Predicting recessions with Factor Linear Dynamic Harmonic ...
Predicting recessions with Factor Linear Dynamic Harmonic Regression Models
Marcos Bujosa Dpto. de Fundamentos del An´ alisis Econ´ omico II. Universidad Complutense de Madrid
Antonio Garc´ıa-Ferrer Dpto. de An´ alisis Econ´ omico: Econom´ıa Cuantitativa. Universidad Aut´ onoma de Madrid
Ar´ anzazu de Juan Dpto. de An´ alisis Econ´ omico: Econom´ıa Cuantitativa.
c 2010
Last Revision Date: June 16, 2010
⇑
Universidad Aut´ onoma de Madrid
Heading
1
Oficina Econ´ omica del Presidente. December 2007 ⇑
Heading
2
”While the latest data confirm the expected weakening of real GDP growth in mid-2008 after exceptionally strong growth in the first quarter, the economic fundamentals of the euro area are sound”. J.C. Trichet, President of the European Central Bank (July 3, 2008) Notice, especially that in 2006, a loud alarm has been sounded, making a a recession in 2007 a virtual certainty. I don’t think so, but that is what these data suggest. Edward Leamer. Macroeconomic Patterns and Stories. 2009. US economic indicators would have to get much worst to pass the recession threshold. Edward Leamer. August 2008.
2
⇑
Contents
3
• Introduction
• Methodology
• Turning points characterization of the Spanish Economy – Building the composite leading indicator for the Spanish economy • Empirical results – In-Sample Results: Growth cycles, Classical IPI cycles – Out-of-sample results: IPI & GDP forecast (2007–2009) • Conclusions ⇑
GDP
4
Not the favorite economic aggregate of many analysts, including us. Reasons: • Publication lag • Often quarterly revisions
• Annual revisions reflect more complete information
• Benchmark or historic revisions take every five years or so. Results: • Many papers in the literature with radically different results depending on the use of original or revised data • Due to its publication delay, not a very useful indicator to monitor the current state of the economy. ⇑
Alternatives
5
Monthly economic indicators are published promptly including information about: • Labor market • Housing market
• Financial market
• Expectation variables
• Others Objective: identifying a subset of variables to construct a leading indicator index ⇑
Alternatives
6
Problems: • Categories such as leading, coincidental, and lagging are not permanent through time • How to use standartization when building the composite index?
• The issue is not volatility but predictability. A low volatility indicator might be a terrible predictor • Temporal orderings of the individual indicators: which comes first?
3
⇑
LDHR model general specification: frequency
7
Bujosa, Garc´ıa-Ferrer, & Young (2007) Series yt is a sum of sinusoids plus noise: yt =
R X aj t cos(ωj t) + bj t sin(ωj t) + et ;
t = 0, 1, 2, . . .
(1)
j=0
ω(j=0) = 0 ω(j6=0) (Seasonal frequency and its harmonics)
→ →
Tt St
yt = Tt + St + et .
⇑
(2)
LDHR model general specification: amplitude
yt =
R X aj t cos(ωj t) + bj t sin(ωj t) + et ;
8
t = 0, 1, 2, . . .
j=0
{aj t } and {bj t } ∼ (possibly non stationary) AR(2) stochastic processes. ( (1 − αj L)(1 − βj L)aj t = ξj t 0 ≤ αj , βj ≤ 1; (1 − αj L)(1 − βj L)bj t = νj t ; ( where
∼ w.n. (0, σe2 ) ∼ w.n. (0, σj2 );
et ξj t , νj t
j = 1, . . . , R
;
uncorrelated.
N V Rj = σj2 /σe2 ⇑
LDHR model: ARIMA spectral representation
9
LDHR model has a non-stationary ARIMA representation with pseudo-spectrum R X θj (e−iω )θj (eiω ) fdhr ω, σ 2 = σe2 + σj2 ; ϕj (e−iω )ϕj (eiω ) j=0
(3)
2 where σ 2 = σe2 , σ02 , . . . , σR ; polynomials ϕj (L) and θj (L) are determined by αj , βj ; and ωj . ⇑
LDHR model: automatic identification
⇑
LDHR model: spectral fitting
10
“Strongest spectral peaks” of time series with trend and seasonal components are due to AR roots with modulus close to one. LDHR automatic identification procedure chooses the values of αj , βj ; analyzing the roots of frequencies ωj of an AR polynomial fitted to the series.
2 σ 2 = σe2 , σ02 , . . . , σR are estimated by OLS:
h i
ˆy − fdhr ω, σ 2 min · I
Ψ(ω)
, 2 σ
where Ψ(ω) its the inverse of the non-stationary AR part of fdhr ω, σ 2 ; and Iˆy is the time series periodogram.
