Firm Volatility in Granular Networks Bryan Kelly Hanno Lustig Stijn Van Nieuwerburgh

Firm Volatility in Granular Networks
Bryan Kelly1
Hanno Lustig2
Stijn Van Nieuwerburgh3
1
Chicago Booth and NBER
2
UCLA Anderson and NBER
3
NYU Stern, NBER, and CEPR
Introduction
Size, Networks, and Volatility
I
Recent research into aggregate volatility and
I
I
I
Volatility of the firm?
I
I
Firm size distribution (Gabaix 2011)
Network connectivity (Acemoglu et al. 2012, Carvalho 2010)
Affects investment, employment, stock prices
How do inter-firm linkages and the size distribution interact to
influence volatility of the firm?
1
Introduction
Our Approach
I
Data on specific network: Customer/supplier sales relationships
I
I
Among firms and among industries
Identify three prominent features of sales networks
1. Firm growth influenced by connected firms
2. Large firms connected to more firms
3. Large firms exert bigger influence on connected firms
I
Propose model
I
I
I
Simple statistical model based only on these features
Rich implications for volatility (cross section and time series)
New empirical facts: Strong comovement between FSD and FVD
2
Illustrative Networks
Customer/Supplier Sales Relationships
1. Firms
I
I
I
Customer/supplier linkages (Cohen and Frazzini 2008)
Subset of CRSP/Compustat, 1980-2009
“firms are required to disclose the identity of any customer
representing more than 10% of total reported sales”
2. Industries
I
I
BEA summary input/output tables
65 industries, 1998-2011
3
Illustrative Networks
Customer/Supplier Sales Relationships
1. Supplier growth rates influenced by customer growth rates
I
I
Transmission appears stronger upstream than downstream
Network-based spatial AR fits significantly better than common
factor model
2. Large suppliers have more customers
I
I
30% for firm-level data (truncation adjusted)
61% correlation between industry size and number of customers
3. Larger customers have stronger links with suppliers
I
I
I
Size of customer j and the weight it exerts on its supplier i
20% correlation at firm level
37% correlation at industry level
4
A Network Model of Size and Volatility
I
Si,t is size, with dynamics: Si,t+1 = Si,t e gi,t+1
I
Supplier i, connected to customers j, has growth rate:
gi,t+1 = µg + γ
N
X
wi,j,t gj,t+1 + εi,t+1
j=1
I
Weight wi,j,t governs strength of firm j’s influence on firm i,
wi,i,t = 0
I
Idiosyncratic growth rate shocks εi,t+1 ∼ N(0, σε2 ), ∀i, t
I
Parameter γ governs the rate of decay as shocks propagate through
network/strength of the network effects
I
gt+1 = (I − γWt )−1 (µg + εt+1 ): Model content is in Wt
5
A Network Model of Size and Volatility
gi,t+1 = γ
N
X
wi,j,t gj,t+1 + εi,t+1
j=1
bi,j,t Sj,t
wi,j,t = P
j bi,j,t Sj,t
I
Does link exist? Link is iid Be(pi,t ) draw,
bi,j,t
pi,t
I
I
=
=
(
1
0
if i connected to j at time t
otherwise,
Si,t −ζ
N
Z
(i.e., Ni ≈ pi N ∝ N 1−ζ )
Probability of connection depends on supplier size
Number of links may increase more slowly than economy (ζ ∈ (0, 1])
I
If so, how strong? Depends on customer size
I
Weights sum to one
6
Firm Volatility in a Granular Network
As the number of firms in the economy N becomes large, firm i’s
volatility behaves as1
κ0
Si
κ1 E [St2 ]
2γ 2
2
Vt (gi,t+1 ) ∼ σε 1 +
+
+
Si N 1−ζ
N E [St ]2
1 − γ NE [St ]
I
Factor structure in firm volatility dynamics
I
Factor is firm size concentration
I
I
I
Larger firms have
I
I
I
Both mean and dispersion of firm volatility depend on concentration
Special cases include
(
exp(σS2 )
if S ∼ LN(·, σS2 )
E [St2 ]
=
E [St ]2
η/(η − 2) if S ∼ PL(η)
lower volatility level
less variable volatility (smaller loading on factor)
Scope for slower volatility decay than that due to pure granularity
7
Firm Volatility in a Granular Network
As the number of firms in the economy N becomes large, firm i’s
volatility behaves as1
κ0
Si
κ1 E [St2 ]
2γ 2
2
Vt (gi,t+1 ) ∼ σε 1 +
+
+
Si N 1−ζ
N E [St ]2
1 − γ NE [St ]
Proof intuition: One-Step Network
gi,t+1 = µg + γ
N
X
gj,t+1
wi,j,t εj,t+1 +εi,t+1
j=1
V (gi,t+1 ) =
σε2
1+γ
2
N
X
!
