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Firm dynamics in news-driven business cycles: the roleof endogenous survival rateHaichao Fana & Zhiwei Xub

a School of International Business Administration, Shanghai University of Finance andEconomics, Shanghai, Chinab Antai College of Economics and Management, Shanghai Jiao Tong University, Shanghai,ChinaPublished online: 20 Feb 2014.

To cite this article: Haichao Fan & Zhiwei Xu (2014) Firm dynamics in news-driven business cycles: the role of endogenoussurvival rate, Applied Economics, 46:15, 1767-1777, DOI: 10.1080/00036846.2014.884701

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Firm dynamics in news-driven

business cycles: the role of

endogenous survival rate

Haichao Fana,* and Zhiwei Xub

aSchool of International Business Administration, Shanghai University ofFinance and Economics, Shanghai, ChinabAntai College of Economics and Management, Shanghai Jiao Tong University,Shanghai, China

Evidences from the structural vector-error correction model shows that the newbusiness formation and stock prices co-moves with output under news shocks.However, simply incorporating firm dynamics into Jaimovich and Rebelo’s(Jaimovich and Rebelo, 2009) model cannot explain these empirical findings.We show that this problem can be resolved by introducing endogenous survivalrates for the new entrants.

Keywords: firm dynamics; aggregate co-movement; expectation-drivenbusiness cycle; news shocks

JEL Classification: E22; E32

I. Introduction

Recent empirical studies (Beaudry and Portier, 2006;Beaudry and Lucke, 2010) have found that expectationsmay be an important source of macroeconomic fluctua-tions. One natural question is whether the anticipativereactions made by forward-looking agents generatedynamic movements that resemble the business cycles.Beaudry and Portier (2006) show that it is difficult forstandard real business cycle (RBC) models to producebusiness cycle co-movements under news shocks. Wang(2012) illustrates that this difficulty can be easily under-stood from a labour market perspective.1 In standard RBCmodels without any real frictions, a positive future totalfactor productivity (TFP) shock will increase future

income and therefore induce forward-looking householdsto raise their current consumptions. The income effectmay also increase households’ leisure or reduce theirlabour supply. As a result, equilibrium labour decreases,causing output fall as well because the capital stock ispredetermined. Consequently, positive news about futureTFP results in opposing movement in output andconsumption.

More recently, Jaimovich and Rebelo (2009) estab-lished a full-fledged but concise RBC model withseveral real rigidities. Their model produces a positiveco-movement of aggregate variables in response to thenews shocks about TFP and investment-specific technol-ogy (IST), thus explaining the expectation-driven businesscycle (EDBC) particularly well.2 Three distinctive

*Corresponding author. E-mail: fan.haichao@mail.shufe.edu.cn1 In a standard RBCmodel, the labour demand curve denotes the relationship between wage and labour demand determined by the firm’soptimal decisions. The shape of the curve thus depends on the form of the production function, while the labour supply curve reflects therelationship between wage and labour supply derived from a household’s optimal labour decision. The shape of the curve is thus mainlyaffected by the utility function.2Other papers also generate an EDBC, for example, Den Hann and Kaltenbrunner (2009), Gunn and Johri (2011), Schmitt-Grohe andUribe (2012) and Karnizova (2010), among others.

Applied Economics, 2014Vol. 46, No. 15, 1767–1777, http://dx.doi.org/10.1080/00036846.2014.884701

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features in Jaimovich–Rebelo’s model play key roles: autility function that yields little income effect on leisure, adynamic adjustment cost in investment and a variablecapacity utilization. With a special form of utility, theirmodel implies that a change in income does not affect thelabour supply curve, and hence it alleviates the problem ofnegative co-movement between consumption and laboursupply. The dynamic adjustment cost smooths the invest-ment decisions intertemporally: the current investmentalso increases in response to an anticipated future increasein investment. Variable capacity utilization allows firms toraise the intensity of capital usage in response to a declinein the relative price of investment. A higher capital utiliza-tion rate further increases the marginal product of labourand hence induces a higher labour supply. Consequently,the business cycle co-movement can be generated.Though Jaimovich and Rebelo (2009) are successful inexplaining EDBCs, their model does not consider firmdynamics. As the literature documents,3 the net entry inthe US economy is strongly procyclical and accounts for alarge fraction of employment variation. This finding sug-gests that firm dynamics should be considered an impor-tant aspect in EDBC modelling as well.