11
(4)
4
⇑
A composite leading indicator: Non-stationary dynamic factors
12
Let y t be an m-dimensional vector of observed time series, y t = Pf t + et where f t is the r-dimensional vector of common nonobserved factors,
P [m×r]
is a factor loading matrix,
and the sequence of vectors et ∼ N {0, Σe } (Σe full rank diagonal matrix). Assume y t is I(d); there are r1 nonstationary factors f1 , and Cy (k) =
1 T 2d+d0
T X
(y t−k − y ¯)(y t−k − y ¯)0 ,
t=k+1
Pe˜ na & Poncela (2006, Theorem 1.): Cy (k) converges to a random matrix Γy that has r1 eigenvalues greater than zero almost sure. The corresponding r1 eigenvalues greater than zero are a basis of the column space of the loading submatrix P1 of the r1 nonstationary factors. ⇑
Building a composite leading indicator: Spanish recession
13
• Non-stationary dynamic factor analysis • Only one common factor
• Weights from the eigenvector associated to the largest eigenvalue of the generalized covariance matrix Cy (k) • Results very robust for different lags k. ⇑
Concepts
14
Garc´ıa-Ferrer & Bujosa-Brun (2000) 1. Anticipation of a recession when the derivative reaches its maximum (TP). 2. Confirmation of recession when the derivative becomes negative and remains so for at least six months 3. Anticipation of a recovery at the derivative minimum (TP) 4. Confirmation of recovery when the derivative becomes positive and remains so for at least nine months
Gross Investment on Fixed Capital - Consumption
Definition of the variable Cement Consumption Construction Production Index (seasonally adjusted) Total Housing Starts (seasonally adjusted) Total Housing Starts Total Building Permits Total Houses Total Oficial Licences Oficial Licences Building Oficial Licences of Civil Buildings
Sample 64.01-09.01 88.01-08.12 04.01-08.09 80.01-08.09 92.01-08.12 92.01-08.11 89.01-08.11 89.01-08.11 89.01-08.11 Mean Range
Confirmation of the Turning Point recession 06.01 07.01 04.09 06.10 03.04 06.05 03.04 06.05 03.03 06.03 05.09 06.06 05.05 06.12 05.05 06.12 05.12 07.01 04.10 06.09 [03.03 - 06.01] [06.03 - 07.01]
Industry Gross Added Value
Definition of the variable Industrial Production Index (total) IPI manufacturing Consumption of Electric Energy Consumption of Electric Energy (seasonally adjusted) IPI - consumption IPI - durable goods IPI - equipment goods IPI - energy Indicator of new industrial orders - general Indicator of new industrial orders - consump. goods Indicador of new industrial orders - intermed. goods Stocks of Industrial Orders Availability of Equipment Goods
Sample 75.01-08.12 75.01-08.12 75.01-09.01 81.01-09.01 92.01-08.12 92.01-08.12 92.01-08.12 92.01-08.12 92.01-08.02 02.01-08.12 02.01-08.12 02.01-08.11 00.01-08.11 Mean Range
Turning Point
Confirmation of the recession
06.03 07.05 06.03 07.05 06.09 08.06 06.09 08.06 06.05 07.04 06.04 07.05 06.03 07.08 06.02 07.03 05.12 07.11 05.12 07.11 05.12 07.11 06.01 07.07 06.08 07.06 06.08 07.09 [05.12 - 06.09] [07.03 - 08.06]
Services Gross Added Value
Definition Total air traffic Passengers entry - Tourists Total tourists Nights spent Transport of passengers by road Activity indicator of services Fuel consumption Workers in SS system - Services sector
Sample 70.01-09.01 95.01-08.12 99.01-08.12 99.01-08.12 85.01-08.12 02.01-08.12 78.01-08.11 85.01-09.01 Mean Range
Turning Point
Confirmation of the recession
06.05 07.10 07.04 07.10 06.04 07.10 07.04 07.10 04.12 06.04 06.04 07.11 06.09 08.06 05.07 --------06.05 07.09 [04.12 - 07.04] [06.04 - 08.06]
Private Consumption
Definition of the variable Availability of Consumption Goods Real wage indicator Car registrations Motorbike registrations Index of retailing sales Index of sales in department stores Consumer confidence indicator Home situation 12 months before Home situation next 12 months Country situation 12 months before Country situation next 12 months Commercial vehicles registration Wage income
Sample
Turning Point
Confirmation of the recession
01.01-08.11 77.01-09.01 70.01-09.01 75.01-09.01 95.01-08.12 95.01-08.12 86.06-09.01 86.06-09.01 86.06-09.01 86.06-09.01 86.06-09.01 75.01-09.01 77.01-09.01 Mean Range
06.04 06.01 06.02 04.09 06.06
07.06 07.11 06.06 07.02 08.02
03.12 05.03 05.12 06.07 03.12 05.01 03.12 04.10 03.09 04.08 04.11 06.09 05.07 07.11 05.02 06.06 [03.12 - 06.04] [04.01 - 08.02]
Labor Market - Afiliations to the SS system
Definition of the variable Workers in SS system - Industry Workers in SS system - Construction Workers in SS system - Total Workers in SS system - Total system - Industry Workers in SS system - Total system - Construction
Sample 85.01-08.12 85.01-08.12 82.01-09.01 95.01-08.12 95.01-08.12 Mean Range
Turning Point
Confirmation of the recession
06.12 07.09 05.07 07.03 05.07 07.11 06.12 07.09 05.07 07.04 06.02 07.07 [05.07 - 06.12] [07.03 - 07.11]
VAT revenues
Definition of the variable VAT revenues
Sample
Turning Point
Confirmation of the recession
86.01-08.11 Mean
05.05 05.05
06.11 06.11
7
⇑
Building the composite leading indicator
15
Leamer (2009) • What are the cycle drivers?
