Can …rm entry explain news-driven ‡uctuations? Oscar Pavlov School of Economics and Finance Queensland University of Technology Australia October 23, 2015

Abstract Most models subjected to news shocks fail to re-produce the basic aggregate comovement facts. This paper proposes that …rm entry can be a channel for the real business cycle model to generate quantitatively realistic expectations-driven ‡uctuations. Endogenous variation in products supports aggregate comovement in response to contemporaneous shocks and news about future technology. This occurs easily even if, as argued by recent empirical studies, markups are procyclical. The model matches the key second moments of U.S. business cycles. The …ndings highlight the importance of future work on the implications of news-driven …rm entry and its interaction with markups for optimal policy. Keywords: Firm entry, markups, expectations-driven business cycles, news-shocks, variety e¤ects. JEL Classi…cation: E32.

School of Economics and Finance, Queensland University of Technology, GPO Box 2434, Brisbane QLD 4001, Australia. E-mail address: [email protected]. Ph:+61 7 3138 2740. Fax:+61 7 3138 1500.

1

1

Introduction

As argued by a recent and fast growing line of research, …rm entry and product creation have an important role in the propagation of economic ‡uctuations. From solving comovement problems in international business cycles (Cavallari, 2013a), to explaining the behavior of pro…ts and markups (Colciago and Etro, 2010; Cavallari, 2013b; Bilbiie et al., 2012), entry models have addressed many important puzzles in the literature. These …ndings are aptly supported by empirical work such as that by Broda and Weinstein (2010) who highlight the procyclical behavior of entry and product creation.1 Yet, there is another role of entry that has not been su¢ ciently addressed in the extant literature: its ability to explain news-driven business cycles. The role of news as a driver of aggregate ‡uctuations has also seen much attention in recent years. Once agents become optimistic about future economic conditions, the news shock story proposes that they will increase consumption and investment, causing an economic boom today. If expectations about the future turn out to be correct, the economy expands further; if news turn out to be false, then the economy contracts, hence resulting in a boom-bust cycle. Empirical evidence by Beaudry and Portier (2006) and Schmitt-Grohé and Uribe (2012) suggests that these anticipated shocks explain about half of U.S. business cycles.2 Unfortunately, most models fail to re-produce the positive comovement between consumption and investment in the absence of changes to fundamentals. Consequently, this paper provides further support for the importance of …rm entry by presenting a 1

Other recent studies include Floetotto and Jaimovich (2008), Lewis (2009) and Bernard et al. (2010). 2 See Lorenzoni (2011) and Beaudry and Portier (2014) for an overview of this growing literature. News shocks have been identi…ed in other economies. For example, Kamber et al. (2014) identify news shocks for Australia, Canada, New Zealand and the United Kingdom.

2

model where entry and exit can overcome this comovement puzzle and generate realistic second moments in response to news about future technology. In a standard one-sector real business cycle (RBC) model, equilibrium in the labor market implies that the wealth e¤ect arising from positive news leads to an inward shift of the upwardly sloping labor supply curve. Since the capital stock is predetermined and current fundamentals are unchanged, the downwardly sloping labor demand curve remains constant. Therefore, there is a comovement puzzle: consumption and leisure increase, while investment and aggregate output contract. The current paper demonstrates that the comovement problem can be solved via endogenous …rm entry determined by a condition of zero pro…ts each period.3 This entry can be more generally interpreted as product creation by new and existing …rms. The variety e¤ect (also known as taste for variety or increasing returns to specialization) implies that the procyclical entry of products brings aggregate e¢ ciency gains and acts as a labor demand shifter. With investment adjustment costs providing an incentive to invest immediately, …rm entry leads to an outward shift of the labor demand curve and to an expectations-driven boom.4 The second contribution of this paper is motivated by markup cyclicality and its interaction with entry. Despite Rotemberg and Woodford’s (1999) claim that markups are countercyclical, Nekarda and Ramey (2013) …nd the reverse: markups in the U.S. are procyclical or acyclical.5 Although not uncontroversial, their result nevertheless questions the plausibility of theo3

This assumption keeps the model tractable and allows for analytical derivations of the comovement conditions in Section 3. Following Ghironi and Melitz (2005), many recent studies assume forward looking …rms and sunk entry costs, which apart from being more realistic, also lead to procyclical pro…ts that the current frictionless entry model cannot deliver. 4 The taste for variety delivers an upwardly sloping equilibrium wage-hours locus and hence, comovement is related to the necessary condition for local indeterminacy in Benhabib and Farmer’s (1994) model. See also Eusepi (2009) and Guo et al. (2012). 5 Khan and Kim (2013) …nd evidence of procyclical markups in Canada.

