How Important Are Sectoral Shocks?
Enghin Atalay
January, 2014
Motivation and Question
Motivation
I
Most analyses of business cycles (especially since Kydland and
Prescott): Fluctuations are caused by economy-wide shocks to
technology, preferences, etc...
I
These shocks may be built up from events at individual …rms
(Gabaix ’11) or industries (Long and Plosser ’83 and
successors).
Question
I
What fraction of aggregate output ‡uctuations come from
industry-speci…c shocks?
Method and Main Result
Method
I
I
Construct a multi-industry general equilibrium model.
I
Shocks to productivity and preferences, each with an
industry-speci…c and aggregate component.
I
Each industry produces using capital, labor, and intermediate
inputs.
Estimate, via MLE:
I
Compare model’s predictions on the evolution of industries’
output, output prices, and intermediate input usage.
I
Infer magnitude of industry-speci…c and aggregate shocks,
elasticities of substitution in preferences and production.
Main result: Industry-speci…c shocks are important; they represent
more than 60% of aggregate volatility.
Related Literature and Contribution
Related Literature: Multi-industry real business cycle models:
Long and Plosser (’83), Horvath (’98, ’00), Dupor (’99), Foerster,
Sarte, and Watson (’11), Acemo¼
glu et al. (’12, ’13)
To the Long and Plosser literature (especially relative to Foerster,
Sarte, Watson), I make 2 contributions:
1. Estimate a more general sectoral production function.
I
I
I
Accommodates empirical input usage patterns.
Foerster et al.: Intermediate input cost shares are constant.
Data: St. Dev. of the growth of these cost shares = 2-3%.
2. Smaller advances:
a. Allow for shocks to preferences.
b. Allow for durability of consumption goods.
c. Apply a dataset that spans the entire economy.
d. Examine data from other countries.
Outline
1. Introduce the multi-industry general equilibrium model.
2. Describe the dataset and a pattern in the data.
3. Present the empirical results.
4. Sensitivity analysis.
5. How are the parameters identi…ed?
1. Model
Model: Preferences
There representative consumer has preferences over consumption
CtJ & labor supply LSt .
(
!
1
N
X
X
t
U=
Dt;Agg
DtJ J
t=0
2
log 4
J =1
N
X
(DtJ
J)
1
"D
(CtJ )
"D 1
"D
J =1
Preferences are such that:
CtJ = DtJ Dt;Agg
Durable goods?
Derivation
! " "D 1 3
D
5
J
PtJ
Pt
"LS
LS
"LS + 1 t
"D
1
Pt
"LS +1
"LS
9
=
;
Model: Production
I
The production technology is a CES function of capital/labor
and intermediate inputs:
QtJ = AtJ At;Agg
VtJ =
KtJ
J
I
I
J
(1
J)
1
"Q
(VtJ )
BtJ Bt;Agg LtJ
1
J
"Q 1
"Q
1
+
1
"Q
J
(MtJ )
"Q 1
"Q
"Q
"Q 1
J
The intermediate input bundle of sector J is a CES aggregate
of the purchases from the other sectors:
h
i
MtJ = C Mt;1!J ; Mt;2!J ; :::Mt;N !J ; "M ; M
I !J
The investment input bundle of sector J is a CES aggregate
of the purchases from the other sectors:
h
i
X
Kt+1;J = (1
)
K
+C
X
;
X
;
:::X
;
"
;
K
tJ
t;1!J
t;2!J
t;N !J X
I !J
Model: Market Clearing
I
Goods market clearing conditions (one for each
I 2 f1; :::; Ng):
X
X
QtI =
CtI
+
Xt;I !J
+
Mt;I !J
|{z}
|{z}
output
consumption
| J {z }
| J {z }
investment purchases
I
Labor market clearing condition:
X
LtJ
LSt =
J
intermediate input purchases
Model: Evolution of Exogeneous Variables
I
I
I
The industry-speci…c components of productivity and
preference shocks:
log At+1;J =
Ind ;A
log AtJ +
Ind ;A
Ind ;A
!tJ
(factor-neutral prod.)
log Bt+1;J =
Ind ;B
log BtJ +
Ind ;B
Ind ;B
!tJ
(labor-aug. prod.)
log Dt+1;J =
Ind ;D
log DtJ +
Ind ;D
Ind ;D
!tJ
(preferences)
And the aggregate components:
log At+1;Agg =
Agg ;A
log At;Agg +
Agg ;A
!tAgg ;A
log Bt+1;Agg =
Agg ;B
log Bt;Agg +
Agg ;B
!tAgg ;B
log Dt+1;Agg =
Agg ;D
log Dt;Agg +
Agg ;D
!tAgg ;D
!s are i.i.d. standard normal random variables.
How are the parameters identi…ed? (much more, later on)
I
The goal of the model is to uncover the "s, s, and s.
Compare data on industries’a) sales, b) output prices,
c) intermediate input purchases to their model-predicted
counterparts.
I
Five main ideas:
1. Relationship between an industry’s output and its output
prices ) "D .
2. Relationship between an industry’s intermediate input prices
and its cost shares ) "Q .
3. Some cross-industry-correlation in activity is due to
input-output linkages, more so the larger are J and
IJ .
4. More cross-industry correlation in sales) Aggregate shocks are
important.
5. More cross-industry correlation in intermediate input purchases
(if "Q 6= 1) ) Aggregate shocks are important.
2. Data
I use two main data sources
I
BEA: 1992 Input/Output Table & Capital Flows
Table. Show Tables
I
Dale Jorgenson: Annual data on industries’production,
input/output prices, & inputs, from 1960 to 2005.