• Investment components of the GDP, durables, new homes and home improvements • These are quite likely to be volatile: they can all be postponed.
• If we all do our postponing at the same time, we will probably have a recession • Workers and capital may be idled, until we finish our waiting ⇑
Spanish recent recession
16
• Housing starts (HS)
• Cement consumption (CC) • Car registrations (CR)
• Commercial vehicle registrations (CVR)
. . . in logs. We use unadjusted monthly data to avoid delays in the recognition of the end of a recession (Matas-Mir et al., 2008). ⇑
Estimated DHR models: Noise Variance Ratios
17
• IRW model for the trend
• RW model for the seasonal components Series
Trend
S12
S6
S4
S3
S2.4
S2
Housing starts Cement consumpt Car Registrat Commercial vehicle reg Industrial Product. Ind.
0.0043 0.0028 0.0017 0.0030 0.0007
0.0070 0.0042 0.0091 0.0038 0.0035
0.0030 0.0045 0.0025 0.0050 0.0012
0.0036 0.0040 0.0057 0.0055 0.0024
0.0072 0.0118 0.0079 0.0100 0.0040
0.0031 0.0091 0.0065 0.0052 0.0030
0.0036 0.0007 0.0006 0.0016 0.0003
(Sample up to 2009.12 )
8
⇑
Spanish recent recession log. Housing starts – 1978.01 to 2009.12
18
log. Car Registrat. – 1970.01 to 2009.12
12.0
12.5
11.5 12.0 11.0 11.5
10.5 10.0
11.0
9.5 10.5 9.0 8.5 70
75
80
85
90
95
00
10.0 70
05
log. Cement consumpt. – 1970.01 to 2009.12 11.0
8.5
10.5
8.0
10.0
7.5
9.5
7.0
9.0
75
80
85
90
95
00
⇑
8.5 70
05
85
90
95
00
05
75
80
85
90
95
00
05
Trend derivatives
2008.06 Housing starts. 1978.01:2009.12
70
80
log. Commercial vehicle reg. – 1975.01 to 2009.12
9.0
6.5 70
75
75
80
85
90
95
00
05
19
2008.07 Cement consumpt. 1970.01:2009.12
70
75
80
85
90
95
00
05
2008.06 Car Registrat. 1970.01:2009.12 2008.07 Commercial vehicle reg. 1975.01:2009.12
70
75
80
85
90
95
00
05
70
75
80
85
90
95
00
05
9
⇑
Composite Leading Indicator cycle
2008.06
Comp. Leading Ind
20
Sample 1978.01:2009.12
+0.030 +0.020 +0.010 +0.000 -0.010 -0.020 -0.030 -0.040 -0.050 -0.060 70
75 2008.10
+0.006 +0.004 +0.002 +0.000 -0.002 -0.004 -0.006 -0.008 -0.010 -0.012 -0.014 70
75
80
85
90
95
Industrial Product. Ind.
80
⇑
85
90
00
05
Sample 1975.01:2009.12
95
00
05 21
Turning points and recessions Series
Turning point
Conf. recession
Turning point
Housing starts Cement consumpt Car Registrat Commercial vehicle reg
200601 200512 200606 200412
200609 200703 200610 200701
200806 200807 200806 200807
Comp. Leading Ind
200601
200610
200806
Industrial Product. Ind.
200602
200702
200810
(Sample up to 2009.12 )
10
⇑
GDP annual growth rate and quarterly Composite L. Indicator
22
0.1
8
6
0.05
4 0 2 -0.05 0 -0.1 -2 -0.15
-4
-6 1979.1
⇑
1983.1
1987.1
1991.1
1995.1
1999.1
2003.1
2007.1
Peaks and troughs of GDP annual growth rate and Leading I.
L.I. 1982.4 1986.4 1991.3 1994.3 1998.3 2006.1 Mean
Peaks GDP # of quarters 1984.1 1987.4 1991.4 1995.1 2000.1 2006.4
5 4 1 2 6 3 3.5
L.I. 1980.2 1984.2 1990.3 1992.4 1995.3 2000.3 2008.3
Troughs GDP # of quarters 1981.2 1985.3 1991.3 1993.1 1996.1 2002.1 2009.2
4 5 4 1 2 6 3 3.6
-0.2
23
11
⇑
Classical IPI cycles
24
First difference of the estimated trend of Comp. Leading Ind. .03 .02 .01 .00 -.01 -.02 -.03 -.04 -.05 -.06 1980
1985
⇑
1990
1995
2000
2005
Classical IPI cycles
25
• CLI and IPI dates where recessions begin
⇑
CLI
IPI
Lead
1979M 2 1983M 4 1989M 7 1995M 4 2000M 3 2006M 10
1980M 2 − 1990M 1 1995M 8 2000M 9 2007M 3
12 FN 6 4 6 5
Out-of-sample forecast
26
• Smooth estimates (taking advantages of full sample information)
• In a true forecasting exercise, however, we can only count on the information available at the beginning of the forecast horizon. • How does the picture change when adding one observation at a time? Composite Leading Indicator: Frames 1989:01 to 2009:12 ⇑
27
Monthly IPI recessions
• CLI leading IPI recessions Recession periods
1990-93
1996
2001
2007-09
CLI IPI Lead (in months)
1990M 2 1990M 11 9
1995M 12 1996M 3 3
2000M 9 2001M 4 5
2007M 5 2007M 11 6
12
⇑
Annual and Quarterly GDP forecasts
28
⇑
Annual and Quarterly GDP forecasts
29
Dymamic model includes lags of GDP and CLI growth rates. • Relative forecast RMSE ratios
⇑
AR
CLI Model
2007 2008 2009
1.00 1.00 1.00
0.714 0.859 0.564
ALL
1.00
0.811
Conclusions
30
• Contrary to “popular” wisdom, clear signals of recession were evident in the economy before the bursting of the financial bubble in August 2007. • For the case of Spain this announcement was genreralized across economic sectors and indicators.