3

ries that utilize countercyclical markups. For example, Pavlov and Weder (2013) demonstrate that because falling markups expand production possibilities, countercyclical markups can also solve the comovement issue described above. The current paper shows that in a model with …rm entry and (as in Galí, 1994) variable markups driven by changes in the composition of aggregate demand, comovement can arise easily even if markups are procyclical.6 This is possible because higher markups (despite their usual distortions that contract output) also induce …rm entry, which through the taste for variety leads to overall e¢ ciency gains. The Simulated Method of Moments is employed to estimate the two parameters important for consumption-investment comovement: the variety e¤ect and the markup elasticity. The model then performs well at matching the main empirical regularities of U.S. ‡uctuations when driven by contemporaneous and anticipated shocks to technology. Simulations further reveal that procyclical markups signi…cantly increase the volatility of entry. The results have implications for optimal policy as important studies addressing welfare and …rm entry like Bergin and Corsetti (2008), Lewis (2013) and Bilbiie et al. (2014) do not consider procyclical markups and only examine contemporaneous shocks. The current paper is the …rst to explicitly study endogenous entry with the taste for variety in the context of news-driven ‡uctuations. Other important work includes Beaudry et al. (2011) who consider news about new markets with exogenous growth of varieties. Fan and Xu (2014) show that the introduction of an endogenous survival rate of …rms in a version of 6

Galí’s (1994) model is ‡exible in the sense that it allows markups to be procyclical or countercyclical. While there are many other theories of variable markups, most only permit countercyclical markup variations with respect to aggregate output. For example, see Rotemberg and Woodford (1999).

4

Jaimovich and Rebelo’s (2009) model with entry and exit restores its ability to generate news-driven ‡uctuations. Finally, Chang et al. (2011) and Pavlov and Weder (2012) examine the conditions for local indeterminacy, while Devereux et al. (1996) assess the e¤ect of contemporaneous technology shocks. The paper is organized as follows. Section 2 outlines the model. Section 3 presents the conditions necessary to generate expectations-driven business cycles. The arti…cial economy is simulated in Section 4. Section 5 concludes.

2

Model

The economy is based on the model with an endogenously variable number of …rms as described by Devereux et al. (1996). There are three crucial di¤erences. First, the variety e¤ect in producing …nal goods is disentangled from the elasticity of substitution between di¤erent intermediate goods. Second, as in Galí (1994), markups can vary endogenously via the composition of aggregate demand. Finally, adjustment costs give an incentive to smooth investment intertemporally.

2.1

Firms

The perfectly competitive …nal goods sector produces the …nal consumption good, Ct ; and the …nal investment good, Xt ; according to the production technologies Ct = Nt1+

1 Nt

Z

Nt1+

1 Nt

Z

1=

Nt

yi;c;t di

0

0; 0 <

<1

0<

< 1:

and Xt =

0

1=

Nt

yi;x;t di

5

Here, yi;c;t (yi;x;t ) is the amount of the unique intermediate good i used in the production of the …nal consumption (investment) good and Nt is the number of intermediate good …rms - though an increase in Nt can also be interpreted as product creation within existing …rms. The functional form implies that the constant elasticities of substitution between intermediate goods are equal to 1=(1

) and 1=(1

). The bene…t to product variety is

governed by , which from now on will be referred to as the variety e¤ect or taste for variety. This formulation follows Benassy (1996): taste for variety does not depend on the elasticities of substitution and is thus independent of the level of market power.7 While the degree of substitutability between intermediate goods may be related to the taste for variety, there is no a priori reason for assuming that

= 1=

1 as in Devereux et al. (1996)

and others. An intermediate good producer i cannot price discriminate between consumption and investment demands and therefore charges the identical price pi;t for its good. From the pro…t maximization problem of the representative …nal consumption good …rm, the conditional demand for intermediate good i is yi;c;t =

1=(

pi;t Pc;t

1)

1

Nt

(1+ ) 1

Ct

with the price index 1

Pc;t = Nt

Z

Nt

( =(

pi;t

0

1)

di

1)=

:

The monopolist faces a similar demand from the …nal investment good …rm. Firm i hires capital, ki;t , and labor, hi;t , via perfectly competitive factor 7

Recent business cycle literature utilizing this formulation includes Bergin and Corsetti (2008) and Bilbiie et al. (2014). Also see the working paper version of Dixit and Stiglitz (1977).

6

markets and produces according to the production function yi;t = yi;c;t + yi;x;t = zt ki;t h1i;t where

0<

< 1;

>0

(1)

denotes …xed overhead costs. Aggregate technology, zt , a¤ects all

…rms equally and follows the process log zt = where

t

log zt

1

+

+

t

0

t l

< 1; l > 0

is the standard contemporaneous shock and

t l

is a news shock

observed and anticipated l periods in the past. Both are i.i.d. disturbances with variances

2

and

2.