1.
YtJ = sales
PtJ QtJ
2.
PtJ = output price
3.
4.
5.
share
MtJ
mat
PtJ
tJ
=
=
=
M
tJ
intermediate inputs cost share
Q tJ
price of intermediate input bundle
mat
PtJ
PtJ
mat
P tJ
P tJ
I make three adjustments, to align the model and the data.
1. Use growth rates of each linearly de-trend each variable.
mat .
2. Subtract o¤ changes in overall price level from YtJ , PtJ , PtJ
3. Trim top/bottom 0:5% of each variable.
Call
z the transformed version of variable Z .
ytI
ptI
mtIshare
ptImat
tI
SD
ytI
1
0.610*
0.107*
0.451*
-0.516*
0.072
ptI
1
-0.010
0.745*
-0.841*
0.048
mtIshare
ptImat
1
0.244*
0.212*
0.025
1
-0.265*
0.027
I make three adjustments, to align the model and the data.
1. Use growth rates of each linearly de-trend each variable.
mat .
2. Subtract o¤ changes in overall price level from YtJ , PtJ , PtJ
3. Trim top/bottom 0:5% of each variable.
Call
z the transformed version of variable Z .
ytI
ptI
mtIshare
ptImat
tI
SD
ytI
1
0.610*
0.107*
0.451*
-0.516*
0.072
ptI
1
-0.010
0.745*
-0.841*
0.048
mtIshare
ptImat
1
0.244*
0.212*
0.025
1
-0.265*
0.027
.06
75
71
-.05
Tobac c o
0
∆π
.05
.1
-.06
s hare
.03
Lumber
C h emic a ls
72
97
92
77 95
04
87
93
88 84
68 0005
99 94 69
98 666362
81
64
65
6173
76
02
03
89
67
96 91 85
01
90
86
82 70
-.03
-.03
Tex tile Mills
R ubber&
Pla s tic s
78
79
Metal
Mining
C o mmun ic .
-.05
∆m
-.01
Paper
74
Petroleum
R efining
s hare
Apparel
83
80
Oil/Gas
Ex trac tion
Publis hing
Trans por tation
0
.01
Elec tric
U tilities
∆m
.03
Why is "Q identi…ed to be less than 1?
-.06
-.03
0
∆π
.03
.06
.06
Tex tile Mills
s hare
.03
Lumber
C h emic a ls
72
97
92
77 95
04
87
93
88 84
68 0005
99 94 69
98 666362
81
64
73
65
6102
76
03
89
67
96 91 85
01
90
86
82 70
-.03
R ubber&
Pla s tic s
78
79
Metal
Mining
C o mmun ic .
-.03
∆m
-.01
Paper
74
Petroleum
R efining
s hare
Apparel
83
80
Oil/Gas
Ex trac tion
Publis hing
Trans por tation
0
.01
Elec tric
U tilities
∆m
.03
Why is "Q identi…ed to be less than 1?
75
-.05
0
∆π
.05
-.06
-.05
71
Tobac c o
.1
-.06
-.03
0
∆π
.03
First-order condition on intermediate input purchases)
share
= log
log MtJ
share
mtJ
= (1
J
+ (1
"Q )
"Q ) log
tJ
+ ("Q
tJ
+ ("Q
1) log (AtJ At;Agg )
1) ( atJ +
Takeaway: Positive correlation) "Q < 1.
at;Agg )
.06
3. Estimation and Results
I apply a mix of moment matching and MLE
I
Production function and consumption shares are inferred
using data from ’92.
I
I
I
These parameters are informative only about the steady-state
allocation/prices.
K
Data from IO Table and Capital Flows Table ) M
I !J , I !J .
Data used to infer J (capital intensity), J (intermediate
input intensity), J (preference for good J):
Industry
1. Agriculture
2. Metal Mining
...
32. Wholesale & Retail Trade
33. Finance, Insurance, R.E.
34. Personal & Bus. Services
sK
sL
sM
19.3%
20.5%
...
13.0%
42.5%
11.0%
23.7%
21.8%
...
48.1%
23.5%
53.7%
57.0%
57.7%
...
38.9%
34.0%
35.4%
Consum.
Share
2.2%
0.1%
...
11.1%
16.6%
22.3%
I apply a mix of moment matching and MLE
I
Production function and consumption shares are inferred
using data from ’92 (from previous slide).
I
Other parameters ( ,
I
Estimate other parameters (elasticities of substitution &
dynamics of productivity and preference shocks), via MLE.
I
I
I
I
"LS ) taken from previous papers.
ytI (output)
ptI (output prices)
mtIshare (intermediate input cost shares)
Assume
I
K,
mtIshare is measured with error.
Measurement error has both a industry-speci…c and aggregate
component.
MLE Estimates
Speci…cation
"D (preference)
"Q (between M and K -L)
"M (among intermediate inputs)
"X (among investment inputs)
(industry factor-neutral)
B ;Ind (industry labor-aug.)
D ;Ind (industry preference)
A;Agg (agg. factor-neutral)
B ;Agg (agg. labor-aug.)
D ;Agg (agg. preference)
A;Ind
Log Likelihood
Robustness Checks
(1)
0.654
0.046
0.034
2.870
0.046
0.110
0.062
0.010
0.040
0.001
6743.0
(2)
1
0.020
1
1
0.042
0.110
0.103
0.008
0.040
0.000
6397.6
(3)
0.587
1
0.128
2.313
0.034
0.000
0.061
0.010
0.001
0.050
-94288.6
(4)
1
1
1
1
0.034
0.000
0.105
0.007
0.015
0.021
-94677.1
MLE Estimates
Speci…cation
"D (preference)
"Q (between M and K -L)
"M (among intermediate inputs)
"X (among investment inputs)
(industry factor-neutral)
B ;Ind (industry labor-aug.)