• Four leading variables used to construct the CLI which provides a similar (clear) message regarding recession announcement. • Does it pay to be a party pooper?
index was next to last in the head-to-head competition.
13
Predicted Probabilities of Ends of Expansions “The party was over” Best Model (Spread, Crude, Permits) Shaded Regions the Year Before Recessions (Predicted Probabilities of Endsare of Expansions Leamer, 2009, pp. 213-214)
⇑
1.0 FP 0.8
214
0.6
13 More Clues: Components of Leading Indicators
Figure 13.6 illustrates the predicted probabilities of recessions coming from 0.4 the best model reported in Table 13.4. Compare this figure with the predicted probabilities based on the interest rate spreadFP alone, Fig. 13.5, and on the Conference Board combination, FPFig. 13.4, to see how much better this model is doing 0.2 than either of them. Here it is hard to see the shaded years-before-recession because the probabilities jump up virtually to one. Otherwise the probabilities are mostly 0.0 close to zero. Here we see a mild false alarm in 1965 and in 1987, and a short-lived 60 65 70 75 80 85 90 95 00 05 major alarm in 1998. Fig. 13.6especially Predicted probabilities of imminent based on three best indicators Notice, that in 2006, a loudrecessions alarm has been sounded, making a recession in 2007 a virtual certainty. I don’t think so, but that is what these data suggest. List of Slides 1
Heading
Appendix: 2 Heading Description of Leading Indicators 3 Contents 4 GDP Source: http://www.conference-board.org/economics/bci/component.cfm 5 Alternatives Leading Index Components 6 Alternatives 7 LDHR model general specification: frequency 8 LDHR model general specification: amplitude 9 LDHR model: ARIMA spectral representation BCI-01 Average Weekly Hours, Manufacturing 10 LDHR model: automatic identification 11 average LDHR model: spectral fitting The hours worked per week by production workers in manufacturing indus12 A composite leading indicator: Non-stationary dynamic factors tries tend to the business cycle because employers usually adjust work hours 13 Building alead composite leading indicator: Spanish recession before increasing or decreasing their workforce. 14 Concepts 15 Building the composite leading indicator 16 Spanish recent recession 17 Estimated DHR models: Noise Variance Ratios BCI-05 Average Weekly Initial Claims for 18 Spanish recent recession Unemployment Insurance 19 Trend derivatives 20 Composite Leading Indicator cycle The of new claims filed for unemployment insurance are typically more 21 number Turning points and recessions sensitive than either total employment or unemployment to overall business condi22 GDP annual growth rate and quarterly Composite L. Indicator 23 Peaks GDP annual growth rate and Leading I. tions, and and thistroughs seriesof tends to lead the business cycle. It is inverted when included 24 Classical IPI cycles in the leading index; the signs of the month-to-month changes are reversed, because 25 Classical IPI cycles initial claims increase 26 Out-of-sample forecast when employment conditions worsen (i.e., layoffs rise and new fall). 27 hirings Monthly IPI recessions 28 Annual and Quarterly GDP forecasts 29 Annual and Quarterly GDP forecasts 30 Conclusions BCI-08 Manufacturers’ New Orders, Consumer Goods, 31 “The party was over”
and Materials (in 1996 $)
These goods are primarily used by consumers. The inflation-adjusted value of new orders leads actual production because new orders directly affect the level of both unfilled orders and inventories that firms monitor when making production deci-
31
14
References Bujosa, M., Garc´ıa-Ferrer, A., & Young, P. C. (2007). Linear dynamic harmonic regression. Comput. Stat. Data Anal., 52 , 999–1024. 3 Garc´ıa-Ferrer, A. & Bujosa-Brun, M. (2000). Forecasting OECD industrial turning points using unobserved components models with business survey data. International Journal of Forecasting, 16 , 207–227. 4 Leamer, E. E. (2009). Macroeconomic Patterns and stories. Berlin: Springer-Verlag. 7, 13 Matas-Mir, A., Osborn, D. R., & Lombardi, M. J. (2008). The effect of a seasonal adjustment on the properties of business cycle regimes. Journal of Applied Econometrics, 23 , 257–278. 7 Pe˜ na, D. & Poncela, P. (2006). Nonstationary dynamic factor analysis. Journal of Statistical Planning and Inference, 136 , 1237–1257. 4
Marcos Bujosa Dpto. de Fundamentos del An´ alisis Econ´ omico II. Universidad Complutense de Madrid
Antonio Garc´ıa-Ferrer Dpto. de An´ alisis Econ´ omico: Econom´ıa Cuantitativa. Universidad Aut´ onoma de Madrid
Ar´ anzazu de Juan Dpto. de An´ alisis Econ´ omico: Econom´ıa Cuantitativa.
