Competition, markups, and predictable returns
Alexandre Corhay
∗
Howard Kung†
Lukas Schmid‡§
May 2017
When markups are high, new innovators can aggressively undercut incumbents to capture market
share. Sensitivity to entry risk intensifies during times of high profit margins, and in high average
markup industries. We show that strategic interactions among firms in product markets provide
a risk amplification mechanism and an endogenous source of time-varying risks. Our estimated
general equilibrium asset pricing model explains a sizable equity premium, predictable excess
returns, and an initially downward-sloping term structure of equity. Consistent with the data,
the model predicts that higher markups are associated with higher expected returns, both in the
time-series and in the cross-section.
Keywords: Imperfect competition, strategic interactions, time-varying risk premia, stock return
predictability, markups, entry and exit, recursive preferences
∗
Rotman School, University of Toronto. [email protected]
London Business School. [email protected]
‡
Fuqua School of Business, Duke University & CEPR. [email protected]
§
We thank Ravi Bansal, Diego Comin, Ian Dew-Becker, Francisco Gomes, Ralph Koijen, Kai Li, Lars Lochstoer,
Erik Loualiche, Lasse Pedersen, Sheridan Titman, Amir Yaron, Lu Zhang and seminar participants at Boston College, Collegio Carlo Alberto, Copenhagen Business School, Duke University, Durham University, HKUST, London
Business School, Stockholm School of Economics, University of Alberta, University of British Columbia, UC Berkeley, UCLA, University of Hong Kong, University of Piraeus, Peking University, CKGSB, ASU Sonoran Conference,
Econometric Society World Congress, European Finance Association, NBER Capital Markets, NBER Asset Pricing,
Red Rock Finance Conference, FIRN Asset Pricing Research Group Annual Meeting, and Society for Economic
Dynamics for helpful comments and discussions.
†
1
1
Introduction
Firms compete in environments that evolve with macroeconomic conditions. In economic contractions, less successful companies are driven out of business, while in expansions, new entrepreneurs
are attracted by more profitable business opportunities. Firms strategically tailor their pricing
and production decisions in response to changes in the competitive landscape. Indeed, firm entry
rates, product creation, and R&D expenditures are procyclical. Naturally, the risk exposure of
firms to entry and macroeconomic risks depend on the dynamics of product market competition.
Incumbent firms with more market power charge higher markups, but can be undercut more aggressively by new entrants. A heightened sensitivity to entry risk in high markup environments
is associated with higher expected returns. In this paper, we examine how strategic interactions
among firms provide a supply-side explanation for stock return predictability.
We build a general equilibrium asset pricing model where firms producing differentiated products strategically compete for market power. Firms internalize the impact of their production,
pricing, and innovation decisions on industry demand. Our model accounts for both the extensive and intensive margins of innovation, labeled as product and process innovation, respectively.
Product innovation refers to the resources devoted to creating new products. Process innovation
refers to the resources devoted to accumulating intangible capital. We show that product innovation provides an short-run risk amplification mechanism and an endogenous source of volatility
risks, while process innovation provides a growth propagation mechanism that generates endogenous long-run risks. We assume a representative agent with Epstein-Zin recursive preferences so
that low-frequency growth and volatility risks are priced in equilibrium. Our benchmark model
features only a single aggregate shock that is stationary and homoskedastic. Thus, the rich growth
and volatility dynamics are generated endogenously. We quantitatively evaluate the model by
estimating key parameters using a simulated method of moments (SMM) approach.
Our paper makes two sets of contributions. First, we theoretically illustrate how the presence
of strategic interactions provides an endogenous mechanism linking product innovation to timevarying risk premia. Understanding the origins of risk premia fluctuations is a first-order issue in
asset pricing, especially in light of the vast empirical literature documenting that excess returns
are predictable.1 To the best of our knowledge, this is the first paper to quantitatively relate
strategic competition to stock return predictability in the time series. Second, we provide novel
1
See, for example, Cochrane (2008) for a survey on the evidence.
2
empirical evidence supporting our mechanism. We find that measures of market power, such as
markups and the number of firms, are strong predictors of future excess stock returns in the data,
consistent with the model predictions.
When estimating and calibrating parameters to fit macroeconomic data, such as consumption,
investment, markup, firm entry dynamics, the model quantitatively explains salient unconditional
and conditional moments of stock market returns. In particular, the model generates a sizable
equity premium and an initially downward-sloping term structure of equity returns, as documented
in Binsbergen, Brandt, and Koijen (2012) and Binsbergen, Hueskes, Koijen, and Vrugt (2013).
Future excess stock returns are also forecastable with the price-dividend ratio, with a magnitude
of predictability that accords with the data.
We discipline our main time-series predictions by examining the cross-sectional linkages between strategic competition and expected returns. To this end, we construct an extension of our
benchmark model that allows for cross-sectional heterogeneity and dispersion in market power.
We find that higher markups are associated with more systematic risk and higher expected returns, both in the time-series and the cross-section. Higher markups (i.e., greater market power),
either over time or across firms, are associated with a heightened sensitivity to entry risk and
macroeconomic fluctuations, which translates to higher expected returns. Furthermore, our model
also predicts that high-markup industries exhibit more time-series predictability than low-markup
ones. The cross-sectional predictions of our model are consistent with the data and reinforce our
main aggregate time-series results.
The relation between market power and expected returns are shaped by the presence of strategic interactions among firms. The relation is also time-varying due to the procyclical entry of
firms through product innovation. When firms internalize the impact of their actions on industry
outcomes, the price elasticity of demand is a function of the number of competitors in equilibrium.
Consequently, industry markups also depend on the number of firms in the industry. We show that
the equilibrium relation between markups and the number of firms is negative and convex, which
captures the notion that when there are less firms, a marginal entrant erodes the market power of
incumbent firms more significantly than when there are many firms. Thus, higher (lower) market
power, either over time or across industries, imply that markup policies are more (less) sensitive
to entry risk and macroeconomic fluctuations. Across firms, higher markup industries have higher
market betas and are associated with larger expected returns, consistent with empirical evidence
3
from Bustamante and Donangelo (2017). Over time, markup sensitivity is countercyclical, which
produces endogenous countercyclical macroeconomic volatility. With recursive preferences, countercyclical volatility risks translate to a countercyclical equity premium, forecastable by measures
of market power.
The negative relation between markups and the number of firms, along with procyclical entry,
implies that markups are countercyclical. Countercyclical markups give rise to a short-run risk
amplification mechanism through the impact of markups on conditional factor demands for capital
and labor inputs. In bad (good) times, higher (lower) markups depress (stimulate) factor demands,
and magnifies recessions (expansions). The amplification of short-run cash flow risks is quantitatively significant, such that, the model generates a downward-sloping equity term structure for the
initial four years, which as documented in Binsbergen, Brandt, and Koijen (2012) and Binsbergen
and Koijen (2017), is a challenge for standard fundamentals-based asset pricing models that imply
upward-sloping equity term structures.
The dynamics of long-term growth are determined by process innovation. The presence of
positive aggregate spillover effects from investment in research and development (R&D) creates a
link between long-term trend growth and the state of the economy, which is a standard feature
in endogenous growth models.2 As demonstrated in Kung (2015) and Kung and Schmid (2015),
the endogenous growth channel provides a long-run growth propagation mechanism that leads to
substantial equilibrium long-run risks in macroeconomic quantities, such as consumption and dividends. Given that an agent with recursive preferences is strongly averse to long-run consumption
growth uncertainty, the exposure of consumption and dividends to long-run risks leads to a sizable
equity premium, as in Bansal and Yaron (2004).
Aside from the asset market evidence, we also provide direct empirical support for our core
mechanisms using macroeconomic data. The product innovation channel predicts that macroeconomic volatility is forecastable by measures of market power. We verify that both markups and
the number of firms are statistically meaningful predictors of future macroeconomic volatility, with
magnitudes that are comparable between the model and the data. The process innovation channel
predicts that economic growth rates are forecastable by measures of R&D. We find that empirical measures of R&D intensity and the accumulation of intangible capital are indeed significant
predictors of future growth, with the degree of explanatory power that increases with horizon,
2
See, for example, Romer (1990), Aghion and Howitt (1992), Peretto (1999), and Comin and Gertler (2006).
4
consistent with the model.
Our model provides a quantitatively relevant account of key aspects of asset market, industry, and macroeconomic data. Due to the presence of strategic interactions, changes in product
innovation generate time-variation and cross-sectional variation in risk premia that are consistent with empirical patterns. Overall, we illustrate the importance of strategic competition for
understanding stock return predictability.
Our paper relates to a growing literature examining the link between competition and asset
prices, such as, Hou and Robinson (2006), Hoberg and Phillips (2010), Corhay (2015), Opp,
Parlour, and Walden (2014), and Opp (2016). Our paper is most closely related to Binsbergen
(2016), Loualiche (2014), and Bustamante and Donangelo (2017), which are also studies that
examine the theoretical link between stock returns and competition. The key distinguishing feature
of our paper is that we focus on time-series return predictability, while the aforementioned papers
study cross-sectional return predictability. From a theoretical perspective, Binsbergen (2016) and
Loualiche (2014) feature demand-side channels to generate cross-sectional dispersion in pricing and
competition, while our paper relies on a supply-side mechanism arising from strategic interactions.
Bustamante and Donangelo (2017) also feature strategic interactions, but in a partial equilibrium
setting with an exogenous pricing kernel. Our general equilibrium growth framework allows us to
jointly study asset prices with business cycle fluctuations and long-term growth. We extend their
cross-sectional analysis to show that the positive relation between markups and expected returns
documented in the cross-section also projects to the time-series dimension. Finally, we differ from
these paper in that we also demonstrate how incorporating strategic competition can help standard
production-based models reconcile the equity term structure evidence.
The endogenous growth margin in our model that produces equilibrium long-run risks builds on
the framework of Kung (2015) and Kung and Schmid (2015). These papers illustrate how aggregate
spillover effects from R&D (labeled as process innovation in this paper) provide an aggregate
growth propagation mechanism that generates equilibrium long-run risks. Paired with recursive
preferences, the growth channel explains a sizable equity premium jointly with macroeconomic
dynamics. However, absent exogenous heteroskedasticity, risk premia is constant in these models.
Thus, a differentiating feature of our paper is to show how incorporating product innovation in
the presence of strategic interactions, along the lines of Jaimovich and Floetotto (2008), generates
endogenous countercyclical macroeconomic volatility. With recursive preferences, these volatility
5
dynamics lead to a countercyclical equity premium. In sum, process innovation is important for
explaining the unconditional equity premium, while product innovation (i.e., the new margin in
this paper) is important for explaining the dynamics of the conditional equity premium.3
The paper is organized as follows. Section 2 outlines the benchmark and extended models.
Section 3 qualitatively discusses the core mechanisms. Section 4 describes the estimation of the
model and presents the quantitative results. Section 5 concludes.
2
Model
This section presents the benchmark model featuring the product and process innovation margins.
We use this framework to link asset prices to changes in the strategic competitive environment of
firms. Households are characterized by a representative agent and markets are complete. Households accumulate the physical and intangible capital stocks in the economy. Production consists
of two sectors, final goods and intermediate goods. A representative final goods firm produces
final goods in two stages. First, a finite measure of differentiated products are packaged together
to form an industry good. Second, there are a continuum of industry goods that are combined to
form the final goods used for consumption. Each product is produced by an intermediate firm.
The intermediate firms are monopolistic and compete strategically within an industry, and the
measure of firms – in each industry and in each period – is determined by a free entry condition.