In this article, we first extend Beaudry and Lucke’s(2010) empirical exercise by adding the new businessformation (NF) into their baseline system. We find firmentry positively co-moves with output under favourablenews about future TFP and that the pattern is statisticallysignificant. To account for our empirical findings, we thenincorporate endogenous firm dynamics into Jaimovich–Rebelo’s model. However, simply incorporating firmentry decisions into their model cannot explain our empiri-cal findings: the economy experiences a recession insteadof a boom under a favourable future TFP shock. Themodel can no longer produce an EDBC because theadvances in future technology make producing today rela-tively less profitable than producing in the future. Giventhis expectation, potential firms have an incentive to waitand enter the market at a later date. As a result, the totalnumber of incumbents in the current period decreases dueto a sharp fall-off in the entry rate. As the demand forlabour and capital decreases, the representative house-hold’s income level decreases correspondingly. Thereduction in income causes further declines in consump-tion. Eventually, the economy is trapped into a recession.The key reason for the failure to generate an EDBC (undergood news about future TFP) is that the survival rate ofnew entrants is assumed to be constant.4 As there is nomarginal cost for a large change in the number of firms that

enter the market, NF in the model is extremely volatile. Inlight of this logic, we endogenize the survival rate as adecreasing function of the entry mass. With this smallmodification, the Jaimovich–Rebelo model augmentedby an endogenous firm entry is able to explain the positiveco-movement of output, consumption, investment, hoursworked, asset price and firm entry mass. The decreasingsurvival rate, which resembles the adjustment cost, pre-vents a significant increase in the number of new entrantsand thus leads to relatively little competition from newentrants after the news shock is realized and, in turn, ahigher value for each operating firm. To take advantage ofthis profitable opportunity, more forward-looking firmswill enter the market immediately when expecting a posi-tive economic future. As a result, both asset price and firmmass increase when good news about TFP hits theeconomy.

However, the situation changes slightly when a favour-able future IST shock hits the economy. The impulseresponses show that the model with an exogenous survi-val rate can still produce the business-cycle co-move-ments among output, consumption, total investment,hours worked and firm entry mass. The explanation isas follows. Distinct from the TFP case, good news aboutfuture IST decreases the future relative price of invest-ment in units of consumption. Because of the investmentadjustment cost, the marginal value of installed capitaldeclines in the current period in accordance with thedecline in the future price of investment.5 This furtherinduces firms to increase investments and raise theircapacity utilization.6 As a result, hours worked, outputand consumption all increase. Moreover, higher aggre-gate demand attracts more firms to enter the economy.However, because the survival rate of new entrants isconstant, the free-entry condition implies the firm value(or stock price (SP)) is always constant along the busi-ness cycle, which is definitely inconsistent with theempirical finding. Therefore, to mimic the positive co-movement between SPs and output, endogenous survivalrate is still necessary when studying the effect of newsshock about future IST.

The remainder of the article is organized as follows.Section II presents a structural VECM analysis on a four-variable system to investigate firm dynamics under newsshocks. In Section III, a model is constructed with firmentry based on Jaimovich and Rebelo (2009). Section IVdescribes the model’s dynamics in an environment with orwithout endogenous survival rate of the entrants. SectionV concludes the article.

3 See Jaimovich and Floetotto (2008) and Wang and Wen (2011), among others.4 To the best of our knowledge, the literature often assumes the failure rate of new entrants is constant or zero, for example, Jaimovich(2007)and Bilbiie, Ghironi and Melitz (2008).5 This is because the marginal value of installed capital becomes persistent when there is the investment adjustment cost.6A favourable future neutral TFP shock would have little effect on the current relative price of investment.

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II. Empirical Evidence from US Data

We now investigate the dynamic effects of news shockson firm entry by analysing the US macroeconomic data.The variables of interest are TFP, which describes theexogenous process of technology7; SP,which containsthe information about the future; real GDP (Y), whichcaptures the macroeconomic condition; and NF, whichrepresents the number of firms that enter the market. Allof the variables are transformed into per-capita variablesusing the total US population count between the ages of16 to 64. The last three series are presented in logs.Data are quarterly, running from 1955Q1 to 2009Q4.The “Appendix” section provides further details of ourdata.

To identify the news shock, we employ the Beaudry–Lucke identification strategy. We first arrange the orderof structural shocks such that the first is a surprise tech-nology shock, the second is a news shock about TFP andthe last two are short-run shocks (e.g. demand shocks).The econometric model we use is a four-variablestructural vector error correction model (SVECM).Specifically, as in Beaudry and Lucke (2010), we con-sider an environment where a four-dimensional vector ofXt (ordered as ½TSP; SP; Y; NF� is integrated of orderone,8 and can be represented as a vector autoregressive(VAR) p rocess of order p < 1. Allowing for r0 < 4cointegration vectors, the error-correction representationof the process Xt takes the form

