Technological Standardization, Endogenous
Productivity and Transitory Dynamics
Justus Baron1
1
Julia Schmidt2
Northwestern University, Mines ParisTech
2
Banque de France
Joint French Macro Workshop / BdF – 5 June 2014
A never-ending story ...
• What drives business cycles?
• Technology as a popular explanation for business cycle fluctuations
• Question of technology-induced fluctuations remains on the research
agenda of macroeconomists due to the difficulty of identifying technology
shocks.
• Literature on investment-specific technological (IST) change (Greenwood
et al., 1988) and “news shocks” (Beaudry and Portier, 2006; Jaimovich
and Rebelo, 2009): Revival of role of (embodied) technology for business
cycle fluctuations
2/40
Opening the black box of technology shocks
• Aggregate macroeconomic movements stem most likely from general
purpose technologies (GPTs)
• ICT = dominant GPT of the last decades (Basu and Fernald, 2008)
3/40
Opening the black box of technology shocks
• Aggregate macroeconomic movements stem most likely from general
purpose technologies (GPTs)
• ICT = dominant GPT of the last decades (Basu and Fernald, 2008)
• Fundamental characteristics of GPTs:
• Network externalities
• Compatibility requirements
→ Necessity to agree on a minimal set of rules for all users of the network
technology
3/40
Opening the black box of technology shocks
• Aggregate macroeconomic movements stem most likely from general
purpose technologies (GPTs)
• ICT = dominant GPT of the last decades (Basu and Fernald, 2008)
• Fundamental characteristics of GPTs:
• Network externalities
• Compatibility requirements
→ Necessity to agree on a minimal set of rules for all users of the network
technology
• Standardization = process of establishing these rules
3/40
The interaction between technology and the cycle
Macroeconomics / Business cycle activity
Economic incentives
Financing opportunities
InnovaRandom
tive input: + science
R&D
flow
Initial shocks
Expectations
New
Selection Standartechnodization
logies
Economic
incentives
Uncertainty
reduction
Technology
diffusion
Actual
impact on
cycle
Adoption
Commercialization
Existing indicators:
t
R&D
expenditures
(Shea, 1999)
Patents
(Shea, 1999)
Standards
(This paper)
Technology books Corrected
(Alexopoulos,
Solow
2011)
residuals
(Basu et al,
2006)
4/40
Goal of this paper
• Identification of an important microeconomic mechanism which predates
technology adoption
• Analysis of macroeconomic aggregates’ reaction to technology shocks
5/40
Goal of this paper
• Identification of an important microeconomic mechanism which predates
technology adoption
• Analysis of macroeconomic aggregates’ reaction to technology shocks
• Summary of results:
1 Slow diffusion → positive, S-shaped reaction of output and investment
Temporary slowdown of disembodied productivity (TFP)
2 Analogy with “news shocks” as stock market indices react positively on
impact
5/40
Existing indicators of technology
• Derivation of technology shocks using long-run restrictions (Galı́, 1999)
• Correction of Solow residuals for capacity utilization, increasing returns,
imperfect competition and aggregation effects (Basu et al., 2006)
• Relative price of investment goods (Greenwood et al., 2000; Fisher, 2006)
• Direct indicators of technology:
• Patent data (Shea, 1999; Kogan et al., 2012)
• Transfer of ownership of patents (Serrano, 2007)
• Technology publications such as manuals (Alexopoulos, 2011)
6/40
What constitutes a good indicator of technology (adoption)?
• Central question: What is a technology shock?
• Science and technological inventions lead to an expansion of the technology
frontier.
• However, the shock itself happens when technologies are adopted
(= catch-up with the technology frontier).
• GPTs: technological/economic necessity to standardize
• A technology shock affects all major industries and production processes.
7/40
What constitutes a good indicator of technology (adoption)?
• Central question: What is a technology shock?
• Science and technological inventions lead to an expansion of the technology
frontier.
• However, the shock itself happens when technologies are adopted
(= catch-up with the technology frontier).
• GPTs: technological/economic necessity to standardize
• A technology shock affects all major industries and production processes.
• A good indicator should ...
• ... be closely related to the adoption and commercialization, and not the
invention, of a new technology.