Absent cross-sectional heterogeneity, the aggregate relations between macroeconomic quantities
in our benchmark model are readily comparable to the real business cycle (RBC) model, the
workhorse framework of the production-based asset pricing literature.4 We begin with a bird’s-eye
view of the model to highlight the similarities and departures from the canonical RBC model. We
then describe the microfoundations of the model, which is followed by an exposition of how the
departures from the neoclassical paradigm contribute to the core asset pricing mechanisms. At
the end of this section, we consider an extension of the benchmark model that allows for ex-post
heterogeneity in the composition of the final goods sector. We use the cross-sectional predictions
of the extended model to discipline our aggregate time-series results.
3
Other fundamentals-based models that examine the equity term structure include Belo, Colin-Dufresne, and
Goldstein (2015), Favilukis and Lin (2015), and Croce, Lettau, and Ludvigson (2014).
4
Examples include production-based models with habits (e.g., Jermann (1998) and Boldrin, Christiano, and
Fisher (2001)), long-run risks (e.g., Kaltenbrunner and Lochstoer (2010) and Croce (2014)), and disasters (e.g.,
Gourio (2012) and Kuehn, Petrosky-Nadeau, and Zhang (2014)).
6
2.1
Resource constraint
Aggregate output, Yt is divided into consumption, Ct , investment in physical capital, It , creation
of new firms, Jt , and research and development (R&D), St :
Yt “ Ct ` It ` Jt ` St .
(1)
Product innovation is defined as the resources expended towards creating new firms and products
(corresponding to Jt ) and process innovation as the resources devoted towards accumulating intangible capital (corresponding to St ). Relative to the RBC paradigm, our model has two additional
endogenous innovation processes, varying at the intensive and extensive margins. We show that
these two margins provide powerful amplification and propagation channels for macroeconomic
risks that are important for explaining asset prices.
2.2
Households and preferences
We assume a representative household that is assumed to have Epstein-Zin preferences defined
over aggregate consumption, Ct , and labor, Lt :
`
˘ 1
1´θ 1´θ
,
Ut “ u pCt , Lt q ` β Et rUt`1
s
(2)
1´γ
where θ ” 1 ´ 1´1{ψ
, γ captures the degree of relative risk aversion, ψ is the elasticity of intertem-
poral substitution, and β is the subjective discount rate. We assume that the utility kernel is
additively separable in consumption and leisure:
1´1{ψ
p1 ´ Lt q1´χ
C
1´1{ψ
u pCt , Lt q “ t
` Zt
χ0
,
1 ´ 1{ψ
1´χ
(3)
where χ captures the Frisch elasticity of labor and χ0 is a scaling parameter.5 We assume that
ψ ą γ1 , so that the agent has a preference for early resolution of uncertainty following the long-run
risks literature (e.g., Bansal and Yaron (2004)).
The household accumulates the stock of aggregate physical capital, Kt , by making making
1´1{ψ
5
We scale the second term by an aggregate productivity trend Zt
become trivially small along the balanced growth path.
7
to ensure that utility for leisure does not
investments, It , through the following law of motion:
ˆ
Kt`1 “ p1 ´ δk qKt ` Φk
It
Kt
˙
Kt ,
(4)
where δk is the depreciation rate, and Φk p¨q captures convex adjustment costs.
The aggregate stock of intangible capital is interpreted as the stock of knowledge in the economy.
Increasing the stock of intangible capital makes production more efficient. The household also
accumulates the aggregate stock of intangible capital, Zt , by making R&D investments, St , through
the following law of motion:
ˆ
Zt`1 “ p1 ´ δz qZt ` Φz
St
Zt
˙
Zt ,
(5)
where δz is the depreciation rate for intangible capital.6
The household provides capital and labor services in competitive markets, and receives the
rental rate Rj,t , for j “ k, z for capital services and the wage rate Wt for labor services. The
household owns all firms and receives the aggregate payout, Πt .
The household maximizes lifetime utility, defined recursively in Eq. (2), subject to the budget
constraint:
Ct ` It ` St “ Πt ` Wt Lt ,
(6)
and the laws of motion for physical and intangible capital (Eqs. (4) and (5), respectively). We
relegate the details of the household optimality conditions to Appendix A.1.
The stochastic discount factor implied by these preferences is given by:
˜
Mt`1 “ β
¸´θ ˆ
Ut`1
1
1´θ 1´θ
Et pUt`1
q
Ct`1
Ct
˙´ ψ1
,
where the first term, involving the continuation utility, captures sensitivity regarding uncertainty
about long-run growth prospects.
6
We assume the following functional form for the adjustment cost function: Φj pxq “
α1,j
1´ ζ1
j
j “ k, z.
8
1´ ζ1
pxq
j
` α2,j , for
2.3
Production technology
Final goods are produced by using a constant elasticity of substitution (CES) aggregator to bundle
together a continuum of differentiated industry goods, Yj,t , on a unit measure, j P r0, 1s:
ˆż 1
Yt “
ν1 ´1
ν1
Yj,t
1
˙ ν ν´1
1
,
dj
(7)
0
where ν1 ą 0 is the elasticity of substitution between industry goods.
Within a particular industry j, a CES aggregator bundles together a finite measure, Nj,t , of
differentiated products, Xi,j,t , according to:
Yj,t “
˜N
j,t
ÿ
ν2 ´1
ν2
Xi,j,t
2
¸ ν ν´1
2
,
(8)
i“1
where ν2 ą 0 is the elasticity of substitution between products. We focus on a case where the
elasticity of substitution is higher within than across industries (i.e., ν2 ą ν1 ).7
Product i P r0, 1s in industry j, Xi,j,t , is produced by using the following technology:
`
˘1´α
η
α
Xi,j,t “ Ki,j,t
At Zi,j,t
Zt1´η Li,jt
,
(9)
where Ki,j,t and Zi,j,t are the firm-specific physical and intangible capital inputs, respectively, Li,j,t
¯
ş1 ´řNj,t
Z
dj is the aggregate stock of intangible capital. The only
is the labor input, and Zt ” 0
i,j,t
i“1
exogenous forcing process in the benchmark model is the stationary and homoskedastic aggregate
productivity shock, At , that affects all intermediate firms across all industries symmetrically, and
evolves as an AR(1) process in logs:
at “ p1 ´ ρqa‹ ` ρat´1 ` σt ,
where t „ iidN p0, 1q.
7
Note that we do not impose this parameter relation in our estimation of ν2 .
9
(10)
2.4
Industry and product demand
A competitive representative final goods firm produces the final goods by first packaging products
into industry goods according to Eq. (8), and then packaging the industry goods into final goods
according to Eq. (7). The static profit maximization problem for the final goods firm yields a
conditional demand schedule for industry good j:
ˆ
Yj,t “ Yt
Pj,t
PY,t
˙´ν1
,
(11)
and for product i in industry j:
ˆ
Xi,j,t “ Yj,t
´ş
1
P 1´ν1 di
0 j,t
Pi,j,t
Pj,t
˙´ν2
,
(12)
1
¯ 1´ν
1
is the final goods price index (numeraire), Pi,j,t is the price of
¯ 1
´ř
Nt
1´ν2 1´ν2
product i in industry j, and Pj,t ”
is the price index of industry j. Details of
i“1 Pi,j,t
where PY,t ”
the final goods firm’s problem is contained in Appendix A.2.
Combining Eqs. (11) and (12) yields the conditional industry demand for product i in industry
j, in terms of the final goods:
Θj,t pPi,j,t q ” Yt pPi,j,t q´ν2 pPj,t qν2 ´ν1 .
(13)
An intermediate firm is a local monopolist that takes this demand schedule and the production
technology specified in Eq. (9) as given when making pricing and production decisions for product
i. Intermediate firms within an industry compete strategically due to the assumption that firms are
not atomistic. The presence of strategic interactions provides an endogenous source of time-varying
risk premia that is the centerpiece of this paper.
The two-stage final goods production that features a continuum of industries allows for a
tractable way to embed an industry equilibrium with strategic interactions in a general equilibrium setting. This environment implies that intermediate firms are “large” in their industry (and
therefore compete in an oligopolistic fashion), but are “small” relative to the aggregate economy.
As a result, intermediate firms influence (and internalize their impact) on industry-level prices,
but do not affect aggregate factor prices, such as rental rates and wages, nor national income.
10
Consequently, this structure retains the tractability of the partial equilibrium solution to a single stage game with oligopolistic firms, where factor prices are take as given, albeit determined
endogenously in competitive factor markets in general equilibrium.
2.5
Equilibrium markups
Intermediate firms internalize their impact on the industry price index, which is reflected in the
price elasticity of demand faced by firms in industry j, that is a function of the number of competitors:
ξj,t ”
´ν2 Nj,t ` ν2 ´ ν1
.
Nj,t
(14)
If firms were atomistic (i.e., Nj,t Ñ 8), as in the canonical monopolistic competition framework,
the price elasticity of demand would be constant (limNj,t Ñ8 ξj,t “ ´ν2 ), and it follows that firms
would set a constant markup policy. In contrast, with strategic interactions, the price elasticity
of demand and markup policy depend on the number of firms. While intermediate firms impact
industry prices, they do not affect aggregate prices, given that industries are atomistic relative to
the overall economy. Below, we characterize the optimal markup policy equating marginal revenue
to marginal costs of the monopolistic intermediate firms.
We now suppress firm and industry subscripts for notational simplicity, but still taking into
account that products and industry goods are differentiated. An intermediate firm in a particular
industry solves a sequence of static profit maximization program in each period t:
max
Pt ,Kt ,Zt ,Nt
Dt ” Pt Xt ´ Wt Lt ´ Rk,t Kt ´ Rz,t Zt ,
(15)
subject to the demand constraint defined in Eq. (13),
Xt ď Θt pPt q.
(16)
A full characterization of an intermediate firms’ problem is outlined in Appendix A.3.
The firm’s optimal pricing decision yields a markup policy (ϕt ” Pt {M Ct ) that depends on the
11
number of firms:
ϕt “
´ν2 Nt ` pν2 ´ ν1 q
.
´pν2 ´ 1q Nt ` pν2 ´ ν1 q
(17)
When the substitutability of goods is higher within industries than across (ν2 ą ν1 ), an increase
in the number of firms decreases markups.
The remaining first-order conditions yield conditional factor demands for physical capital, intangible capital, and labor:
α Yt
,
ϕt Kt
ηp1 ´ αq Yt
“
,
ϕt
Zt
p1 ´ αq Yt
“
.
ϕ t Lt
Rkt “
(18)
Rzt
(19)
Wt
(20)
Therefore, assuming ν2 ą ν1 , more competition depresses markups and increases demand for factor
inputs. The degree of competition in an industry is determined endogenously through the entry
and exit of firms.
2.6
Entry and exit
We assume that setting up a new firm in an industry entails the fixed cost FE,t ” κZt .8 These
costs are funded by the households each period, and in return, the households are entitled to the
future cash flows. We assume that a newly created firm today at time t will start producing its
new product in the following period, at time t ` 1.
The finite measure of firms in an industry evolves as:
Nt`1 “ p1 ´ δn qpNt ` NE,t q,
where NE,j,t is the number of new entrants and δn is the constant fraction of products, randomly
chosen each period, that become obsolete.
A free-entry condition endogenously determines the number of intermediate firms in a particular
8
Note that these costs are multiplied by the aggregate trend in technology to ensure that the entry costs do not
become trivially small along the balanced growth path.
12
industry:
p1 ´ δn qEt rMt,t`1 Vt`1 s “ FE,t ,
(21)
where Vt “ Dt ` p1 ´ δn qEt rMt`1 Vt`1 s is the market value of an intermediate firm. Therefore,
changes in expected profit opportunities and discount rates lead to fluctuations in the number of
entering firms.
2.7
Aggregation and equilibrium
In our benchmark model, there is no heterogeneity among firms, and consequently we focus on
a symmetric equilibrium where firms make identical decisions. After imposing the symmetric
equilibrium conditions, we can obtain an expression that relates aggregate output, Yt , to aggregate
factor inputs:
Yt “ pT F Pt ˚ Lt q1´α Ktα .
