Technological Change and Reallocation∗

Junghoon Lee†

September 14, 2017

Abstract

This paper considers a technological change that can be utilized only

by production units adapting to new technology. A simple firm dynam-

ics model is used to show how such an innovation enhances reallocation,

whereas a technological advance that is available to all production units

does not. This implication is used in structural vector autoregressions

to study the driving force behind cyclical movements in reallocation and

the rival/nonrival nature of technology. This paper finds that one sin-

gle shock explains most of the unpredictable movements in reallocation

over a three- to ten-year horizon and that this shock is closely related

to the investment-specific technology shock identified by long-run re-

strictions. The investment-specific technology shock also accounts for

more than 35 percent of hours forecast errors over a two- to ten-year

horizon. These findings imply that technology shocks responsible for a

large portion of economic fluctuations are the main driving force behind

cyclical variations in reallocation, confirming a rival or Schumpeterian

nature of technological progress.

∗I thank R. Anton Braun, Thorsten Drautzburg, Shigeru Fujita, Andre Kurmann, B.Ravikumar, Harald Uhlig, Tao Zha, and especially Steven J. Davis for their helpful commentsand suggestions. All remaining errors are my own.†Department of Economics, Emory University, 1602 Fishburne Drive, Atlanta, GA 30322,

USA. Email: junghoon.lee@emory.edu.

1

1 Introduction

This paper seeks to answer the following questions. What types of shocks

drive cyclical movements in reallocation? What do fluctuations in reallocation

tell us about the nature—rival or nonrival—of technological change?

Reallocation is a pervasive feature of market economies.1 Reallocation also

accounts for a large portion of productivity growth2 and the pace of realloca-

tion varies considerably over time.3 These facts have motivated many studies

to investigate the role of reallocation shocks.4

Whether technology is rival or nonrival has also received a lot of attention

in the literature (see Acemoglu, 2009). The standard Solow and neoclassical

growth models assume that technology is a nonrival good: once a new tech-

nology is developed, it can be used by any producer without precluding its

use by others. In contrast, the Schumpeterian growth models (e.g., Aghion

and Howitt, 1992) feature the rival nature of technology so that a technologi-

cal innovation can be utilized only by some producers that adapt to the new

knowledge.5

1For example, Davis and Haltiwanger (1999a) document that more than one in ten jobsis either created or destroyed every year in the U.S. Baldwin et al. (1993) show that entryand exit accounts for about 40 percent of job creation and destruction over a five-year span inthe U.S. and Canada manufacturing sectors between 1972 and 1982. Eisfeldt and Rampini(2006) report that the reallocation of existing capital of publicly traded firms comprisesabout one quarter of the U.S. total investment from 1971 to 2000.

2Foster et al. (2001), for example, find that over 50 percent of productivity growth inthe U.S. manufacturing sector between 1977 and 1987 is attributed to reallocation; entryand exit in turn account for half of this contribution.

3Davis and Haltiwanger (1999a) document that the job destruction rate ranges from 2.9percent to 10.8 percent per quarter, while the job creation rate ranges from 3.8 percent to10.2 percent for the U.S. manufacturing sector from 1947:I to 1993:IV.

4To name a few, Lilien (1982), Abraham and Katz (1986), and Blanchard and Diamond(1989) are early contributions to this large literature.

5Hence, like these different strands of the growth literature, I broadly interpret therival/nonrival nature of technology as including all factors affecting the ease of technologyadoption rather than the intrinsic nature of technology per se.

2

This paper addresses the two questions above jointly by finding a strong

link between technology shocks and reallocation shocks. By reallocation shocks,

I mean shocks that account for the most variation in reallocation. I show that

investment-specific technology shocks account for over 50 percent of all un-

predictable movements in reallocation over a four- to ten-year horizon. These

results hold for various reallocation measures over the period 1993-2014; i.e,

establishment turnover (entry plus exit) rates, job reallocation (creation plus

destruction) rates, and capital turnover rates. Hence, investment-specific tech-

nology shocks are the main driving force behind cyclical movements in reallo-

cation.

My findings also reveal the rival nature of investment-specific technology.

If new technology is nonrival and readily available, all production units can

avoid becoming obsolete and aggregate productivity can grow without the need

for restructuring. Technological progress entails incessant reallocation only

when new knowledge is rival, thereby involving the replacement of outdated

units by new ones. Hours worked rise gradually after an investment-specific

technology shock, which explains more than 35 percent of the unpredictable

variations in hours over a two- to ten-year horizon.6 Therefore, technology

shocks responsible for a large portion of aggregate fluctuations are rival and

disruptive, leading to increased reallocation.

In sum, this paper finds that technological progress fostering ongoing real-

location is a major driver of economic fluctuations. This finding confirms the

importance of Schumpeterian creative destruction for reallocation and macroe-

conomic fluctuations.

6These findings are consistent with the business cycle literature documenting investment-specific technological change as a major source of business cycle fluctuations (e.g., Green-wood et al., 2000; Fisher, 2006; Justiniano et al., 2010).

3

My analysis starts by constructing a simple firm dynamics model and

demonstrates the different impact of various types of technological change on

reallocation. The economy consists of plants and potential entrants. Plants

produce aggregate output with their plant-specific productivity and can exit

the market by selling off their capital. Potential entrants are those who possess

new technology and they can build new plants by purchasing capital goods.

There are four types of technology shocks. First, nonrival investment-neutral

technology shocks enhance the productivity of all plants. Second, nonrival

investment-specific technology shocks lower the price of capital goods traded

by all plants. Third, rival investment-neutral technology shocks increase the

average productivity level of new technology (e.g., new skills or organization)

that can be implemented by startups only. Finally, rival investment-specific

technology shocks improve the efficiency of new vintage capital. The second

and fourth types of shocks lower the quality-adjusted price of capital. The lat-

ter two types of technology are distinctive in that they can be taken advantage

of by entrants only and not by all production units.

All four types of shocks in this economy encourage entry and result in an

economic boom. However, only the third and fourth types—both of which are

rival technology shocks—increase exit as well. Only new plants become more

productive and the widened productivity gap between entrants and incumbents

makes old plants less valuable in production. In contrast, the other two types

of shocks do not encourage exit because they affect new and old plants equally.

I then consider a vector autoregression (VAR) that combines reallocation

variables with standard macroeconomic aggregates. I first identify a realloca-

tion shock as one that accounts for most of the forecast error variance (FEV) of

the reallocation rate over the business cycle horizon.7 This data-driven iden-

7This identification of the reallocation shock is different from previous works, which

4

tification quantitatively uncovers the most important shock for reallocation

but does not offer any economic interpretation. I then interpret this shock

by examining its impulse responses through the lens of the theoretical model.

The responses of entry/exit, job creation/destruction, and capital reallocation

to this reallocation shock are similar to what is seen in the rival technology

shock in my firm dynamics model.

The identified reallocation shock accounts for over 50 to 75 percent of all

unpredictable fluctuations in reallocation over a three- to ten-year horizon.

This shock persistently lowers the quality-adjusted price of capital goods. It is

then compared to the investment-specific technology shock identified by long-

run restrictions in the manner of Fisher (2006), which is the only shock to

have a long-run effect on the capital goods price. I find that these two shocks

are highly correlated with a correlation coefficient larger than 85 percent and

their estimated impulse responses are also very similar. This finding suggests

that the investment-specific technology shocks featured in the business cycle

literature are the main driving force behind cyclical movements in reallocation

and that this Schumpeterian or disruptive technological change is a major

source of business cycle fluctuations.

1.1 Related Literature

The cyclicality of reallocation has been studied in many previous works. For

example, Davis and Haltiwanger (1992) and Davis et al. (2006) document con-

typically identify the reallocation shock as the shock orthogonal to the aggregate shock (see,for example, Blanchard and Diamond, 1989; Davis and Haltiwanger, 1999b; Caballero andHammour, 2005). In other words, previous studies extract the shock affecting the remainingvariations in reallocation after controlling for the effect of aggregate activity (expansion orcontraction) on the reallocation, whereas the reallocation shock in this study achieves themaximal variation in reallocation.