• ... be relevant in terms of technological and economic significance.
• ... be an objective measure and directly linked to technology.
7/40
A novel indicator of technology diffusion
• Technological standard = document which describes the required technical
features of products and processes
• A4 paper size, electricity plugs, quality standards such as ISO 9001, ...
→ Industry-wide coordination efforts to ensure compatibility of technical
devices
• Explicit economic mechanism that predates technology implementation
• Direct link to point in time when technology is adopted
• High technological and economic content of each standard
• Use of ICT standards due to the nature of ICT as a general purpose
technology (GPT) (Basu and Fernald, 2008)
→ Analysis of a specific technology shock which is interpreted as one of
radical technical change in production processes (i.e. as opposed to
political reforms)
8/40
A popular example of standardization
• 1G, 2G and 3G represent different standard families in the wireless
telecommunications sector
9/40
A popular example of standardization
• 1G, 2G and 3G represent different standard families in the wireless
telecommunications sector
• First generation (1G): analog telecommunications systems (1980’s)
9/40
A popular example of standardization
• 1G, 2G and 3G represent different standard families in the wireless
telecommunications sector
• First generation (1G): analog telecommunications systems (1980’s)
• Second generation (2G): digital mobile phone systems in the 1990’s
9/40
A popular example of standardization
• 1G, 2G and 3G represent different standard families in the wireless
telecommunications sector
• First generation (1G): analog telecommunications systems (1980’s)
• Second generation (2G): digital mobile phone systems in the 1990’s
• Third generation (3G): high speed data transmission and mobile Internet
access available as of 2000’s
9/40
A popular example of standardization
• 1G, 2G and 3G represent different standard families in the wireless
telecommunications sector
• First generation (1G): analog telecommunications systems (1980’s)
• Second generation (2G): digital mobile phone systems in the 1990’s
• Third generation (3G): high speed data transmission and mobile Internet
access available as of 2000’s
• Forth generation (4G): super high speed...
9/40
Standard setting
• Types of standard setting:
• De facto: market selection processes, traditional use or monopolistic supply
(proprietary standards)
• Voluntary/informal: industry organizations (non-proprietary standards)
• Formal: standard setting organizations with binding decisions
• Standard setting organizations (SSOs):
• International: International Organization for Standardization (ISO),
International Telecommunication Union (ITU)
• Regional: European Telecommunications Standards Institute (ETSI),
European Committee for Standardization (CEN)
• National: American National Standards Institute (ANSI), Association
française de normalisation (AFNOR), Deutsches Institut für Normung (DIN)
• > 100,000 standards in the US today developed by > 600 SSOs
• US: 90% of all standards are set by the 20 largest SSOs
10/40
Standards data
Table 1 : Characteristics by ICS classification 1975Q1–2011Q4
Number
Health/safety/environment/agriculture
ICT
Engineering/electronics
Materials technologies
Transport/construction
Generalities/infrastructures/sciences/etc.
Total
% new
US
US Int
US
US+Int
10 140
9 603
27 772
30 801
30 782
7 432
107 480
20 032
62 753
49 064
41 004
40 108
16 327
209 988
47
68
45
32
46
40
44
51
56
51
37
47
51
49
+
11/40
Figure 1 : Standard series
Standards ICT (US)
Standards (US)
200
1000
150
750
100
500
50
250
1975
1980
1985
1990
1995
2000
2005
2010
(a) ICT Standards and all standards (US)
200
2000
Standards ICT (US)
Standards ICT (US+Int)
1500
150
1000
100
500
50
1975
1980
1985
1990
1995
2000
2005
2010
(b) ICT Standards (US and Int)
12/40
Economic implications of standardization
• Compatibility and network effects. Need for compatibility in order to
benefit from positive externalities (Katz and Shapiro, 1985, 1986; David
and Greenstein, 1990; Farrell and Saloner, 1988).
• Economic significance and “lumpy” adoption. Standards comprise
several inventions, relate to other standards and are adopted in “bundles”.
• Selection mechanism. Choice of one practice among competing ones in
order to identify relevant technologies (Rysman and Simcoe, 2008).
• Reduction of uncertainty and expectations. Standardization defines the
direction towards an industry is heading and anchors technological
expectations.