(22)
The expression above for aggregate technology resembles the neoclassical one used in the RBC
framework, except that in our model, measured total factor productivity (TFP) is endogenous:
1
T F Pt ” At Zt Ntpν2 ´1qp1´αq
´η
.
(23)
The exogenous component, At , is stationary and captures cyclical fluctuations in the level of aggregate productivity. The remaining two terms are endogenous. The aggregate stock of intangible
capital, Zt , is the endogenous trend component driven by process innovation. The final term relates to the aggregate number of firms, Nt , which is a cyclical component that captures business
cycle variation from the extensive margin, determined by product innovation.
2.8
Extension with heterogeneity
We have abstracted from cross-sectional heterogeneity in our benchmark model by focusing on a
symmetric equilibrium. This section outlines an extension of our baseline model that allows for
ex-post cross-sectoral heterogeneity. We use the extended model to examine the cross-sectional
implications of our benchmark framework.
13
We model cross-sectoral heterogeneity by modeling two types of atomistic industries h P t1, 2u,
equally-distributed on the unit interval. Aggregate output is defined as:
ˆż 1
Yt “
ν1 ´1
ν1
Yh,t
1
˙ ν ν´1
1
dh
(24)
0
ˆ
“
1 ν1 ´1
1 ν1ν´1
Y1,t 1 ` Y2,tν1
2
2
˙ ν ν´1
1
1
.
(25)
For simplicity, we assume that the elasticity of substitution across sectors is identical to the one
across industries (set at ν1 ), and that the household accumulates physical and intangible capital
separately for each type of industry.
Our model with endogenous growth places restrictions on the extent of heterogeneity that is
consistent with balanced growth. For the two types of industries to grow at the same long-run
rate rules out ex-ante heterogeneity across the industries (e.g., differences in parameters relating
to technology). As a result, we focus on modeling ex-post heterogeneity through industry-specific
shocks. We consider a specification where the costs of entry – previously held constant – are
stochastic and industry-specific. Thus, the two types of industries face the same parameters for
technology and the forcing processes, but only differ by the ex-post realization of their entry cost
shocks, κh,t . The evolution of entry costs for industry type h is specified as:
log pκh,t q “ log pκ̄q ` ηh,t ,
ηh,t “ ρη ηh,t´1 ` ση η,t ,
(26)
(27)
where η,t „ iidN p0, 1q is a industry h-specific shock.
3
Economic mechanisms
The core asset pricing mechanisms are driven by aggregate innovation policies operating at the
intensive and extensive margins. The benchmark model only features a single exogenous shock that
is stationary and homoskedastic. Therefore, the rich time-varying growth and volatility dynamics
are produced by the industry structure and innovation policies. Due to the presence of strategic
interactions, product innovation provides a (i) risk amplification mechanism that helps the model
explain an initially downward-sloping term structure of equity and (ii) an endogenous source of
14
volatility risks. Due to the positive aggregate spillovers from R&D activity, process innovation
provides a growth propagation mechanism that generates endogenous long-run risks.
The process and product innovation channels impact macroeconomic dynamics at different
frequencies. From the TFP decomposition in Eq. (23), product innovation only affects the short-run
cyclical component, while process innovation affects the long-run trend component. The frequency
at which the innovation channels impact macroeconomic quantities hinges on the origins of the
technological spillovers, and ultimately, the source of sustained endogenous growth. There are
endogenous growth models where trend growth arises from positive externalities along the extensive
margin (e.g., expanding variety model of Romer (1990)) or the intensive margin (e.g., creative
destruction models like Aghion and Howitt (1992) and Peretto (1999)). Our model falls in the
later category where sustainable endogenous growth is due to spillovers from vertical innovations.
3.1
Product innovation
The rich asset pricing dynamics from product innovation arise because of strategic interaction
among firms, which endogenously links markups to industry competition in a nonlinear fashion.
The assumption that number of competitors in an industry is finite implies that intermediate firm
decisions have a nontrivial impact on the industry price index. As firms internalize this, the price
elasticity of industry demand depends on the number of firms; and it follows that in the industry
equilibrium, the industry markup, ϕp¨q, derived from the optimal pricing decision, depends on the
number of firms in the industry, Nt , for ν2 ‰ ν1 :
ϕt “ ϕpNt q ”
´ν2 Nt ` pν2 ´ ν1 q
.
´pν2 ´ 1q Nt ` pν2 ´ ν1 q
(28)
When the substitutability of goods is higher within than across industries (ν2 ą ν1 ), as in our
benchmark parametrization, the markup-competition relation is negative and convex (φ1 pNt q ă 0,
φ2 pN q ą 0 for N ą 1). When the substitutability of goods is higher across than within industries,
the markup-competition relation is positive and concave (φ1 pNt q ą 0, φ2 pN q ă 0 for N ą 1). Either
case implies that the sensitivity of markups to changes in competition is larger when N is smaller.
Since entry dynamics depend on macroeconomic risk, markup sensitivity is also time-varying and
related to aggregate fluctuations.
The number of competitors in an industry depends on the economic incentives for product in-
15
novation. During expansions, more firms enter as they are attracted by higher profit opportunities,
and vice versa in contractions. Firms enter up until the point where expected benefits equal the
costs for the marginal entrant, characterized by the free entry condition:
p1 ´ δn qEt rMt,t`1 Vt`1 s “ FE,t ,
(29)
where Vt “ Dt `p1´δn qEt rMt`1 Vt`1 s is the present value of current and future expected monopoly
profit opportunities, tDj u8
j“t , for a new entrant. In good times (e.g., after a series of positive
technology shocks), profitability is higher, while marginal utility of the representative household
is lower, which both raise valuations. Higher valuations increase firm entry up until the free entry
condition is satisfied. Thus, entry dynamics are procyclical.
Procyclical number of firms implies that markup sensitivity to industry and macroeconomic risk
are countercyclical. Given the properties of the markup relation, ϕpN q, for ν2 ‰ ν1 outlined above,
in bad (good) times when there are less (more) firms, markup sensitivity to small disturbances
to N increases (decreases). The left panel of Fig. 1 plots markups as function of the number
of firms for the benchmark parametrization, ν2 ą ν1 . When N is small (i.e., during recessions),
the markup relation is in the support of the domain where the curvature is highest. Intuitively,
when N is smaller, incumbent firms have more market power and a stronger influence on the
industry equilibrium, but are more susceptible to having their market share undercut by a marginal
entrant. In contrast, when N is large (i.e., during expansions), the relation is in the flatter region
of the support (and approaching the constant markup limit for N Ñ 8). The effects of strategic
interactions are muted when there are many firms, and an individual firm has less influence over
prices in the industry equilibrium. The time-varying markup sensitivity also transmits to real
activity through the factor demands for capital and labor inputs, as given in Eqs. (18)–(20).
Therefore, the higher markup and demand sensitivity to entry risk in bad times translates to
countercyclical macroeconomic volatility. With recursive utility, these volatility dynamics imply a
countercyclical equity risk premium, forecastable by markups and the number of firms. The same
intuition follows for the case where ν2 ă ν1 , as the curvature of the markup relation increases as N
decreases. Overall, product innovation in the presence of strategic actions generates countercyclical
risk premia.
The relative magnitude between the elasticity parameters, ν2 and ν1 , dictates the degree of
curvature in the markup relation, ϕp¨q, and therefore determines the magnitude of excess return
16
predictability. In the benchmark case, where ν2 ą ν1 , decreasing ν2 , while holding ν1 fixed, increases the curvature of the relation, which is depicted in Fig. 1.9 More curvature increases markup
and demand sensitivity to entry risk in bad times, which magnifies the degree of heteroskedasticity
in macroeconomic quantities. More variation in macroeconomic volatility increases the degree of
predictable variation in risk premia.
While the mechanism for generating countercyclical risk premia only depends on ν2 ‰ ν1 ,
the cyclicality of markups depends critically on whether substitutability is (i) higher within than
across industries (ν2 ą ν1 ) or (ii) higher across that within industries (ν2 ă ν1 ). When ν2 ą ν1 , the
markup relation to the number of firms is negative. Given that entry is procyclical, this parameter
configuration implies countercyclical markups. When ν2 ă ν1 , the relation is positive, which implies
procyclical markups. Given most empirical studies find that markups are countercyclical and the
intuitive interpretation of the elasticity parameters, we focus on the case where ν2 ą ν1 . Indeed,
the cyclicality of markups is an important identifying moment in the structural estimation of ν2 .10
Countercyclical markups provide a short-run risk amplification mechanism. In good (bad) times,
markups are lower (higher) which induces more (less) investment and hiring. This amplification
mechanism helps make short-term dividends riskier relative to longer-term ones, and provides a
potential explanation for the downward-sloping equity term structure documented in Binsbergen,
Brandt, and Koijen (2012).
Absent strategic interactions, as in the limiting case of atomistic firms (i.e., N Ñ 8) assumed
in Dixit and Stiglitz (1977), markups are constant:
lim ϕpNt q “
Nt Ñ8
ν2
.
ν2 ´ 1
(30)
Therefore, the rich dynamics generated by product innovation are attributed to strategic interactions among firms. The presence of strategic competition creates a time-varying link between
markups and macroeconomic risk, which accounts for the main asset pricing results of this paper.
9
Given the steady-state values for the markup (ϕ ą 1) and the number of firms N ą 1, and the parameter
restriction ν2 ą ν1 , we can establish the following bounds ν2 ą ϕ{pϕ ´ 1q ą ν2 . Thus, as ν2 Ñ ϕ{pϕ ´ 1q, the
curvature of the equilibrium markup relation approaches 8.
10
Some examples of empirical studies documenting countercyclical markups include Bils (1987), Rotemberg and
Woodford (1999), Chevalier, Kashyap, and Rossi (2003), Hong (2016), and Gilchrist, Schoenle, Sim, and Zakrajšek
(2017).
17
3.2
Process innovation
The process innovation channel provides a long-term growth propagation channel due to the presence of positive aggregate spillover effects from the accumulation of intangible capital (through
R&D investments). The spillover effects are specified such that the equilibrium accumulation of
intangible capital exactly offset the effects of diminishing marginal returns to production – to allow for sustained long-run growth – and is standard in endogenous growth models.11 As a result,
growth in the model arises through aggregate market clearing forces that equate optimal household
supply and firm demand for intangible capital. Indeed, expected log TFP growth in our model is
directly related to the accumulation of intangible capital in equilibrium:
Et r∆tf pt`1 s « ∆zt`1 ,
(31)
where approximation relies on the log stationary productivity shock, at , and the log aggregate
number of firms, nt ” logpNt q, to be persistent and stationary, so that the corresponding growth
rates ∆at and ∆nt are approximately iid. Absent the spillover effects, the effects of diminishing
returns would dominate, such that growth would converge to zero in the steady-state.
As shown in Kung (2015) and Kung and Schmid (2015), the endogenous growth mechanism provides powerful low-frequency growth propagation mechanism that generates significant
innovation-driven long-run risks. Persistent stationary shocks are transmitted to expected growth
rates through the endogenous accumulation of intangible capital as per Eq. (31). A positive technology shock raises the marginal product of intangible capital, which persistently induces more
R&D expenditures. An increase in intangible capital raises the level of output, but due to positive
spillover effects, there is also a persistent increase to the trend component. As the representative
household with recursive preferences is strongly averse to persistent uncertainty about long-term
growth, these growth dynamics lead to a sizable average equity premium.
4
Quantitative results
This section presents a quantitative analysis of our model. We begin with a description of the data
used in the estimation and for model comparison. Then, we describe the estimation strategy to
11
The spillover effects are specified such that aggregate production technology is linear homogeneous in the
accumulating factors, K and N , which can be seen in Eqs. (22) and (23)
18
identify key model parameters. After describing the parametrization, we examine the asset pricing
and macroeconomic implications of the model, and relate it to the product and process innovation
channels.
