19971998
19992000
20012002
20032004
20052006
20072008
20092010
20112012
20132014
20152016
-0.05
-0.04
-0.03
-0.02
-0.01
0.00
0.01
0.02
0.03
0.04Cyclical output production function
(1-α)(lnH-lnH*)
The output gap and the contribution of the labour force (N)
19851986
19871988
19891990
19911992
19931994
19951996
19971998
19992000
20012002
20032004
20052006
20072008
20092010
20112012
20132014
20152016
-0.05
-0.04
-0.03
-0.02
-0.01
0.00
0.01
0.02
0.03
0.04
Cyclical output production function
(1-α)(lnN-lnN*)
Another look at labour input and its driving factors
19851986
19871988
19891990
19911992
19931994
19951996
19971998
19992000
20012002
20032004
20052006
20072008
20092010
20112012
20132014
20152016
-0.05
-0.04
-0.03
-0.02
-0.01
0.00
0.01
0.02
0.03
0.04
0.05(1-α)(lnN-lnN*)
(1-α)(lnH-lnH*)
(1-α)(u*-u)
(1-α)(lnL-lnL*)
More stylised business cycle facts
10. TFP varies in a procyclical manner, explaining most of the variation in the business cycle, particularly at turning points
11. Most of the variation in total labour input reflects cyclical unemployment but average hours worked and to some extent labour force vary pro-cyclically
Should we worry about capital?
19851986
19871988
19891990
19911992
19931994
19951996
19971998
19992000
20012002
20032004
20052006
20072008
20092010
20112012
20132014
20152016
-0.05
-0.04
-0.03
-0.02
-0.01
0.00
0.01
0.02
0.03
0.04
0.05
ln(B)-ln(B*) α(lnKadj-lnKadl*) (1-α)(lnL-lnL*) Cyclical output production function
Measuring the factors determining labour’s input with capital taken into account
19851986
19871988
19891990
19911992
19931994
19951996
19971998
19992000
20012002
20032004
20052006
20072008
20092010
20112012
20132014
20152016
-0.03
-0.02
-0.01
0.00
0.01
0.02
0.03
(1-α)(lnN-lnN*) (1-α)(lnH-lnH*) (1-α)(u*-u)
(1-α)(lnL-lnL*)
We want to develop an aggregate supply and demand model of the economy
Rational expectations
€
Xte
Subjective expectations}
= E[Xt | It−1]
Objective conditional expectations6 7 4 8 4
A closing note: A comparison of Canadian and US Cycles
6.6
6.7
6.8
6.9
7
7.1
7.2
7.3
7.4
7.5
7.6
7.7
-0.20
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
0.20Canada
RecessionsCycleLn(GDP)Ln(GDP poten-tial)
8.8
8.9
9
9.1
9.2
9.3
9.4
9.5
9.6
9.7
9.8
9.9
-0.20
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
0.20United States
RecessionsCycleLn(GDP)Ln(GDP potential)
Data on potential GDP from OECD Economic Outlook database