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tercyclical fluctuations in job reallocation and Campbell (1998) reports that

the entry rate is procyclical, whereas the exit rate is countercyclical. These

studies, however, are based on unconditional correlations and are not contra-

dictory to my findings that the job reallocation and establishment turnover

rates rise conditional on expansionary technology shocks.8 My time-series re-

sults are also in line with the cross-section results of Samaniego (2009), who

finds that industry turnover rates are positively related to the industry rates

of investment-specific technological change.

Ravn and Simonelli (2007), Balleer (2012), and Canova et al. (2013) also

use long-run restrictions in VAR9 to study the effects of technology shocks

on labor market dynamics. These authors are, however, motivated by search

models and analyze cyclical movements in worker flow such as job finding

and separation rates. In contrast, this paper is interested in the effects of

technological progress on restructuring production units, thereby focusing on

job flow as well as establishment/capital turnover.

The most closely related paper is Michelacci and Lopez-Salido (2007). They

apply the same long-run restrictions and find that investment-specific technol-

ogy shocks decrease job reallocation and that investment-neutral technology

shocks increase it, which is in contrast to the positive reallocation effect of

investment-specific technology shocks in this paper. While their results are

8The countercyclicality of job reallocation in Davis and Haltiwanger (1992) and Daviset al. (2006) comes from the fact that job destruction varies more over time than job cre-ation. Foster et al. (2014), however, argue that this pattern is reversed during the GreatRecession—job creation became more cyclically sensitive and reallocation fell. My resultscan be explained by these new patterns in the recent data.

9The use of long-run restrictions in VAR for identifying technology shocks build onGali (1999) and Fisher (2006). Gali (1999) identifies technology shocks as the only shocksthat have a long-run impact on labor productivity. Fisher (2006) decomposes technologyshocks into investment-specific and investment-neutral components; only the former affectsthe relative price of capital goods to consumption goods in the long run.

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found on job flow data in the manufacturing sector for 1972:I–1993:IV, my

finding is based on the total private sector job flow data for 1993:II–2014:II.10

This finding of subsample instability is not new. For example, Fernald (2007)

shows that there was a structural change around 1997 and that this break

complicates inference about labor productivity and hours. Interestingly, I find

that the investment-specific technology shocks account for less than 30 percent

of the permanent change in labor productivity in 1972:I–1993:IV, whereas they

account for about 80 percent in 1993:II–2014:II. Hence the primary technology

shocks—investment-neutral in the early periods and investment-specific in the

later periods—enhance job reallocation. These findings suggest a change in

the nature of labor market or technology progress and call for further investi-

gation.

Although Michelacci and Lopez-Salido (2007) and this paper share a com-

mon theme of technology shocks and job flows, there are important differences.

First, this paper focuses on what the reallocation dynamics reveal about the

rival/nonrival nature of technological change, whereas Michelacci and Lopez-

Salido (2007) are interested in how investment-specific/neutral technology

shocks interact differently with search frictions in the labor market. To inves-

tigate the effects of technological progress on restructuring production units

in general, this paper examines establishment turnover (entry plus exit) and

capital reallocation as well as job flow. Of course, search frictions and the ri-

val/nonrival nature of technology offer two complementary, not contradictory,

perspectives in interpreting the reallocation patterns in the data. Second, by

constructing reallocation shocks, this paper also seeks to discover the dom-

10The job flow data in the total private sector is available only from 1993. Michelacciand Lopez-Salido (2007) note that manufacturing employment closely tracks aggregate em-ployment only in the period 1972:I–1993:IV.

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inant driving force behind reallocation fluctuations. I find that technology

shocks not only have a positive impact on reallocation but are also the single

most important force behind cyclical variations in reallocation.

My findings are also related to a growing literature on capital realloca-

tion and liquidity. Using Compustat data, Eisfeldt and Rampini (2006) show

that capital reallocation between firms is procyclical. Standard heterogeneous

firm models, however, imply contercyclical or acyclical reallocation because

unproductive firms are more willing to sell off their capital in recessions when

profitability is low. To explain the procyclical capital reallocation, Eisfeldt and

Rampini (2006) suggest that capital liquidity is procyclical, that is, frictions

hindering capital redeployment rise in recessions.

Various channels have been proposed through which the procyclical capital

reallocation and liquidity arise. Cui (2013) shows that a positive credit shock

relaxes the borrowing constraint and allows productive firms to expand, which

in turn raises input costs and drives unproductive firms out of the market.

Lanteri (2014) emphasizes that new and used capital are imperfect substitutes.

A shock to aggregate total factor productivity (TFP) shifts the supply curve

of used capital from disinvesting firms inward and the demand curve of used

capital from expanding firms outward, thereby raising the price of used capital.

For low elasticity of substitution between new and used capital, the rise in used

capital price is large enough to offset the inward shift in supply and increase the

equilibrium quantity of used capital supplied. Li and Whited (2015) instead

assume that new and used capital are perfect substitutes and focus on the

adverse selection problem11 in which buyers of used capital do not know the

11Eisfeldt (2004), Kurlat (2013), and Bigio (2015) analyze how adverse selection endoge-nously determines asset liquidity. A rise in aggregate TFP (Eisfeldt, 2004, and Kurlat, 2013)or a fall in the dispersion of capital quality (Bigio, 2015) increases liquidity by increasingthe average quality of assets supplied in the market.

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quality of capital. The price of used capital reflects a mix of good and bad

capital. An aggregate TFP shock raises the price of used capital and elicits

more high-quality capital in the resale market, thereby mitigating adverse

selection and leading to more sales of used capital. Cao and Shi (2016) feature

search friction in the capital market. An aggregate TFP shock raises the value

of firms and induces more buyers to enter the capital market, which increases

the selling probability of capital, thereby increasing capital reallocated.

All these channels, however, generate procyclical reallocation by shifts in

investment demand and would imply a procyclical price of investment (new

capital).12 Hence, these channels are at odds with the close relationship be-

tween reallocation shocks and investment-specific technology shocks found in

this paper; that is, a rise in reallocation comes with a fall in investment good

price. This paper emphasizes investment supply13 and offers an alternative

and complementary explanation for procyclical capital reallocation: if rival or

Schumpeterian innovation that widens the gap between good and bad produc-

tion units is a major source of business cycles, it can generate a procyclical

reallocation without time-varying capital liquidity.

The rest of this paper is organized as follows. Section 2 uses a firm dynamics

model to derive the different effects of various technological shocks. Section 3

explains my empirical approach. Section 4 presents the empirical results and

12These models assume that the supply of new capital is perfectly elastic and its priceis fixed at one in units of output. In the case of imperfectly elastic supply, demand-drivenfluctuations lead to a procyclical price of new capital.

13Investigating how asset liquidity channels respond to an investment-specific technologyshock would be of substantial interest. The rise in the value of used capital or firm drivesan increase in capital liquidity in those models. They consider aggregate shocks that do notchange the price of new capital and study how increased investment raises the used capitalprice by lowering the resale discount. An investment-specific technology shock, however,lowers the value of new capital and it is not clear whether the value of used capital or firm(thereby capital liquidity) will rise or fall even if high investment lowers the resale discount.

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Section 5 concludes.

2 Theory

This section derives different effects of various technology shocks on realloca-

tion from a general equilibrium model of entry and exit. Four types of shocks

are considered depending on whether technological change is rival or nonrival

and whether it is investment-specific or neutral.

It is important to note that the rival/nonrival distinction is orthogonal to

the investment-specific/neutral distinction. The investment-specific/neutral—

capital embodied/disembodied—distinction focuses on whether a technologi-

cal advance is mediated through capital formation. On the other hand, the

rival/nonrival distinction is about whether a technological advance is medi-

ated through unit formation. Accordingly, rival or Schumpeterian innovation

can be called a unit-embodied technological change (Caballero and Hammour,

1996). Hence, both investment-specific and neutral technologies can be either

rival or nonrival depending on the ease of adoption.