4.1
Data
Data series for macroeconomic variables, such as consumption, physical investment, and output,
are from the Bureau of Economic Analysis (BEA). The consumer price index (CPI) and labor hours
are from the Bureau of Labor Statistics (BLS). Asset price data are from Center for Research in
Security Prices (CRSP). Nominal variables are deflated using the CPI. The measures of process
innovation, R&D expenditures and intangible capital, are obtained from the National Science
Foundation (NSF) and the BLS, respectively. R&D flows correspond to the private business R&D
expenditures from the NSF. Intangible capital is measured as the stock of R&D, constructed
recursively by the BLS using the R&D flow series from above.
Empirical measures of product innovation (markups and the number of firms) are computed
in the following ways. Our empirical measure of markups follows the macroeconomics literature
(e.g., Bils (1987), Rotemberg and Woodford (1999), and Campello (2003)), who relate markups to
the labor share through an equilibrium relation:
ϕt “ ´sL,t ´ ωL lt ,
(32)
where sL,t is the log labor share and lt is log hours. Labor share data are obtained from the BLS.
We construct an aggregate measure for the number of operating firms in the following steps. For
the period, 1948 - 1964, we use Table B-72 from the Economic Report of the President (ERP). This
data series is discontinued in 1965 and replaced by the series from the Business Dynamics Statistics
(BDS) in 1977, which we use from 1977-2014. For the missing observations for the period, 1965
- 1976, we regress the growth rate of the number of firms onto the change in the NBF index for
where the periods of the series overlap. Using the fitted values from the estimated relation, we
construct a proxy for the number of firms for the period, 1965 - 1976. We use a bandpass filter to
detrend and obtain the cyclical component of this series. Our data sample is from 1948 (starting
date of the ERP data) to 2015.
19
4.2
Estimated parameters
We estimate five structural parameters, Θ ” rζk , ζz , a‹ , β, ν2 s, using the simulated methods of
moments approach. This procedure chooses values for Θ̂ in order to minimize the distance between
a vector of identifying moments from the data and the corresponding moments generated from
model simulations:
Θ̂ “ argmin rm̂ ´ mpΘqs1 W ´1 rm̂ ´ mpΘqs ,
(33)
Θ
where W is a weighting matrix, m̂ is a vector of empirical moments, and mpΘq is the vector
of model-implied moments obtained by assuming a value of Θ for the structural parameters.12
Although the estimator, Θ̂, is consistent for any positive-definite matrix, W , we follow the literature
and set W equal to the inverse of the covariance matrix of the moments. This specification allocates
more weight to moments estimated with greater precision, which has the advantage of minimizing
the asymptotic variance of Θ̂. To estimate the covariance matrix of the moments, we use the
influence function approach of Erickson and Whited (2000).
The five structural parameters, Θ, are estimated using seven empirical targets, summarized
in Panel A of Table 1. The curvature of the capital and technology adjustment costs, ζk and
ζz , affect the speed to which firms change their physical and R&D investment in response to
aggregate productivity shocks. The parameters, ζk and ζz , are primarily identified by the relative
volatility of physical and R&D investment growth, respectively. We also include the volatility of
consumption growth as a target moment to discipline the quantity of aggregate risk in the model.
The unconditional mean of the forcing process, a‹ , is a scale parameter that affects the average
growth rate of the economy, and is determined by using average output growth. The subjective
discount factor, β, is identified by the average risk-free rate.
The elasticity parameter, ν2 , is important for determining the sign of the equilibrium markup
relation with the number of firms, φ1 pN q, and therefore dictates the cyclicality of markups. Thus,
to identify this parameter, we use two moments, the elasticity of output to the number of firms
and the elasticity of markups to the number of firms. Since the empirical measure of markups is
countercyclical, we obtain an estimate for ν2 that satisfies ν2 ą ν1 (and implies that φ1 pN q ă 0).13
12
Model moments are computed over 100 samples of length similar to the data, with a burning-in period of 100
quarters.
13
While the cyclicality of aggregate markups has been subject to debate, recent studies using micro data, such
as Bils (2013, 2014) and Hong (2016) find strong evidence in support of countercyclical price markups.
20
In particular, conditional on the calibrated value of ν1 (“ 1.165), we obtain an estimate for ν2
of 8.740.14 The parameter relation ν2 ą ν1 that we find is also consistent with estimates from
micro-data. Broda and Weinstein (2010) estimate the within- and across-industry elasticities
(corresponding to ν2 and ν1 , respectively) using bar-code-level product data, and find that the
elasticities of substitution are unequivocally higher within than across industries over the entire
distribution of product share ratios.
4.3
Calibrated parameters
The remaining ten parameters, Γ ” [ψ, γ, χ, η, δk , δz , δn , ν1 , ρ, σ], are pinned down by values
from the existing literature or set to match steady-state evidence. The preference parameters
controlling risk tastes, ψ (intertemporal elasticity of substitution) and γ (coefficient of relative risk
aversion), are calibrated to 1.85 and 10, respectively, and in the standard range values in the longrun risks literature (e.g., Bansal and Yaron (2004)). This preference configuration implies that
the representative agent prefers an early resolution of uncertainty (i.e., ψ ą 1{γ), which implies
that the price of risk for low-frequency consumption growth uncertainty is positive.15 The labor
elasticity parameter, χ, is set to 3. This value implies a Frisch elasticity of labor supply of 2{3,
which is consistent with estimates from the microeconomics literature (e.g. Pistaferri (2003)).
The capital share, α, is set to 0.33 and the quarterly depreciation rate for physical capital,
δk , is set to 2%. These are standard values in the macroeconomics literature and designed to
match steady-state evidence. The quarterly depreciation rate of the R&D capital stock δz is set to
3.75%, and is the value that the BLS uses in its construction of the R&D capital stock (referred
to as intangible in this paper). The degree of technological appropriability η is calibrated to 0.1,
in order to match the steady-state level of R&D intensity (i.e., the ratio of the R&D flows to
the R&D stock), as in Kung (2015). The exogenous firm exit shock δn is set to 2%, in line with
Bilbiie, Ghironi, and Melitz (2012). The elasticity parameter that determines the substitutability
of goods across industries, ν1 , is set to match average markups. Finally, the persistence parameter,
ρ, and volatility parameter, σ, corresponding to the aggregate productivity shock are calibrated
14
We also run the estimation conditional on a wide range of values for ν1 (between 1 and 20), and we get that
the 95% confidence interval for ν2 exceeds ν1 in each case.
15
A preference for a late resolution of uncertainty makes it difficult to explain the equity premium jointly with
a stable riskfree rate. Namely, a high risk aversion would be required to match the equity premium, but to satisfy
ψ ă 1{γ, requires a very small ψ (i.e., far less than 1). A low IES has several counterfactual implications: (i) excess
sensitivity of the riskfree rate to changes in expected consumption growth, (ii) negative relation between valuation
ratios and growth, and (iii) positive relation between valuation ratios and uncertainty.
21
to annualized values of 0.95 and 1.75%, designed to match the dynamics of R&D intensity, as in
Kung (2015).
We also compare our benchmark model to an analogous model that shuts down the product
innovation channel (i.e., assuming that the number of firms in an industry is fixed), which is
referred to as the ‘No-Entry’ model. For a fairer comparison between models, we recalibrate ζk ,
ζz , β, a˚ , and σ to match the relative investment volatility, the relative R&D volatility, riskfree
rate, and the first and second moments of consumption growth from the benchmark model. We
compare these models in the tables and figures to elucidate the role of product innovation for asset
prices.
Overall, our parameterization of the benchmark model provides a good fit to basic macroeconomic fluctuations (Panel A of Table 2), as targeted in the estimation and calibration. In the
following sections, we describe how product innovation generates significant endogenous variation
in the conditional equity premium while the process innovation contributes to a sizable unconditional equity premium.
4.4
Product innovation
Given the parameter configuration, ν2 ą ν1 , established from the estimation results above, the
presence of strategic interactions among firms implies that the relation between markups and the
number of firms is negative and convex. This equilibrium relation is important for driving the
main asset pricing results relating to the product innovation channel. We find direct empirical
support for this nonlinear relation through the following estimated regression:
ϕ̂t “ ´0.004 ´ 0.70˚˚˚ n̂t ` 18.83˚˚˚ n̂2t ,
where ϕ̂t is log markups and n̂t is the detrended log number of firms. The slope coefficients on
n̂t and n̂2t are negative and positive, respectively, which implies a negative and convex relation
between markups and the number of firms, in levels.
As the number of firms respond positively to positive productivity shocks (that raise valuations
of new products through the free entry condition), entry dynamics are therefore procyclical. Since
there is a negative relation between markups and the number of firms, procyclical entry leads to
countercyclical markups. Panel D of Table 3 confirms these relations, as markups are negatively
22
correlated with output while the number of firms are positively related to output, both in the model
and the data. Panels B and C of Table 3 show that the volatility and persistence of markups and
entry dynamics from the model accord with the data. Thus, the model endogenously produces
realistic time-series processes for variables associated with product innovation, which, in turn, are
important for the key asset pricing results of this paper.
4.4.1
Endogenous time-varying risk premia
The nonlinear relation between markups and the number of firms endogenously generates timevarying macroeconomic volatility, forecastable by markups and the number of firms. When there
are less firms, markup sensitivity to entry risk is higher than when there are many firms. The
dependence of markup sensitivity to the number of firms is illustrated graphically in Fig. 1. The
slope of the markup function is larger in magnitude as the number of firms decline. The conditional
markup sensitivity is transmitted to aggregate quantities through impact of markups on factor
demands for capital and labor inputs. Fig. 3 provides a visual depiction of how the elevated
sensitivity of markups to entry risk, when there are less firms, is reflected in macroeconomic
quantities. This figure plots impulse response functions to a positive productivity shock conditional
on less firms (dashed line) and on more firms (solid line). In the bottom row, it is evident that the
responses of markups, TFP growth, and consumption growth are significantly larger when there
are less firms in an industry.
As the incentives for firm entry are procyclical, the higher markup and factor input sensitivities,
conditional on less firms, imply countercyclical macroeconomic volatility. Table 4 examines the
consumption growth volatility dynamics generated by the product innovation channel, in conjunction with strategic interactions. Panel A reports the mean, volatility, and persistence of realized
consumption volatility from the model and the data. The model-generated volatility risks are quantitatively significant, and explains around 40% of the observed variation in consumption volatility.
Absent strategic interactions and variation at the extensive margin, consumption volatility would
be constant as in Kung and Schmid (2015). Thus, we interpret the persistent consumption heteroskedasticity in our model as the endogenous component of consumption volatility attributed to
strategic interactions in product markets.
Panel B of Table 4 presents evidence consistent with the model prediction that macroeconomic
volatility is countercyclical and negatively related to the price-dividend ratio. Panels C and D
23
test the novel prediction in the model that time-variation in macroeconomic volatility is related
to strategic competition in product markets. Panel C reports the consumption volatility forecast
at a one-year horizon using markups. Both in the model and the data, the slope coefficients are
positive and statistically significant, while the R2 are of a comparable magnitude. Panel D reports
a similar forecasting regression, but using the detrended number of firms as a predictive variable.
The slope coefficients are negative and statistically significant. In short, the model generates
realistic variation and patterns in consumption volatility dynamics.