D ;Ind (industry preference)
A;Agg (agg. factor-neutral)
B ;Agg (agg. labor-aug.)
D ;Agg (agg. preference)
A;Ind
Log Likelihood
Robustness Checks
(1)
0.654
0.046
0.034
2.870
0.046
0.110
0.062
0.010
0.040
0.001
6743.0
(2)
1
0.020
1
1
0.042
0.110
0.103
0.008
0.040
0.000
6397.6
(3)
0.587
1
0.128
2.313
0.034
0.000
0.061
0.010
0.001
0.050
-94288.6
(4)
1
1
1
1
0.034
0.000
0.105
0.007
0.015
0.021
-94677.1
MLE Estimates
Speci…cation
"D (preference)
"Q (between M and K -L)
"M (among intermediate inputs)
"X (among investment inputs)
(industry factor-neutral)
B ;Ind (industry labor-aug.)
D ;Ind (industry preference)
A;Agg (agg. factor-neutral)
B ;Agg (agg. labor-aug.)
D ;Agg (agg. preference)
A;Ind
Log Likelihood
Robustness Checks
(1)
0.654
0.046
0.034
2.870
0.046
0.110
0.062
0.010
0.040
0.001
6743.0
(2)
1
0.020
1
1
0.042
0.110
0.103
0.008
0.040
0.000
6397.6
(3)
0.587
1
0.128
2.313
0.034
0.000
0.061
0.010
0.001
0.050
-94288.6
(4)
1
1
1
1
0.034
0.000
0.105
0.007
0.015
0.021
-94677.1
Industry-speci…c shocks account for 60% of aggregate
output volatility
Speci…cation
Aggregate Shocks
Aggregate, Factor-Neutral Prod.
Aggregate, Labor-Augmenting Prod.
Aggregate, Demand
Industry-Speci…c Shocks
Industry, Factor-Neutral Prod.
Industry, Labor-Augmenting Prod.
Industry, Demand
Which Elasticities are
Restricted to 1?
(1)
36.9
10.0
26.9
0.0
63.1
21.3
40.2
1.7
None
(2)
41.4
11.8
29.7
0.0
58.6
17.9
36.5
4.1
"D
"M
"X
(3)
56.6
36.2
0.1
20.3
43.4
37.8
0.0
5.6
(4)
52.0
28.4
18.7
4.8
48.0
35.5
0.0
12.5
"Q
All
4. Robustness Checks
Robustness Checks
I
The plan for the next few slides: Sensitivity to...
a. ... the sample period.
b. ... the parameterization of the stochastic processes.
I
If you like, we could also talk about: Sensitivity to...
c. ... how industries are de…ned.
d. ... the country.
e. ... the treatment of trends.
f. ... assumptions on measurement error in intermediate input
purchases.
g. ... the period length.
h. ... the calibration of the steady state parameters.
i. ... the trimming of outlier observations.
j. ... the choice of shocks to include.
Robust to Time Period?
Period
"Q (btw. M and K -L)
Log Likelihood
Aggregate Shocks
Factor-Neutral
Labor-Augmenting
Demand
Ind.-Speci…c Shocks
Factor-Neutral
Labor-Augmenting
Demand
1960-2005
0.046
1
6743 -94677
36.9
52.0
10.0
28.4
26.9
18.7
0.0
4.8
63.1
48.0
21.3
35.5
40.2
0.0
1.7
12.5
1960-1982
0.055
1
3146 -48566
39.8
67.8
11.5
34.0
27.8
33.8
0.5
0.0
60.2
32.2
22.2
26.6
37.1
0.0
0.9
5.6
1983-2005
0.063
1
3544 -35526
30.4
27.8
5.5
1.6
24.9
23.3
0.0
3.0
69.6
72.2
24.0
45.4
43.7
0.0
2.0
26.8
Robust to Assumptions on the Stochastic Processes?
Reminder: The shock processes, in the benchmark speci…cation,
look like Z 2 fA; B; Dg:
log Zt+1;J =
log Zt+1;Agg =
Period
"Q
Log Likelihood
Aggregate
Middle Nest
Industry
Ind ;Z
Agg ;Z
log ZtJ +
Ind ;Z
log Zt;Agg +
Benchmark
0.046
6743
36.9
1
-94677
52.0
63.1
48.0
Ind ;Z
!tJ
Agg ;Z
Di¤erent s, s
!tAgg ;Z
Di¤. s, s +
Middle Nest
Robust to Assumptions on the Stochastic Processes?
Now the shock processes are sector-speci…c
S 2 fprimary inputs, durable goods, non-durable goods, servicesg:
log Zt+1;J =
log Zt+1;Agg =
Period
"Q
Log Likelihood
Aggregate
Middle Nest
Industry
S
Ind ;Z
S
Agg ;Z
Ind ;Z
S
Ind ;Z !tJ
Agg ;Z
S
log Zt;Agg + Agg
;Z !t
log ZtJ +
Benchmark
Di¤erent s, s
0.046
6743
36.9
1
-94677
52.0
0.027
7200
38.2
1
-94416
49.5
63.1
48.0
61.8
50.5
Di¤. s, s +
Middle Nest
Robust to Assumptions on the Stochastic Processes?