c 2010
Last Revision Date: June 16, 2010
⇑
Universidad Aut´ onoma de Madrid
Heading
1
Oficina Econ´ omica del Presidente. December 2007 ⇑
Heading
2
”While the latest data confirm the expected weakening of real GDP growth in mid-2008 after exceptionally strong growth in the first quarter, the economic fundamentals of the euro area are sound”. J.C. Trichet, President of the European Central Bank (July 3, 2008) Notice, especially that in 2006, a loud alarm has been sounded, making a a recession in 2007 a virtual certainty. I don’t think so, but that is what these data suggest. Edward Leamer. Macroeconomic Patterns and Stories. 2009. US economic indicators would have to get much worst to pass the recession threshold. Edward Leamer. August 2008.
2
⇑
Contents
3
• Introduction
• Methodology
• Turning points characterization of the Spanish Economy – Building the composite leading indicator for the Spanish economy • Empirical results – In-Sample Results: Growth cycles, Classical IPI cycles – Out-of-sample results: IPI & GDP forecast (2007–2009) • Conclusions ⇑
GDP
4
Not the favorite economic aggregate of many analysts, including us. Reasons: • Publication lag • Often quarterly revisions
• Annual revisions reflect more complete information
• Benchmark or historic revisions take every five years or so. Results: • Many papers in the literature with radically different results depending on the use of original or revised data • Due to its publication delay, not a very useful indicator to monitor the current state of the economy. ⇑
Alternatives
5
Monthly economic indicators are published promptly including information about: • Labor market • Housing market
• Financial market
• Expectation variables
• Others Objective: identifying a subset of variables to construct a leading indicator index ⇑
Alternatives
6
Problems: • Categories such as leading, coincidental, and lagging are not permanent through time • How to use standartization when building the composite index?
• The issue is not volatility but predictability. A low volatility indicator might be a terrible predictor • Temporal orderings of the individual indicators: which comes first?
3
⇑
LDHR model general specification: frequency
7
Bujosa, Garc´ıa-Ferrer, & Young (2007) Series yt is a sum of sinusoids plus noise: yt =
R X aj t cos(ωj t) + bj t sin(ωj t) + et ;
t = 0, 1, 2, . . .
(1)
j=0
ω(j=0) = 0 ω(j6=0) (Seasonal frequency and its harmonics)
→ →
Tt St
yt = Tt + St + et .
⇑
(2)
LDHR model general specification: amplitude
yt =
R X aj t cos(ωj t) + bj t sin(ωj t) + et ;
8
t = 0, 1, 2, . . .
j=0
{aj t } and {bj t } ∼ (possibly non stationary) AR(2) stochastic processes. ( (1 − αj L)(1 − βj L)aj t = ξj t 0 ≤ αj , βj ≤ 1; (1 − αj L)(1 − βj L)bj t = νj t ; ( where
∼ w.n. (0, σe2 ) ∼ w.n. (0, σj2 );
et ξj t , νj t
j = 1, . . . , R
;
uncorrelated.
N V Rj = σj2 /σe2 ⇑
LDHR model: ARIMA spectral representation
9
LDHR model has a non-stationary ARIMA representation with pseudo-spectrum R X θj (e−iω )θj (eiω ) fdhr ω, σ 2 = σe2 + σj2 ; ϕj (e−iω )ϕj (eiω ) j=0
(3)
2 where σ 2 = σe2 , σ02 , . . . , σR ; polynomials ϕj (L) and θj (L) are determined by αj , βj ; and ωj . ⇑
LDHR model: automatic identification
⇑
LDHR model: spectral fitting
10
“Strongest spectral peaks” of time series with trend and seasonal components are due to AR roots with modulus close to one. LDHR automatic identification procedure chooses the values of αj , βj ; analyzing the roots of frequencies ωj of an AR polynomial fitted to the series.
2 σ 2 = σe2 , σ02 , . . . , σR are estimated by OLS:
h i
ˆy − fdhr ω, σ 2 min · I
Ψ(ω)
, 2 σ
where Ψ(ω) its the inverse of the non-stationary AR part of fdhr ω, σ 2 ; and Iˆy is the time series periodogram.
