Transcript Estimating potential output business survey data in a SVAR

Estimating potential output using
business survey data in a SVAR
framework
3° annual WORKSHOP
on Macroeconomic Forecasting
Montreal 5-6 october 2007
Tatiana Cesaroni
ISAE-ITALY
Motivation
 Potential output and the related concept of output gap
represent important concepts for economic policy
evaluation and analysis
 Most macroeconomic models include estimates of
potential output
 Potential output plays a key role in business cycle
research
Contribution
 Provide potential output and output gap estimates for
Italy using information coming from business survey data
 Compare the estimated output gap obtained with
different methods (univariate vs multivariate
decompositions)
 Evaluate the reliability of the estimates at the end of
sample
 Compare peaks and troughs of the estimated output gap
with turning points of the Italian official cyclical
chronology
Definitions
Potential output
It is defined as the maximum capacity of a given
economy
Output gap
 It is defined as the difference between actual level of output and its
potential.
y
t

 y tT  100
 It is used as indicator of the cyclical position of the economy
Measurement problems
 Potential output represents a theoretical concept it is not
observed and for this reason need to be estimated
 The empirical evidence shows a significant sensibility of
the estimates with respect to the method used (see
Orphanides, and Van Norden, 2001)
 The choice of the methodology is not unique since
depends on more factors like the aim of the research,
the statistical properties of data used etc.
Univariate detrending methods
 Deterministic trend (quadratic trend)
 Filters (Hodrick Prescott, Band Pass)
 Unobserved components models
Drawback
We cannot use information coming from
external data
Structural VAR decomposition
The multivariate trend cycle decomposition method used is based
on SVAR models with long run restrictions (Blanchard and
Quah,1989)
 Advantages
 Possibility to give an economic interpretation to the shocks
 Absence of a priori restrictions on the dynamics of trend/cycle
components
 Absence of end of sample problems (VAR is a backward method)
The model
MA Representation of the structural form model is given by
xt  k  S L vt
where vt indicate vector of the aggregate shocks such that
E (v t v t )  I
'
and Xt= [Dyt, bst]. The AR representation of the reduced form (R.F)
xt   0  1 Lxt 1   t
where
 t represents the residuals vector and 

 
 E  t  t' is the VCV matrix
The associated MA representation of the Reduced Form
xt  K  C L  t
The structural shocks can be derived from the innovations of the reduced form
model:
S 0vt   t
Knowledge of S(0) allows to obtain structural shocks from the innovations
Identification scheme
 
S 0vt   t
 
E  t  t  S 0E v v S 0  
'
'
'
t t
Bivariate model
2
2

S11 0  S12 0
S11 0S 21 0  S12 0S 22 0


2
2
S 21 0  S 22 0
S11 0S 21 0  S12 0S 22 0

:
Var  yt   S11 0  S12 0
2
2
Cov yt  ct   S11 0S 21 0  S12 0 S 22 0
Var ct   S210  S22 0
2
C11 LS12 0  C12 LS 22 0  0
Restriction: Only supply shocks can produce a long run impact on
GDP
2
SVAR Trend/Cycle decomposition
 Trend is a measure of potential output
 The cyclical component is a measure of output gap
 Case of bivariate model
vt  vst , vdt 
xt  yt , ct 
xt  K  S L vt  K  C L S 0vt
Considering only the first equation we have:
yt  K1  S11Lvst  S12 Lvdt
yt
pot
y
gap


 K1  S11 L vst  K1    11S11 0vst i  K1  S11 0  i11vst i
i
i 0

t
i 0

 S12 L vdt    11S12 0vdt i  S12 0  i11vdt i
i
i 0
i 0
Business survey data
Cross correlations with GDP
(period 1986q1-2003q4)
t-4
t-3
t-2
t-1
t
t+1
t+2
t+3
t+4
Plant
utilizatio
n
-0.06
0.17
0.39
0.59
0.71
0.74
0.68
0.58
0.46
Inventori
es
0.58
0.47
0.30
0.08
-0.14
-0.29
-0.37
-0.4
-0.38
Prod.
level
-0.42
-0.17
0.11
0.38
0.57
0.66
0.64
0.57
0.48
Order
book
-0.46
-0.21
0.08
0.34
0.57
0.68
0.69
0.62
0.53
Prod.
exp
-0.42
-0.26
-0.03
0.23
0.45
0.57
0.60
0.54
0.44
Climate
-0.52
-0.32
-0.04
0.26
0.50
0.63
0.66
0.61
0.52
Empirical results
 Data
 Output: Italian GDP quarterly data seasonally adjusted (at constant
prices and base 1995) 1980Q1-2005Q1 Source:ISTAT
 Degree of plants utilization: quarterly frequency 1985Q1-2005Q1
 Source:ISAE





Trend/cycle decompositions used
Quadratic trend
Hodrick Prescott filter
Baxter and King filter
Bivariate SVAR model (GDP and degree of capacity
utilization)
SVAR model
0.0015
12.47
0.001
12.42
0.0005
12.37
0
12.32
-0.0005
12.27
-0.001
12.22
12.17
-0.0015
12.12
-0.002
1985 1986 1987 1988 1989
1990
1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004
Trend
P IL
Output gap
 Reliability of real time estimates
 For short term analysis purposes is important to obtain reliable
estimates at the end of sample
 Impact of revisions
 The availability of new information allow to identify more precisely
the cyclical position of the economy
 Revisions formula
( yt / t T  yt / t i )  100
 where y t / t T indicates the estimates at time t, obtained using
information available in t+T and yt / t i indicates the estimates at
period t, made using the informative set available in t+i con i<T.
Impact of revisions
t=2002:4
Pt/t+9Pt/t+1
Pt/t+9Pt/t+2
Pt/t+9Pt/t+3
Pt/t+9Pt/t+4
Pt/t+9Pt/t+5
Pt/t+9Pt/t+6
Pt/t+9Pt/t+7
Pt/t+9Pt/t+8
Pt/t+9Pt/t+9
SAMPLE
1980:1
2003:1
1980:1
2003:2
1980:1
2003:3
1980:1
2003:4
1980:1
2004:1
1980:1
2003:2
1980:1
2004:3
1980:1
2004:4
1980:
1
2005:
1
TL
1.03
0.89
0.78
0.65
0.52
0.40
0.3
0.16
0
TQ
0.54
0.45
0.38
0.3
0.25
0.21
0.19
0.11
0
HP
0.84
0.55
0.39
0.23
0.15
0.12
0.11
0.06
0
SVAR
0.015
0.016
0.010
0.008
0.008
0.010
0.008
0.007
0
Analysis of turning points of output gap
indicators
 It is important to evaluate of the ability of the cyclical
components obtained through the different methods to
indicate the turning points of the cyclical official
chronology for Italy.
 Cyclical official dating chronology
 Turning points are determined on the basis of the
dynamics of the series included in the coincident
indicator for the italian economy ( information on GDP,
ind. Production, imports of investment goods, share of
over time hours, railway transport of goods,
 (see Altissimo et al., 1999)
Detecting turning points
(quadratic trend)
Detecting turning points
(Hodrick Prescott)
Detecting turning points
(Baxter and King)
Detecting turning points
(SVAR)
Conclusions
 The output gap estimates are sensitive to the different trend cycle
estimation techniques
 The use of business survey data into multivariate models allow to
capture information on business cycle activity.
 The analyisis of the impact of revisions due to the availability of new
information, highligths an high degree of reliability of real time
estimates obtained with SVAR models
 The output gap estimates obtained with VAR models are able to
detect quite precisely the turning points of the cyclical official
chronology as well as traditional unvariate decompositions