2
wi,j,t
j=1
| {z }
Hi
Hi
N→∞
≈
2
1 E [S ]
pi NE [S]2
⇒
V (gi ) ≈ σε2 1 +
κ0 E [S 2 ]
Si N 1−ζ E [S]2
3
γ4
1 κ = γ 2 Z and κ = 2γ +
0
1
1−γ
(1−γ)2
8
Other Implications
2
a
] depends on same factor σs,t
1. Variance of aggregate growth Vt [gt+1
ga,t+1 =
X
i
S
E [St2 ]
P i,t gi,t+1 , with variance Vt (ga,t+1 ) ∝ σε2
⊥ζ
NE [St ]2
i Si,t
2. Insufficiency of factor models in sparse networks
gi = γ
N
X
bi,j Sj
P
gj +εi 6= γ
k Sk
j=1
|
{z
}
Avg. growth of links
N
X
j=1
|
Sj
P
k
{z
Sk
gj
+εi
}
Avg. growth of economy
res
3. “Idiosyncratic” variance (gi,t+1
= gi,t+1 − βi ga,t+1 ) inherits same
factor structure
4. Rich aggregate dynamics coming from network effects (γ 6= 0)
I
Firm size → network structure → firm volatility → firm size
I
Moments of FSD and FVD display substantial time variation
9
Empirical Facts
10
Data, Definitions, Etc.
I
Market (CRSP) and fundamentals (Compustat) data
I
Everything annual
I
Firm size: Market cap or annual sales
I
Firm volatility: Std. dev. of returns or sales growth
I
Concentration: Standard deviation of log size
11
Average Firm Volatility and Dispersion in Firm Size
Average Volatility and Dispersion in Firm Size, 0.72 correlation
2.5
2
1.5
1
0.5
0
−0.5
−1
−1.5
Mean Log Vol based on equity return
Std log size based on mkt cap
−2
1930
1940
1950
1960
I
Firm size dispersion (mkt cap)
I
Mean firm volatility (returns)
1970
1980
1990
2000
2010
12
Dispersion in Firm Volatility and Dispersion in Firm Size
Dispersion in Volatility and Dispersion in Firm Size, 0.79 correlation
1.5
1
0.5
0
−0.5
−1
−1.5
Std Log Vol based on equity return
Std log size based on mkt cap
−2
1930
1940
1950
1960
1970
I
Firm size dispersion (mkt cap)
I
Firm volatility dispersion (returns)
1980
1990
2000
2010
13
Average Firm Volatility and Dispersion in Firm Size (2)
Size and volatility based on sales data
Average Volatility and Dispersion in Firm Size, 0.87 correlation
1
0.5
0
−0.5
−1
−1.5
−2
Mean Log Vol based sales
Std log size based on sales
−2.5
1930
1940
1950
1960
1970
I
Firm size dispersion (sales)
I
Mean firm volatility (sales growth)
1980
1990
2000
2010
14
Factor Structure in Volatility
1 (Small)
2
3
4
5 (Big)
Average Log Return Volatility
−2.5
−3
−3.5
−4
−4.5
1930
1940
1950
1960
1970
1980
1990
2000
2010
0.45
Volatility of Volatility
0.4
0.35
0.3
0.25
Small
2
3
4
Big
15
Factor Structure in Volatility
log Vi,t+1 = ai + bi factort + ei,t+1
Panel A: Total Volatility
Panel B: Residual Volatility
Factors
σs,t
µσ,t
Factors
µσ,t+1
σs,t
µσ,t
µσ,t+1
Factor Model R 2 , All Firms
Return Volatility
24.4
25.9
39.3
24.7
26.5
37.5
Sales Gr. Volatility
21.8
23.4
24.3
21.4
25.8
27.8
(1) Small
1.25
1.09
1.18
1.32
1.10
1.19
(2)
1.12
0.92
1.05
1.21
0.93
1.05
(3)
1.07
0.85
0.99
1.15
0.84
0.97
(4)
0.92
0.74
0.90
0.97
0.69
0.83
(5) Big
0.80
0.65
0.84
0.81
0.55
0.71
Volatility Loadings by Size Quintile
16
Network/Size Uniquely Important for Volatility
Dependent Variable: Log Firm Volatility
(1)
Log Sales
(3)
(4)
(5)
(6)
(7)
(8)
(9)
-0.16
-0.14
-0.13
-0.12
-0.13
-0.12
-16.71
-15.57
-33.10
-19.93
-20.61
-17.78
Netw. Conc.