11
(4)
4
⇑
A composite leading indicator: Non-stationary dynamic factors
12
Let y t be an m-dimensional vector of observed time series, y t = Pf t + et where f t is the r-dimensional vector of common nonobserved factors,
P [m×r]
is a factor loading matrix,
and the sequence of vectors et ∼ N {0, Σe } (Σe full rank diagonal matrix). Assume y t is I(d); there are r1 nonstationary factors f1 , and Cy (k) =
1 T 2d+d0
T X
(y t−k − y ¯)(y t−k − y ¯)0 ,
t=k+1
Pe˜ na & Poncela (2006, Theorem 1.): Cy (k) converges to a random matrix Γy that has r1 eigenvalues greater than zero almost sure. The corresponding r1 eigenvalues greater than zero are a basis of the column space of the loading submatrix P1 of the r1 nonstationary factors. ⇑
Building a composite leading indicator: Spanish recession
13
• Non-stationary dynamic factor analysis • Only one common factor
• Weights from the eigenvector associated to the largest eigenvalue of the generalized covariance matrix Cy (k) • Results very robust for different lags k. ⇑
Concepts
14
Garc´ıa-Ferrer & Bujosa-Brun (2000) 1. Anticipation of a recession when the derivative reaches its maximum (TP). 2. Confirmation of recession when the derivative becomes negative and remains so for at least six months 3. Anticipation of a recovery at the derivative minimum (TP) 4. Confirmation of recovery when the derivative becomes positive and remains so for at least nine months
Gross Investment on Fixed Capital - Consumption
Definition of the variable Cement Consumption Construction Production Index (seasonally adjusted) Total Housing Starts (seasonally adjusted) Total Housing Starts Total Building Permits Total Houses Total Oficial Licences Oficial Licences Building Oficial Licences of Civil Buildings
Sample 64.01-09.01 88.01-08.12 04.01-08.09 80.01-08.09 92.01-08.12 92.01-08.11 89.01-08.11 89.01-08.11 89.01-08.11 Mean Range
Confirmation of the Turning Point recession 06.01 07.01 04.09 06.10 03.04 06.05 03.04 06.05 03.03 06.03 05.09 06.06 05.05 06.12 05.05 06.12 05.12 07.01 04.10 06.09 [03.03 - 06.01] [06.03 - 07.01]
Industry Gross Added Value
Definition of the variable Industrial Production Index (total) IPI manufacturing Consumption of Electric Energy Consumption of Electric Energy (seasonally adjusted) IPI - consumption IPI - durable goods IPI - equipment goods IPI - energy Indicator of new industrial orders - general Indicator of new industrial orders - consump. goods Indicador of new industrial orders - intermed. goods Stocks of Industrial Orders Availability of Equipment Goods
Sample 75.01-08.12 75.01-08.12 75.01-09.01 81.01-09.01 92.01-08.12 92.01-08.12 92.01-08.12 92.01-08.12 92.01-08.02 02.01-08.12 02.01-08.12 02.01-08.11 00.01-08.11 Mean Range
Turning Point
Confirmation of the recession
06.03 07.05 06.03 07.05 06.09 08.06 06.09 08.06 06.05 07.04 06.04 07.05 06.03 07.08 06.02 07.03 05.12 07.11 05.12 07.11 05.12 07.11 06.01 07.07 06.08 07.06 06.08 07.09 [05.12 - 06.09] [07.03 - 08.06]
Services Gross Added Value
Definition Total air traffic Passengers entry - Tourists Total tourists Nights spent Transport of passengers by road Activity indicator of services Fuel consumption Workers in SS system - Services sector
Sample 70.01-09.01 95.01-08.12 99.01-08.12 99.01-08.12 85.01-08.12 02.01-08.12 78.01-08.11 85.01-09.01 Mean Range
Turning Point
Confirmation of the recession
06.05 07.10 07.04 07.10 06.04 07.10 07.04 07.10 04.12 06.04 06.04 07.11 06.09 08.06 05.07 --------06.05 07.09 [04.12 - 07.04] [06.04 - 08.06]
Private Consumption
Definition of the variable Availability of Consumption Goods Real wage indicator Car registrations Motorbike registrations Index of retailing sales Index of sales in department stores Consumer confidence indicator Home situation 12 months before Home situation next 12 months Country situation 12 months before Country situation next 12 months Commercial vehicles registration Wage income
Sample
Turning Point
Confirmation of the recession
01.01-08.11 77.01-09.01 70.01-09.01 75.01-09.01 95.01-08.12 95.01-08.12 86.06-09.01 86.06-09.01 86.06-09.01 86.06-09.01 86.06-09.01 75.01-09.01 77.01-09.01 Mean Range
06.04 06.01 06.02 04.09 06.06
07.06 07.11 06.06 07.02 08.02
03.12 05.03 05.12 06.07 03.12 05.01 03.12 04.10 03.09 04.08 04.11 06.09 05.07 07.11 05.02 06.06 [03.12 - 06.04] [04.01 - 08.02]
Labor Market - Afiliations to the SS system
Definition of the variable Workers in SS system - Industry Workers in SS system - Construction Workers in SS system - Total Workers in SS system - Total system - Industry Workers in SS system - Total system - Construction
Sample 85.01-08.12 85.01-08.12 82.01-09.01 95.01-08.12 95.01-08.12 Mean Range
Turning Point
Confirmation of the recession
06.12 07.09 05.07 07.03 05.07 07.11 06.12 07.09 05.07 07.04 06.02 07.07 [05.07 - 06.12] [07.03 - 07.11]
VAT revenues
Definition of the variable VAT revenues
Sample
Turning Point
Confirmation of the recession
86.01-08.11 Mean
05.05 05.05
06.11 06.11
7
⇑
Building the composite leading indicator
15
Leamer (2009) • What are the cycle drivers?