And, I add a "middle nest" stochastic processes
S 2 fprimary inputs, durable goods, non-durable goods, servicesg:
log Zt+1;J =
log Zt+1;Agg =
log Zt+1;S =
Period
"Q
Log Likelihood
Aggregate
Middle Nest
Industry
S
Ind ;Z
S
Agg ;Z
S
Mid ;Z
Ind ;Z
S
Ind ;Z !tJ
Agg ;Z
S
log Zt;Agg + Agg
;Z !t
Mid ;Z
S
log ZtS + Mid
;Z !tS
log ZtJ +
Benchmark
Di¤erent s, s
0.046
6743
36.9
1
-94677
52.0
0.027
7200
38.2
1
-94416
49.5
63.1
48.0
61.8
50.5
Di¤. s, s +
Middle Nest
0.075
1
7203
-79671
28.2
53.2
6.0
4.9
65.7
41.9
5. How Are the
Parameters Identi…ed?
How are the parameters identi…ed?
I
Four results:
1. Relationship between an industry’s sales prices and its sales )
"D .
2. Relationship between an industry’s intermediate input prices
and cost shares ) "Q .
3. More cross-industry correlation in sales) Aggregate shocks are
important.
4. More cross-industry correlation in intermediate input purchases
(if "Q 6= 1)) Aggregate shocks are important.
I
Two tacks:
1. A numerical example, varying parameters around the MLE
estimates.
2. A worked-out example, using a simpli…ed version of the model.
Go to Simple Example
.01
∆ y, ∆ p)
.005
Cov(
0
Covariance
.015
.02
Varying "D , holding all other parameters …xed
.3
.5
.7
Goods are Complements
.9
εD
1.1
1.3
1.5
Goods are Substitutes
Varying "Q , holding all other parameters …xed
)
,∆ p
mat
)
-.00015
0.05 0.10 0.15
0
s hare
s hare
)
0
SD( ∆ m
-.0003
Covariance
∆m
Cov(
.1
.3
.5
Inputs are Complements
.7
.9
εQ
1.1
1.3
1.5
Inputs are Substitutes
Standard Deviation
mat
.00015
.0003
SD( ∆ p
Working through a simple example
I
Assume:
1. no capital (
J
= 0)
2. consumption goods are not durable
3. productivity and preferences are not persistent
4. consumption shares are identical (
J
=
1
N)
5. intermediate input intensities are identical (
6. "M = 0,
I
M
I !J
=
J
= )
1
N
From Assumptions (1)-(3) :
I
The model can be solved period by period (drop t subscripts).
I
The parameters we care about (the "s, s) are identi…ed from
the covariance matrix of the observed variables (the PPJ s, YPJ s,
and MJshare s).
Working through a simple example
Reminder, the production function for an industry:
QJ = AJ AAgg
2
4(1
1
) "Q (BJ BAgg LJ )
"Q 1
"Q
+
1
"Q
1
min MI !J
N I
"Q 1
"Q
3
"Q
"Q 1
5
Taking …rst-order conditions, with respect to MtJ , the equilibrium
intermediate input share satis…es:
PJmat =
@QJ
PJ ) ... )
@MJ
MJshare =
(AJ AAgg )"Q
1
PJmat
PJ
1 "Q
(1)
How are the parameters identi…ed?
The cost minimization condition of each industry also implies that:
PJ =
=
AJ
AJ
1
AAgg
"
(1
)
2
1
4(1
AAgg
)
W
BJ BAgg
1 "Q
W
BJ BAgg
1 "Q
1 "Q
PJmat
+
N
X
PI
+
I =1
N
!1
#
1
1 "Q
"Q
5
Solving this system of equations:
log
PJmat
PJ
1 X
log
N
I
AI
AJ
(1
) log
BI
BJ
(2)
Plug (2) into (1):
log MJshare = log
+ ("Q
1) log AAgg
("Q
1) (1
3
) log BJ
1
1 "Q
From the last slide:
log MJshare = log
+ ("Q
1) log AAgg
("Q
1) (1
) log BJ
(3)
Also:
log
log
YJ
P
PJ
P
=
=
1 X
log
N
I
1 X
N
1
AI
AJ
(1
1
I
+ log
"D (1
1
1
) log
BI
BJ
[log AI + log AAgg ]
"LS
[log DI + log DAgg ]
"LS + 1
AI
BI
)) log
+ (1
) log
AJ
BJ
DJ
+ (1
) log
DI
+ log BI + log BAgg +
+ (1
"Q )
+ (1
(4)
(5)
From the last slide:
log MJshare = log
+ ("Q
1) log AAgg
("Q
1) (1
Sensitivity of MJshare of shocks is U-shapred in "Q .
Also:
1 X
AI
PJ
=
log
log
+ (1
) log
P
N
AJ
I
log
YJ
P
=
1 X
N
1
(1
1
I
+ log
"D (1
1
1
BI
BJ
[log AI + log AAgg ]
"LS
[log DI + log DAgg ]
"LS + 1
AI
BI
)) log
+ (1
) log
AJ
BJ
DJ
+ (1
) log
DI
+ log BI + log BAgg +
+ (1
"Q )
) log BJ
(3)
(4)
(5)
From the last slide:
log MJshare = log
+ ("Q
1) log AAgg
("Q
1) (1
Sensitivity of MJshare of shocks is U-shapred in "Q .
Also:
1 X
AI
PJ
=
log
log
+ (1
) log
P
N
AJ
I
) log BJ
(3)
BI
BJ
(4)
Relative price of industry J is inversely related to AJ and BJ .
log
YJ
P
=
1 X
N
1
(1
1
I
+ log
"D (1
1
1
[log AI + log AAgg ]
"LS
[log DI + log DAgg ]
"LS + 1
AI
BI
)) log
+ (1
) log
AJ
BJ
DJ
+ (1
) log
DI
+ log BI + log BAgg +
+ (1
"Q )
(5)
How are the parameters identi…ed?