Log Age
(2)
0.88
0.17
0.55
0.13
0.74
0.17
7.14
3.09
8.69
3.27
28.54
8.81
None
None
Ind.
Ind.
171,034 38,030 37,202 145,247 32,901 32,901 171,034 38,030
37,202
...
Leverage
...
Ind. Conc.
...
Inst. Hldg.
...
...
FE
Obs.
Adj. R 2
None
0.329
0.048
0.361
Cohort Cohort Cohort
0.405
0.307
0.448
Ind.
0.386
0.218
0.425
17
Model Calibration
18
Goals of Calibration
I
Quantitative match of size, volatility, network data?
1. Amount of variability in FSD and FVD generated by model
2. Cross-correlations of moments of FSD and FVD
3. Cross-sectional correlation of network structure and size/volatility
I
Dynamics (birth/death of firms, persistence in links) add further
complexity
I
Even this simple model produces complex, analytically intractable
behavior
I
Certain network features difficult to ascertain due to data truncation
and selection
19
Benchmark Calibration 1
Model Dynamics
I Basic model setup as described earlier
gi,t+1 = 0 + 0.95
N
X
wi,j,t gj,t+1 + 0.22εi,t+1
j=1
Si,t
bi,j,t Sj,t
P
, bi,j,t ∼ iidBe(pi,t ), pi,t =
wi,j,t = P
b
S
0.35
i,j,t
j,t
j Sj,t
j
I Initialize with log normal sizes, µS,0 = 10.20, σS,0 = 1.06
I Extra persistence in links: pi,j,t = pi,t + 0.5 if i, j connected at t − 1
Firm Death
I Exogenous rate δ = 5%
I Replace from initial distribution
Addressing Data Limitations
I N = 2, 000, track largest 1,000 to treat selection (public firms only)
I wi,j,t < 0.1 is set to zero to treat truncation (only weights> 0.10)
20
Benchmark Calibration 2
I Basic model setup as described earlier
gi,t+1 = 0 + 0.95
N
X
2
wi,j,t gj,t+1 + σε,i,t
εi,t+1
j=1
2
σε,i,t
= (0.4)2 − 0.9
log Si,t − E [log(St )]
E [log(St )]
I Large firms experience less volatile primitive shocks
I Motivated by internal diversification
I Network effects remain crucial. If γ = 0, focal moments change sign (higher size
dispersion lowers average vol)
21
Size Distribution Moments
All
Avg
SD
5%
25%
Med
75%
95%
9.61
1.79
6.86
8.33
9.48
10.77
12.76
SD of σS,t
AR(1) σS,t
0.24
0.947
Top 1000
Model 1
Cross-sectional Moments of Log Size
11.63
1.06
10.38
10.78
11.39
12.25
13.64
Model 2
11.63
1.07
10.32
10.79
11.42
12.25
13.68
12.03
1.03
10.69
11.19
11.86
12.71
13.92
Time Series Properties of Size Distribution
0.14
0.939
0.19
0.995
0.44
0.998
22
Volatility Distribution Moments
All
Avg
SD
5%
25%
Med
75%
95%
Top 1000
Model 1
Model 2
Cross-sectional Moments of Firm Volatility
0.40
0.96
0.19
0.29
0.40
0.56
0.90
0.30
0.73
0.17
0.24
0.30
0.38
0.54
0.37
0.45
0.26
0.31
0.36
0.42
0.54
0.36
0.71
0.20
0.28
0.36
0.46
0.65
Cross Section Moments of Joint Size-Vol Distribution
Corr (Si,t , Vi,t+1 )
β(Si,t , Vi,t+1 )
−0.57
−0.32
SD of µσ2 ,t
SD of σσ2 ,t
Corr (σS,t , µσ2 ,t )
Corr (σS,t , σσ2 ,t )
0.69
0.18
0.71
0.76
−0.33
−0.23
−0.42
−0.18
−0.62
−0.46
Time Series Properties of Volatility Distribution
0.64
0.12
0.55
0.76
0.20
0.05
0.95
0.77
0.37
0.11
0.90
0.91
23
Network Moments
All
Top 1000
Model 1
Model 2
Cross-sectional Moments of Network
median # customers
1.00
1.00
1.71
0.48
99th % # customers
3.38
3.32
4.66
7.39
median Hi
0.05
0.04
0.60
0.12
99th % Hi
0.95
0.54
1.00
0.56
Corr (Hi , Si )
−0.31
−0.08
−0.71
−0.54
Corr (Hi , Vi )
0.15
0.08
0.54
0.43
24
Additional Considerations
I
Sample composition
I
I
Private vs. public firms
Entry and exit
I
Internal vs. external diversification
I
Upstream vs. downstream shock transmission
I
Retail sector
I
Aggregate shocks
I
High or low frequency dynamics?