With recursive preferences, the countercyclical consumption volatility leads to a countercyclical
equity premium. Table 5 presents excess stock return forecasts with the log price-dividend ratio
averaged across short-samples matching the length of observations in the empirical counterpart
(Panel A) and in the population regressions (Panel B). In Panel A, the slope coefficients are negative
and statistically significant, the R2 are increasing with horizon, and the degree of predictability
is of a comparable magnitude as in the data. In Panel B, we compare the price-dividend ratio
forecasting regressions between the benchmark model and an analogous model that shuts down
the product innovation channel, referred to as the ‘No-Entry’ model. The population regressions
in the benchmark model confirm the countercyclical risk premia evidence from the short-sample
regressions in Panel A. However, the No-Entry model does not produce any predictability in excess
returns, as consumption volatility is constant. Thus, the time-varying risk premia arising in our
model is attributed to product innovation in the presence of strategic interactions.
Table 6 reports the novel excess stock return forecasting regressions using markups and the
number of firms. To account for the small sample properties of our test and for the cross-sectional
and time-series dependence in innovations, we block-bootstrap our p-values and report coefficients
adjusted for the Stambaugh bias. Panel A reports the forecasting regressions with markups. The
slope coefficients are positive and statistically significant, and both the coefficients and R2 ’s are
increasing with horizon, consistent with the data. Panel B reports the forecasting regressions with
the detrended number of firms. The slope coefficients are negative and statistically significant, and
the magnitude of the slope coefficients and the R2 ’s are increasing with horizon, as in the data.
These predictive regressions lend empirical support to our key mechanism linking countercyclical
risk premia to product innovation dynamics. The first two rows of Fig. 4 summarize this mechanism
using impulse response functions. A positive technology shock raises valuations and induces more
entry through the free entry condition. Due to the presence of strategic interactions, the level of
24
markups and sensitivity of markups to entry risk declines. The fall in markup sensitivity transmits
to aggregate quantities through the factor demands, and therefore the volatility of consumption
decreases. With recursive preferences, the decline in consumption volatility leads to a fall in first
and second moments of the conditional equity premium.
Table 7 quantitatively explores the role of the elasticity parameters, ν1 and ν2 , for our endogenous return predictability results. As discussed in Section 3.1, these parameters determine the
sign and shape of the equilibrium markup relation with the number of firms. Given the parameter
configuration, ν2 ą ν1 , Fig. 1 illustrates how decreasing ν2 steepens the markup relation. The
increased curvature enhances the sensitivity of markups and factor demands in bad times when
there are less firms, which is reflected in a greater amount consumption heteroskedasticity. More
variation in consumption volatility then translates to a higher degree of return predictability. Indeed, Panel A of Table 7 illustrates how decreasing ν2 increases consumption volatility risks, while
Panel B shows how decreasing ν2 increases the degree of excess return predictability, reflected in
higher R2 ’s and slope coefficients that are larger in magnitude.
Panel C of Table 7 examines the less intuitive case where the higher degree of substitutability
is higher across than within industries (i.e., ν2 ă ν1 ), which is the opposite of our benchmark
parametrization. While the cyclicality of markups flips in this case, the mechanism for countercyclical risk premia is robust to the alternative parametrization. As mentioned in Section 3.1,
when ν2 ă ν1 , the markup relation is positive and concave (rather than negative and convex).
Importantly, the relation in this alternate case is still steeper when there are less firms. Thus,
macroeconomic volatility and risk premia are higher in bad times. The countercyclical risk premia
is manifested in excess return forecasts with the price-dividend ratio with negative slope coefficients and sizable R2 ’s, as in our benchmark parametrization. However, as markups are procyclical
(rather than countercyclical), the forecasting regressions with markups flip signs. Therefore, the
model mechanism for generating a countercyclical equity risk premium only requires that ν2 ‰ ν1 .
However, to explain the observed countercyclical markups requires ν2 ą ν1 .
4.4.2
Term structure of equity
The negative relation between markups and the number of firms implied by the parameter configuration, ν2 ą ν1 , leads to countercyclical markups. Such markup dynamics provide a short-run risk
amplification mechanism. In good times, lower markups stimulate demand for factor inputs and
25
boost expansions, while in bad times, higher markups discourage demand and deepen recessions.
The amplification of macroeconomic quantities attributed to the product innovation channel is exhibited in Table 2. Absent strategic interactions or variation in entry dynamics, markups would be
constant. With countercyclical variation in markups, the benchmark model generates significantly
higher labor hours and output volatility.
From an asset pricing perspective, the short-run amplification in macroeconomic quantities
increases the riskiness of short-run cash flows relative to longer-term ones sufficiently, such that,
the term structure of equity returns is downward-sloping. The price of a claim to the aggregate
dividend strip of maturity k is defined as:
pkq
Pt
” ErMt,t`k Dt`k s,
(34)
and the corresponding unconditional risk premium is
”
RP pkq ” E
pkq
pk´1q
pkq
Rt`1
ı
´ Rf,t ,
(35)
pkq
where Rt`1 ” Pt`1 {Pt ´1 is the holding-period return. Fig. 2 plots the risk premium of dividend
strips as a function of maturity. The benchmark model (dashed line) produces a downward-sloping
term structure for the initial four years, consistent with the findings from Binsbergen, Brandt, and
Koijen (2012) and Binsbergen, Hueskes, Koijen, and Vrugt (2013). In contrast, in the analogous
model with constant markups (solid line), the term structure is upward-sloping like in standard
fundamentals-based models, such as the long-run risks paradigm. Thus, our paper illustrates how
accounting for strategic competition provides a potential explanation for reconciling the long-run
risks paradigm with the empirical evidence on the equity term structure.
4.5
Process innovation
The presence of spillover effects from the accumulation of intangible capital provides a long-run
growth propagation mechanism akin to Kung (2015) and Kung and Schmid (2015). Consequently,
the low-frequency macroeconomic dynamics in our model are driven by process innovation.
26
4.5.1
Endogenous long-run risks
The growth propagation mechanism provides an endogenous source of long-run risks. A positive
productivity shock raises the marginal product of intangible capital. In equilibrium, households
increase R&D expenditures to raise the stock of intangible capital. Through aggregate spillovers
from accumulating intangible capital (via the production technology of intermediate firms), an
increase in intangible capital raises the trend component of measured TFP persistently. The lowfrequency TFP dynamics are inherited by macroeconomic quantities, such as consumption, output,
and dividends, through the impact of TFP on the marginal product of factor inputs. The last
row of Fig. 4 provides a visual depiction of these endogenous growth mechanics through impulse
response functions. The equilibrium relation between expected TFP growth and the accumulation
of R&D from the model are summarized compactly in Eq. (31).
We provide empirical support for the innovation-driven growth dynamics in Table 8. Panels A
and B report output growth forecasts with R&D intensity and the growth rate of intangible capital,
respectively. Consistent with the benchmark model, measures of process innovation forecast future
output growth with positive and statistically significant slope coefficients, and with sizable R2 ’s
that increase with horizon. Panels C and D repeat these forecasting regressions with TFP growth,
and we find similar results. While there is some endogenous interaction between the process
and product innovation channels (the channels positively reinforce each other), the low-frequency
movements are primarily driven by the process innovation channel. In the last two columns of
Table 8, we see that the TFP and output growth forecasts are quantitatively similar between the
benchmark model and model without entry.
The low-frequency growth dynamics paired with recursive preferences translates to a sizable
equity premium, reported in Panel B of Table 2. The representative household is strongly averse
to persistent consumption uncertainty. As consumption and aggregate dividends share a common
persistent trend, the household requires a sizable risk compensation to hold the dividend claim
in equilibrium. The long-run consumption uncertainty also induces a strong precautionary savings motive that leads to a low riskfree rate in equilibrium. The benchmark model also generates
a moderately larger equity premium compared to the model without entry. There are two primary reasons for the disparity. First, with recursive preferences, the countercyclical consumption
volatility risks are priced. Second, the countercyclical markups increase the comovement between
dividends and consumption.
27
4.6
Cross-section of returns
In the extension of our benchmark model that allows for cross-sectional heterogeneity (outlined
in Section 2.8) is examined in here. We use cross-sectional moments to discipline the equilibrium
time-series relations documented above. Ex-post heterogeneity across the industries is introduced
through industry-specific entry cost shocks specified in Eqs. (26) and (27). In the model simulations, we sort the two types of industries based on the level of markup into a high-markup industry
and a low-markup industry, each period.
In the data, we sort firms into terciles based on a lagged measure of industry competition. The
average industry price markup, in a given year, is measured as the sum of the operating profits in
the industry divided by total industry sales:
Markupj,t “
Salesj,t ´ Cogsj,t
,
Salesj,t
(36)
where Salesj,t is the sum of firm’s sales in industry j, and Cogsj,t is the sum of cost of goods sold
in industry j. The data is from Compustat and spans 1962 to 2016.16 We define an industry as all
firms within the same 3-digit Standard Industrial Classification (SIC) code. We exclude financial
industries (SIC codes from 6000 to 6999) and regulated industries (SIC codes from 4900 to 4999).
Panel A of Table 9 compares the cross-sectional implications of the extended model to the data.
The persistence and volatility of the industry-specific shocks are calibrated to match the average
dispersion in markups between the high- and low-markup industries. We find that high-markup
industry is associated with higher expected returns than the low-markup industry – both in the
model and the data – and is also consistent with the findings from Bustamante and Donangelo
(2017). In our model, the high-markup industry faces higher entry costs (i.e., due to a sequence
of positive entry cost shocks), and therefore has less firms than the low-markup industry. Due to
the presence of strategic interactions, markup sensitivity to entry risk is higher when there are less
firms, as the markup relation is in the steeper portion of the domain. Through the impact of the
conditional markup sensitivity on factor demands, the production decisions and cash flows of the
high-markup industry face a greater average exposure to both industry and aggregate risk. The
greater exposure to systematic risk is reflected in the higher CAPM betas and higher expected
16
Although this measure is only available for publicly traded firms, Bustamante and Donangelo (2017) find no
evidence of a significant bias in this markup measure as compared to one that consists of a broader sample including
both private and public firms.
28
returns, consistent with the data.
Panel B of Table 9 considers time-series return predictability across the high- and low-markup
industries. As the high-markup industry exhibits greater sensitivity to aggregate risk, the conditional betas exhibit more predictable variation in the time-series than the low-markup industry.
Consistent with the model predictions, we find in the data that the high-markup industry exhibits
significantly more excess return predictability in the time-series than the low-markup industry. We
find that higher markups are associated with higher systematic risk and expected returns, both
in the time-series and in the cross-section. The presence of strategic interactions determine the
conditional relations between market power and systematic risk, while endogenous entry dynamics
produce the time-series fluctuations and cross-sectional dispersion in the relations.
5
Conclusion
This paper illustrates how product innovation in the presence of strategic competition provides
an endogenous source of time-varying risks. Strategic interactions among firms shape the equilibrium relation between product market competition and systematic risk. When incumbent firms
have more market power and charge higher markups, new entrants can undercut markups more
aggressively, while stealing market share. In equilibrium, the heightened sensitivity to the threat
of entry when markups are high correspond to higher systematic risk. The endogenous entry of
firms, depending on economic and industry conditions, generates time-variation and cross-sectional
dispersion in markups. We find that higher markups predict higher expected stock returns over
time and across industries, consistent with patterns in the data. Strategic competition also leads
to countercyclical markups, which provides a powerful short-run risk amplification mechanism that
can help explain an initially downward-sloping term structure of equity. Overall, we show that
accounting for strategic interactions provides a macroeconomic foundation for understanding stock
return predictability.
29
Appendix A. Optimality conditions
A.1 Household
The representative household maximizes utility by participating in financial markets, investing in capital and
technology, and supplying labor. The household position in the stock market is denoted by Ωt , and her position in
the government bond market by Bt . The household owns a stock of physical and intangible capital, that are rented
to firms for a period return of Rkt and Rzt , respectively. The (real) budget constraint of the household is
Ct ` Q`
t Ωt`1 ` Bt`1 ` It ` St
k
z
“ Wt Lt ` pQ´
t ` Dt q Ωt ` Rf,t Bt ` Rt Kt ` Rt Zt ,
`
where Q´
t and Qt are vectors containing the ex-dividend stock prices of all firms that are present at the beginning
and at the end (i.e. including entrants) of period t respectively, Dt is the aggregate dividend paid by all surviving
firms at the beginning of time t, Rf,t is the gross risk free rate, and Wt is the wage rate.