Cov
log
PJmat
PJ
; log MJshare
= (1
)2 (1
"Q )
2
B ;Ind
Result 1. Slope of the relationship between intermediate input prices
and cost shares ) "Q .
How are the parameters identi…ed?
PJ
P
PJ
YJ
log
; log
P
P
Var
Cov
log
=
+ (1
)2
"D (1
))
2
A;Ind
= (1
2
B ;Ind
2
A;Ind
+ (1
)2
2
B ;Ind
Combining these two equations:
E log PPI log YPI
E log PPI
2
Cov log PPI ; log YPI
Var log PPI
1
Result 2. Regression coe¢ cient of sales on prices ) "D
"D (1
).
How are the parameters identi…ed?
Cov
log
YI
YJ
; log
P
P
=
1
(1
+
h
2
A;Ind
Cov log MIshare ; log MJshare = ("Q
Result 4. Co-movement of
Industry-speci…c.
MIshare
2
"LS
"LS + 1
)2
+ 1I =J (1
YI
P
2
A;Agg +
1
2
B ;Agg
Result 3. Co-movement of
2
"Q )
+ (1
1)2
2
D ;Agg
2
D ;Ind
)2
2
A;Agg
+ (1
2
B ;Ind
i
+ 1I =J ("Q
)Aggregate vs. Industry-speci…c.
(if "Q 6= 1))Aggregate vs.
"D (1
))2
1)2
2
B ;Ind
How are the parameters identi…ed?
Cov
log
YI
YJ
; log
P
P
=
1
(1
+
h
2
A;Ind
Cov log MIshare ; log MJshare = ("Q
Result 4. Co-movement of
Industry-speci…c.
MIshare
2
"LS
"LS + 1
)2
+ 1I =J (1
YI
P
2
A;Agg +
1
2
B ;Agg
Result 3. Co-movement of
2
"Q )
+ (1
1)2
2
D ;Agg
2
D ;Ind
)2
2
A;Agg
+ (1
2
B ;Ind
i
+ 1I =J ("Q
)Aggregate vs. Industry-speci…c.
(if "Q 6= 1))Aggregate vs.
"D (1
))2
1)2
2
B ;Ind
How are the parameters identi…ed?
Cov
log
YI
YJ
; log
P
P
=
1
(1
+
h
2
A;Ind
Cov log MIshare ; log MJshare = ("Q
Result 4. Co-movement of
Industry-speci…c.
MIshare
2
"LS
"LS + 1
)2
+ 1I =J (1
YI
P
2
A;Agg +
1
2
B ;Agg
Result 3. Co-movement of
2
"Q )
+ (1
1)2
2
D ;Agg
2
D ;Ind
)2
2
A;Agg
+ (1
2
B ;Ind
i
+ 1I =J ("Q
)Aggregate vs. Industry-speci…c.
(if "Q 6= 1))Aggregate vs.
"D (1
))2
1)2
2
B ;Ind
How are the parameters identi…ed?
Cov
log
PI
PJ
; log
P
P
= 1I =J
h
2
A;Ind
+ (1
)2
2
B ;Ind
Result 5. Volatility of industry-speci…c prices ) industry-speci…c
productivity shocks
i
How are the parameters identi…ed?
Cov
log
YI
YJ
; log
P
P
=
1
(1
"Q )
1
2
2
A;Agg +
2
"LS
2
+
D ;Agg
"LS + 1
h
+ 1I =J (1
)2 D2 ;Ind + (1
2
B ;Agg
2
A;Ind
+ (1
)2
2
B ;Ind
i
"D (1
Result 6. Covariance of YPI s) Volatility of industry-speci…c and
aggregate preference shocks.
))2
Appendix Slides
Robust to Period Length?
Period Length
"Q (between M and K -L)
Log Likelihood
Aggregate Shocks
Factor-Neutral Prod.
Labor-Augmenting Prod.
Demand
Industry-Speci…c Shocks
Factor-Neutral Prod.
Labor-Augmenting Prod.
Demand
Go Back , Robustness, Table of Contents
1 year
0.046
1
6743.0 -94677.1
36.9
52.0
10.0
28.4
26.9
18.7
0.0
4.8
63.1
48.0
21.3
35.5
40.2
0.0
1.7
12.5
2 years
0.031
1
2486.8 -20266.3
44.2
55.0
12.8
26.7
31.4
28.1
0.0
0.2
55.8
45.0
19.9
35.2
34.6
0.0
1.2
9.8
Robust to Calibration of
Period Length
"Q (between M and K -L)
Log Likelihood
Aggregate Shocks
Factor-Neutral Prod.
Labor-Augmenting Prod.
Demand
Industry-Speci…c Shocks
Factor-Neutral Prod.
Labor-Augmenting Prod.
Demand
Go Back , Robustness, Table of Contents
J,
J,
J,
and
Original (1992)
0.046
1
6743.0 -94677.1
36.9
52.0
10.0
28.4
26.9
18.7
0.0
4.8
63.1
48.0
21.3
35.5
40.2
0.0
1.7
12.5
M
I !J ?
Alternative (1972)
0.056
1
5368.2 -96087.4
25.4
63.4
9.7
0.0
15.7
9.1
0.0
54.4
74.6
36.6
16.7
3.5
23.8
0.0
34.0
33.0
Robust to Cut-o¤?