• Discontinuous technologies which incentivize incremental innovation.
Standards as indicators of radical technological change → Backwards
non-compatibility and need for further investment and innovation.
• Long-term impact and “QWERTY-nomics” (David, 1985). Network
externalities, path dependence and irreversibility of investment make
future technology a function of today’s standardization choices.
13/40
Data
Quarterly data for the US, 1975Q1-2011Q4
Variable
Description
Source
Standards
Number of standards released per quarter by American standard
setting organizations
ICT sector: ICS classes 33 (Telecommunications) and 35
(Information technology)
PERINORM database
Macroeconomic
variables
Business output
Non-residential investment in equipment and software
Consumption of goods and services
Hours worked
Capacity utilization
Price indices for investment
BLS
NIPA tables (BEA)
NIPA tables (BEA)
BLS
FRB
NIPA tables (BEA)
TFP
Utilization-adjusted total factor productivity in “investment
sector” (equipment and consumer durables) and in
“consumption sector” (non-equipment)
John Fernald (San
Francisco Fed)
Stock market
indices
S&P 500
NASDAQ Composite index
Datastream
Interest rate
Federal Funds rate
FRB
14/40
Procyclical standardization (1)
Figure 2 : ICT Standards and business output
Standards ICT (US)
Output
0
0
1975
1980
1985
1990
1995
2000
2005
2010
Notes: Data are in logs, and HP-detrended (with smoothing parameter 1600). Output is seasonally adjusted. Standard
data are averaged over a centered window of 9 quarters. Shaded areas correspond to NBER recession dates.
15/40
Procyclical standardization (2)
Figure 3 : Cross-correlations of ICT Standards and macro variables
Output
Investment
TFP (adj.)
0.5
0.4
0.3
0.2
0.1
0
−0.1
−0.2
−0.3
−0.4
−0.5
−8
−7
−6
−5
−4
−3
−2
−1
0
1
2
3
4
5
6
7
8
Notes: The x-axis shows quarters and the y axis the estimated cross-correlations. Cross-correlations
were calculated based on the data which are in logs, seasonally adjusted and HP-detrended. Standard
data are averaged over a centered window of 5 quarters.) The above graph shows that standards are
lagging output and investment.
16/40
Procyclicality (3)
• Idea: check procyclicality in a VAR framework using an agnostic business
cycle shock
• Variables in baseline VAR: Output, Investment, TFP, Standards
• Business cycle shock:
• Identification based on Giannone et al. (2012a) who modify the approach of
DiCecio and Owyang (2010)
• Extraction of a shock process which is a linear combination of all the shocks
in the VAR system (except the technology shock) that leads to a high
variation in output at business cycle frequencies
• Identification of the technology shock is left unchanged
Details
17/40
Figure 4 : IRFs: Business cycle shock
Output
Investment
0.012
0.025
0.01
0.02
0.015
0.008
0.01
0.006
0.005
0.004
0
0.002
−0.005
0
4
12
−0.01
16
x 10
8
12
16
12
16
Standards
0.06
5
0.04
4
0.02
3
0
2
−0.02
1
−0.04
0
4
TFP
−3
6
8
4
8
12
−0.06
16
US
4
8
US+Int
18/40
Econometric approach
• What do we know about technology from innovation economics?
• Procyclicality/endogeneity → Use of vector autoregressions
• Slow technology diffusion (Griliches, 1957; Comin and Hobijn, 2010)
19/40
Econometric approach
• What do we know about technology from innovation economics?
• Procyclicality/endogeneity → Use of vector autoregressions
• Slow technology diffusion (Griliches, 1957; Comin and Hobijn, 2010)
• How to tackle slow diffusion?