Consider, for example, investment-specific technology. Its advance can

represent either a fall in the cost of producing capital goods or a quality

improvement of a new vintage of capital. As Greenwood et al. (1997) show,

these two interpretations are equivalent in a representative firm economy as

the same representative firm replaces old capital with new. This equivalence,

however, no longer holds in a heterogenous firm economy if a new vintage

of capital cannot be easily deployed. A less expensive capital good affects

investment and disinvestment decisions of all production units; whereas, only

a production unit that possesses the necessary skills or knowledge can adopt

a new vintage of capital. Hence, although a fall in capital good price and

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a rise in capital quality both cause a decline in the quality-adjusted price of

capital goods—which is the main evidence for identifying investment-specific

technological progress—the former is nonrival and the latter is rival in this

case.

The model in this section builds on a standard firm dynamics model (e.g.,

Hopenhayn, 1992, and more closely, Campbell, 1998) with one main difference.

The standard models assume that a new entrant discovers its idiosyncratic

productivity only after entry, whereas this paper follows Lee and Mukoyama

(2007) and assumes a prospective entrant decides on entry after observing its

productivity. The latter assumption enables the endogenous determination of

the average productivity of new entrants.

2.1 The Model

The economy consists of plants, potential entrants, and households. I use

the term “plants” loosely in this section to mean production units at various

levels of disaggregation. The entry and exit dynamics in the model will be later

compared to the entry and exit of establishments, the creation and destruction

of jobs, and the flow of capital across firms in the data.

A continuum of production units exists. Each plant behaves competitively

and produces the consumption good using a Cobb-Douglas production func-

tion:

yt = ezt+ωt(ewk)1−αnαt .

The plant’s output is yt and its labor input is nt. The plant’s capital k is a

fixed factor at the plant level and is normalized to one. ew is the efficiency of

capital of a given vintage that is determined at the birth of the plant.14 The

14How the efficiency of a new vintage of capital evolves over time will be detailed later.

11

plant cannot adjust its capital over its life cycle and all variation in aggregate

capital comes from the extensive margin: that is, from the entry and exit of

plants. In contrast, labor can be freely adjusted.

The plant’s productivity consists of two components: zt, which is the aggre-

gate productivity common across all plants, and ωt, which is the idiosyncratic

productivity specific to each plant. Aggregate and idiosyncratic productivities

follow independent random walks:

zt+1 = µz + zt + σzεzt+1, εzt+1 ∼ i.i.d. (across time) N(0, 1),

ωt+1 = ωt + σωεωt+1, εωt+1 ∼ i.i.d. (across time/plants) N(0, 1). (1)

Note that zt represents the nonrival investment-neutral technology available

to all plants.

Building a new plant means combining physical capital with new plant-

specific technology. In each period, there is a fixed mass of potential entrants

who possess new technology. The initial productivity of new technology is

drawn from a normal distribution:

ωt ∼ N(ut, σ2e). (2)

Once adopted at the plant level, the idiosyncratic productivity of new tech-

nology also evolves by equation (1). I call this idiosyncratic technology before

adoption by the plant an idea.

ut is the aggregate level of the technology that affects the pool of new ideas

and evolves by:

ut+1 = µu + ut + σuεut+1, εut+1 ∼ i.i.d. N(0, 1).

12

ut represents the rival investment-neutral technology exclusively available to

new plants only.

The potential entrant (i.e., the idea owner) makes a once-and-for-all deci-

sion about entry. If the productivity of the idea is not good enough, the idea

owner decides against entry and the idea disappears. If the idea owner decides

to enter the market, the owner then builds a plant by purchasing a unit of

capital good. The cost of producing a capital good is time varying so that the

price of the capital good is given by e−xt , where xt also follows a random walk:

xt+1 = µx + xt + σxεxt+1, εxt+1 ∼ i.i.d. N(0, 1).

Once a plant is built, it acquires a disinvestment option and decides when to

sell off its capital and leave the economy. If a plant decides to exit, it can

recover a (1 − η)e−xt unit of consumption good. Note that except for the

resale loss of η, all plants—both new and incumbent—trade capital goods at

the same price governed by xt. Hence, xt represents the nonrival investment-

specific technology applicable to all plants.

In each period, a new vintage of capital goods is produced and its quality

is also time varying. More specifically, the efficiency of new vintage capital is

given by ewt , which evolves by:

wt+1 = µw + wt + σwεwt+1, εwt+1 ∼ i.i.d. N(0, 1).

The efficiency of capital deployed by entrants at time t is fixed at wt and

is not affected by any further change in vintage. Hence, wt represents the

rival investment-specific technology only available to entrants adopting a new

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vintage of capital.15 Note that e−xt represents the quality-unadjusted price of

capital goods, whereas e−xt−wt is the quality-adjusted price.

Now consider the entry and exit decision. The idea owner enters the market

if and only if the level of productivity is good enough. Similarly, the incumbent

plant exits if and only if its productivity is bad enough. The optimal entry

decision is therefore characterized by the productivity thresholds ωt, above

which the idea owner builds a plant and begins operation. The exit decision

is in turn characterized by the productivity thresholds ωt, below which the

plant exits. I assume that plants die at probability δ, which can be justified

by capital depreciation.

Finally, the economy is populated by a unit measure of identical households

with the following utility function in consumption ct and labor nt:

vt = maxct,nt

(1− β) [log ct − κnt] + βEt[vt+1].

Households supply the labor and finance the investments in plants so that

their wealth is held as shares in plants.

2.2 Solving Equilibrium

To characterize the equilibrium, I solve the social planner’s problem.16 Let

Kt(·) and Ht(·) denote measures over the plants’ and ideas’ productivity, re-

15I assume that the efficiency of capital is retained by the initial owner only and isnot transferred to a new plant when capital is reallocated. This is consistent with theconcept of rival technology, which is unit-specific and determined by the entity that deploysit. Accordingly, the resale value of capital, (1 − η)e−xt , is the same for all exiting plantsindependently from its original vintage. This assumption also makes it unnecessary to keeptrack of the distribution of different vintages: capital efficiency can simply be treated as aproductivity shifter for entrants; that is, ωt—the initial productivity of the idea owner—becomes ωt + (1− α)wt after entry.

16The competitive equilibrium is presented in Appendix B.

14

spectively. Also, let φ(·) denote the pdf of the standard normal distribution.

The social planner’s problem is then

V (Kt(·), H t, zt, xt, ut, wt) = maxCt,Nt,nt(·),ωt,ωt

(1− β) [logCt − κNt]

+βEt[V (Kt+1(·), H t+1, zt+1, xt+1, ut+1, wt+1)

],

subject to

Yt = Ct + e−xt[∫ ∞

ωt

Ht(ωt)dωt − (1− η)

∫ ωt

−∞Kt(ωt)dωt

], (3)

Yt =

∫ ∞−∞

ezt+ωtnt(ωt)αKt(ωt)dωt, (4)

Nt =

∫ ∞−∞

nt(ωt)Kt(ωt)dωt,

Kt+1(ωt+1) = (1− δ)∫ ∞ωt

1

σωφ

(ωt+1 − ωt

σω

)Kt(ωt)dωt (5)

+

∫ ∞ωt

1

σωφ

(ωt+1 − ωt − (1− α)wt

σω

)Ht(ωt)dωt,

Ht(ωt) =1

σeφ

(ωt − utσe

)×H t, (6)

where H t is a fixed mass of new idea discovery.17 The social planner optimally

chooses aggregate consumption Ct, aggregate labor Nt, labor allocation at

each plant nt(·), and entry and exit thresholds (ωt and ωt). Note that the

plant’s output is ezt+ωtnt(ωt)α in equation (4) because the efficiency of capital

is incorporated into the plant-specific productivity ωt (see footnote 15).

Equation (5) captures the main dynamics. Ht(·) represents the current

stock of ideas. Ideas with good enough productivity (higher than ωt) are

adopted and added to the stock of plants Kt+1(·) in the next period; by using

a new vintage of capital, the productivity of entrants is shifted by (1− α)wt.

17More precisely, Ht exogenously grows with the stochastic trend of the economy.