ΔXt ¼ ab0Xt�1 þ

Xp�1

j¼1

ΓjΔXt�j þ ut (1)

where a and b are 4� r0 matrices of loading coefficients

and cointegrating vectors, respectively; the Γj

� �p�1

jare

4� 4 coefficient matrices; and ut are the nonorthogonalerror terms. Our exercise aims to identify a vector oforthogonal/structural shocks, εt satisfying ut ¼ Bεt whereB is a nonsingular impact matrix. In particular, we assumethe ordering in the vector εt is TFP shock, news shockabout TFP and two short-run shocks. By applying theGranger representation theorem, process (1) can beexpressed as (see Lütkepohl (2005))

Xt ¼ X 0 þX1j¼1

ΞjBεt�j þ LXt�1

j¼1

εj þ Bεt (2)

where X 0 is a vector of initial conditions, the matricesΞj

� �1jare absolutely summable ðlimj!1 Ξj ¼ 0Þ, L is the

long-run multiplier matrix of the structural shocks εt and Bis the corresponding short-run impact matrix.

To jointly identify matrices L and B we must imposesix restrictions on their elements. Specifically, we assumethat the news shock (the second shock in εt) has noimpact on today’s TFP but can affect today’s SP. Thatis, the (1,2) element in the B matrix is zero.9 Regardingtwo short-run shocks (the third and fourth shocks in εt),we assume that they are independent of the exogenousTFP process and have no long-run effects on TFP. Thisassumption means the (1,3) and (1,4) elements in both Band L are set at zero. Finally, to distinguish two short-runshocks, we force the (3,4) element in B to be zero. Withthese aforementioned six restrictions, all of the structuralshocks are fully identified. To summarize, the impactmatrix B and the long-run matrix L can be shown expli-citly as

B ¼� 0 0 0� � � �� � � 0� � � �

2664

3775; L ¼

� � 0 0� � � �� � � �� � � �

2664

3775 (3)

To study the dynamic responses to the new shocks, wefirst estimate a SVECM for the four-variable system(TFP, SP, Y, NF). We use three criteria to determine theappropriate lag length. Specifically, the AkaikeInformation Criterion and the Final Prediction ErrorCriterion suggest four lags in levels, that is, p ¼ 3 inthe representation (1), while the Schwarz Criterion sug-gests three lags in levels. Therefore, we estimate thesystem with four lags in levels.10

We now turn to the cointegration properties. As shownin Table 1, the Johansen trace test significantly rejects onecointegration relationships ðr0 ¼ 1Þ at the 5% level andmarginally rejects two cointegration relationshipsðr0 ¼ 2Þ at the 5% level. Since in our SVECM there isonly one explicit trend for the TFP series, a naturalassumption on cointegration rank is three, that is, rejectingtwo cointegration relationships in the Johansen test.Taking this into account, as in Beaudry and Portier(2006), we conservatively choose three cointegration rela-tionships instead of two. Our results are robust to the valueof the cointegration rank.

Figure 1 presents the responses of TFP, SPs, output andNF to a one-SD of positive news shock. The top left panelshows that under a positive news shock, TFP initially

7 Ideally, the IST series should also be added to the system to identify news shocks about IST. However, as there is no such variable (likeTFP) that can capture the exogenous changes in IST, we only study the news about TFP.8 The ADF test shows that all of four series are Ið1Þ processes.9As the news shock has the ability to predict the TFP in the long run, the (1,2) element in the long-run matrix L is not necessarily zero.10We also estimate the system with three lags in levels for the robustness check. The main results in our article change little.

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decreases and after approximately 1.5 years, it reversesand gradually increases. The dynamics of TFP share simi-lar patterns to those found in Beaudry and Lucke (2010),thus suggesting that our SVECM system, despite thevariables being considered, contains as much informationas does the Beaudry–Lucke system to recover the newsabout TFP. Moreover, other panels in Fig. 1 show thatthere are statistically significant positive effects of a newsshock about future TFP on output, SP and NF.Furthermore, the responses of these three variables presenta similar hump shape. In particular, they increase in thefirst five quarters and gradually decrease thereafter, finallytending to flatten out 15 quarters later. Overall, thedynamics of output and SP, as in Beaudry and Lucke(2010), highly co-move with the news shock about futureTFP. The novel finding in our exercise is that the firm entryappears to demonstrate a similar pattern of co-movement.

Intuitively, the phenomenon in which positive newsinduces more new business incorporations is mainly dueto the potential firms’ expectation that their firm value willincrease in the future due to the higher level of productiv-ity. This point is well reflected by the significant co-move-ment relationship between firm entry and SP. In the next

section, we incorporate the firm dynamics into theJaimovich–Rebelo model and provide the theoreticalrationale for our previous empirical findings.