Cuto¤
"Q (btw. M and K -L)
Log Likelihood
Aggregate Shocks
Factor-Neutral
Labor-Augmenting
Demand
Ind.-Speci…c Shocks
Factor-Neutral
Labor-Augmenting
Demand
Go Back
,
0.25%
0.049
1
6493 -19032
34.6
46.1
8.5
39.5
26.2
3.2
0.0
3.3
65.4
53.9
21.9
39.6
41.1
0.0
2.4
14.3
Robustness, Table of Contents
0.5%
0.046
1
6743 -94677
36.9
52.0
10.0
28.4
26.9
18.7
0.0
4.8
63.1
48.0
21.3
35.5
40.2
0.0
1.7
12.5
1.0%
0.043
1
6980 -11496
35.4
55.2
6.1
39.4
29.3
6.5
0.0
9.3
64.6
44.8
22.0
32.8
40.5
0.0
2.0
12.0
Robust to Industry Classi…cation?
Industry Classi…cation
"Q (between M and K -L)
Log Likelihood
Aggregate Shocks
Factor-Neutral Prod.
Labor-Augmenting Prod.
Demand
Industry-Speci…c Shocks
Factor-Neutral Prod.
Labor-Augmenting Prod.
Demand
Go Back , Robustness, Table of Contents
Original:
34 industries
0.046
1
6743.0 -94677.1
36.9
52.0
10.0
28.4
26.9
18.7
0.0
4.8
63.1
48.0
21.3
35.5
40.2
0.0
1.7
12.5
Coarse:
8 industries
0.020
1
1975.3 -8106.8
29.3
35.2
0.0
20.7
28.9
5.5
0.5
9.1
70.7
64.8
38.9
46.1
33.8
11.4
1.0
7.3
Robust to Country? (1)
Country
"Q (btw. M and K -L)
Log Likelihood
Aggregate Shocks
Factor-Neutral
Labor-Augmenting
Demand
Ind.-Speci…c Shocks
Factor-Neutral
Labor-Augmenting
Demand
Go Back
,
Denmark
0.036
1
2415 -52262
4.5
10.6
3.6
0.0
0.0
0.0
0.8
10.6
95.5
89.4
18.7
16.3
29.9
42.5
46.9
30.6
Robustness, Table of Contents
Netherlands
0.148
1
3814 -12633
27.0
41.1
14.4
39.5
12.3
0.0
0.3
1.6
73.0
58.9
13.8
9.3
22.4
33.5
36.8
16.2
Spain
0.042
1
2183 -11458
5.0
42.0
5.0
33.9
0.0
0.9
0.0
7.2
95.0
58.0
10.5
7.3
25.0
21.5
59.5
29.3
Robust to Country? (2)
Country
"Q (btw. M and K -L)
Log Likelihood
Aggregate Shocks
Factor-Neutral
Labor-Augmenting
Demand
Ind.-Speci…c Shocks
Factor-Neutral
Labor-Augmenting
Demand
Go Back
,
France
0.118
1
1716 -10578
44.4
7.7
44.4
0.0
0.0
6.6
0.0
1.1
55.6
92.3
5.1
6.0
14.4
18.8
36.1
67.5
Robustness, Table of Contents
Italy
0.068
1
2568 -27190
91.6
34.4
67.6
0.0
22.7
11.5
1.3
22.9
8.4
65.6
1.5
7.3
3.5
25.1
3.4
33.3
Japan
0.027
1
1766 -17110
37.3
8.2
1.3
4.0
35.9
0.1
0.1
4.1
62.7
91.8
3.8
7.8
9.5
14.9
49.3
69.1
Robust to Country? (3)
60
Why does "Q 6= 1 lead to higher estimates for some countries, and
lower estimates for others?
0
Denmark
-20
Netherlands
USA
Spain
1
1.2
1.4
Ratio of Correlations: Sales vs.
Intermediate Input Cost Shares
Go Back
,
France
20
Japan
-40
Free - Restricted: Importance
of Sectoral Shocks
40
Italy
Robustness, Table of Contents
1.6
How to deal with trends in the data?
I
In the benchmark speci…cation, I linearly de-trend each data
series.
I
Two concerns:
1. De-trending removes potentially useful variation.
2. Parameter estimates may be sensitive to the de-trending
procedure (Canova ’13).
I
Ways to address these concerns:
1. Try di¤erent de-trending procedures (next slide).
2. Include trends, permanent shocks, and stationary shocks in the
model.
Robust to De-trending Procedure?
De-trending
Procedure
"Q (btw. M and K -L)
Log Likelihood
Aggregate Shocks
Factor-Neutral
Labor-Augmenting
Demand
Ind.-Speci…c Shocks
Factor-Neutral
Labor-Augmenting
Demand
Go Back
,
Linear
0.046
6743
36.9
10.0
26.9
0.0
63.1
21.3
40.2
1.7
Robustness, Table of Contents
1
-94677
52.0
28.4
18.7
4.8
48.0
35.5
0.0
12.5
Linear +
Break at 1983
0.050
1
6887
-83620
36.8
52.1
9.1
28.6
27.7
18.7
0.0
4.8
63.1
47.9
21.3
35.9
40.6
0.0
1.2
12.0
HP Filter
0.039
8230
23.5
10.1
13.4
0.0
76.4
27.4
48.5
0.6
1
-45668
60.7
0.0
52.4
8.3
39.3
33.6
0.0
5.7
Robust to Measurement Error?
=
M ;Agg =
"Q (between M and K -L)
Log Likelihood
Aggregate Shocks
Factor-Neutral Prod.
Labor-Augmenting Prod.
Demand
Industry-Speci…c Shocks
Factor-Neutral Prod.
Labor-Augmenting Prod.