I
Micro Foundations
25
Additional Considerations
I
Sample composition
I
I
Private vs. public firms
Entry and exit
I
Internal vs. external diversification
I
Upstream vs. downstream shock transmission
I
Retail sector
I
Aggregate shocks
I
High or low frequency dynamics?
I
Micro Foundations
26
Sample Composition
Private vs. Public Firms
Dynamics of FSD and FVD dispersion are similar for publicly-listed and
privately-held firms
I
Census Sample 1: Size concentration (measured from # employees)
similar dynamics as Compustat sample
I
Census Sample 2: TFP volatility (al mfg firms, Bloom et al. (2012))
has 50% correlation with sales growth volatility of Compustat firms
I
Compustat Private Sample: Strong positive correlation between
I
I
Size concentration of public firms and that of private firms
Mean volatility of public firms and that of private firms
27
Sample Composition
Stratified Samples
# Firms
3004
ρ(σsubset,s,t , σs,t )
-
ρ(µσ,t , σs,t−1 )
71.7%
ρ(σσ,t , σs,t−1 )
79.3%
1158
3018
347
500
64.2%
89.9%
78.1%
90.5%
62.1%
58.1%
44.5%
64.9%
77.6%
40.7%
62.7%
80.7%
By size
Smallest third
Middle third
Largest third
1000
1000
1003
67.7%
87.7%
86.8%
71.7%
61.6%
55.9%
51.9%
69.8%
73.4%
By industry
Consumer Non-Dur.
Consumer Durables
Manufacturing
Energy
Technology
Telecom
Retail
Healthcare
Utilities
Other
248
107
528
140
413
55
310
188
112
904
91.4%
87.6%
91.9%
72.9%
88.1%
23.6%
86.5%
69.5%
67.8%
82.8%
64.4%
33.4%
53.1%
68.4%
85.2%
14.3%
69.0%
69.4%
19.7%
63.3%
72.3%
74.9%
79.8%
67.9%
58.2%
10.6%
69.8%
50.6%
64.8%
65.7%
All stocks
By sample period / exchange
NYSE only
Non-NYSE
At least 50 yrs
Random 500
28
Sample Composition
Exit and Entry
0.14
Exit
Entry
0.13
0.12
0.11
0.1
0.09
0.08
1976
1982
1987
1993
1998
2004
2009
2015
Annual data, 1977-2009. Source: U.S. Small Business Administration Office of
Advocacy (based on data provided by the U.S. Census Bureau, Business Dynamics
Statistics)
29
Additional Considerations
I
Sample composition
I
I
Private vs. public firms
Entry and exit
I
Internal vs. external diversification
I
Upstream vs. downstream shock transmission
I
Retail sector
I
Aggregate shocks
I
High or low frequency dynamics?