Setting up the household problem in Lagrangian form:
Ut
`
˘ 1
1´θ 1´θ
“ max u pCt , Lt q ` β Et rUt`1
s
`
˘
`
k
z
` Λt Wt Lt ` pQ´
t ` Dt qΩt ` Rf,t Bt ` Rt Kt ` Rt Zt ´ Ct ´ Qt Ωt`1 ´ Bt`1 ´ It ´ St
` ΛK
t pp1 ´ δk qKt ` Φk,t Kt ´ Kt`1 q
` ΛZ
t pp1 ´ δz qZt ` Φz,t Zt ´ Zt`1 q
Z
where Λt , ΛK
t , and Λt are the Lagrange multipliers on the budget constraint, physical accumulation and intangible
capital accumulation, respectively.
Taking first order conditions with respect to It , St , Kt`1 , Zt`1 , Ωt`1 , Bt`1 , and Lt yield four intertemporal Euler
equations and one intratemporal condition for labor supply:
¯ fi
´
´ ¯
It
1
Rkt`1 ` Φ1´1
`
Φ
1
´
δ
´
Φ
k
k,t`1
k,t`1 Kt
k,t`1
fl
Et –Mt,t`1
1´1
Φk,t
¯ fi
´
´ ¯
»
St
1
Rzt`1 ` Φ1´1
z,t`1 1 ´ δz ´ Φz,t`1 Zt ` Φz,t`1
fl
Et –Mt,t`1
Φ1´1
z,t
«
ff
Dt`1 ` Q´
t`1
Et Mt,t`1
Q`
t
»
1
“
1
“
1
“
1
“
Wt
“
Et rMt,t`1 Rf,t`1 s
χ0 p1 ´ Lt q´χ 1´1{ψ
Zt
´1{ψ
Ct
30
where Φ1k,t “
BΦk,t
BKt ,
Φ1z,t “
BΦz,t
BZt ,
and Mt`1 is the one-period stochastic discount factor:
˛´θ
¨
Mt`1 “ β ˝
ˆ
Ut`1
1
‚
1´θ 1´θ
Et pUt`1
q
Ct`1
Ct
˙´ ψ1
Imposing the symmetry condition across firms and using the evolution of the number of firms, we have that
`
Q´
t “ Nt Qt , and Qt “ pNt ` NE,t qQt . Thus, the cum-dividend value of a firm simplifies to:
Vt
Dt ` p1 ´ δn qEt rMt,t`1 Vt`1 s
“
The aggregate resource constraint is obtained after imposing market clearing in financial markets (i.e. Ωt “ 1 and
Bt “ 0), goods markets and production input markets as well as using the symmetric nature of the economy. We
obtain,
Ct ` NE,t ` It ` St
“
Wt Lt ` Nt Dt ` Rkt Kt ` Rzt Zt
which after replacing for Dt , and using the free entry condition (i.e. Qt “ FE,t ), simplifies to:
Ct ` NE,t FE,t ` It ` St
“ Yt
A.2 Final goods sector
The final goods firm’s problem consists of choosing the optimal bundle of products tXi,j,t ujPr0,1s,i“1,...,Nj,t , in order
to maximize the firm’s profit. The production function is:
ˆż 1
Yt
ν1 ´1
ν1
Yj,t
“
1
˙ ν1ν´1
dj
0
˜N
j,t
ÿ
Yj,t
“
ν2 ´1
ν2
2
¸ ν2ν´1
Xi,j,t
i“1
The problem is solved in two steps. First, we derive the optimal demand for products Xi,j,t within industry j to
maximize industry output Yj,t for any given expenditure level ξj,t :
Nj,t
ÿ
Pi,j,t Xi,j,t “ ξj,t
(A.1)
i“1
The Lagrangian of the problem is:
Lξ,j,t “
max
tXi,j,t ui“1,Nj,t
˜N
j,t
ÿ
ν2 ´1
ν2
2
¸ ν2ν´1
˜
` Λξ,j,t
Xi,j,t
i“1
ξj,t ´
ÿ
i“1
31
¸
Nj,t
Pi,j,t Xi,j,t
where Λξ,j,t is the associated Lagrange multiplier. The first order necessary conditions are:
˜N
j,t
ÿ
ν2 ´1
ν2
2 ´1
¸ ν2ν´1
´
1
ν2
“ Λξ,j,t Pi,j,t ,
Xi,j,t
Xi,j,t
for i “ 1, ..., Nj,t
i“1
Using the expression above, for any two products i, and k,
ˆ
Xi,j,t “ Xk,j,t
ν2 ´1
ν2 ,
Now, raising both sides of the equation to the power of
of
ν2
ν2 ´1 ,
Pi,j,t
Pk,j,t
˙´ν2
(A.2)
summing over i and raising both sides to the power
we get
˜N
j,t
ÿ
ν2 ´1
ν2
2
¸ ν2ν´1
Xi,j,t
´ř
Nj,t
i“1
“ Xk,j,t
1´ν2
Pi,j,t
2
¯ ν ν´1
2
´ν2
Pk,j,t
i“1
Substituting for the industry production function in the left-hand side and rearranging terms,
Yj,t
´ν2
Pk,j,t
Xk,j,t
˜N
j,t
ÿ
“
´ν2
¸ 1´ν
2
1´ν2
Pi,j,t
(A.3)
i“1
The industry j price index is the price Pj,t such that Pj,t Yj,t “ ξj,t . Using the expenditure function, Eq. A.1, along
with Eq. A.2, we get
Nj,t
Xk,j,t ÿ 1´ν2
Pi,j,t “ ξj,t “ Pj,t Yj,t
´ν2
Pk,j,t
i“1
(A.4)
Putting Eq. A.3 together with Eq. A.4, we obtain the expression for the industry price index Pj,t :
Pj,t “
˜N
j,t
ÿ
1
¸ 1´ν
2
1´ν2
Pi,j,t
i“1
Therefore the demand for intermediate firm pi, jq output is:
ˆ
Xi,j,t “ Yj,t
Pi,j,t
Pj,t
˙´ν2
(A.5)
In the second step, we derive the optimal demand for each industry good Yj,t in order to maximize the final goods
firm profit, that is
ˆż 1
max
tYj,t ujPr0,1s
PY,t
ν1 ´1
ν1
Yj,t
1
˙ ν1ν´1
dj
0
ż1
Pj,t Yj,t dj
´
0
where PY,t is the price of the final good (taken as given), Yj,t is the amount of industry good purchased from
industry j and Pj,t is the price of that good j P r0, 1s.
32
The first-order condition with respect to Yj,t is
ˆż 1
PY,t
ν1 ´1
ν1
Yj,t
1 ´1
˙ ν1ν´1
dj
´
1
Yj,t ν1 ´ Pj,t “ 0
0
which can be rewritten as
ˆ
Yj,t “ Yt
Pj,t
PY,t
˙´ν1
(A.6)
Using the expression above, for any two industry goods j, k P r0, 1s,
ˆ
Yj,t “ Yk,t
Pj,t
Pk,t
˙´ν1
(A.7)
Since markets are perfectly competitive in the final goods sector, the zero profit condition must hold:
ż1
PY,t Yt “
Pj,t Yj,t dj
(A.8)
0
Substituting (A.7) into (A.8) gives
Yj,t “ PY,t Yt ş1
0
´ν1
Pj,t
1´ν1
Pj,t
dj
(A.9)
Substitute (A.6) into (A.9) to obtain the price index
1
˙ 1´ν
1
ˆż 1
1´ν1
Pj,t
PY,t “
dj
0
A.3 Intermediate firms
Using the demand faced by a firm i in sector j (Eq. A.5), and the demand faced by industry j (Eq. A.6), the
demand faced by firm (i,j) can be expressed as
˙´ν2 ˆ
˙´ν1
Pj,t
Pi,j,t
Pj,t
PY,t
´
¯´ν2 ´
¯ν2 ´ν1
“ Yt P̃i,j,t
P̃j,t
ˆ
Xi,j,t
where P̃i,j,t ”
Pi,j,t
PY,t
and P̃j,t ”
“ Yt
(A.10)
(A.11)
Pj,t
PY,t .
The (real) source of funds constraint is
Di,j,t “ P̃i,j,t Xi,j,t ´ Wt Li,j,t ´ Rkt Ki,j,t ´ Rzt Zi,j,t
Taking the input prices and the pricing kernel as given, firm (i,j)’s problem is to maximize shareholder’s wealth
33
subject to the firm demand emanating from the rest of the economy:
«
Vi,j,t “
ff
8
ÿ
s
max
Et
Mt,t`s p1 ´ δn q Di,j,t`s
tLi,j,t ,Ki,j,t ,Zi,j,t ,P̃i,j,t utě0
s“0
´
¯´ν2 ´
¯ν2 ´ν1
s.t. Xi,j,t “ Yt P̃i,j,t
P̃j,t
where Mt,t`s is the marginal rate of substitution between time t and time t ` s.
The Lagrangian of the problem is
Qi,j,t
“
´
¯1´α
η
α
P̃i,j,t Ki,j,t
At Zi,j,t
Zt1´η Li,j,t
´ Wt Li,j,t ´ Rkt Ki,j,t ´ Rzt Zi,j,t
ˆ
´
¯1´α
´
¯´ν2 ´
¯ν2 ´ν1 ˙
η
α
`Λdi,j,t Ki,j,t
At Zi,j,t
Zt1´η Li,j,t
´ Yt P̃i,j,t
P̃j,t
The corresponding first order necessary conditions are
Rkt
Rzt
Wt
Xi,j,t
Xi,j,t
pP̃i,j,t ` Λdi,j,t q
Ki,t
Xi,j,t
“ ηp1 ´ αq
pP̃i,j,t ` Λdi,j,t q
Zi,j,t
Xi,j,t
“ p1 ´ αq
pP̃i,j,t ` Λdi,j,t q
Li,j,t
«
“ α
“
Λdi,j,t Yt
´ν2 ´1
´ν2 P̃i,j,t
Pj,t ν2 ´ν1
` pν2 ´
´ν2 ν2 ´ν1 ´1
ν1 qP̃i,j,t
P̃j,t
B P̃j,t
B P̃i,j,t
ff
where Λdi,j,t is the Lagrange multiplier on the inverse demand function.
Using the definition of the industry price index,
B P̃j,t
“
B P̃i,j,t
˜
P̃i,j,t
P̃j,t
¸´ν2
Imposing the symmetry condition across industries implies that P̃j,t “ 1. In addition, the symmetry across firms
ν2
1
ν2 ´1
ν2 ´1
within an industry implies that P̃i,j,t “ P̃t “ Nj,t
, so that Yj,t “ Nj,t
Xj,t and the i subscript can be dropped.
Our set of equilibrium conditions simplifies to:
Rkt
Rzt
Wt
1
Yj,t
“ α
Nj,t Kj,t
˜
1`
Λdj,t
¸
P̃t
˜
¸
Λdj,t
Yj,t
“ ηp1 ´ αq
1`
Nj,t Zj,t
P̃t
˜
¸
d
Λj,t
Yj,t
“ p1 ´ αq
1`
Nj,t Lj,t
P̃t
“
Λdj,t “
P̃t
´1
´ν2 ` pν2 ´ ν1 qNj,t
34
‰
References
Aghion, P., P. Howitt, 1992. A model of growth through creative destruction. Econometrica 60(2),
323–351.
Bansal, R., A. Yaron, 2004. Risks for the long run: A potential resolution of asset pricing puzzles.