Demand
Go Back , Robustness, Table of Contents
M ;Ind
0:2%
0:2%
0.046
6743.0
36.9
10.0
26.9
0.0
63.1
21.3
40.2
1.7
0:1%
0:1%
0.045
6493.3
35.8
10.6
25.1
0.0
64.2
21.6
41.0
1.7
0:4%
0:2%
0.046
6758.0
37.6
10.2
27.4
0.0
62.4
21.4
39.3
1.7
0:2%
0:4%
0.047
6748.1
31.1
8.5
22.6
0.0
68.9
23.4
43.6
1.8
Other Estimates of "D and "Q
I
"Q (between intermediate inputs and capital/labor)
I
I
I
Bruno (’84): 0.3
Rotemberg and Woodford (’96): 0.7
"D (preference elasticity)
I
I
Go Back
Ngai and Pissarides (’07), and Acemo¼
glu and Guerrieri (’08):
<1.
Not appropriate: Broda and Weinstein (’06) or Foster,
Haltiwanger, and Syverson (’08): 1.
Robust to Choice of "LS ?
"Q (between M and K -L)
Log Likelihood
Aggregate Shocks
Factor-Neutral Prod.
Labor-Augmenting Prod.
Demand
Industry-Speci…c Shocks
Factor-Neutral Prod.
Labor-Augmenting Prod.
Demand
Go Back , Robustness, Table of Contents
"LS = 1
0.046
1
6743.0 -94677.1
36.9
52.0
10.0
28.4
26.9
18.7
0.0
4.8
63.1
48.0
21.3
35.5
40.2
0.0
1.7
12.5
"LS = 2
0.046
1
6735.3 -16209.9
32.6
38.8
20.3
6.3
23.7
31.4
8.9
1.1
67.4
61.2
19.9
45.3
34.6
0.0
1.2
15.9
Robust to Choice of Shocks?
I
Alter the capital accumulation condition of each industry to:
Kt+1;J = (1
+
I
tJ
K)
t;Agg
KtJ
h
C Xt;1!J ; Xt;2!J ; :::Xt;N !J ; "X ;
X
I !J
i
In one-sector analyses, shocks to the s explain a substantial
fraction of output variation (Fisher ’06, Justiniano, Primiceri,
and Tambalotti ’10)
Go Back
,
Robustness, Table of Contents
Robust to Inclusion of Investment Shocks?
Benchmark
"Q (btw. M and K -L)
Log Likelihood
Aggregate Shocks
Factor-Neutral
Labor-Augmenting
Demand
Investment
Ind.-Speci…c Shocks
Factor-Neutral
Labor-Augmenting
Demand
Investment
Go Back
,
0.046
6743
36.9
10.0
26.9
0.0
1
-94677
52.0
28.4
18.7
4.8
63.1
21.3
40.2
1.7
48.0
35.5
0.0
12.5
Robustness, Table of Contents
Investment
Shocks
0.052
1
6766 -94629
37.1
68.7
12.4
8.3
24.7
0.0
0.0
0.0
0.0
60.5
62.9
31.3
15.9
10.0
23.0
2.0
1.5
0.0
22.4
19.3
Robust to Choice of Shocks?
Benchmark
"Q (btw. M and K -L)
Log Likelihood
Aggregate Shocks
Factor-Neutral
Labor-Augmenting
Demand
Investment
Ind.-Speci…c Shocks
Factor-Neutral
Labor-Augmenting
Demand
Investment
Go Back
,
0.046
6743
36.9
10.0
26.9
0.0
1
-94677
52.0
28.4
18.7
4.8
63.1
21.3
40.2
1.7
48.0
35.5
0.0
12.5
Robustness, Table of Contents
Investment
Shocks
0.052
1
6766 -94629
37.1
68.7
12.4
8.3
24.7
0.0
0.0
0.0
0.0
60.5
62.9
31.3
15.9
10.0
23.0
2.0
1.5
0.0
22.4
19.3
No LaborAug. Shocks
0.754
1
-88401 -94677
69.5
48.3
43.2
48.3
26.3
0.0
30.5
6.9
51.7
38.4
23.5
13.2
Why do the results change so drastically when I set
B = 0?
I
Reminder, from the simple example:
Cov log MIshare ; log MJshare = ("Q
1)2
2
A;Agg ++1I =J
("Q
I
When B2 ;Ind = 0, only common, factor-neutral productivity
shocks can explain volatile intermediate input cost shares.
I
Because the movements in intermediate input cost shares are
so uncorrelated, the likelihood drops substantially.
Go Back
,
Robustness, Table of Contents
1)2
2
B
Destination Industry
There are substantial ‡ows of intermediate inputs, across
industries
2%
4%
8%
16%
32%
Primary+
Cons truc ti on
Manufacturing
Originating Industry
Go Back
T rans port
Servic es
+ Utilities
Destination Industry
A small number of industries produce most of the
investment goods
2%
4%
8%
16%
32%
Primary+
Cons truc ti on
Manufacturing
Originating Industry
Go Back
T rans port
Servic es
+ Utilities
Model: Preferences (With Durable Goods)
Preferences are described by:
U=
1
X
t=0
2
log 4
t
(
N
X
Dt;Agg
(DtJ
N
X
DtJ
J =1
J)
1
"D
(
CJ
J
!