→ Not trivial to deal with macroeconometrically (Lippi and Reichlin, 1993)
→ Use of meaningful information to capture the point in time when a
technology is adopted or its future adoption is announced
→ Lag truncation bias (Ravenna, 2007; Chari et al., 2008)
19/40
A BVAR that accounts for diffusion lags (1)
• Slow technology diffusion requires the use of long lags → high estimation
uncertainty
• Bayesian shrinkage deals with overparameterization by combining the
likelihood of the data with informative priors
• Minnesota prior where prior coefficients aijl approximate the time series
behaviour of the data
aijl =
δi
0
if i = j and s = 1
otherwise
• δi = 1 (unit root behaviour) for macroeconomic variables
• δi = 0 (substantial mean reversion) for standards
20/40
A BVAR that accounts for diffusion lags (2)
• Bayesian VAR approach in order to allow for a large number of lags and a
differentiated lag structure among the variables in the VAR
• Informativeness of the prior:

φ1


for i = j, i 6= k, l = 1, . . . , p (own lags)

 φ4
 lφ φ σ 2
1
2
i
V aijl =
for i =
6 j, i 6= k, l = 1, . . . , p (lags of other variables)

 lφ4,j σ 2

j


2
φ3 σi
for the constant
21/40
A BVAR that accounts for diffusion lags (3)
• Choice of hyperparameters:
• Quadratic lag decay (φ4,j = 2) and uninformative prior for the constant
• Long lags of the standard series s are “allowed to speak”: φ4,s = 0
• Symmetric treatment of all equations (Kadiyala and Karlsson, 1997; Sims
and Zha, 1998) → φ2 = 1
• Overall prior variance: φ1 is estimated from the data by maximizing the
marginal likelihood of the model (empirical Bayes method following Canova,
Technical details
2007; Giannone et al., 2012b; Carriero et al., 2011)
• Posterior simulations using the Normal-Wishart prior (implemented using
dummy observations) in order to allow for a non-diagonal
variance-covariance matrix and compute IRFs
22/40
Table 2 : Estimated lag decay parameters
(a) Standard series used: US
Implied decay at different lags
φ4,j
Output
Investment
TFP (adj.)
Standards
0.6990
1.0721
0.8707
0.5083
4
8
12
2.6
4.4
3.3
2.0
4.3
9.3
6.1
2.9
5.7
14.4
8.7
3.5
(b) Standard series used: US and Int
Implied decay at different lags
φ4,j
Output
Investment
TFP (adj.)
Standards
0.4023
0.6384
0.4935
0.0777
4
8
12
1.7
2.4
2.0
1.1
2.3
3.8
2.8
1.2
2.7
4.9
3.4
1.2
23/40
Identification of the technology shock
• Variables in baseline VAR: Output, Investment, TFP, Standards
• Technology shock:
• Cholesky decomposition
• Ordering: Output, investment, TFP and standards
• Similar to Shea (1999)
• Idea: Standardization is the first step in the adoption of a new technology,
necessity to invest in incremental innovation before actual
commercialization
24/40
Figure 5 : IRFs: Responses to a technology shock
Output
−3
15
x 10
Investment
0.025
0.02
10
0.015
5
0.01
0.005
0
0
−5
8
24
32
8
TFP (adj.)
−3
6
16
−0.005
x 10
16
24
32
24
32
Standards
0.35
0.3
4
0.25
2
0.2
0
0.15
0.1
−2
−4
0.05
8
16
24
0
32
US
8
16
US+Int
Beaudry and Portier (2006)
25/40
S-shaped technology diffusion
• Empirical evidence of diffusion patterns starting with Griliches (1957)
show that technology diffusion follows a logistic curve.
Figure 6 : Diffusion of consumer goods
Source: New York Times (2008)
25/40
Figure 7 : IRFs: Responses to a technology shock
Output
−3
15
x 10
Investment
0.025
0.02
10
0.015
5
0.01
0.005
0
0
−5
8
24
32
8
TFP (adj.)
−3
6
16
−0.005
x 10
16
24
32
24
32
Standards
0.35
0.3
4
0.25
2
0.2
0
0.15
0.1
−2
−4
0.05
8
16
24
0
32
US
8
16
US+Int
Beaudry and Portier (2006)
25/40
Are we picking up the right stuff?
• Add sectoral measures of investment one by one
• Estimation of a block exogeneity VAR to ensure consistent estimation of
technology shock
26/40
Table 3 : Impact of a technology shock, IRF at horizon 20
Investment series
Equipment
a Information processing equipment
aaa Computers and periphal equipment
aaa Other information processing equipment
a Industrial equipment
a Transportation equipment
a Other equipment
Intellectual property products
a Software
a Research and development
a Entertainment, literary, and artistic originals
US
US+Int
0.93*
1.59*
3.59*
0.61*
0.42*
0.72*
0.44*
1.11*
2.74*
0.52*
0.58*
0.82*
1.40*
2.78*
0.62*
0.39*
0.45
0.75*
0.71*
1.81*
0.02
0.46*
“*” denotes significance at the 5th/95th percentile.