The Journal of Finance 59(4), 1481–1509.
Belo, F., P. Colin-Dufresne, R. S. Goldstein, 2015. Dividend dynamics and the term structure of
dividend strips. The Journal of Finance 70(3), 1115–1160.
Bilbiie, F. O., F. Ghironi, M. J. Melitz, 2012. Endogenous entry, product variety, and business
cycles. Journal of Political Economy 120(2), 304–345.
Bils, M., 1987. The cyclical behavior of marginal cost and price. The American Economic Review
77(5), 838–855.
Binsbergen, J. v., 2016. Good-Specific Habit Formation and the Cross-Section of Expected Returns.
The Journal of Finance 71(4), 1699–1732.
Binsbergen, J. v., M. Brandt, R. Koijen, 2012. On the timing and pricing of dividends. The
American Economic Review 102(4), 1596–1618.
Binsbergen, J. v., W. Hueskes, R. Koijen, E. Vrugt, 2013. Equity yields. Journal of Financial
Economics 110(3), 503–519.
Binsbergen, J. v., R. S. Koijen, 2017. The term structure of returns: Facts and theory. Journal of
Financial Economics 124(1), 1–21.
Boldrin, M., L. J. Christiano, J. D. Fisher, 2001. Habit persistence, asset returns, and the business
cycle. American Economic Review 91(1), 149–166.
Broda, C., D. E. Weinstein, 2010. Product creation and destruction: Evidence and price implications. The American economic review 100(3), 691–723.
Bustamante, M. C., A. Donangelo, 2017. Product market competition and industry returns. Review
of Financial Studies, Forthcoming.
35
Campello, M., 2003. Capital structure and product markets interactions: evidence from business
cycles. Journal of Financial Economics 68(3), 353–378.
Chevalier, J. A., A. K. Kashyap, P. E. Rossi, 2003. Why don’t prices rise during periods of peak
demand? Evidence from scanner data. The American Economic Review 93(1), 15–37.
Cochrane, J. H., 2008. The dog that did not bark: A defense of return predictability. Review of
Financial Studies 21(4), 1533–1575.
Comin, D., M. Gertler, 2006. Medium-term business cycles. The American Economic Review 96(3),
523–551.
Corhay, A., 2015. Industry competition, credit spreads, and levered equity returns. Working Paper,
University of Toronto.
Croce, M. M., 2014. Long-run productivity risk: A new hope for production-based asset pricing?.
Journal of Monetary Economics 66, 13–31.
Croce, M. M., M. Lettau, S. C. Ludvigson, 2014. Investor information, long-run risk, and the term
structure of equity. Review of Financial Studies 28(3), 706–742.
Dixit, A. K., J. E. Stiglitz, 1977. Monopolistic competition and optimum product diversity. The
American Economic Review 67(3), 297–308.
Erickson, T., T. M. Whited, 2000. Measurement error and the relationship between investment
and q. Journal of Political Economy 108(5), 1027–1057.
Favilukis, J., X. Lin, 2015. Wage rigidity: A quantitative solution to several asset pricing puzzles.
Review of Financial Studies 29(1), 148–192.
Gilchrist, S., R. Schoenle, J. Sim, E. Zakrajšek, 2017. Inflation dynamics during the financial crisis.
The American Economic Review 107(3), 785–823.
Gourio, F., 2012. Disaster risk and business cycles. The American Economic Review 102(6), 2734–
2766.
Hoberg, G., G. Phillips, 2010. Real and financial industry booms and busts. The Journal of Finance
65(1), 45–86.
36
Hong, . S., 2016. Markup Cyclicality: A Tale of Two Models. Working Paper, Princeton University.
Hou, K., D. T. Robinson, 2006. Industry concentration and average stock returns. The Journal of
Finance 61(4), 1927–1956.
Jaimovich, N., M. Floetotto, 2008. Firm dynamics, markup variations, and the business cycle.
Journal of Monetary Economics 55(7), 1238–1252.
Jermann, U. J., 1998. Asset pricing in production economies. Journal of Monetary Economics
41(2), 257–275.
Kaltenbrunner, G., L. A. Lochstoer, 2010. Long-run risk through consumption smoothing. Review
of Financial Studies 23(8), 3190–3224.
Kuehn, L.-A., N. Petrosky-Nadeau, L. Zhang, 2014. Endogenous disasters. Working Paper,
Carnegie Mellon University.
Kung, H., 2015. Macroeconomic linkages between monetary policy and the term structure of
interest rates. Journal of Financial Economics 115(1), 42–57.
Kung, H., L. Schmid, 2015. Innovation, growth, and asset prices. The Journal of Finance 70(3),
1001–1037.
Loualiche, E., 2014. Asset pricing with entry and imperfect competition. Working Paper, Massachusetts Institute of Technology.
Opp, C. C., 2016. Venture Capital and the Macroeconomy. .
Opp, M. M., C. A. Parlour, J. Walden, 2014. Markup cycles, dynamic misallocation, and amplification. Journal of Economic Theory 154, 126–161.
Peretto, P. F., 1999. Industrial development, technological change, and long-run growth. Journal
of Development Economics 59(2), 389–417.
Pistaferri, L., 2003. Anticipated and unanticipated wage changes, wage risk, and intertemporal
labor supply. Journal of Labor Economics 21(3), 729–754.
Romer, P. M., 1990. Endogenous technological change. Journal of Political Economy 98(5), 71–102.
37
Rotemberg, J. J., M. Woodford, 1999. The cyclical behavior of prices and costs. Handbook of
Macroeconomics 1, 1051–1135.
38
Table 1: Simulated Moments Estimation
Panel A: Moments
Data
Description
Average output growth
Average risk-free rate
Relative investment volatility (σ∆i {σ∆c )
Relative R&D volatility (σ∆s {σ∆c )
Consumption growth volatility (∆c)
Elasticity of number of firms w.r.t output
Elasticity of markup w.r.t the number of
firms
Simulated moments
2.20%
1.00%
4.38
3.44
1.4
0.119
-0.372
ζk
ζz
Panel B: Parameter estimates
a‹
0.676
(0.025)
0.668
(0.013)
0.377
(0.094)
2.20%
1.11%
3.04
2.84
1.48
0.148
-0.307
β
ν2
0.988
(0.001)
8.740
(0.163)
This table reports the results of the SMM estimation. Structural parameters are estimated by matching simulated
moments from the model to the corresponding empirical moments. Panel A reports the empirical targets and corresponding simulated moments. Panel B reports the estimated structural parameters, standard errors are reported
in parenthesis. ζk and ζz captures the curvature of the capital and R&D capital adjustment cost function. a‹ is the
unconditional mean of technology process at . β is the subjective discount factor. ν2 is the price elasticity within
industries.
39
Table 2: Aggregate Moments
Data
Benchmark
No-Entry
A. Macro moments
E[∆c]
2.20%
2.20%
2.20%
σ∆c {σ∆y
σ∆i {σ∆c
σ∆s {σ∆c
σ[∆c]
σ[l]
0.64
4.38
3.44
1.40%
1.52%
0.43
3.04
2.84
1.48%
1.98%
0.70
3.04
2.84
1.48%
0.83%
B. Asset pricing moments
E[rf ]
E[rd ´ rf ]
E[pd]
1.00%
7.74%
3.50%
1.11%
3.02%
2.45%
1.11%
1.52%
2.55%
σ[rf ]
σ[rd ´ rf ]
σ[pd]
1.49%
16.44%
0.42%
1.02%
4.70%
0.06%
0.21%
2.17%
0.06%
This table reports macroeconomic and asset pricing moments from the data (column 1), the benchmark model
(column 2), and the No-Entry model (column 3). The No-Entry model is obtained after recalibrating ζk , ζz , β,
a‹ , and σ to match the relative investment volatility, the relative R&D volatility, the mean risk free-rate, and
the first and second moments of realized consumption growth of the benchmark model. Reported model moments
are averaged across 100 simulations that are equivalent in length to the data sample. Growth rate moments are
annualized percentage. Moments for log-hours (l) are reported in percentage of total time endowment. The risk
premiums are levered following Boldrin, Christiano, and Fisher (2001).
40
Table 3: Industry Moments
Data
Benchmark
0.30
0.30
B. Standard deviations
σ[ϕ]
σ[∆tf p]
σ[∆z]
σ[N E]
2.43%
1.72%
2.25%
0.06
1.62%
2.54%
2.27%
0.09
C. Autocorrelations
AC1[ϕ]
AC1[∆tf p]
AC1[∆z]
AC1[N E]
0.918
0.166
0.868
0.779
0.988
0.211
0.872
0.697
D. Correlations
corr[ϕ, N E]
corr[ϕ, Y ]
corr[N, Y ]
-0.196
-0.184
0.250
-0.164
-0.333
0.465
A. Means
E[ϕ]
This table presents the means, standard deviations, autocorrelations, for key macroeconomic variables from the
data and the benchmark model. The growth rate of technology (∆z), and measured technology growth (∆tf p) are
annualized. Correlation coefficients are obtained after HP-filtering both series with a smoothing parameter of 1,600
(6.25) when the data frequency is quarterly (annual). Reported model moments are averaged across 100 simulations
that are equivalent in length to the data sample.
41
Table 4: Consumption Volatility Dynamics
Data
Benchmark
A. Summary statistics
E[V olt,t`4 ]
1.46%
σ[V olt,t`4 ]
1.00%
AC1[V olt,t`4 ] 0.27
1.31%
0.39%
0.16
B. Forecasts with price-dividend ratio
β
S.E.
R2
-0.416
0.094
0.174
-0.280
0.109
0.099
C. Forecasts with markups
β
S.E.
R2
0.202
0.100
0.041
0.236
0.113
0.082
D. Forecasts with number of firms
β
S.E.
R2
-0.275
0.159
0.075
-0.170
0.117
0.049
This table presents summary statistics (Panel A) and forecasting regressions (Panels B to D) for realized consumption growth volatility from the data and the model. Forecasting regressions are obtained as follows:
V olt`1,t`5 “ α ` βxt ` t`1 , where xt corresponds to the Price-Dividend Ratio (Panel B), the price markup
(Panel C), and the number of firms (panel D), respectively. The series for realized consumption growth volatility
is computed following Bansal, Kiku, and Yaron (2012). First, consumption growth is fitted to an AR(1) process:
∆ct “ β0 ` β1 ∆ct´1 ` ut . Next, the annual realized volatility is computed by summing the absolute value of
ř4´1
residuals, i.e. V olt,t`4 “ j“0 |ut`j |. All variables have been normalized. Reported model moments are averaged
across 100 simulations that are equivalent in length to the data sample.
42
Table 5: Stock Return Predictability with the Price-Dividend Ratio
1
Horizon (in years)
2
3
4
5
Panel A. Short-sample
β pnq (Data)
S.E. (Data)
R2 (Data)
-0.107
0.042
0.073
-0.187
0.075
0.125
-0.234
0.089
0.151
-0.275
0.093
0.177
-0.360
0.093
0.254
β pnq (Benchmark) -0.123
S.E. (Benchmark) 0.041
R2 (Benchmark) 0.039
-0.240
0.075
0.076
-0.353
0.105
0.111
-0.457
0.131
0.144
-0.557
0.156
0.175
Panel B. Long-sample
β pnq (Benchmark)
R2 (Benchmark)
-0.071
0.022
-0.140
0.044
-0.205
0.064
-0.268
0.083
-0.327
0.100
β pnq (No-Entry)
R2 (No-Entry)
0.007
0.001
0.014
0.002
0.020
0.003
0.026
0.003
0.032
0.004
This table reports excess stock return forecasts for horizons of one to five years using the log-price-dividend ratio:
pnq
ex
´ yt “ αn ` β logpPt {Dt q ` t`1 . Panel A presents the forecasting regressions from the data and the
rt,t`n
benchmark model in the short sample. The empirical data sample is 1948-2015. Reported model moments are
averaged across 100 simulations that are equivalent in length to the data sample. Panel B presents population forecasting regressions for the Benchmark model and the No-Entry model. The forecasting regressions use overlapping
quarterly data. The risk premiums are levered following Boldrin, Christiano, and Fisher (2001).
