Estimating potential output using Estimating potential output using business survey data in a SVAR business survey data in a SVAR

frameworkframework

3° annual WORKSHOP3° annual WORKSHOPon Macroeconomic Forecastingon Macroeconomic Forecasting

Montreal 5-6 october 2007Montreal 5-6 october 2007

Tatiana CesaroniTatiana Cesaroni

ISAE-ITALYISAE-ITALY

MotivationMotivation

Potential output and the related concept of output gap Potential output and the related concept of output gap represent important concepts for economic policy represent important concepts for economic policy evaluation and analysisevaluation and analysis

Most macroeconomic models include estimates of Most macroeconomic models include estimates of potential outputpotential output

Potential output plays a key role in business cycle Potential output plays a key role in business cycle researchresearch

ContributionContribution

Provide potential output and output gap estimates for Italy Provide potential output and output gap estimates for Italy using information coming from business survey datausing information coming from business survey data

Compare the estimated output gap obtained with different Compare the estimated output gap obtained with different

methods (univariate vs multivariate decompositions)methods (univariate vs multivariate decompositions)

Evaluate the reliability of the estimates at the end of sampleEvaluate the reliability of the estimates at the end of sample

Compare peaks and troughs of the estimated output gap Compare peaks and troughs of the estimated output gap with turning points of the Italian official cyclical chronologywith turning points of the Italian official cyclical chronology

DefinitionsDefinitions

Potential outputPotential output It is defined as the maximum capacity of a given It is defined as the maximum capacity of a given economy economy

Output gapOutput gap It is defined as the difference between actual level of output and its It is defined as the difference between actual level of output and its

potential.potential.

It is used as indicator of the cyclical position of the economyIt is used as indicator of the cyclical position of the economy

100 Ttt yy

Measurement problemsMeasurement problems

Potential output represents a theoretical concept it is not Potential output represents a theoretical concept it is not observed and for this reason need to be estimatedobserved and for this reason need to be estimated

The empirical evidence shows a significant sensibility of The empirical evidence shows a significant sensibility of the estimates with respect to the method used (see the estimates with respect to the method used (see Orphanides, and Van Norden, 2001)Orphanides, and Van Norden, 2001)

The choice of the methodology is not unique since The choice of the methodology is not unique since depends on more factors like the aim of the research, depends on more factors like the aim of the research, the statistical properties of data used etc.the statistical properties of data used etc.

Univariate detrending methodsUnivariate detrending methods

Deterministic trend (quadratic trend)Deterministic trend (quadratic trend) Filters (Hodrick Prescott, Band Pass)Filters (Hodrick Prescott, Band Pass) Unobserved components modelsUnobserved components models

DrawbackDrawback

We cannot use information coming from We cannot use information coming from external dataexternal data

Structural VAR decompositionStructural VAR decomposition

The multivariate trend cycle decomposition method used is based The multivariate trend cycle decomposition method used is based

on SVAR models with long run restrictions (Blanchard and on SVAR models with long run restrictions (Blanchard and Quah,1989)Quah,1989)

AdvantagesAdvantages Possibility to give an economic interpretation to the shocksPossibility to give an economic interpretation to the shocks

Absence of a priori restrictions on the dynamics of trend/cycle Absence of a priori restrictions on the dynamics of trend/cycle componentscomponents

Absence of end of sample problems (VAR is a backward method)Absence of end of sample problems (VAR is a backward method)

The modelThe modelMA Representation of the structural form model is given byMA Representation of the structural form model is given by

wherewhere vt vt indicate vector of the aggregate shocks such that indicate vector of the aggregate shocks such that

and Xt= [Dyt, bst]. The AR representation of the reduced form (R.F)and Xt= [Dyt, bst]. The AR representation of the reduced form (R.F)

where represents the residuals vector and is the VCV matrixwhere represents the residuals vector and is the VCV matrix

The associated MA representation of the Reduced FormThe associated MA representation of the Reduced Form

The structural shocks can be derived from the innovations of the reduced form The structural shocks can be derived from the innovations of the reduced form model:model:

Knowledge of S(0) allows to obtain structural shocks from the innovationsKnowledge of S(0) allows to obtain structural shocks from the innovations

'ttE

tt vLSkx IvvE tt )( '

ttt xLx 110

tt LCKx

ttvS 0

t

Identification schemeIdentification scheme

Bivariate modelBivariate model

::