III. The Model

Consider a closed economy, which is characterized by arepresentative household, a representative firm producingfinal goods and a continuum of differentiated monopolis-tically competitive intermediate firms. The mass of inter-mediate firms is endogenously determined by their entryand exit decisions.

Final goods firms

The final goods firms maximize their period-by-periodprofit with the technology constraint, which is a CESaggregation of a continuum of intermediate goods indexedby i:

Yt ¼ðNt

0yit� �σ

di

� �1=σ

(4)

5 10 15 20 25 30 35 40–0.01

–0.005

0

0.005

0.01TFP

5 10 15 20 25 30 35 400

0.02

0.04

0.06

0.08

0.1Stock Price

5 10 15 20 25 30 35 400

0.002

0.004

0.006

0.008

0.01Output

5 10 15 20 25 30 35 40

–0.02

–0.01

0

0.01

0.02

New Firms

Fig. 1. Responses to news shock in the four-variable SVECM systemNotes: The figure shows percentage responses (0.01 corresponds to 1%). The horizontal axes indicate quarters. In each panel, the bluesolid line represents the impulse response. The red dashed lines are 95% bootstrapped confidence interval computed (200 replications) byHall’s percentile interval. All the estimations are conducted in the software JMulTi.

Table 1. Results in Johansen trace test

Cointegration rank: r0 0 1 2 3

p-Value 0.0000 0.0194 0.0503 0.2610

Notes: Four lags (in levels) and one intercept are included. The test is implemented in JMulTi.

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where yit is the production of the intermediate firm i, Nt isthe mass of the intermediate firms and σ 2 ð0; 1Þ governsthe elasticity of substitution across intermediate goods.

The final goods producers’ profit maximization yields

yit ¼ pit� � 1

σ�1Yt (5)

and the price index function is

Pt ¼ðNt

0pit� � σ

σ�1di

� �σ�1σ

(6)

where pit is the optimal price set by the intermediate firmi and Pt denotes the aggregate price index hereafter nor-malized to one.

Incumbent intermediate firms

We first consider a typical incumbent firm. Each inter-mediate good, yit, is produced by the firm i using theefficient capital, uitk

it , and the labour, lit , with the

Cobb–Douglas production function:

yit ¼ AtðuitkitÞαðlitÞ1�α (7)

where At denotes the aggregate technology and uit is avariable rate of capital utilization. The rate of capitalutilization determines the intensity of the use of capi-tal, which affect the rate of capital depreciation. We letδ uit� �

represent the rate of capital depreciation andassume that depreciation is convex to the rate of uti-lization: δ0ð�Þ > 0, δ00ð�Þ > 0. The total cost to produceyit can be obtained by

min rtuitk

it þ wtl

it

s:t:At uitk

it

� �αlit� �1�α � yit (8)

where rt represents the rental rents per unit of efficientcapital, wt is the real wage and let f

it be the marginal cost.

We then have the following:

rt ¼ αfit

yituitk

it

;wt ¼ 1� αð Þfit

yitlit

(9)

Using the aforementioned two equations, we can derivethat in a symmetric equilibrium the marginal cost fi

t is

fit ¼

1

At

wt

1� α

� 1�α rtα

� α(10)

Each intermediate firm i maximizes its static period oper-ating profits:

πit ¼ pit � fit

� �yit (11)

The previous expression yields that optimal price andprofit at each period are

pit ¼ fit=σ; π

it ¼ ð1� σÞpityit (12)

Because the intermediate firms’ technology is symmetricwith respect to all inputs, we focus hereafter on the sym-metric equilibrium: uit ¼ ut, kit ¼ kt, lit ¼ lt, yit ¼ yt,

rit ¼ rt, fit ¼ ft and πit ¼ πt. The representative house-

hold provides labour, Lt and capital, Kt, to firms forproduction activities. In a symmetric equilibrium, theresource constraint on the labour and capital marketsimplies Lt ¼ Ntlt and Kt ¼ Ntkt. The aggregate price

index from Equation 6 implies pt ¼ N1�σσ

t . Also, the tech-

nology of producing the final goods implies yt ¼ N1�σσ

t yt.Finally, the aggregate final output, the equilibrium rentalrate and wage, and the intermediate firm’s operating profitare given by

yt ¼ AtN1σ�1t ðutKtÞαL1�α

t (13)

wt ¼ 1� αð Þσ YtLt

(14)

rt ¼ ασYtutKt

(15)

πt ¼ ð1� σÞYt=Nt (16)