Given the demand for its unique good, each mo-

nopolist sets the pro…t maximizing price such that the markup, 1 i;t

=

1 yi;c;t

+

1 yi;c;t

+

1

1 yi;x;t 1 yi;x;t

i;t ,

equals

:

The real wage earned for labor services and the rental rate on capital services satisfy wt = (1

)

pi;t yi;t + hi;t i;t

and

rt =

pi;t yi;t + : ki;t i;t

(2)

In a symmetric equilibrium, all monopolists produce an identical amount and charge the same price, pi;t = pt . The functional form of the …nal good production functions implies that the prices of the …nal goods are equal and setting them as the numeraire, Pc;t = Px;t = 1, results in pt = N t : Higher number of …rms and varieties therefore reduce the prices of …nal goods relative to that of intermediate goods. Each period, free entry and exit into the intermediate goods sector proceeds until each active …rm earns zero pro…t. Using (1) and (2) with the zero pro…t condition leads to yt = t

7

1

and to aggregate output zt N t

Yt =

t

Kt Ht1

(3)

where aggregate capital and hours are Kt = Nt kt and Ht = Nt ht . The e¢ ciency wedge, zt Nt = t ; is a positive function of technology and the number of …rms, and it is negatively related to the markup. The number of …rms moves positively with aggregate output and the markup: Nt =

Yt

1

t

1=(1+ )

:

(4)

The markup can be written as 1 t

1 1

= 1

where st

(1

(1

st ) + st ) +

1

1 1

1

st

st

(5)

1

Xt =Yt is the share of investment in aggregate output. If

=

the markup is constant and completely irrelevant for local dynamics due to the instantaneous entry and exit (see Kim, 2004). If

> ; intermediate

goods are more substitutable in the production of consumption goods and the markup is procyclical with respect to st . As demand for investment increases, the monopolist confronts a less elastic demand curve and this permits it to charge a higher markup. Setting the steady state markup, ; and its elasticity with respect to the investment share, " calibrates

and

indirectly. Since

> 1 and

;

(@ =@s)(s= ),

2 (0; 1); the markup

elasticity is constrained by 1

where s =

<" <

1

s 1

s

(6)

=( + ) is the steady state investment share. While " strictly

determines the markup’s relationship with st , it can be shown that the latter

8

comoves positively with Yt . That is, " > 0 (" < 0) also implies that the markup is procyclical (countercyclical) with respect to aggregate output.8 As can be seen from (4), higher markups lead to additional …rm entry. This link between entry and markups is an important distinction between the taste for variety and other forms of increasing returns to scale, such as productive externalities. The relationship between …rms and markups also di¤ers to what has been commonly assumed in other entry models. For example, strategic interactions in Floetotto and Jaimovich (2008) and demand-side pricing complementarities in Bilbiie et al. (2012) imply that there is a direct relationship between the number of …rms and the price elasticity of demand. While in monetary models, like Cavallari (2013b), markup variability is generated by sticky prices. In these studies, …rm entry leads to a fall in markups.

2.2

Agents

The representative agent chooses a sequence of consumption and hours worked to maximize lifetime utility: E0

1 X t=0

1 1+

t

ln Ct

Ht1+ 1+

!

> 0;

> 0;

0

where E0 denotes the expectation conditional on period 0 information; the discount rate, and

is

is the inverse of the Frisch labor supply elasticity.9

The agent owns all …rms and receives any pro…ts,

t;

that they potentially

generate. The budget is thus constrained by wt Ht + rt Kt + 8

t

Xt + Ct :

(7)

See the model simulations in Section 4 and Appendix B for details. This functional form of additively-separable preferences is compatible with balanced growth. A further advantage of this formulation is that it gives clear-cut analytical expressions for comovement as shown in Section 3. 9

9

The capital stock evolves according to the law of motion Kt+1 = (1 where

Xt Xt 1

)Kt + Xt 1

0<

<1

(8)

is the depreciation rate and the adjustment cost function follows 0 (1)

(1) =

= 0;

0:10 The …rst-order conditions from the agent’s

00 (1)

maximization problem are Ht Ct = wt t

1 = Ct where

1

t

t

Xt Xt 1

= Et Xt Xt 1

rt+1 + Ct+1 0

Xt Xt 1

(9)

t+1 (1

)

1 Et + 1+

(10)

t+1

Xt+1 Xt

2

Xt+1 Xt (11) 0

is the multiplier associated with (8). Equation (9) is the usual

labor supply equation, (10) is the intertemporal Euler equation and (11) governs optimal investment dynamics in the presence of adjustment costs.

3

Macroeconomic comovement

This section demonstrates that the model with …rm entry and su¢ ciently high taste for variety can generate the macroeconomic comovement necessary for expectations-driven business cycles. That is, as observed in the data, good news about a future change to fundamentals leads to a joint increase in consumption, investment and hours worked. Furthermore, the interaction between entry and markups allows this comovement to occur even if markups are procyclical (as argued by Nekarda and Ramey, 2013). To analytically show that consumption and investment can move together in the absence of changes to current technology, the static equilibrium 10

See Christiano et al. (2005).