27/40
Table 4 : Variance decompositions at different frequencies
(a) Standard series used: US
Business cycle shock
Technology shock
Frequency (quarters)
8–32
33–200
8–32
33–200
Output
Investment
TFP (adj.)
Standards
0.47
0.27
0.21
0.07
0.17
0.10
0.13
0.07
0.06
0.05
0.06
0.68
0.19
0.14
0.14
0.26
(b) Standard series used: US and Int
Business cycle shock
Technology shock
Frequency (quarters)
8–32
33–200
8–32
33–200
Output
Investment
TFP (adj.)
Standards
0.58
0.43
0.18
0.08
0.20
0.17
0.15
0.11
0.05
0.05
0.06
0.75
0.16
0.11
0.11
0.18
28/40
Figure 8 : Variance decompositions for different frequencies (US)
Business cycle shock → Standards
Technology shock → Macro variables
0.16
0.25
Output
Investment
TFP (adj.)
Share of variance decomposition
Share of variance decomposition
0.14
0.12
0.1
0.08
0.06
0.04
0.2
0.15
0.1
0.05
0.02
0
0
0.4
0.8
Frequency
1.2
0
0
0.4
0.8
Frequency
1.2
29/40
Figure 9 : Variance decompositions for different frequencies (US+Int)
Technology shock → Macro variables
0.2
0.18
0.18
Share of variance decomposition
Share of variance decomposition
Business cycle shock → Standards
0.2
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
Output
Investment
TFP (adj.)
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
0.4
0.8
Frequency
1.2
0
0
0.4
0.8
Frequency
1.2
30/40
Technological change and expectations
• Slow technology diffusion leads to the effects of a shock materializing only
with a considerable delay
• Technology shocks identified from standardization data could show similar
patterns as “news shocks”.
• Do results hold when stock market data are included?
• S&P500
• NASDAQ Composite index
31/40
Figure 10 : IRFs: Responses to a technology shock and news
Output
−3
12
x 10
Investment
−3
20
10
x 10
TFP (adj.)
−3
6
15
4
6
10
2
4
5
0
0
−2
x 10
8
2
0
−2
−5
8
16
24
32
−4
8
Standards
16
24
32
8
S&P500
0.35
0.05
0.3
0.04
16
24
32
NASDAQ
0.06
0.04
0.25
0.03
0.2
0.02
0.02
0.15
0.01
0.1
0
0
0.05
0
−0.01
8
16
24
32
−0.02
8
16
US
24
32
8
16
24
32
US+Int
32/40
Robustness — Weighting standards by their relative importance
1
Pages
• Every line of text that is added to a standard represents a compromise
• Lengthy standard = indicator of the complexity of the technology
2
References
• Referencing = explicit link to an already existing standards by ulterior
standard documents
• Referenced standard = technological importance
• Window: 4 years (→ only use of data up to 2009)
• Weighting schemes follow Trajtenberg (1990) who constructs
citation-weighted patent counts
WSCxt =
nt
X
(1 + xi,t )
where x = p, r
(1)
i=1
33/40
Figure 11 : Weighting standard counts
Output
Investment
0.03
0.025
Output
0.04
0.018
0.035
0.016
0.03
0.014
0.025
0.012
Investment
0.035
0.03
0.025
0.02
0.02
0.015
0.02
0.01
0.01
0.015
0.008
0.01
0.006
0.005
0.004
0
0.002
0.015
0.01
0.005
0
−0.005
−0.005
8
16
24
32
16
24
8
6
0.9
5
16
24
32
x 10
16
24
32
24
32
Standards
1
0.9
0.8
4
0.7
8
TFP (adj.)
−3
1
0.8
0
−0.005
32
Standards
0.005
0
0
8
TFP (adj.)