Potential entrants

In order to enter the market, the potential entrants have topay fe units of final goods as the cost of entry. We assumethat a start-up becomes a functioning new firm, acting as aproduct monopoly with an endogenous probability qt. Theempirical literature provides fruitful evidence that thesurvival rate of new entries is negatively correlated withthe level of industrial density. Mata and Portugal (1994)investigate the Portuguese manufacturing data and find thenew firm failure varies positively with the extent of entryinto the industry; Audretsch, et al. (2000) find a similarpattern using the Netherlands entry data; Hannan et al.(1995), using Belgium, France, Germany and Italy data,find that during the mature stage of the industry the survi-val rate is negatively affected by the density of entry due to

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the competition effect. Taking this correlation intoaccount, we assume qt is a decreasing function of theentry rate nt

Nt�1

11:

qt ¼ qnt

Nt�1

� �(17)

where nt denotes the mass of potential entrants and the

elasticity of qt at steady state,q0 nNq , is in ½�1; 0� This

specification is a generalized version of that used inBeaudry et al. (2011). They assume that nt start-ups com-pete to secure the εtNt�1 (εt is an exogenous shock) newmonopoly positions. This is to say, the survival rate qt hasa form of εtNt�1

nt. The exogenous εt is assumed to be an

increasing function of the entry rate: g ntNt�1

� ; with

0 � g0 nNg � 1: The increasing feature of gð:Þ indicates that

the more start-ups there are, the more vacancies will be

generated. This is equivalent toq0nNq 2 �1; 0�:

Each incumbent firm faces a natural death rate δN . Thus,only a proportion 1� δN of existing firms will survive intothe next period. We also assume that the period-t entrantsproduce in the current period, that is, there is no time-to-build.12 Therefore, the law of motion for the total massimplies

Nt ¼ ð1� δN ÞNt�1 þ qtnt (18)

Finally, the free-entry condition implies that the potentialfirms are willing to enter as long as the expected value forthe start-up is higher than the cost of entry. Therefore, inthe equilibrium, we have

fe ¼ qtVt (19)

where Vt denotes the present discounted value ofexpected profits for the incumbent firm, which corre-sponds to the SP in the real world. Note that the free-entry condition is crucial to understand the dynamics ofSP Vtð Þ. With an exogenous survival rate (qt is a con-stant), the SP does not respond to any exogenous shocks.Therefore, in order to capture the cyclicity in SP asobserved from the SVECM exercise, it is necessary toendogenize the survival rate qt.

Households

The household side is similar to what is presented inJaimovich and Rebelo (2009). The representative

household has preferences over random stream of con-sumption Ct and labour Lt with the following lifetimeutility function:

E0

X1t¼0

βtCt � ψLθt Xt

� �1���1

1� �(20)

where

Xt ¼ Cγt X

1�γt�1 (21)

We assume that 0 < β < 1, θ > 1, ψ > 0, and � > 0The presence of Xt means that preferences is nontime-separable in consumption and labour. When γ ¼ 1 weobtain KPR preferences, and when γ ¼ 0, we obtainthe GHH preferences. In each period, the representa-tive household maximizes its utility (20) subject to thefollowing sequence of constraints:

Ct þ It=Zt þðNt

0Vts

itdi �wtLt þ rtutKt

þðNt

0πts

itdiþ ð1� δN Þ

ðNt�1

0Vts

it�1di

(22)

Ktþ1 ¼ 1� δtð ÞKt þ 1� ’ItIt�1

� �� �It (23)

where sit denotes the share of firm i purchased by thehousehold in period t; Zt is the IST shock. An increasein Zt reflects technological progress in IST. As in

Jaimovich and Rebelo (2009), ’0 It

It�1

� It is the adjustment

cost in investment such that ’ð1Þ ¼ 0, ’0ð1Þ ¼ 0and ’00ð1Þ > 0. The first-order conditions forfC;X ; L; u; I ;K; Sg are

λt ¼ ðCt � ψLθt XtÞ�� þ μtγCγ�1t X 1�γ

t�1 (24)

μt ¼ βEt ð1� γÞμtþ1Cγtþ1X

�γt

�� Ct � ψLθt Xt

� ���ðψLθt Þ(25)

λtwt ¼ ðCt � ψLθt XtÞ��ψXtθLθ�1t (26)

11Assuming qt is a decreasing function of either ntNt�1

, ntNt

or nt does not affect our final results. This is because Nt is a stock variable that isless volatile than nt , and thus dynamics of qt is mainly driven by nt.12 The time-to-build assumption does not matter in model’s dynamics, except for the response of the total mass Nt at the first period.