10

equations are log-linearized.11 Then taking into account that news do not a¤ect current technology and that the capital stock is predetermined, some algebra yields the following expression: (1

)

C^t = (1

)(1 + ) +

+" ( (1

(1 +

)( (1 ( ) + )(1 + )

) + )(1 + ) 1) 1+ 1+" 1

^ t : (12) X

Here hatted variables denote percent deviations from the steady state. If there is no taste for variety ( = 0) and markups are constant (" = 0); ^ t is negative as in the standard RBC model and then the term in front of X news-driven ‡uctuations cannot arise. Good news leads to an increase in consumption via a positive wealth e¤ect and to an inward shift of the labor supply curve. Since the labor demand curve remains constant, hours worked and investment both decline. Clearly, this response is not the news-driven boom as identi…ed by Beaudry and Portier (2006) and others. Let us now consider the case of positive taste for variety ( > 0) and constant markups (" = 0): The variety e¤ect implies that …rm entry leads to an endogenous rise in the e¢ ciency wedge (an outward shift of the labor demand curve). The su¢ cient and necessary condition for positive consumptioninvestment comovement is12 >

( + )=(1

) > 0:

If the taste for variety is su¢ ciently high, despite an inward shift of the labor supply curve, …rm entry is able to raise hours and investment via its 11

These are: the symmetric equilibrium version of the real wage (2), equations (3), (4), (5), (9), the investment share st = Xt =Yt ; and the resource constraint Yt = Ct + Xt : See Appendix A. 12 Though not presented to preserve space, it can be shown that satisfying the comovement conditions also ensures positive consumption-hours comovement and an upwardly sloping wage-hours locus.

11

e¤ect on labor demand. Calibrating the standard parameters as = 0:025;

= 0:01,

= 0 (indivisible labor) implies that

= 0:3;

= 0:429. While

a variety e¤ect of this magnitude is unlikely to be empirically plausible, variable markups can bring the required value considerably lower. Next, let us consider the situation where there is no taste for variety ( = 0) but markups are variable (" 6= 0). The su¢ cient and necessary condition for positive comovement is " <"

( + ) < 0: ) + )(1 + )

( (1

Here, su¢ ciently variable countercyclical markups ("

< 0) can expand

the e¢ ciency wedge and generate news-driven business cycles. Procyclical markups on the other hand cannot generate comovement on their own as higher markups contract production possibilities. Finally, what happens if variety e¤ects and variable markups are both relevant? Substituting (4) into (3) yields the reduced form production function: Yt =

t

1

zt t

1+

Kt Ht1

:

Note that the …rst term in brackets becomes larger with a higher markup. This implies that higher markups can expand or contract the e¢ ciency wedge depending on the size of the taste for variety. This is due to the relationship between entry and markups: as …rms raise markups, the higher potential pro…ts encourage more …rms to enter.13 In (12), if " (1+ then the required

) > 0;

for positive comovement is lower. Therefore, procyclical

markups expand the e¢ ciency wedge if

>

1. The variety e¤ect is

su¢ ciently large such that the e¢ ciency gains from entry dominate the contractionary e¤ect of higher markups. In contrast, countercyclical markups 13

Similar to (12), it can be shown that positive comovement between …rms and markups always exists if " > 0:

12

make positive comovement less likely due to their negative e¤ect on entry. If

<

1, then …rm entry is not enough to o¤set higher markups that

contract production possibilities. In this case countercyclical markups make comovement more plausible. So far this paper has shown that …rm entry can solve the comovement puzzle, yet, a noticeable aspect about the presented conditions is that they are completely independent of investment adjustment costs. As explained in the next section, these prove to be important in generating the empirically supported direction of comovement.

4

Estimation and simulations

This section evaluates whether the news-driven ‡uctuations of the arti…cial economy are quantitatively realistic. To do this, the model described in the previous sections is extended by variable capital utilization. The reason for this is twofold. First, comovement becomes signi…cantly more plausible with respect to the size of the variety e¤ect, . Second, the utilization rate is used to adjust the innovations to technology measured via the model’s equilibrium conditions. Then the Simulated Method of Moments (SMM) is used to select parameters by minimizing the distance between the empirical and theoretical moments.14 Finally, the model’s second moments are compared to the Hodrick-Prescott …ltered U.S. quarterly time series counterparts (see Appendix D for the data sources).

4.1

Measuring technology shocks

In the extended model, the aggregate production function is Yt =

zt N t t

14

(Ut Kt ) Ht1

See Karnizova (2010) for a similar application of SMM.