I
Micro Foundations
30
Internal vs. External Diversification
I
Internal diversification alone is unable to match focal time series
moments of data
Calibration 2 described earlier:
gi,t+1 = 0.95
N
X
2
wi,j,t gj,t+1 + σε,i,t
εi,t+1
j=1
2
σε,i,t
= (0.4)2 − 0.9
log Si,t − E [log(St )]
E [log(St )]
I
If γ = 0, higher size dispersion lowers average volatility
I
Internal diversification helps cross section spread in vols with less
network concentration
31
Additional Considerations
I
Sample composition
I
I
Private vs. public firms
Entry and exit
I
Internal vs. external diversification
I
Upstream vs. downstream shock transmission
I
Retail sector
I
Aggregate shocks
I
High or low frequency dynamics?
I
Micro Foundations
32
Downstream Transmission of Shocks
Model
I
No change, reinterpret firm-level herfindahl as concentration of its
suppliers
Data
I
Firm size and volatility distribution unaffected
I
Model predicts “in-herfindahl” (supplier concentration) drives firm
volatility, absent in data
I
Does not generate correlation between “out-herfindahl” (customer
concentration) and volatility, which is significant in data
33
Additional Considerations
I
Sample composition
I
I
Private vs. public firms
Entry and exit
I
Internal vs. external diversification
I
Upstream vs. downstream shock transmission
I
Retail sector
I
Aggregate shocks
I
High or low frequency dynamics?
I
Micro Foundations
34
Retail Sector?
I
Retailers’ customers are households which are not modeled explicitly
in network (leakage)
I
But, if markets are incomplete, then some of the labor income risk
that is specific to non-retail firms affects the consumption decisions
of workers at these firms
I
That in turn exposes retail firms to upstream risk from non-retail
firms
Let wl,m = 0, m = 1, . . . , N and vl,m denote the link strength of retailer l to customers
working at supplier m.
gi,t+1
=
µg + γ
N+k
X
wi,j,t gj,t+1 + εi,t+1 , i = 1, . . . , N.
j=1
gl,t+1
=
µg + ψ
N+k
X
vl,m,t gm,t+1 + εl,t+1 , l = N + 1, .., N + k.
m=1
ψ governs how much firm-specific idiosyncratic risk is transferred to consumption.
35
Additional Considerations
I
Sample composition
I
I
Private vs. public firms
Entry and exit
I
Internal vs. external diversification
I
Upstream vs. downstream shock transmission
I
Retail sector
I
Aggregate shocks
I
Amplifies size/vol dispersion with less idiosyncratic risk, but can
overstate concentration
I
High or low frequency dynamics?
I
Micro Foundations
36
Additional Considerations
I
Sample composition
I
I
Private vs. public firms
Entry and exit
I
Internal vs. external diversification
I
Upstream vs. downstream shock transmission
I
Retail sector
I
Aggregate shocks
I
High or low frequency dynamics?
I
Micro Foundations
37
Average Volatility and Size Concentration: Detrended
Average Volatility and Dispersion in Firm Size − cyclical components, 0.29 correlation
1.5
1
0.5
0
−0.5
Mean Log Vol based on equity return
Std log size based on mkt cap
−1
1930
1940
1950
1960
1970
1980
1990
2000
2010
38
Volatility Dispersion and Size Concentration: Detrended
Dispersion in Volatility and Dispersion in Firm Size − cyclical components, 0.66 correlation
1
0.5
0
−0.5
−1
Std Log Vol based on equity return
Std log size based on mkt cap
1930
1940
1950
1960
1970
1980
1990
2000
2010
39
Average Volatility and Size Concentration: Detrended
Sales and Sales Growth Volatiltiy
Average Volatility and Dispersion in Firm Size − cyclical components, 0.44 correlation
0.6
0.4
0.2
0
−0.2
−0.4
−0.6
Mean Log Vol based sales
Std log size based on sales
1930
1940
1950
1960
1970
1980
1990
2000
2010
40
Additional Considerations
I
Sample composition
I
I
Private vs. public firms
Entry and exit
I
Internal vs. external diversification
I
Upstream vs. downstream shock transmission
I
Retail sector
I
Aggregate shocks
I
High or low frequency dynamics?