Restriction: Only supply shocks can produce a long run impact on Restriction: Only supply shocks can produce a long run impact on GDPGDP

212

211 00 SSVar yt 2

222

21 00 SSVar ct

0000 22122111 SSSSCov ctyt 000 22121211 SLCSLC

ttvS 0 ''' 00 SvvESE tttt

2

222

2122122111

221221112

122

11

000000

000000

SSSSSS

SSSSSS

SVAR Trend/Cycle decompositionSVAR Trend/Cycle decomposition

Trend is a measure of potential outputTrend is a measure of potential output The cyclical component is a measure of output gapThe cyclical component is a measure of output gap Case of bivariate modelCase of bivariate model

Considering only the first equation we have: Considering only the first equation we have:

isti

iist

i

ist

pott vSKvSKvLSKy

0

11111110

111111 00

idti

iidt

i

idtt

gap vSvSvLSy

0

1112120

1112 00

ttt vSLCKvLSKx 0

dtstt vLSvLSKy 12111

ttt cyx , dtstt vvv ,

Business survey dataBusiness survey data

-80

-60

-40

-20

0

20

40

60

60

65

70

75

80

85

Confidence climate Inventories Prod. Expectations Order book level Prod. Level Plant utilization

t-4t-4 t-3t-3 t-2t-2 t-1t-1 tt t+1t+1 t+2t+2 t+3t+3 t+4t+4

Plant Plant utilizatioutilizationn

-0.06-0.06 0.170.17 0.390.39 0.590.59 0.710.71 0.740.74 0.680.68 0.580.58 0.460.46

InventoriInventorieses

0.580.58 0.470.47 0.300.30 0.080.08 -0.14-0.14 -0.29-0.29 -0.37-0.37 -0.4-0.4 -0.38-0.38

Prod. Prod. levellevel

-0.42-0.42 -0.17-0.17 0.110.11 0.380.38 0.570.57 0.660.66 0.640.64 0.570.57 0.480.48

Order Order bookbook

-0.46-0.46 -0.21-0.21 0.080.08 0.340.34 0.570.57 0.680.68 0.690.69 0.620.62 0.530.53

Prod. Prod. expexp

-0.42-0.42 -0.26-0.26 -0.03-0.03 0.230.23 0.450.45 0.570.57 0.600.60 0.540.54 0.440.44

ClimateClimate -0.52-0.52 -0.32-0.32 -0.04-0.04 0.260.26 0.500.50 0.630.63 0.660.66 0.610.61 0.520.52

Cross correlations with GDPCross correlations with GDP(period 1986q1-2003q4)(period 1986q1-2003q4)

Empirical resultsEmpirical results DataData Output: Italian GDP quarterly data seasonally adjusted (at constant Output: Italian GDP quarterly data seasonally adjusted (at constant

prices and base 1995) 1980Q1-2005Q1 Source:ISTATprices and base 1995) 1980Q1-2005Q1 Source:ISTAT

Degree of plants utilization: quarterly frequency 1985Q1-2005Q1Degree of plants utilization: quarterly frequency 1985Q1-2005Q1 Source:ISAESource:ISAE

Trend/cycle decompositions usedTrend/cycle decompositions used Quadratic trendQuadratic trend Hodrick Prescott filterHodrick Prescott filter Baxter and King filterBaxter and King filter Bivariate SVAR model (GDP and degree of capacity Bivariate SVAR model (GDP and degree of capacity

utilization)utilization)

SVAR modelSVAR model

12.12

12.17

12.22

12.27

12.32

12.37

12.42

12.47

1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004

-0.002

-0.0015

-0.001

-0.0005

0

0.0005

0.001

0.0015

Trend P IL Output gap

Reliability of real time estimatesReliability of real time estimates

For short term analysis purposes is important to obtain reliable For short term analysis purposes is important to obtain reliable estimates at the end of sampleestimates at the end of sample

Impact of revisionsImpact of revisions The availability of new information allow to identify more precisely The availability of new information allow to identify more precisely

the cyclical position of the economythe cyclical position of the economy

Revisions formulaRevisions formula

where indicates the estimates at timewhere indicates the estimates at time t, t, obtained using obtained using information available in information available in t+Tt+T and indicates the estimates at and indicates the estimates at period period t, made t, made using the informative set available in using the informative set available in t+i t+i con con i<T.i<T.