43
44
1.277
0.700
0.053
0.057
-0.026
0.017
0.080
0.023
-0.060
0.027
0.020
0.069
-0.092
0.035
0.012
0.141
2.301
1.399
0.096
0.113
3
-0.110
0.046
0.017
0.184
2.884
1.649
0.090
0.173
4
-0.115
0.059
0.042
0.166
3.760
2.032
0.072
0.185
-0.011
0.003
0.001
0.065
0.405
0.146
0.009
0.035
Horizon (in years)
5
1
pnq
-0.025
0.005
0.001
0.158
0.795
0.263
0.006
0.069
2
-0.039
0.007
0.001
0.256
1.159
0.367
0.005
0.100
3
Model
-0.051
0.009
0.001
0.341
1.506
0.462
0.005
0.131
4
-0.062
0.010
0.001
0.398
1.837
0.551
0.005
0.159
5
ex
This table reports excess stock return forecasts for horizons of one to five years, i.e. rt,t`n
´ yt “ αn ` β xt ` t`1 , where xt is the predicting variable.
The different panels present forecasting regressions using different predicting variables: the aggregate price markup (panel A), and the the aggregate number
of firms (panel B). The forecasting regressions use overlapping quarterly data for panel A and annual data for panel B. The estimated coefficients β pnq are
corrected for the Stambaugh (1986) bias. Standard errors, S.E., are corrected for heteroscedasticity using Newey-West with k ` 1 lags. The one-sided p-value
is obtained by block-bootstrapping with replacement over 10,000 samples and computing the empirical probability of obtaining, under the null, a coefficient
that is of the same sign and as large as the data estimates. The data sample is 1948-2015. Model moments are averaged across 100 simulations that are
equivalent in length to the data sample. The risk premiums are levered following Boldrin, Christiano, and Fisher (2001).
β pnq
S.E.
p-value
R2
2
1.571
1.092
0.112
0.100
B. Number of firms
β pnq
S.E.
p-value
R2
A. Markup
1
Data
Table 6: Stock Return Predictability
Table 7: Sensitivity analysis
Panel A: Consumption heteroskedasticity
σ[V olt,t`4 ]
ν2 “ 10
ν2 “ 8.74
ν2 “ 7
0.30%
0.39%
0.60%
Panel B: Return predictability
Log PD Ratio (horizon in years)
1
2
3
4
5
1
Markup (horizon in years)
2
3
4
5
Case I: ν1 “ 1.17, ν2 “ 10.00
β pnq
R2
-0.058
0.019
-0.113
0.037
-0.166
0.054
-0.216
0.070
-0.263
0.086
0.200
0.019
0.390
0.036
0.566
0.052
0.730
0.066
0.884
0.081
0.749
0.060
0.969
0.077
1.175
0.094
1.144
0.064
1.482
0.083
1.800
0.100
Case II: ν1 “ 1.17, ν2 “ 8.74
β pnq
R2
-0.071
0.022
-0.140
0.044
-0.205
0.064
-0.268
0.083
-0.327
0.100
0.264
0.022
0.515
0.041
Case III: ν1 “ 1.17, ν2 “ 7.00
β pnq
R2
-0.094
0.025
-0.186
0.049
-0.274
0.072
-0.357
0.094
-0.436
0.115
0.402
0.023
0.785
0.044
Panel C: ν1 “ 8.74 ą ν2 “ 4.50
Log PD Ratio (horizon in years)
1
2
3
4
5
β pnq
R2
-0.158
0.016
-0.317
0.032
-0.468
0.047
-0.611
0.062
1
-0.738
0.075
-1.665
0.015
Markup (horizon in years)
2
3
4
-3.242
0.028
-4.720
0.041
-6.121
0.053
5
-7.451
0.065
This table reports comparative statics for different values of ν2 . Panel A reports the standard deviation of realized
consumption growth volatility, σ[V olt,t`4 ]. Panel B reports population excess stock return forecasts for horizons of
pnq
ex
one to five years, i.e. rt,t`n
´ yt “ αn ` β xt ` t`1 , where xt is the predicting variables for the log price-dividend
ratio (left column of panel B), and the aggregate price markup (right column of panel B). Panel C reports excess
stock return forecasts for a calibration where ν1 ą ν2 for the log price-dividend ratio (left column of panel C), and
the aggregate price markup (right column of panel C). The forecasting regressions use overlapping quarterly data.
The risk premiums are levered following Boldrin, Christiano, and Fisher (2001).
45
Table 8: Growth Forecasts
1
Data
Benchmark
2
Horizon (in years)
1
2
3
3
No-Entry
1
2
3
A. Output forecasts with R&D intensity
β
0.024 0.053 0.082
S.E. 0.010 0.019 0.026
R2
0.076 0.149 0.216
0.136 0.228 0.303
0.046 0.092 0.139
0.203 0.213 0.215
0.094 0.150 0.198
0.032 0.063 0.093
0.175 0.178 0.181
B. Output forecasts with intangible capital
β
0.403 0.769 1.137
S.E. 0.125 0.262 0.384
R2
0.132 0.177 0.245
0.592 0.985 1.309
0.198 0.396 0.595
0.205 0.214 0.217
0.491 0.843 1.144
0.224 0.438 0.630
0.138 0.157 0.164
C. Total Factor Productivity forecasts with R&D intensity
β
0.012 0.028 0.044
S.E. 0.007 0.012 0.018
R2
0.037 0.095 0.148
0.172 0.299 0.402
0.036 0.076 0.119
0.348 0.341 0.323
0.088 0.131 0.164
0.039 0.078 0.113
0.123 0.125 0.130
D. Total Factor Productivity forecasts with intangible capital
β
0.294 0.518 0.766
S.E. 0.102 0.174 0.232
R2
0.137 0.206 0.289
0.744 1.292 1.735
0.154 0.325 0.510
0.352 0.344 0.325
0.422 0.681 0.890
0.277 0.536 0.762
0.094 0.110 0.118
This table presents output growth and total factor productivity growth forecasts for horizons of one, two, and three
řn
years using R&D intensity and the growth in the stock of technology. The n-year regressions, j“1 ∆xt`j´1,t`j “
řn
α ` βpst ´ zt q ` t`1 and j“1 ∆xt`j´1,t`j “ α ` β∆zt ` t`1 , are estimated via OLS with Newey-West standard
errors with k ` 1 lags and overlapping annual observations. The data sample is 1953-2015 for st ´ zt , and 1949-2014
for ∆zt . Reported model moments are averaged across 100 simulations that are equivalent in length to the data
sample.
46
Table 9: Cross-sectional asset pricing moments
High
Model
Low
H-L
0.156
2.91%
0.856
0.282
0.70%
0.294
High
Data
Low
H-L
0.489
9.29%
1.633
0.202
7.22%
1.400
0.287
2.07%
0.233
1.361
0.811
0.028
1.868
0.040
Panel A: Moments
E[Markup] 0.438
E[rd ´ rf ] 3.61%
βCAPM
1.150
Panel B: Predictibility regressions with EP
β
S.E.
R2
0.744
0.298
0.069
-0.179
0.364
0.013
0.923
0.056
3.230
1.110
0.068
This table reports key statistics for the multi-industry version of the model along with their empirical moments,
conditional on the level of industry markups. Model moments are obtained by simulating a two-industry version
of the model with heterogenous entry cost shocks. At each point in time, we sort firms depending on the level of
industry markup. We discard observations in the lowest tercile of the difference in markup across industries. We
then compute the moments conditional on this classification. The empirical moments are obtained by sorting firms
into terciles based on the average industry markup. Panel A reports a series of asset pricing moments. E[rd ´ rf ]
is the average annual excess return, and βCAP M is the annual conditional CAPM β for portfolios sorted on lagged
measure of competition. Panel B reports the results for one-year excess stock returns predictive regressions using
pnq
ex
lagged Earnings-Price ratio, i.e. rt`1,t`4
´ yt “ α ` β EPt ` t`1 . Reported model moments are averaged across
100 simulations that are equivalent in length to the data sample. Standard errors for regressions are corrected for
heteroscedasticity.
47
Figure 1: Equilibrium markup relation
∂markup/∂N
markup
1.6
Low ν 2
-0.2
1.5
Benchmark
High ν 2
-0.4
1.4
-0.6
1.3
-0.8
1.2
-1
1.1
-1.2
N
N
This figure plots the relationship between the level of price markup and the number of firms (left), and the first
derivative of the price markup with respect to the number of firms (right) for three values of ν2 . The Low and High
ν2 cases are obtained by setting ν2 to 6 and 20, respectively.
Figure 2: Term structure of equity returns
Expected returns
6
12
Benchmark
No-Entry
4.5
8.5
3
5
1.5
1.5
0
0
5
10
15
-2
20
This figure compares the term structure of equity returns in the Benchmark model and in the No-Entry model. All
values on the y-axis are annualized percentage.
48
Figure 3: Responses conditional on competition
a
1.8
High N
Low N
1.6
v
1.6
1.4
1.4
1.2
1.2
1
1
0.02
0.01
0.8
10
20
30
40
markup
0.2
0
10
0.5
-0.2
0.4
-0.4
0.3
-0.6
20
30
40
E[ ∆tfp]
0.6
0
20
quarters
30
40
10
20
30
40
30
40
E[ ∆c]
1.5
1
0.5
0.2
10
N
0.03
0
10
20
quarters
30
40
10
20
quarters
This figure compares the impulse response functions to a positive technology shock, conditional on the number of
firms in the economy, Nt , for the exogenous technology process (a), the firm value (v), the number of firms (N), the
price markup (markup), expected total factor productivity growth (E[∆tf p]), and expected consumption growth
(Er∆cs). The High N (Low N ) case corresponds to the average responses accross 250 draws in the highest (lowest)
quintile sorted on Nt . The data for the sorting is obtained by simulating the economy for 50 periods prior to the
realization of the positive technology shock. All values on the y-axis are percentage deviation from the steady state.
Growth rates variables are annualized.
49
Figure 4: Product and Process Innovation
a
2
v
1.5
Benchmark
No-Entry
N
0.02
1
1.5
0.01
0.5
1
0
10
20
30
40
markup
0
0
10
20
30
40
σ [rd - rf]
0.01
10
0
-0.01
-0.05
30
40
30
40
30
40
E[r d - rf]
0.05
0
20
-0.2
-0.4
-0.02
10
20
30
40
E[ ∆s]
0.6
-0.1
10
0.4
0.2
0.2
30
40
E[ ∆tfp]
0.6
0.4
20
10
20
E[ ∆c]
1
0.5
0
0
10
20
quarters
30
40
0
10
20
quarters
30
40
10
20
quarters
This figure compares the impulse response functions to a positive productivity shock in the Benchmark model
(dashed line), and the No-Entry model (solid line) for the exogenous technology process (a), the firm value (v), the
number of firms (N), the price markup (markup), the conditional volatility of the risk premium (σrrd ´ rf s), the
conditional risk premium (Errd ´ rf s), expected R&D growth (Er∆ss), expected total factor productivity growth
(E[∆tf p]), and expected consumption growth (Er∆cs). The No-Entry model is obtained after recalibrating ζk , ζz ,
β, a‹ , and σ to match the relative investment volatility, the relative R&D volatility, the mean risk free-rate, and
the first and second moments of realized consumption growth of the benchmark model. All values on the y-axis are
percentage deviation from the steady state. Growth rates and asset prices variables are annualized.
50