0.01
0.005
0.7
3
0.6
0.6
2
0.5
0.5
1
−0.005
0.4
0.4
0
0.3
−0.01
−0.015
8
16
US baseline
24
0.1
−2
0
−3
32
US Page−weighted
0.3
−1
0.2
8
16
24
US Reference−weighted
(a) Standard series used: US
32
0.2
0.1
0
8
16
US+Int baseline
24
32
US+Int Page−weighted
8
16
US+Int Reference−weighted
(b) Standard series used: US and Int
34/40
Robustness — Radical vs. incremental innovation
• A substantial number of standard in our dataset consist of upgraded
versions of already existing standards
35/40
Robustness — Radical vs. incremental innovation
• A substantial number of standard in our dataset consist of upgraded
versions of already existing standards
• Radical innovation: Series which excludes upgraded versions of prior
released standards from our standard count
• Incremental innovation: Series which only consists of upgraded versions
35/40
Figure 12 : Radical vs. incremental innovation
Output
Investment
0.025
0.035
0.03
0.02
0.025
0.015
0.02
0.01
0.015
0.005
0.01
0
0.005
−0.005
0
8
24
32
8
TFP (adj.)
−3
10
16
x 10
16
24
32
24
32
Standards
1
0.9
8
0.8
6
0.7
4
0.6
2
0.5
0
0.4
−2
0.3
−4
0.2
−6
0.1
−8
0
8
16
US radical
24
32
US+Int radical
8
US incremental
16
US+Int incremental
36/40
Robustness — Larger VAR system
• Additional variables: Consumption, Hours worked, Capacity utilization,
TFP in the consumption sector, Relative price of investment, Federal
Funds rate
• Identification as before: Technology shocks impact contemporaneously
only on standardization and stock market indices
37/40
Figure 13 : IRFs from large system
15
x 10
−3
Output
Investment
0.03
15
10
0.02
10
5
0.01
5
0
0
0
x 10
−3
−3
Consumption
10
Hours
x 10
5
0
−5
−0.01
8
16
24
−5
32
8
−3
Capacity util.
0.6
15
0.4
x 10
16
24
−5
32
8
TFP (adj.) Inv.
3
x 10
16
24
32
TFP (adj.) Cons.
10
16
24
32
Rel. price Inv.
0.01
2
0.2
8
−3
0.005
1
0
0
−0.005
5
0
0
−0.2
−0.4
−5
8
16
24
32
8
Fed funds rate
16
24
−1
−0.01
−2
−0.015
32
8
Standards
0.4
0.2
16
24
32
8
S&P500
16
24
32
24
32
NASDAQ
0.4
0.08
0.08
0.3
0.06
0.06
0.2
0.04
0.04
0.1
0.02
0.02
0
0
0
−0.1
−0.02
−0.02
0
−0.2
−0.4
8
16
24
32
8
16
24
32
US
8
US+Int
16
24
32
8
16
38/40
Some more robustness
• Inclusion of more standard classes (ICS 31: Electronics / ICS 37: Image
technology)
Figure
• Replacement of ICT standards with standards from other sectors
(manufacturing, services, ...)
• Responses are similar, but muted and more often insignificant
39/40
Summary of results and conclusions
• Caution: Technology adoption is cycle-driven (especially at lower
frequencies)
40/40
Summary of results and conclusions
• Caution: Technology adoption is cycle-driven (especially at lower
frequencies)
1
Positive impact of technology shocks on the cycle
• S-shaped technology diffusion
• Rich transitory dynamics of disembodied productivity
→ Reconciliation of the fact that productivity slowdowns are observed in the
data with the notion of an ever-evolving technology frontier.
2
Propagation of our identified technology shock shows a similar pattern as
the one of “news shocks” (due to slow technological diffusion).
40/40
Summary of results and conclusions
• Caution: Technology adoption is cycle-driven (especially at lower
frequencies)
1
Positive impact of technology shocks on the cycle
• S-shaped technology diffusion
• Rich transitory dynamics of disembodied productivity
→ Reconciliation of the fact that productivity slowdowns are observed in the
data with the notion of an ever-evolving technology frontier.
2
Propagation of our identified technology shock shows a similar pattern as
the one of “news shocks” (due to slow technological diffusion).