100)( // ittTtt yy

Ttty /

itty /

Impact of revisionsImpact of revisions

t=2002:4t=2002:4 Pt/t+9-Pt/Pt/t+9-Pt/t+1t+1

Pt/t+9-Pt/t+9-Pt/t+2Pt/t+2

Pt/t+9-Pt/t+9-Pt/t+3Pt/t+3

Pt/t+9-Pt/t+9-Pt/t+4Pt/t+4

Pt/t+9-Pt/t+9-Pt/t+5Pt/t+5

Pt/t+9-Pt/Pt/t+9-Pt/t+6t+6

Pt/t+9-Pt/Pt/t+9-Pt/t+7t+7

Pt/t+9-Pt/Pt/t+9-Pt/t+8t+8

Pt/t+9-Pt/t+9-Pt/t+9Pt/t+9

SAMPLESAMPLE 1980:11980:1

2003:12003:1

1980:11980:1

2003:22003:2

1980:11980:1

2003:32003:3

1980:11980:1

2003:42003:4

1980:11980:1

2004:12004:1

1980:11980:1

2003:22003:2

1980:11980:1

2004:32004:3

1980:11980:1

2004:42004:4

1980:1980:11

2005:2005:11

TLTL 1.031.03 0.890.89 0.780.78 0.650.65 0.520.52 0.400.40 0.30.3 0.160.16 00

TQTQ 0.540.54 0.450.45 0.380.38 0.30.3 0.250.25 0.210.21 0.190.19 0.110.11 00

HPHP 0.840.84 0.550.55 0.390.39 0.230.23 0.150.15 0.120.12 0.110.11 0.060.06 00

SVARSVAR 0.0150.015 0.0160.016 0.0100.010 0.0080.008 0.0080.008 0.0100.010 0.0080.008 0.0070.007 00

Analysis of turning points of output gap Analysis of turning points of output gap indicatorsindicators

It is important to evaluate of the ability of the cyclical It is important to evaluate of the ability of the cyclical components obtained through the different methods to components obtained through the different methods to indicate the turning points of the cyclical official chronology indicate the turning points of the cyclical official chronology for Italy.for Italy.

Cyclical official dating chronologyCyclical official dating chronology

Turning points are determined on the basis of the Turning points are determined on the basis of the dynamics of the series included in the coincident indicator dynamics of the series included in the coincident indicator for the italian economy ( information on GDP, ind. for the italian economy ( information on GDP, ind. Production, imports of investment goods, share of over Production, imports of investment goods, share of over time hours, railway transport of goods, time hours, railway transport of goods,

(see Altissimo et al., 1999)(see Altissimo et al., 1999)

Detecting turning pointsDetecting turning points(quadratic trend)(quadratic trend)

-0,04

-0,03

-0,02

-0,01

0

0,01

0,02

0,03

0,04

Trend quadratico

Detecting turning pointsDetecting turning points(Hodrick Prescott)(Hodrick Prescott)

-0.03

-0.02

-0.02

-0.01

-0.01

0.00

0.01

0.01

0.02

0.02

Filtro di Hodrick P rescott

Detecting turning pointsDetecting turning points(Baxter and King)(Baxter and King)

-0.02

-0.02

-0.01

-0.01

0.00

0.01

0.01

0.02

0.02

Filtro di Baxter e King

Detecting turning pointsDetecting turning points(SVAR)(SVAR)

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

VAR1

ConclusionsConclusions The output gap estimates are sensitive to the different trend cycle The output gap estimates are sensitive to the different trend cycle

estimation techniquesestimation techniques

The use of business survey data into multivariate models allow to The use of business survey data into multivariate models allow to capture information on business cycle activity. capture information on business cycle activity.

The analyisis of the impact of revisions due to the availability of new The analyisis of the impact of revisions due to the availability of new information, highligths an high degree of reliability of real time information, highligths an high degree of reliability of real time estimates obtained with SVAR modelsestimates obtained with SVAR models

The output gap estimates obtained with VAR models are able to The output gap estimates obtained with VAR models are able to detect quite precisely the turning points of the cyclical official detect quite precisely the turning points of the cyclical official chronology as well as traditional unvariate decompositionschronology as well as traditional unvariate decompositions