15

This entry deploys∫∞ωtHt(ωt)dωt amount of capital goods, which represents

the total measure of entrants or aggregate investment in this economy. Plants

with sufficiently bad productivity (lower than ωt) exit and disappear from the

next period’s stock of plants. This exit releases (1− η)∫ ωt−∞Kt(ωt)dωt amount

of capital goods, which represents the total measure of exit or aggregate dis-

investment.

Four technology processes (zt, xt, ut, and wt) have distinct effects on this

economy. Nonrival investment-neutral technology zt raises the productivity

of new and old plants altogether. Nonrival investment-specific technology xt

affects both the investment and disinvestment margins equally in equation (3).

Rival technologies, wt and ut, improve the productivity level of entrants only

in equations (5) and (6), respectively. Investment-specific technologies, xt and

wt, lower the quality-adjusted price of capital goods:

Pt = e−xt−wt .

Table 1 summarizes four types of technology in the model.

The equilibrium conditions of the model (see Appendix A) are functional

equations that require solving for the distribution of plant productivity. To

deal with this infinite dimensional problem, I adopt an approach developed by

Campbell (1998) of approximating the distribution functions by their values at

a large but finite set of grid points and then applying a perturbation method

that can handle many state variables relatively easily. I obtain the solution by

using Dynare++ (Kamenik, 2011).

16

investment-specific investment-neutral

rival w u

nonrival x z

Table 1: Technology classification.

2.3 Parameter Choices

The model period is a quarter. The labor income share is set equal to α = 2/3.

Greenwood et al. (2000) document that the average annual rate of decline in

the relative real quality-adjusted price of equipment is 3.2 percent per year,

adding 0.81 percent to the balanced growth rate of output. The quarterly

contribution of 0.2 percent is split equally between two investment-specific

technologies so that µx = µw = 0.002.18 µz = µu = 0.005 is then set in order

to imply a 1.4 percent annual growth rate of output per capita. The time

discount factor β is set to match an annual interest rate of 4 percent. The

capital depreciation rate δ = 0.025 is typical in the literature and the disutility

of labor κ = 2.50 is chosen so that the steady-state level of labor is 1/3.

The estimate for idiosyncratic volatility σω varies in the literature. For

example, σω = 0.011 in Khan and Thomas (2008), whereas σω = 0.047 in

Bachmann et al. (2013). The entry and exit response results are robust over

this range of values and I report results with σω = 0.03.

An increase in the resale loss η lowers the exit rate, which also represents

the capital turnover rate in the model.19 Eisfeldt and Rampini (2006) report

that, depending on the measure of the capital stock, between 1.4 and 5.5

percent of the capital stock turns over each year. I set η = 0.15 so that the

18In the model, output grows at the rate of 1α (µz + (1− α)µx + µu + (1− α)µw) in the

deterministic steady state.19Capital recovered from exiting plants is reallocated to the entering plants.

17

annual turnover rate of capital is 3.2 percent in the steady state.20

Finally, the standard deviation of the entrant’s initial productivity distri-

bution is set to σe = 0.09, which is much larger than the idiosyncratic volatility

σω based on the finding that entering plants face a higher productivity uncer-

tainty than old plants (Bartelsman and Dhrymes, 1999). I experiment with a

wide range of values for this parameter as well as others and the qualitative

results remain intact.

2.4 Effects of Technology Shocks

Figure 1 displays the impulse responses of the entry and exit thresholds (ωt

and ωt), the entry and exit rates21, and the quality-adjusted price of capital

goods Pt to four technology shocks in the model.22 The stochastic trend of

output in the model is 1α

(zt + (1− α)xt + ut + (1− α)wt). Hence, I consider

a 1 percent shock to each technology—zt, (1− α)xt, ut, (1− α)wt—so that all

four shocks have the same size effect on output—a 1α

percent increase—in the

long run. The pool of new ideas H t is also set to jump upon impact to a new

steady state value.

All four technology shocks encourage entry. Although the new idea pool

increases by the same percentage, a rise in entry is bigger than an increase in

the steady state level during the transition; this results in a lower entry thresh-

old for nonrival technology shocks. The incumbent plants then compete with

new plants that have lower productivity, thereby reducing the exit threshold

and the exit rate. In contrast, rival technology shocks induce a rise in the

20More precisely, η and the (normalized) level of the new idea pool—H?

in AppendixA—are set to imply a capital turnover rate of 3.2 percent and an investment to output ratioof 20 percent in the steady state.

21

∫∞ωtHt(ωt)dωt∫∞

−∞Kt(ωt)dωtand

∫ ωt−∞Kt(ωt)dωt∫∞−∞Kt(ωt)dωt

.

22See Appendix C for the impulse responses of key macroeconomic variables.

18

10 20 30 40−8

−6

−4

−2

0x 10

−4

quarters

Entry threshold

10 20 30 40−6

−4

−2

0x 10

−4

quarters

Exit threshold

10 20 30 400

0.02

0.04

0.06

0.08

pe

rce

nt

quarters

Entry rate

10 20 30 40−0.02

−0.01

0

0.01

pe

rce

nt

quarters

Exit rate

10 20 30 40−1

−0.5

0

0.5

1

pe

rce

nt

quarters

Capital price

10 20 30 40−2

−1.5

−1

−0.5

0x 10

−3

quarters

Entry threshold

10 20 30 40−2

−1.5

−1

−0.5

0x 10

−3

quarters

Exit threshold

10 20 30 400

0.1

0.2

0.3

pe

rce

nt

quarters

Entry rate

10 20 30 40−0.06

−0.04

−0.02

0

0.02

pe

rce

nt

quarters

Exit rate

10 20 30 40−3

−2

−1

0

pe

rce

nt

quarters

Capital price

10 20 30 400

0.002

0.004

0.006

0.008

0.01

quarters

Entry threshold

10 20 30 400

0.002

0.004

0.006

0.008

0.01

quarters

Exit threshold

10 20 30 400

0.05

0.1

0.15

pe

rce

nt

quarters

Entry rate

10 20 30 400

0.05

0.1

0.15

0.2

pe

rce

nt

quarters

Exit rate

10 20 30 40−1

−0.5

0

0.5

1

pe

rce

nt

quarters

Capital price

10 20 30 40−4

−3

−2

−1

0x 10

−3

quarters

Entry threshold

10 20 30 400

0.002

0.004

0.006

0.008

0.01

quarters

Exit threshold

10 20 30 400

0.05

0.1

0.15

pe

rce

nt

quarters

Entry rate

10 20 30 400

0.05

0.1

0.15

0.2p

erc

en

t

quarters

Exit rate

10 20 30 40−3

−2

−1

0

pe

rce

nt

quarters

Capital price

Figure 1: Impulse responses of entry and exit to a 1 percent increase in nonrivalinvestment-neutral technology zt (top panel), nonrival investment-specific technol-ogy (1 − α)xt (second panel), rival investment-neutral technology ut (third panel),and rival investment-specific technology (1− α)wt (bottom panel).

productivity of new plants and the resulting competition with a better cohort

of entrants pushes out old plants. Note that although the entry threshold for

new ideas drops in the case of a rival investment-specific technology shock

(bottom panel), those ideas are equipped with a better quality capital so that

the productivity of new plants rise.23 Hence, the exit rate rises for both rival

23In fact, if we plot the entry threshold for an entrant’s productivity after her productivityis enhanced by more efficient capital (ωt in Appendix A), the response is exactly the sameas that of a rival investment-neutral technology shock. See footnote 15 and Appendix A.

19

technology shocks.