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λtrt ¼ ηtδ0t (27)

λt=Zt ¼ ηt 1� fItIt�1

� �� f

0 ItIt�1

� �ItIt�1

�

þ βEt ηtþ1f0 Itþ1

It

� �Itþ1

It

� �2" # (28)

ηt ¼ βEt ηtþ1ð1� δtþ1Þ þ λtþ1rtþ1utþ1

�(29)

Vt ¼ πt þ β 1� δNð ÞEtλtþ1

λtVtþ1

� �(30)

where μt, λt and ηt are the Lagrangian multipliers asso-ciated with Equations 21, 22 and 23, respectively. Finally,the market clearing condition implies

Ct þ lt=Zt þ ntfe ¼ Yt (31)

Note that, as in Jaimovich and Rebelo (2009), the value ofinstalled capital in units of consumption can be defined asηt=λt From Equation 28, ηt=λt is mainly determined by theIST shock Zt and the investment dynamics. Equation 27implies that the optimal capacity utilization is decreasingin the value of installed capital.

IV. Exogenous Versus Endogenous SurvivalRate

We now analyse how the model economy responds to anews shock about future TFP or ISTwhen the survival rateis either constant or endogenous. As in Jaimovich andRebelo (2009), the timing of the news shock that weconsider is as follows. At time zero, the economy is in asteady state. At time one, the unanticipated news arrives.Agents learn that there will be a 1% permanent increase inAt (or Zt) beginning four periods later, in period five.

Table 2 presents the values assigned to the calibratedparameters. For those parameters also present inJaimovich–Rebelo model, we simply use the same values.In particular, the time unit corresponds to one quarter. Thediscount factor, β, is calibrated at 0.985, which implies asteady state annual real interest rate of 6%. The value ofintertemporal elasticity of substitution, �, is set as 1 corre-sponding to the logarithmic utility. The value of is γ set to0.01 such that the preference is close to GHH specifica-tion. The value of θ chosen to be 1.4 implies that the

elasticity of the labour supply is 2.5 when the preferencetakes the GHH form. On the production side, the share ofcapital α is set to 0.36, as commonly used in the literature.The steady state capital depreciation rate δk is calibrated at0.025, which corresponds to the 10% annual depreciationrate found in the data. We choose the second derivative ofthe adjustment-cost functions evaluated at the steady state,’00, to equal 1.3. For the elasticity δ00ðuÞu=δ0ðuÞ evaluatedin the steady state, we set it to 0.15. For those parametersabsent in the Jaimovich–Rebelo model, we set σ at 1=1:2,implying that the steady state mark-up is 20%. The naturaldeath rate of firms, δN is set at 0.025, which implies a 10%annual rate of exogenous exit in our model. This assump-tion is consistent with the empirical result that the annualjob destruction rate in the United States is approximately10%. The survival rate for new entrants at steady state, q,is set to be 1� δN . In order to make the start-ups not toomany, we set the initial fixed cost, fe, at 0.12.

13 Finally,

we set the elasticity of the survival rate at steady state,q0 nNq ,

to be –0.5. Our robustness check shows the results holdover a wide range.

Before discussing the impulse responses, we brieflydiscuss the dynamics in the labour market under differentnews shocks. Consider an extreme case where γ ¼ 0, Xt isconstant, and the utility function becomes the GHH pre-ference.14 Equations 24 and 26 imply

wt ¼ ψθLθ�1t (32)

Table 2. Calibrated parameters

Parameter Value Description

β 0.985 Subjective discount factorξ 1 Intertemporal elasticity of substitutionθ 1.4 Corresponds to an elasticity of labour

supply of 3.3 when preferences takethe GHH form

γ 0.01 The extent of nontime-separablepreference in consumption andlabour 0 for GHH preference, 1 forKPR preference

’00 1.3 Second derivative of investmentadjustment cost function

δ00ðuÞu=δ0ðuÞ 0.15 Elasticity of δ0ðuÞ at steady stateΑ 0.36 Capital share in productionΣ 1/1.2 Corresponds to 20% mark-upδk 0.025 Steady-state depreciation rate of capitalδN 0.025 Corresponds to 10% annual rate of

exogenous exitfe 0.12 Fixed entry costq0 nNq −0.5 Elasticity of survival rate at steady state

13 It is easy to show that the steady state share of the initial entry cost in output equals to δN ð1�σÞq1�βð1�δN Þ . And according to our calibration, this

share equals 10.25%. However, the value of fe has no effect on our results regarding impulse responses.14 There exists income effect when γ > 0. The range of the value of γ is set to maintain the co-movement among the aggregate variables.