13

where Ut stands for the utilization rate of capital set by its owners (see Appendix C for further details). The conventional de…nition of the Solow residual, SRt ; would thus imply SRt = Y^t

^t K

(1

^ t = z^t + N ^t + U ^t )H

^t:

The procyclical movement of …rms and the rate of utilization would give an upward bias to SRt as an estimator of zt ; while procyclical markups would ^t have the opposite e¤ect. Using the static equilibrium equations, ^ t and N are eliminated to yield15 z^t =

1 ^ Yt 1+

^t K

^t U

1

+"

(1 +

)( + (1 ))(1 + ) ( 1)(1 + )

^ t: H (13)

The above expression is used to estimate z^t from observable data. Before estimating the AR(1) process and the variance of innovations (

2+

2 ),

the

data (in natural logs) is linearly de-trended.

4.2

Simulated method of moments

As in Section 3, standard parameters are set as is common in the real business cycle literature:

= 0:3;

= 0:025;

= 0:01 and

= 0. Follow-

ing Jaimovich and Rebelo (2009), the adjustment cost parameter is set to 00 (1)

= 1:3. Beaudry and Portier (2006) identify anticipated shocks to to-

tal factor productivity via a vector autoregressive model and their variance decompositions indicate that news shocks explain roughly 50 percent of business cycle ‡uctuations. Schmitt-Grohé and Uribe (2012) use Bayesian and maximum likelihood methods to estimate the contribution of anticipated shocks and likewise …nd that these account for about half of the variance of the main macroeconomic aggregates. Guided by these results, the variances of the anticipated and standard technology shocks are set to 15

See Devereux et al. (1996) and Floetotto and Jaimovich (2008).

14

2

=

2

(i.e. 50 percent of the shocks are anticipated). The steady state markup is calibrated to

= 1:3; which lies in the middle of the estimates of U.S.

markups in value added data (see Floetotto and Jaimovich, 2008). As for its elasticity, two alternative calibrations are employed. First, the markup is restricted to be constant (" = 0). Second, in light of Nekarda and Ramey’s (2013) …ndings, the possibility of procyclical markups ("

0) is consid-

ered. Since there is no direct evidence on the size of this elasticity and also no straightforward way to pin down the magnitude of the variety e¤ect, ; these are then estimated by SMM. The standard deviation of aggregate output,

Y;

and the correlation of

consumption with investment, (C; X); provide information on the variety e¤ect and the markup elasticity. Recall that

and " determine whether

positive comovement and thus expectations-driven business cycles are possible. In particular, under constant or procyclical markups, consumption moves in the opposite direction to investment in response to news if the variety e¤ect is not su¢ ciently large. Thus, the vector of parameters estimated by SMM is M

[

Y;

[ ; " ] and the vector of targeted moments is

(C; X)].

For each parameter constellation, after obtaining the total variance of technology shocks,

2

+

2;

and the persistence parameter

via (13), the

model is simulated N S = 20 times for 276 periods (corresponding to the 1967:I-2010:IV period, T = 176; plus 100 initial periods that are later purged).16 This procedure is replicated 500 times. Each of the replications generates a vector of parameter values NST arg min S N T +1

^ 16

ME

! PS S 1 N M ( ) N S t=1 t

ME

!0 PS S 1 N M ( ) N S t=1 t

Because the values of 2 + 2 and obtained from the U.S. data depend on the parameters in (13), they are recalculated for each and " pair in the estimation process.

15

Table 1: Estimated and Implied Parameters Calibration Estimated Implied 2+ 2 " " =0 0:1349 0:4183 0:9678 (0:0078)

"

0

0:0625 (0:0003)

0:2063 (0:0046)

0:3788

0:9651

" and are directly estimated by SMM and together with the rest of the parameters imply values for 2 + 2 and . Standard deviations are in parentheses. 2 + 2 is reported in percent terms.

that minimizes the distance between the theoretical (simulated) moments, MtS ( ); and empirical moments, M E . Here,

is the variance-covariance

matrix of the empirical moments (see Appendix E). Finally,

and " are

calculated by taking the average across the replications. Table 1 presents the estimated and implied parameters based on anticipation periods l = 3.17 Note that only parameters in vector

have

been directly estimated by SMM, and that these determine the total variance of technology shocks,

2

+

2;

and the shock persistence parameter

.

The estimated variety e¤ect, which is critical for the positive consumptioninvestment comovement, is not too large to be implausible.

When the

markup is allowed to vary (last row of Table 1), SMM picks a procyclical markup that has a negative impact on the e¢ ciency wedge and this leads to a higher estimate of the variety e¤ect. Importantly, the estimates in both cases are consistent with realistic news-driven business cycles. This is illustrated next. 17

l = 3 provided a closer match to the empirical moments than l = 4.