The different signs of the exit responses, of course, depend on how elas-

tically the pool of new ideas responds to the shocks; however, the different

sizes of the exit responses are more robust. Note that the response of the exit

rate is an order of magnitude smaller than that of the entry rate in the case

of nonrival technology shocks. This comes from the fact that these shocks

do not affect new and old plants differentially: a nonrival investment-neutral

technology shock makes both new and old capital more productive, while a

nonrival investment-specific technology shock lowers the value of new capital

as well as the scrap value of old capital. In contrast, rival technology shocks

increase both the entry and exit rates by a similar magnitude; only new units

become more productive and this widened productivity gap between entrants

and incumbents makes old plants more valuable in a sell-off as their capital

can be deployed by more productive entrants.24

I will later show that the empirical impulse responses to the investment-

specific technology shocks are characterized by a lead-lag pattern—the entry

and job creation rates rise on impact, whereas the exit and job destruction

rates initially fall but subsequently rise above the average for an extended

amount of time. This response is predicted by a version of the model, which

is extended to assume that more than one time period is required for an exit

and job destruction.25

24This result is similar to Michelacci and Lopez-Salido (2007), who show in a searchmodel that investment-neutral technological advances increase job destruction and realloca-tion; whereas, investment-specific technological advances that make new capital equipmentless expensive reduce job destruction. The authors assume old plants can adopt investment-neutral technology with a small probability; hence, this technology is closer to rival tech-nology than the nonrival investment-neutral technology studied in my model.

25The responses of the existing plants to a new wave of entrants are likely to take asubstantial time in the real world. Liquidating and selling off existing assets takes time. Inaddition to physical frictions, the delay can be due to informational frictions: the incumbents

20

3 Empirical Approach

3.1 Identification

Consider the vector moving average representation of a VAR:

yt = C(L)ut, (7)

where yt is a n×1 vector, C(L) = I+C1L+C2L2+. . . is a matrix of polynomials

in the lag operator L, and ut is a n × 1 vector of one-step ahead forecasting

errors with a variance-covariance matrix E[utu′t] = Σ. Identification of the

structural shocks amounts to finding a matrix A and a vector of mutually

orthogonal shocks εt, such that ut = Aεt.

The elements of yt are [∆pt,∆at,∆ht, enrt, exrt]′, where pt is the log of the

quality-adjusted capital good price, at is the log of labor productivity, ht is

the log of per capita hours worked,26 enrt is the entry rate, exrt is the exit

rate, and ∆ = 1− L.

This paper identifies the reallocation shock by extracting the shock that

explains the maximal amount of the FEV over the business cycle horizon up to

32 quarters for the turnover rate enrt + exrt.27 First, fix A to some arbitrary

might not immediately realize that the entrants have better productivity. See Appendix Dfor the impulse responses with a time-to-exit assumption.

26I consider the differenced hours as my benchmark case. The literature on the long-run identification of technology shocks reaches different conclusions depending on how re-searchers deal with the low frequency variation in hours (e.g., Gali, 1999, and Christianoet al., 2004). This literature typically finds that the technology shocks are less expansion-ary and account for a smaller fraction of hours variation when hours enters the VAR as indifferences rather than in levels. I indeed find stronger results with the level specification.

27This identification strategy to extract shocks that explain the majority of FEV of atarget variable is developed by Uhlig (2003) and is adopted in Barsky and Sims (2011),Kurmann and Otrok (2013), and Francis et al. (2014). Such identified shocks in generaldepend on the forecast horizon over which the FEV is maximized. The similarity between areallocation shock and an investment-specific technology shock remains strong in my study

21

matrix satisfying Σ = AA′. Finding A is then equivalent to choosing an

orthonomal matrix Q, such that ut = AQεt. The k-step ahead forecast error

of the turnover rate is given by:

enrt+k + exrt+k − Et(enrt+k + exrt+k) = e′i

[k−1∑l=0

ClAQεt+k−l

],

where ei is a column vector with 1 in the 4th and 5th positions and 0 elsewhere.

Let q be a column vector of Q. I then solve

q = arg maxq

e′i

k∑k=k

k−1∑l=0

ClAqq′AC ′l

ei subject to q′q = 1

so that q′A−1ut is a reallocation shock.

For comparison, I also identify the investment-specific technology shock fol-

lowing Fisher (2006). I impose all first-row elements except the (1, 1) position

of C(1)A to be equal to zero so that only the investment-specific technology

shock has a long-run impact on the capital good price. The investment-neutral

technology shock can in turn be identified by imposing that all second-row el-

ements except the (2, 1) and (2, 2) positions of C(1)A are equal to zero. Table

2 summarizes the long-run restrictions.

ShocksPermanent effects on:

capital price labor productivity

investment-specific technology shock yes yes

investment-neutral technology shock no yes

all other shocks no no

Table 2: Identification by long-run restrictions.

unless I focus on a short forecast horizon of less than three years.

22

3.2 Data

The real price of quality-adjusted capital goods is an investment deflator for

equipment and software divided by a consumption deflator for nondurables

and services. This series is constructed by Liu et al. (2011),28 who adopt the

method used by Fisher (2006)29 and extend the series to more recent periods.

Labor productivity is measured by the nonfarm business series published by

the Bureau of Labor Statistics (BLS).30 Following Fisher (2006), productivity

is also expressed in consumption units using the same consumption deflator

that underlies the capital goods price. Per capita hours are measured with

the BLS hours series for the nonfarm business sector divided by the civilian

noninstitutionalized population over the age of 16.

For the entry and exit rates, I use the rates of total private sector establish-

ment births and deaths from the BLS Business Employment Dynamics (BED)

data. The BED series are quarterly and seasonally adjusted and they have

been available since 1993:II. The BED defines births as those records that

have positive employment in the third month of a quarter and zero employ-

ment in the third month of the previous four quarters. Similarly, deaths are

units that report zero employment in the third month of a quarter and do not

report positive employment in the subsequent third months of the next four

quarters.

28Their benchmark series is the quality-adjusted deflator for equipment and software,nonresidential and residential structures, and consumer durables. I instead use a versionincluding equipment and software only because the technology embodied in equipment andsoftware better represents the type of technology I am interested in; that is, innovationthat requires restructuring the production unit. My results are slightly stronger with thisdeflator for equipment and software only, but the difference is small. Fisher (2006) also usesthe deflator for only equipment and software as his benchmark deflator.

29Fisher (2006) builds on Gordon (1990) and Cummins and Violante (2002).30Fernald (2012) constructs a quarterly utilization-adjusted series on TFP. I also use his

measure of TFP instead of labor productivity and find very similar results.

23

The BLS BED data contain job flow rates as well. Job creation and de-

struction rates are defined as private sector gross job gains and job losses,

respectively, as a percent of employment. This data have also been available

since 1993:II, and these series are quarterly and seasonally adjusted.

I also consider the capital turnover rates used by Eisfeldt and Rampini

(2006). They construct two capital turnover rates from the annual Com-

pustat data—acquisitions divided by lagged total assets as well as sales of

property, plant, and equipment divided by lagged total property, plant, and

equipment. To obtain more observations, I follow Cui (2013) to construct the

corresponding quarterly series from the quarterly Compustat data and apply

a X-12-ARIMA seasonal adjustment.

Appendix E provides a time-series plot and summary statistics of this data.

4 Empirical Findings

The sample period used in this paper is 1993:II–2014:II. The baseline VAR are

estimated with 4 lags of each variable and no time trend. To compute error

bands, I impose a diffuse (Jeffreys) prior and display 68 percent error bands.

4.1 Baseline Estimates

Figure 2 shows the impulse responses to reallocation shocks identified by maxi-

mizing the FEV. The investment price keeps falling and the labor productivity

gradually increases after an initial rise and drop. Hours respond positively and

with a hump shape; the entry rate immediately rises and gradually declines,

whereas the exit rate rises significantly above zero after two-and-a-half years.

Figure 3 displays the fraction of the FEV explained by the reallocation

24

5 10 15 20 25 30 35 40

−3.5

−3

−2.5

−2

−1.5

−1

−0.5

0

Investment price

pe

rce

nt

quarters5 10 15 20 25 30 35 40

0

0.5

1

1.5

2

2.5

Labor productivity

pe

rce

nt

quarters5 10 15 20 25 30 35 40

−3

−2.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

Hours

pe

rce

nt

quarters

5 10 15 20 25 30 35 40

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

Entry rate

pe

rce

nt

quarters5 10 15 20 25 30 35 40

−0.04

−0.02

0

0.02

0.04

0.06

Exit rate

pe

rce

nt

quarters5 10 15 20 25 30 35 40

0

0.02

0.04

0.06

0.08

0.1

0.12

Turnover rate

pe

rce

nt

quarters

Figure 2: Impulse responses to a reallocation shock based on entry and exit data.