Micro Foundations
I
I
I
I
I
Long and Plosser (1983) and emphasized in recent network settings
(Acemoglu et al., Carvalho)
GE network models analytically challenging, typically static
We’ve chosen a statistical route that embeds dynamics,
size-dependent sparsity directly and offers tractability
Gives us an edge to make empirical progress, establish foundation for
next generation micro-founded network models
41
Conclusion
I
New volatility insights due to network and firm size interaction
I
I
Firms as aggregators of idiosyncratic shocks to other firms
Factor structure in firm volatility
I
I
I
I
I
Shocks are size-weighted, slow volatility decay – granularity effect
firm-by-firm (and in aggregate)
Network sparsity slows this decay even further
New empirical facts:
I
I
I
Size concentration is factor governing all volatilities
A firm’s size determines its factor sensitivity
FSD and FVD tightly linked
Factor structure in firm vol, size concentration a successful factor
Simple model unifies a wide range of size/network/volatility facts
42
Extra Slides
43
FSD Leads FVD: Granger Causality Tests in Data
Dependent Variable
Intercept
Independent Variables
µσ,t−1
σs,t−1
µσ,t
Coeff
t-stat.
-1.18
-2.82
0.74
8.31
0.07
2.21
σs,t
Coeff
t-stat.
-0.28
-0.47
-0.11
-0.88
0.97
16.01
Intercept
σσ,t−1
σs,t−1
σσ,t
Coeff
t-stat.
-0.02
-1.48
0.61
5.86
0.04
3.12
σs,t
Coeff
t-stat.
0.20
1.47
-1.19
-2.25
1.04
15.88
44
Firm Size Dispersion with Private Firms
4
7
1.5
Spliced Census
Comp
7
Census
Comp
6.5
6.5
1.4
6
3.5
Comp
Comp
Census
Census
6
5.5
5.5
1.3
5
3
4.5
1976 1982 1987 1993 1998 2004 2009 2015
5
1.2
4.5
1976 1982 1987 1993 1998 2004 2009 2015
Cross-sectional variance of log employment in the Census and Compustat data. Data is annual for
1977-2009. Source: U.S. Small Business Administration, Office of Advocacy, from data provided
by the U.S. Census Bureau, Business Dynamics Statistics. Left panel: splices Census data together
with Compustat data for firms with 10,000+ employees; correlation is 62%. The right panel does
not; correlation is 65%.
45
Log-Normal Size/Vol Distributions
Market
Fundamental
All Years
All Years
Probability Density
Skewness: −0.18
Kurtosis: 3.25
Probability Density
Skewness: 0.27
Kurtosis: 2.93
−10
−5
0
Size (log S/E[S])
5
−10
All Years
−5
0
Size (log S/E[S])
5
All Years
Probability Density
Skewness: 0.26
Kurtosis: 3.25
Probability Density
Skewness: 0.20
Kurtosis: 3.21
−7
−6
−5
−4
−3
−2
Annual Volatility (log RV)
−1
0
−6
−4
−2
0
Annual Volatility (log RV)
2
46
Simulated Size Dispersion and Mean Firm Variance
Average Volatility and Dispersion in Firm Size − Benchmark Model (Last 300 Periods)
1.5
Average Log Volatility
Std. Dev. Log Size
1
0.5
0
−0.5
−1
−1.5
−2
0
50
100
150
200
250
300
47
Simulated Size Dispersion and Variance Dispersion
Dispersion in Volatility and Dispersion in Firm Size − Benchmark Model (Last 300 Periods)
2.5
Std. Dev. Log Volatility
Std. Dev. Log Size
2
1.5
1
0.5
0
−0.5
−1
−1.5
−2
0
50
100
150
200
250
300
48
FSD Leads FVD: Granger Causality Tests in Model
Dependent Variable
Intercept
Independent Variables
µσ,t−1
σS,t−1
µσ,t
Coeff.
t-stat.
-1.16
-14.71
0.63
24.84
0.38
13.95
σs,t
Coeff.
t-stat.
0.02
0.78
0.01
0.61
0.99
93.09
Intercept
σσ,t−1
σS,t−1
σσ,t
Coeff.
t-stat.
0.21
22.03
0.12
3.81
0.18
21.32
σs,t
Coeff.
t-stat.