16

4.3

Business cycle dynamics

Figure 1 plots the impulse response functions of the variable markup economy (" , ; and

from the last row of Table 1) to news arriving in period

t = 1 about a rise in technology, zt ; that will occur in t = 4:18 There are two situations: the expected rise in productivity is realized (news turn out to be correct) or unrealized (news turn out to be incorrect and there is no change to technology). Positive news about the future leads to positive comovement among all the main aggregates. The intuition for this is as follows. Upon receiving news about an increase to future technology, adjustment costs give an incentive to invest today. Since " > 0 ( > ); higher demand for investment induces monopolistic …rms to raise their markups. While higher markups reduce the demand for labor, higher potential pro…ts stimulate greater …rm entry, which through the variety e¤ect leads to an overall increase in the e¢ ciency wedge. The downwardly sloping labor demand curve thus shifts out and hours worked rise. This creates a positive wealth e¤ect that raises consumption and shifts the labor supply curve inward. It is the relatively ‡at dynamics of the interest rate, R; that allow the wealth e¤ect to dominate over the intertemporal substitution e¤ect and this is due to the negative impact of adjustment costs on the return to investment. If technology remains unchanged in t = 4; agents realize that they have overinvested, the expansion comes to a halt and economic activity declines back to the steady state. To test whether the model generates quantitatively realistic ‡uctuations, it is then simulated 1000 times for the two alternative calibrations. Table 2 compares the second moments to those from the U.S. economy. Theory suc18

The impulse response functions of the model with " = 0 are qualitatively identical and are omitted to conserve space.

17

Hours Worked (H) 0.2

0.3

0.15

% deviation

% deviation

Output (Y) 0.4

0.2 0.1

0.1 0.05

0 0

2

4

6

0

8

0

2

Consumption (C)

% deviation

0.05

8

6

8

6

8

0.6 0.4 0.2

0 0

2

4

6

0

8

0

2

4

Markup (µ)

Interest Rate (R) 0.2

0.05

0.1

0.04

% deviation

% deviation

6

0.8

0.1

0 -0.1 -0.2

0.03 0.02 0.01

0

2

4

6

0

8

0

2

Firms (N) 0.15

0.4

% deviation

0.1

0.3 0.2

0.05 0

0.1 0 0

4

Technology (z)

0.5

% deviation

8

1

0.15

-0.3

6

Investment (X)

0.2

% deviation

4

2

4

6

8

realized

-0.05

0

2

4

not realized

Figure 1: Response of the economy to news arriving at t = 1 and a realization/non-realization at t = 4:

18

Table 2: Business Cycle Dynamics Data Model, " = 0 Model, " 0 2.30 (1) 2.10 (1) 2.10 (1) Y 6.03 (2.63) 6.83 (3.26) 6.79 (3.23) X 0.90 (0.39) 1.07 (0.51) 1.08 (0.51) C 1.91 (0.83) 1.32 (0.63) 1.32 (0.63) H 3.81 (1.66) 4.88 (2.33) 4.84 (2.31) s 1.17 (0.51) 1.07 (0.51) 1.08 (0.51) Y =H 1.85 (0.88) 2.76 (1.31) N 0.30 (0.14) (C; X) 0.70 0.64 0.64 (X; Y ) 0.98 0.95 0.95 (C; Y ) 0.82 0.85 0.85 (H; Y ) 0.86 0.90 0.89 (s; Y ) 0.95 0.90 0.89 (Y =H; Y ) 0.56 0.85 0.85 (N; Y ) 1.00 0.98 ( ;Y ) 0.89 See Appendix D for the source of U.S. data. x and (x; Y ) denote the standard deviation of variable x and its contemporaneous correlation with Y . Relative standard deviations are in parentheses. Blank entries for and N are due to data unavailability.

19

cessfully mimics the ranking of cyclical volatilities in output, consumption, investment and hours. The contemporaneous correlations with output are also in line with their empirical counterparts. Consistent with the evidence, the number of …rms (or more generally, products) is also procyclical. Altogether, the statistics are very similar for the two calibrations. As expected from (4), procyclical markups raise the volatility of …rms. There are therefore implications for optimal policy as news shocks and procyclical markups may induce socially wasteful entry. Addressing such questions could be a fruitful avenue for future research. Tables 3 and 4 check the robustness of the results by considering full anticipation of shocks (

2

= 0), higher adjustment costs (from Christiano et

al., 2005), and a lower steady state markup. Expectations-driven business cycles exist under all three calibrations. When all shocks are anticipated, the parameters are less precisely estimated but the model is able to more accurately match the targeted moments. As expected, higher adjustment costs allow the model to better match the volatility of investment and its share in output, yet, the model performs slightly weaker in most other areas. In the case of the lower steady state markup, the moments are almost identical to those from Table 2. The only notable di¤erence being a slightly higher volatility of …rms.

