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. :
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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 are 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.
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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
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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).
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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
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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)).
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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 .
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(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.
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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
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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.
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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: κq ` ηh,t , log pκh,t q “ log p¯ 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
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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-
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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 Zakrajˇsek (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 ˆ in order to minimize the distance between moments approach. This procedure chooses values for Θ a vector of identifying moments from the data and the corresponding moments generated from model simulations: ˆ “ argmin rm ˆ ´ mpΘqs1 W ´1 rm ˆ ´ mpΘqs , Θ
(33)
Θ
where W is a weighting matrix, m ˆ 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 ˆ is consistent for any positive-definite matrix, W , we follow the literature Although the estimator, Θ, 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 ˆ To estimate the covariance matrix of the moments, we use the the asymptotic variance of Θ. 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: ϕˆt “ ´0.004 ´ 0.70˚˚˚ n ˆ t ` 18.83˚˚˚ n ˆ 2t , where ϕˆt is log markups and n ˆ t is the detrended log number of firms. The slope coefficients on n ˆ t and n ˆ 2t 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 P˜i,j,t P˜j,t ˆ
Xi,j,t
where P˜i,j,t ”
Pi,j,t PY,t
and P˜j,t ”
“ Yt
(A.10) (A.11)
Pj,t PY,t .
The (real) source of funds constraint is Di,j,t “ P˜i,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 ,P˜i,j,t utě0 s“0 ´ ¯´ν2 ´ ¯ν2 ´ν1 s.t. Xi,j,t “ Yt P˜i,j,t P˜j,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 P˜i,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 P˜i,j,t P˜j,t
The corresponding first order necessary conditions are Rkt Rzt Wt Xi,j,t
Xi,j,t ˜ pPi,j,t ` Λdi,j,t q Ki,t Xi,j,t ˜ “ ηp1 ´ αq pPi,j,t ` Λdi,j,t q Zi,j,t Xi,j,t ˜ “ p1 ´ αq pPi,j,t ` Λdi,j,t q Li,j,t « ff ˜j,t B P ´ν ´1 ´ν ν ´ν ´1 ν ´ν d 2 2 2 1 2 1 “ Λi,j,t Yt ´ν2 P˜i,j,t Pj,t ` pν2 ´ ν1 qP˜i,j,t P˜j,t B P˜i,j,t
“ α
where Λdi,j,t is the Lagrange multiplier on the inverse demand function. Using the definition of the industry price index, B P˜j,t “ B P˜i,j,t
˜
P˜i,j,t P˜j,t
¸´ν2
Imposing the symmetry condition across industries implies that P˜j,t “ 1. In addition, the symmetry across firms ν2
1
ν2 ´1 ν2 ´1 within an industry implies that P˜i,j,t “ P˜t “ 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
˜
Λdj,t 1` P˜t ˜
¸
¸ Λdj,t Yj,t “ ηp1 ´ αq 1` Nj,t Zj,t P˜t ˜ ¸ Λdj,t Yj,t “ p1 ´ αq 1` Nj,t Lj,t P˜t “
‰ Λdj,t “ ´1 ´ν2 ` pν2 ´ ν1 qNj,t P˜t
34
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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.
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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).
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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.
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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