• Need to understand technology and productivity as multifaceted
phenomena
• Importance of analyzing the microeconomic mechanisms that are at the
basis of the driving forces of macroeconomic fluctuations
40/40
Identification of a business cycle shock (1)
• Notation follows largely Altig et al. (2005).
• Reduced form VAR: Yt = A(L)Yt + ut
• Structural VAR:
B0 Yt = B1 Yt−1 + B2 Yt−2 + . . . + Bp Yt−p + εt
Yt = [I − A(L)]−1 CRR−1 C −1 ut = [I − A(L)]−1 CRε∗t
where A(L) = (B0 )−1 B(L) , C = (B0 )−1 and ε∗t = R−1 C −1 ut
• Implementation: a set of column vectors of C is rotated by R so that the
shock εj,t maximizes the forecast error variance of one of the variables
Yk,t of the vector Yt at business cycle frequencies
• Variance of Yt in the time domain:
−1
E[Yt Yt0 ] = [I − A(L)]−1 CRR0 C 0 I − A(L)0
40/40
Identification of a business cycle shock (2)
• Use of variances in the frequency domain
• Spectral density of the vector Yt :
h
i−1
h
i−1
SY (e−iω ) = I − A(e−iω )
CRR0 C 0 I − A(e−iω )0
• Spectral density of Yt due to shock εt,j :
h
i−1
h
i−1
SY,j (e−iω ) = I − A(e−iω )
CRIj R0 C 0 I − A(e−iω )0
• Identification → Find R which maximizes the share of the forecast error
variance of variable Yk,t due to shock εt,j :
Rb
SY,j (e−iω )dω
2π
2π
Vk,j = ι0k Rab
ιk where a =
, b=
−iω )dω
32
8
S
(e
Y
a
Jump back
40/40
Results from Beaudry and Portier (2006)
Jump back
40/40
Figure 14 : Historical decomposition of TFP (adj.) (US)
0.02
0.01
0
−0.01
Original data
Only business cycle shocks (corr. with original: 0.47)
Only technology shocks (corr. with original: 0.36)
−0.02
−0.03
1985
1990
1995
2000
2005
2010
Jump back
40/40
Figure 15 : Historical decomposition of TFP (adj.) (US+Int)
0.02
0.01
0
−0.01
Original data
Only business cycle shocks (corr. with original: 0.36)
Only technology shocks (corr. with original: 0.45)
−0.02
−0.03
1985
1990
1995
2000
2005
2010
Jump back
40/40
Technical details on ML
• β . . . vectorized VAR coefficients
• Σ . . . variance-covariance matrix of residuals of VAR model
• Prior distributions:
Σ ∼ IW(Ψ, d)
β | Σ ∼ N (b, Σ ⊗ Ω)
• Marginal likelihood:
Z Z
p(Y | β, Σ) p(β | Σ) p(Σ) dβ dΣ
p(Y ) =
• Prior parameters β and Σ depend on a set of hyperparameters Θ
• Empirical Bayes method to estimate Θ from the data:
Θ∗ = arg max ln p(Y )
Θ
Jump back
40/40
Figure 16 : IRFs: Different standard measures
6
x 10
−3
Output
Investment
0.015
4
5
0.01
2
0.005
x 10
−3
−3
Consumption
5
4
4
3
3
2
2
1
0
0
8
4
x 10
−3
16
24
8
−3
Capacity util.
6
3
1
0
32
16
24
0
32
8
TFP (adj.) I
x 10
1
4
0.5
2
0
0
−0.5
Hours
x 10
x 10
−3
16
24
32
8
−3
TFP (adj.) C
2
x 10
16
24
32
Rel. price of I
0
2
1
−2
0
−1
−2
8
16
24
32
−1
8
Fed funds rate
16
24
32
−4
8
Standards
0.2
24
32
8
NASDAQ
0.8
16
24
32
24
32
S&P500
0.04
0.6
0.1
16
0.03
0.03
0.02
0.4
0
0.02
0.2
−0.1
0.01
0.01
0
−0.2
−0.2
8
16
24
32
US ICT (33−35)
0
8
16
24
Intl ICT (33−35)
32
0
8
16
US ICT+Electronics (31−37)
24
32
8
16
Intl ICT+Electronics (31−37)
40/40