5

Conclusion

Can …rm entry explain news-driven business cycles? The current paper takes important steps to address this question. While most models cannot reproduce the macroeconomic comovement necessary for expectations-driven ‡uctuations, a one-sector real business cycle model with endogenous entry and exit of …rms can overcome this shortcoming. Upon good news, the 20

Table 3: Robustness: Estimated and Implied Parameters Calibration Estimated Implied 2+ 2 " 2 =0 0:0580 0:2170 0:3872 0:9661 00 (1)

= 2:5

= 1:2

(0:0152)

(0:0173)

0:0627

0:2444

0:3997

0:9677

0:0446

0:1641

0:4012

0:9667

(0:0001)

(0:0006)

(0:0042)

(0:0043)

Baseline calibration: = 1:3, 00 (1) = 1:3, 2 = 2 , = 0:3, = 0:025, = 0:01, = 0. " and are directly estimated by SMM and together with the rest of the parameters imply values for 2 + 2 and . Standard deviations are in parentheses. 2 + 2 is reported in percent terms.

Table 4: Robustness: Business Data 2 =0 2.30 (1) 2.22 (1) Y 6.03 (2.63) 7.30 (3.28) X 0.90 (0.39) 1.07 (0.48) C 1.91 (0.83) 1.41 (0.64) H 3.81 (1.66) 5.20 (2.34) s 1.17 (0.51) 1.07 (0.48) Y =H 2.85 (1.28) N 0.30 (0.14) (C; X) 0.70 0.69 (X; Y ) 0.98 0.96 (C; Y ) 0.82 0.86 (H; Y ) 0.86 0.92 (s; Y ) 0.95 0.92 (Y =H; Y ) 0.56 0.86 (N; Y ) 0.99 ( ;Y ) 0.92

Cycle Dynamics Model 00 (1) = 2:5 = 1:2 1.84 (1) 2.10 (1) 5.36 (2.92) 6.81 (3.25) 1.17 (0.64) 1.07 (0.51) 1.02 (0.56) 1.32 (0.63) 3.76 (2.05) 4.86 (2.32) 1.17 (0.64) 1.07 (0.51) 2.20 (1.19) 2.85 (1.36) 0.24 (0.13) 0.22 (0.10) 0.57 0.64 0.91 0.95 0.86 0.85 0.80 0.90 0.80 0.90 0.86 0.85 0.98 0.98 0.80 0.90

x and (x; Y ) denote the standard deviation of variable x and its contemporaneous correlation with Y . Relative standard deviations are in parentheses. Blank entries for and N are due to data unavailability.

21

taste for variety implies that the entry of new …rms and products leads to e¢ ciency gains. This then leads to a joint increase in consumption, hours and investment in the absence of changes to current fundamentals. It is then shown that the model can generate realistic second moments in response to news about future technology. The secondary contribution relates to recent empirical …ndings of procyclical markups in the U.S. economy. Since higher markups induce greater …rm entry, quantitatively realistic news-driven business cycles arise easily even if markups are procyclical. The extent to which news and procyclical markups can lead to excessive (welfare reducing) entry is an unexplored area for further research. In particular, incorrect signals triggering a boom-bust cycle propagated by …rm and product creation suggests the development of new rules for optimal policy.

Acknowledgements I would like to thank Begoña Domínguez, Christoph Thoenissen, Mark Weder, the editor of this journal and two anonymous referees for extremely helpful comments.

Appendix A. Deriving the consumption-investment comovement condition Log-linearizing equations (2), (3), (4), (5), (9), st = Xt =Yt ; and Yt = Ct +Xt gives w ^t = Y^t

^t H

^t + K ^ t + (1 Y^t = z^t + N ^t = N

1 ^ 1 Yt + 1+ 1+ 22

^t )H 1

^t

^t

^ t = " s^t ^ t + C^t = w H ^t ^t s^t = X Y^t =

+ (1 +

Y^t

)^ Ct +

+

^t X

^ t = 0 (to re‡ect that news do not a¤ect current technolAfter setting z^t = K ogy and that capital is predetermined), the above equations are then used to solve for the comovement condition (12).

Appendix B. Comovement between the investment share and output This appendix demonstrates that the investment share positively comoves with aggregate output as long as the taste for variety, state markup,

; and the steady

; are not implausibly large. As in the previous appendix,

the linearized equilibrium equations can be used to obtain: ((1

s^t = (1

)(1 + ) + "

) + )(1 + ) (1 + )((1

) + )(1 + ) 1

Y^t :

Negative comovement occurs if the denominator is negative: if " > 0 and (1+

) < 0; or if " < 0 and (1+

case. Here a lower When

) > 0. Let us …rst consider the former

and higher " reduce the value of the denominator.