• Investment components of the GDP, durables, new homes and home improvements • These are quite likely to be volatile: they can all be postponed.
• If we all do our postponing at the same time, we will probably have a recession • Workers and capital may be idled, until we finish our waiting ⇑
Spanish recent recession
16
• Housing starts (HS)
• Cement consumption (CC) • Car registrations (CR)
• Commercial vehicle registrations (CVR)
. . . in logs. We use unadjusted monthly data to avoid delays in the recognition of the end of a recession (Matas-Mir et al., 2008). ⇑
Estimated DHR models: Noise Variance Ratios
17
• IRW model for the trend
• RW model for the seasonal components Series
Trend
S12
S6
S4
S3
S2.4
S2
Housing starts Cement consumpt Car Registrat Commercial vehicle reg Industrial Product. Ind.
0.0043 0.0028 0.0017 0.0030 0.0007
0.0070 0.0042 0.0091 0.0038 0.0035
0.0030 0.0045 0.0025 0.0050 0.0012
0.0036 0.0040 0.0057 0.0055 0.0024
0.0072 0.0118 0.0079 0.0100 0.0040
0.0031 0.0091 0.0065 0.0052 0.0030
0.0036 0.0007 0.0006 0.0016 0.0003
(Sample up to 2009.12 )
8
⇑
Spanish recent recession log. Housing starts – 1978.01 to 2009.12
18
log. Car Registrat. – 1970.01 to 2009.12
12.0
12.5
11.5 12.0 11.0 11.5
10.5 10.0
11.0
9.5 10.5 9.0 8.5 70
75
80
85
90
95
00
10.0 70
05
log. Cement consumpt. – 1970.01 to 2009.12 11.0
8.5
10.5
8.0
10.0
7.5
9.5
7.0
9.0
75
80
85
90
95
00
⇑
8.5 70
05
85
90
95
00
05
75
80
85
90
95
00
05
Trend derivatives
2008.06 Housing starts. 1978.01:2009.12
70
80
log. Commercial vehicle reg. – 1975.01 to 2009.12
9.0
6.5 70
75
75
80
85
90
95
00
05
19
2008.07 Cement consumpt. 1970.01:2009.12
70
75
80
85
90
95
00
05
2008.06 Car Registrat. 1970.01:2009.12 2008.07 Commercial vehicle reg. 1975.01:2009.12
70
75
80
85
90
95
00
05
70
75
80
85
90
95
00
05
9
⇑
Composite Leading Indicator cycle
2008.06
Comp. Leading Ind
20
Sample 1978.01:2009.12
+0.030 +0.020 +0.010 +0.000 -0.010 -0.020 -0.030 -0.040 -0.050 -0.060 70
75 2008.10
+0.006 +0.004 +0.002 +0.000 -0.002 -0.004 -0.006 -0.008 -0.010 -0.012 -0.014 70
75
80
85
90
95
Industrial Product. Ind.
80
⇑
85
90
00
05
Sample 1975.01:2009.12
95
00
05 21
Turning points and recessions Series
Turning point
Conf. recession
Turning point
Housing starts Cement consumpt Car Registrat Commercial vehicle reg
200601 200512 200606 200412
200609 200703 200610 200701
200806 200807 200806 200807
Comp. Leading Ind
200601
200610
200806
Industrial Product. Ind.
200602
200702
200810
(Sample up to 2009.12 )
10
⇑
GDP annual growth rate and quarterly Composite L. Indicator
22
0.1
8
6
0.05
4 0 2 -0.05 0 -0.1 -2 -0.15
-4
-6 1979.1
⇑
1983.1
1987.1
1991.1
1995.1
1999.1
2003.1
2007.1
Peaks and troughs of GDP annual growth rate and Leading I.
L.I. 1982.4 1986.4 1991.3 1994.3 1998.3 2006.1 Mean
Peaks GDP # of quarters 1984.1 1987.4 1991.4 1995.1 2000.1 2006.4
5 4 1 2 6 3 3.5
L.I. 1980.2 1984.2 1990.3 1992.4 1995.3 2000.3 2008.3
Troughs GDP # of quarters 1981.2 1985.3 1991.3 1993.1 1996.1 2002.1 2009.2
4 5 4 1 2 6 3 3.6
-0.2
23
11
⇑
Classical IPI cycles
24
First difference of the estimated trend of Comp. Leading Ind. .03 .02 .01 .00 -.01 -.02 -.03 -.04 -.05 -.06 1980
1985
⇑
1990
1995
2000
2005
Classical IPI cycles
25
• CLI and IPI dates where recessions begin
⇑
CLI
IPI
Lead
1979M 2 1983M 4 1989M 7 1995M 4 2000M 3 2006M 10
1980M 2 − 1990M 1 1995M 8 2000M 9 2007M 3
12 FN 6 4 6 5
Out-of-sample forecast
26
• Smooth estimates (taking advantages of full sample information)
• In a true forecasting exercise, however, we can only count on the information available at the beginning of the forecast horizon. • How does the picture change when adding one observation at a time? Composite Leading Indicator: Frames 1989:01 to 2009:12 ⇑
27
Monthly IPI recessions
• CLI leading IPI recessions Recession periods
1990-93
1996
2001
2007-09
CLI IPI Lead (in months)
1990M 2 1990M 11 9
1995M 12 1996M 3 3
2000M 9 2001M 4 5
2007M 5 2007M 11 6
12
⇑
Annual and Quarterly GDP forecasts
28
⇑
Annual and Quarterly GDP forecasts
29
Dymamic model includes lags of GDP and CLI growth rates. • Relative forecast RMSE ratios
⇑
AR
CLI Model
2007 2008 2009
1.00 1.00 1.00
0.714 0.859 0.564
ALL
1.00
0.811
Conclusions
30
• Contrary to “popular” wisdom, clear signals of recession were evident in the economy before the bursting of the financial bubble in August 2007. • For the case of Spain this announcement was genreralized across economic sectors and indicators.
