“Firm Volatility in Granular Networks” by Bryan Kelly, Hanno Lustig and Stijn van Nieuwerburgh
Discussion Matthias Kehrig (UT Austin)
NBER SI: Capital Markets and the Economy, July 15, 2013
Overview Main questions: 1 How do networks propagate idiosyncratic firm-level shocks? How do networks impact firm volatility? How do networks impact aggregate volatility?
⇒ Write statistical model to study network effects focussing on... Network incompleteness, i.e. a firm’s number of links Network imbalances, i.e. rel. strength of links (given number of links) 2
How do networks form in the first place?
⇒ Incorporate formation of network links into statistical model; then, feedback between formation and consequences of networks Main findings: Networks explain a considerable share of... aggregate volatility firm-level volatility residual volatility 1 / 11
Context & Contributions
Theoretical and empirical Network consists of heterogeneous firms as in Oberfield (2013) and Gabaix (2011) rather than heterogeneous sectors as in Acemoglu et al. (2012) and Carvalho/Gabaix (forthcoming) Paper studies both network formation and network propagation Shocks travel “upstream” rather than “downstream” as in Acemoglu et al. (2012), Basu (1995), Oberfield (2013) Finance aspects (firm and aggregate volatility) of production networks and how size distribution affects that
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1. Network propagation and volatility Firm growth and firm volatility gi,t+1 = µg + γ
N X
wi,j,t gj,t+1 + εi,t+1
j=1
gt+1 = µg + γWt gt+1 + εt+1 = (I − γWt )−1 (µg + εt+1 ) Vt (gt+1 ) = σε2 (I − γWt )−1 (I − γWt0 )−1 ⇒ Wt is the crucial determinant emp. findings: pos. co-movement between size dispersion (Wt ) and average firm volatility volatility dispersion across firms residual volatility of firms at high and low (Campbell et al. (2001)) frequency 3 / 11
2. Network formation
S2
S1
C1
C2
C3
S3
C4
C5
Figure: Incomplete and unbalanced network structure
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Questions & Comments: Why is γ < 1? When shocks travel downstream, this is intuitive: Assume the customer firms buy materials from supplier firms ⇒ How will output shocks in supplier firms affect customer firms? Customer firm j produces output Y using value added V and materials M using the following production function: Yj = eεj Vjα Mjβ yˆj ≡ gj = εˆj + αˆ vj + β m ˆj X = εˆj + αˆ vj + β ωi,j m ˆ i,j i
≈ εˆj + αˆ vj + β
X
mi,j ωi,j ≡ P i mi,j
ωi,j yˆi
i
gj ≈ εˆj + αˆ vj + β |{z} =γ
X
ωi,j gi
i
γ < 1 ⇔ β < 1: this is very likely (empirically: β ≈ 0.45) 5 / 11
Questions & Comments: Why is γ < 1? When shocks travel upstream, the logic runs the other way around: Assume the supplier produces output that is bought as a material by customer firms ⇒ How will a sales shock in customer firms affect supplier firms? Yi =
X
Mi,j
j
yˆi ≡ gj =
X
≈
X
ωi,j m ˆ i,j
j
j
ωi,j
1 1 yˆj − εˆj − αˆ vj yˆ β yˆj j | {z } =γ
γ < 1 is likely if vˆj , εˆj large relative to yˆj (debatable) and/or if α + β > 1 (very unlikely). 6 / 11
Suggestions Size dispersion-volatility link: what really matters is size concentration What matters for volatility in model is concentration of final goods firms only Size concentration-volatility link not monotone unless number of customers stays the same – what is Nt ? Sales of... Case 1 Case 2 C1 10 10 10 C2 10 C3 − 1 Size dispersion 0.25 σε2 0.34 σε2 Supplier volatility 0.50 σε2 0.46 σε2 ⇒ account for entry/exit which alter Nt ⇒ account for M&A (would expect σε2 to fall with lots of M&A) 7 / 11
Causality
Figure 5: Trends in Average Firm Volatility
Average Stock Volatility (demeaned) Regr. Resid. (Using Size Distn.) 0.8
Time Trend Residual Time Trend
Trend Slop e t-stat= 10.9
0.6
0.4
0.2
0
−0.2 Trend Slop e t-stat= 0.4
−0.4
−0.6 1930
1940
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2000
2010
Fig. 5: Average firm volatility raw (black) and after taking out effect of size dispersion (grey)
Notes: The figure plots the average of log stock return variance (black line) as well as the residual from a regression of mean variance on our market-based measure of log firm size dispersion (gray line). It also shows estimated time trends in the original volatility data (black dotted line) and in the residual (gray dotted line), and reports the t-statistic for the time trend coefficient estimate.
for less than 10% of their sales, and this is occasionally (23%other of firms).way The around? Dispersion Granger-causes volatility; how observed is it the Compustat datavariable has been carefully linked be to CRSP market equity data by Cohen and Frazzini (A latent third might driving both.) (2008), which allows us to associate information on firms’ network connectivity with their market equity size and their return volatility.9 The data set covers the period 1980-2009, and
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Networks & volatility – just relevant for Compustat firms? For Compustat firms the size dispersion-volatility link exists Possible issue: Publicly traded firms exhibit different long-run dynamics than privately held firms (Davis et al. (2006)) Kehrig (2013): Long-run firm volatility (productivity dips.) increases: 2
Durables Durables (trend) Non−Durables Non−Durables (trend)
1.8
1.6
1.4
1.2
1
1975
1980
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1990
1995
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2005
Figure: Cross-sectional dispersion of log TFP 9 / 11
Networks & volatility – just relevant for Compustat firms? Bachmann/Kehrig (2013): Size dispersion decreases ⇒ bad news? 1.5
V a r ( log ( Y /L) ) V a r ( log ( Y ) ) V a r ( log ( L) )
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1.1
1
0.9
0.8 1975
1980
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Figure: Cross-sectional dispersion of log output per worker, output and workers
But: Size concentration increases ⇒ good news! 10 / 11
Conclusion
Nice paper with good theoretical and empirical work Reduced-form model could be more tightly linked to empirics Address macro questions surrounding the Great Moderation Financial networks?
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