= 0; and " approaches its positive limit of

1

Section 2.1) the denominator can be written as 1

1

(1 + )

which under Section 4’s calibration is negative if

23

> 3:33:

(1

)+

(recall

Next, the case where " < 0 and (1 + its negative limit of (1 (1

) > 0: When " approaches

)= ; the denominator can be written as (1 +

)(1 + )

For this term to be negative,

)((1

) + )(1 + )

:

must be greater than 0:73.

Appendix C. Capital utilization Section 4’s model contains variable capital utilization. Here, each intermediate good …rm i operates the production technology 1 yi;t = zt (Ut ki;t ) hi;t

where Ut stands for the utilization rate of capital set by its owners. Capital accumulation follows Kt+1 = (1 t

=

1

t )Kt

+ Xt 1

Ut

Xt Xt 1

>1

and the optimal rate of utilization is rt = Ut Ct

1

t:

The steady state equations are used to derive the depreciation elasticity parameter:

= ( + )= = 1:4 (see Wen, 1998).

In the presence of adjustment costs, the current rate of utilization depends on past and (expected) future investment. As a result, the corresponding comovement condition to (12) can no longer be obtained from this version of the model. In the case where adjustment costs are zero, the minimum variety e¤ect required for comovement is

= 0:094 (down from 0.429

under constant utilization). Yet, it can be shown numerically that adjustment costs bring down the requirements for comovement even further. 24

Appendix D. Data sources This appendix details the source and construction of the U.S. data used in Section 4. All data is quarterly and for the period 1967:I-2010:IV. The capital stock, Kt ; was constructed by the perpetual inventory method, taking into account the variable depreciation rate. 1. Personal Consumption Expenditures, Nondurable Goods. Seasonally adjusted at annual rates, billions of dollars. Source: Bureau of Economic Analysis, NIPA Table 1.1.5. 2. Personal Consumption Expenditures, Services. Seasonally adjusted at annual rates, billions of dollars. Source: Bureau of Economic Analysis, NIPA Table 1.1.5. 3. Personal Consumption Expenditures, Durable Goods. Seasonally adjusted at annual rates, billions of dollars. Source: Bureau of Economic Analysis, NIPA Table 1.1.5. 4. Gross Private Domestic Investment. Seasonally adjusted at annual rates, billions of dollars. Source: Bureau of Economic Analysis, NIPA Table 1.1.5. 5. Gross Domestic Product. Seasonally adjusted at annual rates, billions of dollars. Source: Bureau of Economic Analysis, NIPA Table 1.1.5. 6. Gross Domestic Product. Seasonally adjusted at annual rates, billions of chained (2005) dollars. Source: Bureau of Economic Analysis, NIPA Table 1.1.6. 7.

Nonfarm Business Hours.

Index 2005=100, seasonally adjusted.

Source: Bureau of Labor Statistics, Series Id: PRS85006033. 8. Civilian Noninstitutional Population. 16 years and over, thousands. Source: Bureau of Labor Statistics, Series Id: LNU00000000Q.

25

9. GDP De‡ator = (5)=(6): 10. Real Per Capita Consumption, Ct = [(1) + (2)]=(9)=(8): 11. Real Per Capita Investment, Xt = [(3) + (4)]=(9)=(8): 12. Real Per Capita Output, Yt = (10) + (11): 13. Per Capita Hours Worked, Ht = (7)=(8): 14. Investment Share, st = (11)=(12): 15. Labor Productivity, Yt =Ht = (12)=(13): 16. Capital Utilization, Ut , total index, percentage, seasonally adjusted. Source: Board of Governors of the Federal Reserve System, G17/CAPUTL/CAPUTL.B50001.S.Q.

Appendix E. Weighting matrix The construction of the weighting matrix,

; is based on Karnizova (2010).

This matrix depends entirely on empirical data. First, the vector of empirical Hodrick-Prescott …ltered moments is de…ned as m ^ T = [var(Yt ); var(Ct ); var(Xt ); cov(Ct ; Xt )]0 where var(Yt ) = (1=T )

PT

2 t=1 Yt :

The variance-covariance matrix of these

empirical moments is then computed using the Newey-West estimator with a Bartlett kernel with four lags, p = 4; of the series mt = [Yt2 ; Ct2 ; Xt2 ; Ct Xt ]0 : The Newey-West estimator is calculated by ! ^=

0

+

p X

j p+1

1

j=1

where j

= (1=T )

T X

[mt

t=j+1

26

m ^ T ][mt

j

j

+

0 j

m ^ T ]0 :

Next, let a vector x consist of x1

var(Yt ); x2

var(Ct ); x3

var(Xt ); x4

cov(Ct ; Xt ):

The two moments targeted in the simulation are functions of these variances and covariances: Y

g2 (x) =

p p (C; X) = x4 = ( x2 x3 )

Then the weighting matrix is

=

p

g1 (x) =

x1

= [ G(x) ! ^

G(x)0 ]

1

where

G(x) is

the gradient of the function G(x) = [g1 (x); g2 (x)]0 :

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