• Four leading variables used to construct the CLI which provides a similar (clear) message regarding recession announcement. • Does it pay to be a party pooper?
index was next to last in the head-to-head competition.
13
Predicted Probabilities of Ends of Expansions “The party was over” Best Model (Spread, Crude, Permits) Shaded Regions the Year Before Recessions (Predicted Probabilities of Endsare of Expansions Leamer, 2009, pp. 213-214)
⇑
1.0 FP 0.8
214
0.6
13 More Clues: Components of Leading Indicators
Figure 13.6 illustrates the predicted probabilities of recessions coming from 0.4 the best model reported in Table 13.4. Compare this figure with the predicted probabilities based on the interest rate spreadFP alone, Fig. 13.5, and on the Conference Board combination, FPFig. 13.4, to see how much better this model is doing 0.2 than either of them. Here it is hard to see the shaded years-before-recession because the probabilities jump up virtually to one. Otherwise the probabilities are mostly 0.0 close to zero. Here we see a mild false alarm in 1965 and in 1987, and a short-lived 60 65 70 75 80 85 90 95 00 05 major alarm in 1998. Fig. 13.6especially Predicted probabilities of imminent based on three best indicators Notice, that in 2006, a loudrecessions alarm has been sounded, making a recession in 2007 a virtual certainty. I don’t think so, but that is what these data suggest. List of Slides 1
Heading
Appendix: 2 Heading Description of Leading Indicators 3 Contents 4 GDP Source: http://www.conference-board.org/economics/bci/component.cfm 5 Alternatives Leading Index Components 6 Alternatives 7 LDHR model general specification: frequency 8 LDHR model general specification: amplitude 9 LDHR model: ARIMA spectral representation BCI-01 Average Weekly Hours, Manufacturing 10 LDHR model: automatic identification 11 average LDHR model: spectral fitting The hours worked per week by production workers in manufacturing indus12 A composite leading indicator: Non-stationary dynamic factors tries tend to the business cycle because employers usually adjust work hours 13 Building alead composite leading indicator: Spanish recession before increasing or decreasing their workforce. 14 Concepts 15 Building the composite leading indicator 16 Spanish recent recession 17 Estimated DHR models: Noise Variance Ratios BCI-05 Average Weekly Initial Claims for 18 Spanish recent recession Unemployment Insurance 19 Trend derivatives 20 Composite Leading Indicator cycle The of new claims filed for unemployment insurance are typically more 21 number Turning points and recessions sensitive than either total employment or unemployment to overall business condi22 GDP annual growth rate and quarterly Composite L. Indicator 23 Peaks GDP annual growth rate and Leading I. tions, and and thistroughs seriesof tends to lead the business cycle. It is inverted when included 24 Classical IPI cycles in the leading index; the signs of the month-to-month changes are reversed, because 25 Classical IPI cycles initial claims increase 26 Out-of-sample forecast when employment conditions worsen (i.e., layoffs rise and new fall). 27 hirings Monthly IPI recessions 28 Annual and Quarterly GDP forecasts 29 Annual and Quarterly GDP forecasts 30 Conclusions BCI-08 Manufacturers’ New Orders, Consumer Goods, 31 “The party was over”
and Materials (in 1996 $)
These goods are primarily used by consumers. The inflation-adjusted value of new orders leads actual production because new orders directly affect the level of both unfilled orders and inventories that firms monitor when making production deci-
31
14
References Bujosa, M., Garc´ıa-Ferrer, A., & Young, P. C. (2007). Linear dynamic harmonic regression. Comput. Stat. Data Anal., 52 , 999–1024. 3 Garc´ıa-Ferrer, A. & Bujosa-Brun, M. (2000). Forecasting OECD industrial turning points using unobserved components models with business survey data. International Journal of Forecasting, 16 , 207–227. 4 Leamer, E. E. (2009). Macroeconomic Patterns and stories. Berlin: Springer-Verlag. 7, 13 Matas-Mir, A., Osborn, D. R., & Lombardi, M. J. (2008). The effect of a seasonal adjustment on the properties of business cycle regimes. Journal of Applied Econometrics, 23 , 257–278. 7 Pe˜ na, D. & Poncela, P. (2006). Nonstationary dynamic factor analysis. Journal of Statistical Planning and Inference, 136 , 1237–1257. 4
