Networks in Production: Asset Pricing Implications

• DOI: http://doi.org/10.1111/jofi.12684
• Author: BERNARD HERSKOVIC
• Date: 01 August 2018
• Published date: 01 August 2018

THE JOURNAL OF FINANCE •VOL. LXXIII, NO. 4 •AUGUST 2018

Networks in Production: Asset Pricing

Implications

BERNARD HERSKOVIC∗

ABSTRACT

In this paper, I examine asset pricing in a multisector model with sectors connected

through an input-output network. Changes in the network are sources of systematic

risk reflected in equilibrium asset prices. Twocharacteristics of the network matter for

asset prices: network concentration and network sparsity.These two production-based

asset pricing factors are determined by the structure of the network and are computed

from input-output data. Consistent with the model predictions, I find return spreads

of 4.6% and −3.2% per year on sparsity and concentration beta-sorted portfolios,

respectively.

FIRMS USE A VARIETY OF inputs to build their products, collectively spending

trillions of dollars and designing a network of input-output linkages. As tech-

nology evolves, industries use different inputs to produce their products. For

example, since the 1970s, plastics have become a more suitable substitute for

wood and metal materials, reshaping the production process for manufactur-

ing and construction. Changes in the input-output network have implications

for the overall economy as they alter sectoral input-output linkages. In this

paper, I investigate the implications of changes in the input-output network

for asset prices and aggregate quantities such as consumption and GDP. I show

∗Bernard Herskovic is at UCLA Anderson School of Management. I am extremely grateful to

Stijn van Nieuwerburgh for his invaluable support of and input into this project. I also want to

thank Alberto Bisin and Boyan Jovanovic for their numerous comments and suggestions, as well

as Kenneth Singleton (the Editor) and two anonymous referees. I thank Viral Acharya; Daniel An-

drei; David Backus; Jess Benhabib; Clara Bois; Jaroslav Boroviˇ

cka; Katar´

ına Boroviˇ

cka; Joseph

Briggs; Mikhail Chernov; Eduardo Davila; Ross Doppelt; Itamar Drechsler; Vadim Elenev; Xavier

Gabaix; Barney Hartman-Glaser; Eric Hughson; Theresa Kuchler; Elliot Lipnowski; Hanno Lustig;

Cecilia Parlatore; Jo˜

ao Ramos; Alexi Savov; Edouard Schaal; Johannes Stroebel; Avanidhar Sub-

rahmanyam; Alireza Tahbaz-Salehi; Gianluca Violante; Stanley Zin; participants at several stu-

dent seminars at New YorkUniversity; and seminar participants at Arizona State University W.P.

Carey, University of Southern California Marshall, Duke Fuqua, Federal Reserve Board, UCLA

Anderson, Chicago Booth, Northwestern University Kellogg, London School of Economics, Lon-

don Business School, UCSD Rady, UC Berkeley Haas, PUC-Rio, Fundac¸ ˜

ao Get ´

ulio Vargas EPGE,

Insper,Fundac¸˜

ao Get ´

ulio VargasS ˜

ao Paulo, University of Melbourne, Monash University,and Uni-

versity of Wisconsin. I am also grateful for comments and suggestions from Burton Hollifield, who

discussed this paper at the 2015 Western Finance Association meeting in Seattle. Finally,I thank

participants at the 2015 meeting of the Society for Economic Dynamics, 2015 World Congress of

the Econometric Society, and 2015 Southern California Finance Conference. I have no potential

conflicts of interest as identified in the Journal of Finance policy.

DOI: 10.1111/jofi.12684

1785

1786 The Journal of Finance R

that changes in the network are a source of systematic risk that is priced in

equilibrium. To the best of my knowledge, I am the first to explore the asset

pricing implications of a sectoral network model.

The main result of this paper is that two key network factors matter for as-

set prices: network concentration and network sparsity. These network factors

describe specific attributes of the sectoral linkages, based on the fundamentals

of the economy. I demonstrate that concentration and sparsity are sufficient

statistics for aggregate risk. Thus, while the entire input-output linkage net-

work is multidimensional, we may focus on these two characteristics when

assessing systematic risk. I derive concentration and sparsity from a general

equilibrium model and show that they determine the dynamics of aggregate

output and consumption. When I compute innovations in concentration and

sparsity from the data and empirically test these new asset pricing factors, the

return data show that exposure to these network factors is reflected in average

returns as predicted by my model.

Network concentration measures the degree to which equilibrium output is

dominated by a few large sectors. It is a measure of concentration over sectors’

output shares in equilibrium. An individual sector’s equilibrium output share

captures the importance of the sector’s output to all other sectors as an input.

If the output of a sector is widely used as an input by other sectors, then it

has high output share in equilibrium. Whether a sector has high or low output

share depends on the network and therefore concentration is an attribute of

the network.

Network sparsity measures the distribution of sectoral linkages. Sectoral

linkages capture the input flow in the economy and are directly related to the

importance of each input to a particular sector. Sparsity thus measures the

degree of input specialization in the economy and how crowded or dense these

linkages are in the network. A network with high sparsity has fewer linkages,

but these linkages are stronger and, on average, firms rely on fewer sources of

input.

The Bureau of Economic Analysis (BEA) Input-Output Accounts provide a

picture of the production network of the U.S. economy. Figure 1provides a

network representation of the input-output linkages, in which nodes (circles)

represent sectors and edges (arrows) represent input flows between sectors—

an arrow from sector jto sector ishows the input flow from sector jto sector i.

The size of a node represents the sector’s output share, and the thickness of an

edge represents the input expenditure share. Concentration, which captures

the degree to which aggregate output is dominated by few sectors, is reflected

in the concentration over nodes’ size. If there are a few large nodes (sectors

with large output share), as the graph illustrates for the U.S. economy, then

concentration is greater than in an economy in which the nodes have the same

size. Sparsity, which captures the degree of input specialization, is reflected in

the thickness and scarcity of the network edges. An economy with high sparsity

and therefore high input specialization has fewer edges, but these edges are

thicker. Hence, concentration is a characteristic of the nodes’ size distribution,

whereas sparsity is a characteristic of the edges’ thickness distribution.

Networks in Production: Asset Pricing Implications 1787

Figure 1. Input-output network at the sector level. This picture contains a network repre-

sentation of the Bureau of Economic Analysis (BEA) Input-Output Accounts for 2012 at the sector

level, that is, two-digit North American Industry Classification System (NAICS) code level. An

arrow from sector jto sector imeans that jis selling to i; the intensity of the arrow (transparency

and width) indicates how much iis buying from jrelative to other suppliers. Each node (circle)

represents a different sector in the economy, with the size of nodes representing output shares.

Node labels specify the two-digit NAICS sector.

When production is subject to diminishing returns, an economy with high

concentration has a few large sectors with lower returns on investment. The

lower productivity of large sectors of an economy affects other sectors through

equilibrium prices. As a result, high concentration leads to lower aggregate con-

sumption and higher marginal utility. Innovations in concentration therefore

carry a negative price of risk. Assets that have high returns when concentra-

tion increases, that is, assets with high concentration beta, are hedges against

a decline in aggregate consumption and hence should have lower expected