0 10 20 30 400

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Investment price

fra

ctio

n o

f F

EV

exp

lain

ed

quarters0 10 20 30 40

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Labor productivity

fra

ctio

n o

f F

EV

exp

lain

ed

quarters0 10 20 30 40

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Hours

fra

ctio

n o

f F

EV

exp

lain

ed

quarters

0 10 20 30 400

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Entry rate

fra

ctio

n o

f F

EV

exp

lain

ed

quarters0 10 20 30 40

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Exit rate

fra

ctio

n o

f F

EV

exp

lain

ed

quarters0 10 20 30 40

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Turnover rate

fra

ctio

n o

f F

EV

exp

lain

ed

quarters

Figure 3: Fraction of forecast error variance (FEV) explained by reallocation shockbased on entry and exit data.

shock. It is noteworthy that the reallocation shock accounts for most medium-

25

and longer-term variations in the turnover rate. This shock by construction

maximizes its contribution among possible shocks, but nothing requires that

a single shock account for over 50 to 75 percent of all unpredictable fluctua-

tions from one-and-a-half to ten years. Hence, the identified shock is truly a

dominant driving force behind fluctuations in reallocation.

5 10 15 20 25 30 35 40

−3.5

−3

−2.5

−2

−1.5

−1

−0.5

0

Investment price

perc

ent

quarters5 10 15 20 25 30 35 40

0

0.5

1

1.5

2

Labor productivity

perc

ent

quarters5 10 15 20 25 30 35 40

−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5

Hours

perc

ent

quarters

5 10 15 20 25 30 35 40

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

Entry rate

perc

ent

quarters5 10 15 20 25 30 35 40

−0.06

−0.04

−0.02

0

0.02

0.04

0.06

Exit rate

perc

ent

quarters5 10 15 20 25 30 35 40

−0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

Turnover rate

perc

ent

quarters

Figure 4: Impulse responses to an investment-specific technology shock based onentry and exit data.

Figure 4 displays the impulse responses to investment-specific technology

shocks identified by the long-run restrictions. These results are very similar

to the results for reallocation shocks. The initial drop of the exit rate is more

significant, but as mentioned earlier, this pattern of a lagged response of exit

is consistent with a version of the model extended to include the time to

exit. The fraction of the FEV explained by the investment-specific technology

shock (Figure 5) is also very similar.31 The investment-specific technology

31As can be expected from the result that most variations in entry and turnover rates areaccounted for by investment-specific technology shocks, the responses of reallocation rates

26

0 10 20 30 400

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Investment price

fra

ctio

n o

f F

EV

exp

lain

ed

quarters0 10 20 30 40

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Labor productivity

fra

ctio

n o

f F

EV

exp

lain

ed

quarters0 10 20 30 40

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Hours

fra

ctio

n o

f F

EV

exp

lain

ed

quarters

0 10 20 30 400

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Entry rate

fra

ctio

n o

f F

EV

exp

lain

ed

quarters0 10 20 30 40

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Exit rate

fra

ctio

n o

f F

EV

exp

lain

ed

quarters0 10 20 30 40

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Turnover rate

fra

ctio

n o

f F

EV

exp

lain

ed

quarters

Figure 5: Fraction of forecast error variance (FEV) explained by investment-specifictechnology shock based on entry and exit data.

shock accounts for more than 35 percent of hours variation after one year,

confirming that it is a major shock driving the business cycle fluctuations.

Fisher (2006) finds that the investment-specific technology shock accounts for

9 to 22 percent of hours’ FEV in the sample period of 1982:III–2000:IV. Figure

5 shows that the importance of an investment-specific technology shock is even

larger in the more recent periods of 1993:II–2014:II, the time period studied

in this paper.

The identified investment-specific technology shocks are conceptually a

weighted average of rival and nonrival shocks (shocks to w and x in Section 2).

The strong positive effects on reallocation suggest that the identified shocks

to investment-neutral technology shocks (not shown) are weak and the error bands includezero in most periods. In addition, the hours response is no longer robust across differentspecifications: hours fall (rise) after a positive investment-neutral technology shock whenhours enters the VAR in differences (in levels with/without time trends). I find the sameresults for job flow and capital reallocation data as well.

27

5 10 15 20 25 30 35 40−1.8

−1.6

−1.4

−1.2

−1

−0.8

−0.6

−0.4

−0.2

0

Investment price pe

rcen

t

quarters5 10 15 20 25 30 35 40

−0.6

−0.4

−0.2

0

0.2

0.4

Labor productivity

perc

ent

quarters5 10 15 20 25 30 35 40

0

0.5

1

1.5

2

2.5

3

Hours

perc

ent

quarters

5 10 15 20 25 30 35 400

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

Job creation rate

perc

ent

quarters5 10 15 20 25 30 35 40

−0.1

−0.05

0

0.05

0.1

Job destruction rate

perc

ent

quarters5 10 15 20 25 30 35 40

0

0.05

0.1

0.15

0.2

Job reallocation rate

perc

ent

quarters

Figure 6: Impulse responses to an investment-specific technology shock based onjob flow data.

0 10 20 30 400

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Investment price

fract

ion

of F

EV

exp

lain

ed

quarters0 10 20 30 40

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Labor productivity

fract

ion

of F

EV

exp

lain

ed

quarters0 10 20 30 40

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Hours

fract

ion

of F

EV

exp

lain

ed

quarters

0 10 20 30 400

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Job creation rate

fract

ion

of F

EV

exp

lain

ed

quarters0 10 20 30 40

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Job destruction rate

fract

ion

of F

EV

exp

lain

ed

quarters0 10 20 30 40

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Job reallocation rate

fract

ion

of F

EV

exp

lain

ed

quarters

Figure 7: Fraction of forecast error variance (FEV) explained by investment-specifictechnology shock based on job flow data.

28

are mostly rival (shocks to w).32

I also find similar results for other reallocation measures. Figures 6 and 7

show the results when job creation and destruction rates are used in place of

entry and exit rates. As the results for the reallocation shock are very similar,

they are omitted from this paper. The investment-specific technology shock

explains over 50 percent of the job reallocation rate’s FEV for three to ten

years. The impulse responses are similar to that seen in the case of entry and

exit data and the only notable difference is that labor productivity falls below

zero in the medium term. Note, however, that output still rises as the hours

response is larger than the productivity response.

The positive responses of job creation and reallocation rates to an investment-

specific technology shock are different from the results of Michelacci and Lopez-

Salido (2007), who find that this shock leads to a fall in job destruction and

reallocation rates. This difference in findings results from different data sam-

ples being used in these two studies. Michelacci and Lopez-Salido (2007) use a

quarterly series of job flow data in the manufacturing sector for 1972:I–1993:IV;

I in fact find similar results to theirs when using this data (see Appendix F).

Interestingly, the contribution of the investment-specific technology shock

to the long-run variation in labor productivity differs substantially among the

two samples. The investment-specific technology shock accounts for less than

30 percent of the permanent change in labor productivity in the manufacturing

sector for 1972:I–1993:IV, whereas it accounts for about 80 percent in the total

private sector for 1993:II–2014:II (see Table 3). In other words, the technol-

ogy shocks identified by long-run restrictions in the former sample are mostly

32Similarly, the identified reallocation shocks are in principle a combination of multipleshocks; however, the close relationship between reallocation and investment-specific tech-nology shocks suggests that the identified reallocation shocks are mostly investment-specifictechnology shocks (shocks to w).