-0.00
-0.08
0.02
1.28
0.99
193.51
Also: Model generates factor structure in volatility, quantitatively similar
to data
49
Downstream Transmission: Network Moments
All
Returns
Top-33%
Returns
All
Sales
Top-33%
Sales
Model
Panel A: Out-degree Moments
median K out
99th % K out
median H out
99th % H out
Corr (Ktout , St )
Corr (Htout , St )
Corr (Htout , Vt+1 )
1.00
3.38
0.05
0.95
0.01
−0.31
0.15
median K in
99th % K in
median H in
99th % H in
Corr (Ktin , St )
Corr (Htin , St )
Corr (Htin , Vt+1 )
1.00
31.61
0.00
0.28
0.37
−0.26
0.13
1.00
3.32
0.04
0.54
−0.07
−0.08
0.08
–
–
–
–
–
–
0.29
–
–
–
–
–
–
0.10
3.88
6.15
0.25
1.00
0.14
−0.09
0.05
Panel B: In-degree Moments
1.12
16.80
0.00
0.24
0.49
−0.20
0.08
–
–
–
–
–
–
0.08
–
–
–
–
–
–
0.08
1.90
7.39
0.11
0.85
0.59
−0.39
0.32
50
Downstream Transmission: Data on Supplier Networks
wi,j,t
Sj,t
log Si,t
in
Ki,t
log Si,t
log Hi,t
log Hi,t
log σi,t (r)
log Hi,t
log σi,t (s)
Customer Firms (Compustat)
Average
t
0.78
23.4
0.37
21.6
-0.25
-4.3
0.12
0.9
0.08
0.8
Customer Industries (BEA)
Average
t
0.41
44.6
0.46
19.3
0.10
6.0
-
0.26
2.5
51
Network/Size Uniquely Important for Volatility (Detail)
Dependent Variable: Log Firm Volatility
(1)
Log Sales
(2)
(3)
(4)
(5)
(6)
(11)
(12)
(13)
(14)
(15)
-0.14
-0.15
-0.12
-0.14
-0.12
-0.13
-0.12
-0.13
-0.12
-25.56
-23.93
-19.32
-12.10
-33.10
-19.93
-20.61
-17.78
0.88
0.17
0.63
0.17
0.53
0.15
0.55
0.13
0.74
0.17
7.14
3.09
8.74
3.43
7.01
2.65
8.69
3.27
28.54
8.81
Ind. Conc.
-0.05
-0.26
-0.11
-0.08
-0.22
-0.11
-3.07
-11.32
-6.60
-3.52
-6.58
-6.10
0.29
0.10
0.24
0.30
0.04
0.23
0.32
0.13
0.26
3.32
1.08
3.10
4.53
0.48
3.45
4.71
1.87
3.95
0.32
0.36
0.35
0.44
0.41
0.37
0.32
0.30
0.29
1.51
1.32
1.62
2.13
1.35
1.70
2.06
1.45
1.81
-4.01
-3.64
Inst. Hldg.
Adj. R 2
(10)
-15.57
Leverage
Obs.
(9)
-0.16
Log Age
FE
(8)
-16.71
Netw. Conc.
Constant
(7)
-3.91
-3.52
-3.78
-3.92
-3.03
-3.64
-88.45
-54.43
-76.93
-49.72
-39.79
-42.73
None
None
None
None
None
None
-0.03
-0.50
-0.06
-0.39
-5.09
-0.61
-3.80
-2.93
-3.60
-32.42 -30.61
-30.98
None
None
None
-72.31 -50.66
-3.51
-3.75
-59.97 -111.89 -94.74
-3.88
-82.52
Cohort Cohort Cohort
-3.86
Ind.
Ind.
Ind.
171,034 38,030 37,202 145,070 32,887 32,887 113,425 31,318 31,318 145,247 32,901 32,901 171,034 38,030 37,202
0.329
0.048
0.361
0.347
0.228
0.402
0.354
0.281
0.413
0.405
0.307
0.448
0.386
0.218
0.425
Additional Considerations
I
Private vs. public firms
I
I
Upstream vs. downstream shock transmission
I
I
Counterfactual implication: More size dispersion lowers average vol
Aggregate shocks
I
I
Bi-directional, but correlation of volatility with out-Herfindahl
statistically much stronger than with in-Herfindahl
Internal vs. external diversification
I
I
Stratified sample, Compustat private firm data, Census data
Amplifies size/vol dispersion with less idiosyncratic risk, can
overstate concentration
Entry and exit
I
Our focus size/vol feedback, but interesting source of FSD variation
I
Idiosyncratic vs. total volatility
I
High or low frequency dynamics?
I
Retail sector
53