CtJ )
J =1
"D 1
"D
! " "D 1 3
D
5
"LS
LS
"LS + 1 t
Here, CtJ is the stock of the durable good J, is a durable. The
stock evolves according to:
CtJ = Ct
Go Back
1;J
(1
CJ )
~tJ
+C
"LS +1
"LS
9
=
;
Model: Preferences (With Durable Goods)
Name
Construction
Lumber and Wood Products
Furniture and Fixtures
Stone, Clay, and Glass Products
Primary Metals
Fabricated Metal Products
Non-Electrical Machinery
Electrical Machinery
Motor Vehicles
Other Transportation Equipment
Instruments
Miscellaneous Manufacturing
Go Back
Depreciation Rate
2.1%
11.8%
11.8%
16.5%
16.5%
16.5%
16.5%
17.0%
35.3%
16.5%
16.7%
16.2%
Industries in input-output relationships co-move more
strongly
Correlation of Growth Rates Between I and J
-.25
0
.25
.5
.75
Oil E xtrac tion,
Gas Utilities
Oil E xtrac tion,
Refining
W hol es ale/Retail,
Cons truc tion
Non-E lec . Mac hinery,
Non-Metallic Mining
Autos ,
Ships /A irplanes
0
.05
.1
.15
Frac tion of J 's expenditures from I
.2
Equilibrium De…nition
For a given set of initial conditions, a perfectly competitive
equilibrium
consists of shock vectors
n
o1
Ind ;A Agg ;A
Ind ;B Agg ;B
Ind ;D Agg ;D
!tJ ,!t
, !tJ
,!t
, !tJ
,!t
, price vectors
1
t=0
mat , P inv
, and quantity vectors
Wt ; PtJ , PtJ
tJ
t=0
1
S
Lt ; CtJ , QtJ , MtJ , LtJ , XtJ t=0 such that:
1. The representative consumer chooses CtJ and LSt to maximize
expected utility.
2. Each industry chooses LtJ , XtJ , and MtJ to maximize
expected pro…ts.
3. The capital stocks, durable goods stocks evolve as described
in other slides.
4. The demand and productivity stochastic processes evolve as
described in other slides.
5. The labor market and N goods markets clear.
Write the Lagrangian of the social planner:
(
!
X
X
t
L = E0
Dt;Agg
J DtJ
t
J
2"
X
log 4
(
+
X
J
+
X
J
DtJ )
J
1
"D
(CtJ )
"D 1
"D
J
inv
PtJ
[XtJ + (1
"
PtJ QtJ
#
K )KtJ
CtJ
XtJ
"D
"D 1
3
5
X
"LS
LtJ
J
Kt+1;J ]
X
I
Mt;J !I
#)
Take …rst-order conditions with respect to CtJ :
!
X
1
PtJ = Dt;Agg
(DtJ J ) "D (CtJ )
J DtJ
J
X
I
(DtI
I)
1
"D
(CtI )
! "LS +1
"D 1
"D
!
1
1
"D
Re-arrange:
"D
CtJ = (PtJ )
"
X
(
I
"
DtJ
J
DtI )
1
"D
Dt;Agg
(CtI )
J
Note also that:
"D
CtI = (PtI )
"
(CtI )
"D 1
"D
"D 1
"D
N
X
K
X
K
1 "D
I
DtI
Dt;Agg
K
DtK ) "D (CtK )
"D 1
"D
!#"D
(6)
"D 1
"D
"
1
(
"D
Dt;Agg
DtK ) "D (CtK )
DtI
I
I
"
1
(
K =1
= (PtI )
"
DtI
I
#
X
#
N
X
K
K =1
"D
X
K
#1 "D
(
DtK
!#"D
!#"D
K
DtK
I
DtI )
1
"D
1
(7)
CtJ
Plugging Equation (7) into Equation (6):
"
!#"D
X
= (PtJ ) "D Dt;Agg
I DtJ
J
X
1 "D
(PtI )
I
DtI
I
= Dt;Agg
J
DtJ (PtJ )
!
"D
1
"
Dt;Agg
DtJ
J
X
DtK
K
I
X
I
P
K
I
DtI
(PtI )1
K DtK
De…ning the aggregate price level as:
Pt
X
I
We get that:
CtJ = Dt;Agg
Go Back
K
DtI
(PtI )1
D
K
tK
J
DtJ (PtJ )
P
I
"D
"D
!
1
1 "D
(Pt )"D
1
.
!#1
"D
!
"D
1
Conclusion
I
Main result: Industry-speci…c shocks are important (account
for 53 ths of aggregate volatility)
I
I
I
Other studies on the sources of business cycles:
I
I
I
I
Positive correlation between intermediate inputs and
intermediate input prices ) "Q is small.
Movements in intermediate input cost shares are uncorrelated
) industry-speci…c shocks are important.
monetary policy shocks
news about future economic activity
uncertainty about future productivity
Possible avenue for future work: Re-examine these sources of
variation with the understanding that they may come from the
micro level.
Table of Contents
Introduction
Simple Example, Part 1
Industry De…nitions
Challenges
Simple Example, Part 2
Time Period
Method and Main Result
Simple Example, Part 3
Related Literature
Proposition, without Y J
Outline
Robustness, Table of Contents
Intermediate Input Meas. Error
Preferences
Structure of Shocks, 1
Period Length
Production and Market Clearing
Structure of Shocks, 2
Value of "LS
Exogeneous Processes
Comparative Statics, "D
Investment-Speci…c Shocks
Data Sources
Comparative Statics, "Q
Other Estimates of "D and "Q .
A relationship in the data
Calibrate Steady State to 1972
IO and Capital Flows Tables .
Estimation Methodology
Input Relationships and Correlations
Durable Goods
MLE Estimates
Equilibrium De…nition
Proposition, with Y J
Variance Decompositions
Di¤erent Treatment of Trends.
Conclusion
Other Countries
P
Extent of Winsorization
P