29

5 10 15 20 25 30 35 40

−3.5

−3

−2.5

−2

−1.5

−1

−0.5

0

Investment price pe

rcen

t

quarters5 10 15 20 25 30 35 40

0

0.5

1

1.5

2

Labor productivity

perc

ent

quarters5 10 15 20 25 30 35 40

−1

−0.5

0

0.5

1

1.5

2

Hours

perc

ent

quarters

5 10 15 20 25 30 35 40

−0.005

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

Acquisitions turnover rate

perc

ent

quarters5 10 15 20 25 30 35 40

0

0.01

0.02

0.03

0.04

0.05

Property sale turnover rate

perc

ent

quarters5 10 15 20 25 30 35 40

−0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Sum of turnover rates

perc

ent

quarters

Figure 8: Impulse responses to an investment-specific technology shock based oncapital reallocation data.

0 10 20 30 400

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Investment price

fract

ion

of F

EV

exp

lain

ed

quarters0 10 20 30 40

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Labor productivity

fract

ion

of F

EV

exp

lain

ed

quarters0 10 20 30 40

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Hours

fract

ion

of F

EV

exp

lain

ed

quarters

0 10 20 30 400

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Acquisitions turnover rate

fract

ion

of F

EV

exp

lain

ed

quarters0 10 20 30 40

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Property sale turnover rate

fract

ion

of F

EV

exp

lain

ed

quarters0 10 20 30 40

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Sum of turnover rates

fract

ion

of F

EV

exp

lain

ed

quarters

Figure 9: Fraction of forecast error variance (FEV) explained by investment-specifictechnology shock based on capital reallocation data.

30

investment-neutral, whereas they are mostly investment-specific in the latter

one. Hence, the dominant technology shocks enhance job reallocation in both

samples,33 which is in line with the positive relationship between reallocation

and productivity growth documented in the productivity literature.34

Figures 8 and 9 display the results when capital turnover rates are used.

The elements of yt in the VAR system (7) are [∆pt,∆at,∆ht, tr1t , tr

2t ]′, where

tr1t is acquisitions divided by lagged total assets and tr2

t is the sales of property,

plant, and equipment divided by lagged total property, plant, and equipment.35

Note that both turnover rates are reallocation measures,36 whereas only the

sum of the entry and exit rates—or the sum of the job creation and destruction

rates—represents reallocation in the previous cases. This explains why both

rates rise together without a lead-lag pattern. The fraction of the FEV ex-

plained by the investment-specific technology shock is again large—it explains

over 50 percent of the variations of the capital turnover rates after three years.

The tight link between reallocation and investment-specific technology

shocks can also be seen in Table 3. The mean estimates of the correlation

coefficient between the two shocks are over 0.79 for all three reallocation mea-

sures. The contribution of the reallocation shock to the long-run variation in

the capital goods price is also over 0.72. Note that the contribution of the

33However, the hours response differs. The investment-neutral technology shock in theearlier sample is contractionary, whereas the investment-specific technology shock in thelater sample is expansionary.

34The findings in this literature are mainly based on cross-sectional decomposition—thosestudies decompose the total industry-wide productivity growth over the sample period intocomponents that reflect an improvement in individual units and the reallocation of resourcesacross units. They find that the reallocation component is substantial. See Foster et al.(2001) and references therein.

35The correlation coefficient of these two series is 0.56.36A reallocation shock is again identified as a shock that explains the maximum amount

of the FEV of the sum of the two turnover rates tr1t + tr2t . The results are very similar andare therefore omitted.

31

Correlation Contribution of Contribution of

Data between reallocation shock to investment shock to

reallocation and long-run variation long-run variation

investment shocks in capital good price in labor productivity

entry/exit 0.795 0.725 0.802

(0.301) (0.272) (0.242)

job flow 0.925 0.870 0.805

(0.123) (0.156) (0.226)

capital 0.874 0.805 0.787

reallocation (0.204) (0.201) (0.216)

Table 3: Relationship between reallocation and technology shocks. Entries not inparentheses are the mean estimates; the entries in parentheses are the standarddeviations.

investment-specific technology shock is one by definition.37

The final column represents the contribution of the investment-specific

technology shock to the technological change measured by a long-run effect

on labor productivity. These findings show that the investment-specific tech-

nology shock accounts for most of the permanent change in labor productivity,

which is consistent with the findings of Fisher (2006) and Schmitt-Grohe and

Uribe (2011). It also suggests that if a single technology shock is identified

as the only shock to have a long-run effect on labor productivity, as in Gali

(1999), that technology shock would also be very similar to the reallocation

shock. I indeed find that this is the case; the correlation coefficient of a real-

location shock with a single technology shock is almost as high as that seen

with an investment-specific technology shock.

37This contribution is computed by the ratio of the (1,1) element of C(1)Aqq′AC(1) tothe (1,1) element of C(1)ΣC(1)′.

32

4.2 Robustness

This subsection considers a number of potential specification issues. First, the

baseline estimates focus on a 5-variable VAR system primarily because the

quarterly reallocation measures of the total private sector are only available

for a short sample period. However, adding two more variables considered

by Fisher (2006)—nominal interest rate38 and inflation—barely changes the

strong link between the shock driving the reallocation and the investment-

specific technology shock.

Second, the baseline specification has hours included in differences. There

is a disagreement in the literature about the treatment of the low frequency

component of hours (see, for example, Gali, 1999; Christiano et al., 2004;

Francis and Ramey, 2005). The literature also considers the level specification

of hours with linear/quadratic detrending; these specifications lead to different

conclusions about whether hours rise or fall after a positive technology shock

and how important the role of the technology shocks is in explaining hours and

output fluctuations. I find that hours rise after a positive investment-specific

technology shock and that this shock accounts for over 30 percent of hours FEV

after one year for all those specifications. Hence, the prominent contribution

of the investment-specific technology shocks to cyclical fluctuations is very

robust for the sample period in this paper.

More importantly, I examine the robustness of the strong correlation be-

tween the reallocation shock and the investment-specific technology shock. I

find the correlation remains strong except for the entry and exit data; how-

ever, even in this case, the impulse responses to the two shocks are broadly

38Because the zero lower bound becomes binding in the latter part of my sample, I alsouse the Wu-Xia shadow Federal Funds rate (Wu and Xia, 2014) instead of the three-monthTreasury bill rate; however, the results do not change.

33

1996 1998 2000 2002 2004 2006 2008 2010 2012 2014−4

−2

0

2

4

pe

rce

nt

first differenced hours

1996 1998 2000 2002 2004 2006 2008 2010 2012 2014−6

−4

−2

0

2

4

pe

rce

nt

linear time trend

1996 1998 2000 2002 2004 2006 2008 2010 2012 2014−6

−4

−2

0

2

4

pe

rce

nt

quadratic time trend

Figure 10: Comparison of the reallocation shock (solid line) and the investment-specific technology shock (dash-dot line) based on entry and exit data. Correlationcoefficients are 0.92 (0.30, top panel), 0.49 (0.34, middle panel), and 0.53 (0.39,bottom panel). Numbers in parentheses are the standard deviations.

similar. To illustrate the dependence on different specifications, Figures 10,

11, and 12 extract the time series of the reallocation and investment-specific

technology shocks for the mean (OLS) estimates of the VAR parameters and

plot them together.39 I do not show the results for the level specification of

39I find that technology shocks account for a larger fraction of hours variations when thelevel specifications of hours with time trends are considered. This is consistent with thefindings of the aforementioned papers. The contribution to reallocation variations, however,becomes smaller than the benchmark case of differenced hours, as can be seen in the lowercorrelation coefficient.

34

1996 1998 2000 2002 2004 2006 2008 2010 2012 2014−4

−2

0

2

4

perc

ent

first differenced hours

1996 1998 2000 2002 2004 2006 2008 2010 2012 2014−2

−1

0

1

2

3

perc

ent

linear time trend

1996 1998 2000 2002 2004 2006 2008 2010 2012 2014−4

−2

0

2

4

perc

ent

quadratic time trend

Figure 11: Comparison of the reallocation shock (solid line) and the investment-specific technology shock (dash-dot line) based on job flow data. Correlation coeffi-cients are 0.95 (0.12, top panel), 0.82 (0.34, middle panel), and 0.82 (0.28, bottompanel). Numbers in parentheses are the standard deviations.

hours without the time trend because the extracted shocks are almost identical

with a correlation coefficient over 0.95. Although the correlation coefficients

are substantially smaller for the linear/quadratic trending in the case of the

entry and exit data, the two identified shocks broadly move together even in

this case. For all other cases, the two shocks very closely mirror each other

and represent a similar innovation to the economy.