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The last equation implies that a change in consumptionwould not affect the labour supply curve, that is, there isno income effect. Thus, from Equations 13 and 14, wehave

wt ¼ AtN1σ�1t utKtð ÞαL�α

t (33)

which implies that the labour demand curve would only beaffected by the change in total firm mass Nt and capacityutilization ut. Remember that ut largely depends on themarginal value of installed capital ηt=λt as shown inEquation 27. A favourable future TFP shock, comparedto the IST shock, would not significantly change the valueof ηt=λt, and thus the change in ut is relatively small. Inthis case, the firm mass Nt dominates the shift of labourdemand curve. Therefore, whether the model can mimicthe EDBC hinges on the dynamics of the firm mass Nt,

15

while a news shock about future IST would significantlychange the marginal value of installed capital and thus thecapacity utilization ut. In this case, the capacity utilizationut dominates the shift of labour demand curve, and accord-ingly, it is the key variable to generate the EDBC.

Figures 2 and 3 depict the responses under a good newsshock about TFP or IST with exogenous survival rates.The responses in Fig. 2 clearly illustrate the failure of the

Jaimovich–Rebelo model with a constant survival rate fornew entrants in generating positive co-movement under afavourable future TFP shock. In this case, the aggregatevariables, including output, consumption, total invest-ment,16 hours worked and entry numbers, all decline inthe impact period. Therefore, good news leads the econ-omy into a recession, which is contrary to the empiricalfindings. The failure to generate an EDBC in this case ismainly due to the constant survival rate, which imposes noextra cost for a large shift in the number of firms enteringthe market; therefore, the potential firms have an incentiveto enter the economy at the news-realized period.According to the previous analysis on the labour market,the decline in total firm mass causes the model to fail togenerate an EDBC. As shown in Fig. 2, the entry numberdecreases sharply in the first period, which induces lessdemand in labour and capital and thus reduces totalincome. As a result, consumption goes down, and thusthe economy is trapped in a recession because theJaimovich–Rebelo specifications (variable capacity utili-zation, investment adjustment, preference with lowerincome effect) cause the other aggregate variables to posi-tively co-move with consumption. In addition, accordingto the free entry condition, the asset price Vtð Þ in this caseis constant, which is highly inconsistent with the empiricalfindings. Figure 3 reports the responses under a favourable

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1

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6

7Output (Y)

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0

1

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4Consumption (C)

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0

5

10

15Total Investment

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–2

–1

0

1

2

3

4

5Hours Worked (H)

2 4 6 8 10–10

–5

0

5

10

15

20

25

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35Entry Number (n)

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–0.5

0

0.5

1Asset Price (V)

2 4 6 8 100

0.2

0.4

0.6

0.8

1

1.2

1.4News Shock

Fig. 2. Impulse responses to TFP news shock with exogenous survival rateNotes: The figure shows theoretical percentage responses to a favourable news shock about TFP (defined in the last panel). The horizontalaxes indicate quarters.

15More specifically, in a model with an endogenous survival rate, Nt increases in the impact period corresponding to good news aboutTFP, causing other aggregate variables to increase. Therefore, in this case, the EDBC can be explained.16 The total investment consists of the physical capital It/Zt and the entry cost ntfe:

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future ISTshock. As evidenced, the positive co-movementamong output, consumption, investment, hours workedand firm entry mass can be successfully generated eventhough survival rate is constant. Themain reason for this isthat, distinct from the neutral TFP shock, the IST shockwould change the relative price of investment. Thedynamic adjustment cost implies that the reduction in thefuture investment goods prices would reduce the currentinvestment goods price as well. As a result, the capacityutilization increases accordingly, which further raises thehours worked and the total output. Furthermore, house-holds will spend more in consumption because of thehigher income level, and in turn higher demand attractsmore firms to enter the economy. However, according tothe free-entry condition, the asset price Vtð Þ in this case isagain constant, which is inconsistent with the empiricalfinding from the SVECM exercise. To explain our empiri-cal finding from the SVECM, the survival rate is assumedto be endogenous rather than exogenous. With this mod-ification, the Jaimovich–Rebelo model is able to explainthe business cycle co-movements under news shocksregarding future TFP and IST.

Figure 4 shows the dynamic responses under afavourable future TFP shock when survival rate qt isan endogenous function of nt=Nt. Output, consumption,total investment, hours worked and entry number allincrease in response to the news about future TFP.17

In particular, the path of the entry number in this casebecomes much smoother because the endogenous sur-vival rate induces an extra cost for new entrants in the

high-entry rate period. As a result, fewer potential firmsdesire to enter the market at the news-realized period.The reduced competition effect of new entrantsenhances the future profit of production, as shown inEquation 16, and thus raises the asset price of function-ing firms. Under this premise, more start-ups will beestablished by entrepreneurs before the news is realized.Meanwhile, the expansion of firm entry induces higherdemands for labour and capital and therefore increasesthe representative household income. Consequently,the aggregate economy experiences a boom in responseto the news shock. The robustness check indicatesthat keeping other parameters unchanged, the aforemen-

tioned results hold in a wide range ofq0 nNq , namely,

½�1;�0:12� With respect to a favourable future ISTshock, introducing an endogenous survival rate causesan increase in the asset price increase during the impactperiod. Therefore, together with the co-movement ofother aggregate variables, the EDBC, in this case, canbe well explained, as shown in Fig. 5.

V. Conclusions

In the literature, firm dynamics are believed to be animportant mechanism for understanding business cycles,though their role in explaining EDBC remains unknown.By incorporating an endogenous firm entry problem intoJaimovich and Rebelo’s (2009) well-established model,

2 4 6 8 100.5

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1.5

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2.5

3Output (Y)

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0.6

0.8

1

1.2

1.4

1.6Consumption (C)

2 4 6 8 101

2

3

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6Total Investment

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0.5

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2Hours Worked (H)

2 4 6 8 107

8

9

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12Entry Number (n)

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0

0.5

1Asset Price (V)

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0

0.2

0.4

0.6

0.8

1

1.2News Shock

Fig. 3. Impulse responses to IST news shock with exogenous survival rateNotes: The figure shows theoretical percentage responses to a favourable news shock about IST (defined in the last panel). The horizontalaxes indicate quarters.

17As the mass of new functioning firms qtnt is monotonic increasing in the entry number nt, the dynamics of these two variables havesimilar patterns. To save space, we only discuss the entry number.

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we find it generates a recession rather than a boom inresponse to a favourable future TFP shock. This is mainlybecause there is no cost for large movement of firmentry, and thus, when the good news affects the economy,potential firms optimally choose to enter the industry at thenews-realized period. As to a favourable future IST shock,positive co-movement among output, consumption,

investment, hours worked and firm entry still could begenerated in the extended Jaimovich–Rebelo modelwith exogenous survival rates. However, the assetprice is constant, which is sharply inconsistent with theempirical finding. After endogenizing the survival rateof new entry firms, the impulses of main macroeco-nomic variables are smoothed, and hence, the extended

2 4 6 8 100.5

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1.5

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2.5

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4Output (Y)

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7Total Investment

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0.5

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3Hours Worked (H)

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6.5Entry Number (n)

2 4 6 8 101

1.5

2

2.5

3

3.5Asset Price (V)

2 4 6 8 10–0.2

0

0.2

0.4

0.6

0.8

1

1.2News Shock

Fig. 4. Impulse responses to TFP news shock with endogenous survival rateNotes: The figure shows theoretical percentage responses to a favourable news shock about TFP (defined in the last panel). The horizontalaxes indicate quarters.

2 4 6 8 100.2

0.4

0.6

0.8

1

1.2Output (Y)

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0.55

0.6

0.65

0.7

0.75

0.8

0.85Consumption (C)

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0.5

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3.5Total Investment

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0.2

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0.8Hours Worked (H)

2 4 6 8 101.5

1.6

1.7

1.8

1.9

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2.1

2.2Entry Number (n)

2 4 6 8 100.75

0.8

0.85

0.9

0.95

1

1.05

1.1Asset Price (V)

2 4 6 8 10–0.5

0

0.5

1

1.5News Shock

Fig. 5. Impulse responses to IST news shock with endogenous survival rateNotes: The figure shows theoretical percentage responses to a favourable news shock about IST (defined in the last panel). The horizontalaxes indicate quarters.

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Jaimovich–Rebelo model can generate positive co-movement of the main macroeconomic indicators,including output, consumption, investment, labour,entry mass and asset price.

Acknowledgement

We thank anonymous referees for their insightful com-ments that substantially improved the quality of this article.

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Appendix: Data

All of the data used in SVECM analysis are quarterlyfrequency from 1955Q1–2009Q4.

(1) TFP: total factor productivity, adjusted by capitalutilization, downloaded from John Fernald’s web-site: www.frbsf.org/economics/economists/staff.php?jfernald.

(2) SP: real stock price, downloaded from RobertShiller’s website: www.econ.yale.edu/~shiller/data.htm

(3) Y: real GDP series, obtained from St. Louis FEDeconomic database.

(4) NF: the number of new business incorporations isreported by the US Bureau of Economic Analysis

(BEA). The data can be downloaded from thewebsite: www.bls.gov/bdm/. Because the seriesis discontinued (up to 1994Q4) as a result of areprogramming of resources at BEA, we extend itto 2009Q4 using the US Bureau of LaborStatistics (BLS)’s establishment birth and deathdata. To check the robustness of the series, weconduct the dynamic responses exercise by run-ning the data up to 1994Q4; the impulse responsespresent similar patterns as those from the fullsample.

The SP, Y, NF series are transformed in per capita terms bydividing them by the population of age 15 to 64.

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