35

1996 1998 2000 2002 2004 2006 2008 2010 2012 2014−4

−2

0

2

4

perc

ent

first differenced hours

1996 1998 2000 2002 2004 2006 2008 2010 2012 2014−6

−4

−2

0

2

4

perc

ent

linear time trend

1996 1998 2000 2002 2004 2006 2008 2010 2012 2014−6

−4

−2

0

2

4

perc

ent

quadratic time trend

Figure 12: Comparison of the reallocation shock (solid line) and the investment-specific technology shock (dash-dot line) based on capital reallocation data. Cor-relation coefficients are 0.93 (0.20, top panel), 0.87 (0.20, middle panel), and 0.91(0.29, bottom panel). Numbers in parentheses are the standard deviations.

5 Concluding Remarks

This paper studies two related questions: what drives cyclical movements in

reallocation and is the technological change rival or nonrival? By showing the

close link between the main shock affecting reallocation and the investment-

specific technology shock, I address these questions jointly. The investment-

specific technology shock is the dominant driving force behind reallocation; it

is the main technological progress accounting for a large portion of aggregate

36

fluctuations and is rival and disruptive.

My findings are subject to some caveats. Because of the data availability,

this study covers a relatively short sample period, which includes only two

recessions. It is hard to judge at this time whether the difference between my

findings and previous studies are due to a structural change in the 1990s or

factors unique to the Great Recession.

In addition, my results rely on the premise that the long-run restriction

identifies the exogenous technology shocks. A simple demand-side story can-

not explain my results because increased demand would lead to a higher price

of capital goods. However, if a higher demand encourages innovation in the

capital goods producing sector, resulting in a lower quality-adjusted price of

capital (in a way similar to Comin and Gertler, 2006), what I identify as a

disruptive innovation could be the confounding effects of various economic

shocks. Investigating the robustness of my findings to an endogenous techno-

logical change would be important and interesting and I hope to pursue this

matter in future research.

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43

Appendix A First-order Conditions of the So-

cial Planner’s Problem

The social planner’s problem in Section 2.2 can be transformed in the following

ways. First, note that the labor allocation decision is atemporal so it can be

solved separately:

maxnt(·)

Yt =

∫ ∞−∞

ezt+ωtnt(ωt)αKt(ωt)dωt

subject to

Nt =

∫ ∞−∞

nt(ωt)Kt(ωt)dωt. (8)

The solution is

nt(ωt) =e

11−αωt

Kt

Nt, (9)

Yt =

∫ ∞−∞

ezt+ωtnt(ωt)αKt(ωt)dωt = eztK1−α

t Nαt , (10)

where

Kt =

∫ ∞−∞

e1

1−αωtKt(ωt)dωt (11)

is the productivity-weighted capital stock. Second, by replacing Ht(ωt) with

1σeφ(ωt−utσe

)×H t and applying a change of variable ωt = ωt + (1−α)wt, dωt =

dωt, the resulting integrals in equations (3) and (5) become

∫ ∞ωt

1

σeφ

(ωt − utσe

)H tdωt

=

∫ ∞ωt+(1−α)wt

1

σeφ

(ωt − ut − (1− α)wt

σe

)H tdωt,∫ ∞

ωt

1

σωφ

(ωt+1 − ωt − (1− α)wt

σω

)1

σeφ

(ωt − utσe

)H tdωt

44

=

∫ ∞ωt+(1−α)wt

1

σωφ

(ωt+1 − ωt

σω

)1

σeφ

(ωt − ut − (1− α)wt

σe

)H tdωt.

Once we define

ωt = ωt + (1− α)wt,

the social planner’s problem can be rewritten as:40

V (Kt(·), H t, zt, xt, ut, wt) = maxCt,Nt,ωt′ ,ωt′

(1− β) [logCt − κNt]

+βEt[V (Kt+1(·), H t+1, zt+1, xt+1, ut+1, wt+1)

],

subject to

eztK1−αt Nα

t = Ct + e−xt

[∫ ∞ωt

1

σeφ

(ωt − ut − (1− α)wt

σe

)H tdωt (12)

−(1− η)

∫ ωt

−∞Kt(ωt)dωt

],

Kt =

∫ ∞−∞

e1

1−αωtKt(ωt)dωt,

Kt+1(ωt+1) = (1− δ)∫ ∞ωt

1

σωφ

(ωt+1 − ωt

σω

)Kt(ωt)dωt (13)

+

∫ ∞ωt

1

σωφ

(ωt+1 − ωt

σω

)1

σeφ

(ωt − ut − (1− α)wt

σe

)H tdωt.

Note that this social planner’s problem is identical to one in which the capital

efficiency is not time varying and the initial productivity of potential entrants

is drawn from

ωt ∼ N(ut + (1− α)wt, σ2e)

40ωt is a dummy variable that is integrated out; hence, we can use ωt again—or anyletter—to denote this variable.

45

instead of (2).41 Hence two rival technologies, ut and wt, are isomorphic except

that their effects on the quality-adjusted price of capital goods P and the

original entry threshold ωt are different.42

The economy grows because of technological progress. To solve the social

planner’s problem, the problem must be transformed into a stationary one.

Expressing idiosyncratic productivity as a deviation from rival technologies,43

ω?t = ωt − ut−1 − (1− α)wt−1,

and dividing all variables except labor and entry/exit thresholds by the corre-

sponding stochastic trends,

C?t =

Ct

e1α

(zt+(1−α)xt+ut+(1−α)wt), K?

t (ω?t ) =Kt (ω?t + ut−1 + (1− α)wt−1)

e1α

(zt+xt+ut+(1−α)wt), . . . ,

accomplish this transformation. The resulting stationary problem is:

V ?(K?t (·),∆ut + (1− α)∆wt) = max

C?t ,Nt,ω?t ,ω

?t

(1− β) [logC?t − κNt] (14)

+βEt[V ?(K?

t+1(·),∆ut+1 + (1− α)∆wt+1)],

41Because the idea of the potential entrant who decides against entry disappears, allsurviving ideas in a given period are ones that are combined with capital in the sameperiod. Hence, it does not affect the outcome regardless of whether the initial productivityis shifted—ωt becomes ωt + (1− α)wt—before or after entry.

42ωt is the entry threshold for an entrant’s productivity before her initial productivity isshifted by (1− α)wt, whereas ωt is one after the productivity shift.

43Normalizing with respect to the lagged values of rival technologies is convenient be-cause the evolution of the normalized idiosyncratic productivity, ω?t to ω?t+1, is expressedas depending on the aggregate information up to the present, ∆ut + (1−α)∆wt, instead of∆ut+1 + (1− α)∆wt+1.

46

subject to

(K?t )1−αNα

t = C?t +

∫ ∞ω?t

1

σeφ

(ω?t −∆ut − (1− α)∆wt

σe

)H?dω?t

−(1− η)

∫ ω?t

−∞K?t (ω?t )dω

?t ,

K?t =

∫ ∞−∞

e1

1−α (ω?t−∆ut−(1−α)∆wt)K?t (ω?t )dω

?t ,

e1α

(∆zt+1+∆xt+1+∆ut+1+(1−α)∆wt+1)K?t+1(ω?t+1)

= (1− δ)∫ ∞ω?t

1

σωφ

(ω?t+1 − ω?t + ∆ut + (1− α)∆wt

σω

)K?t (ω?t )dω

?t

+

∫ ∞ω?t

1

σωφ

(ω?t+1 − ω?t + ∆ut + (1− α)∆wt

σω

)× 1

σeφ

(ω?t −∆ut − (1− α)∆wt

σe

)H?dω?t ,

where H?

is a constant number.

The Lagrangian for the problem is:

L = max (1− β) [logC?t − κNt] + βEt

[V ?(K?t+1(·),∆ut+1 + (1− α)∆wt+1

)]+Mt

[(K?

t )1−αNαt − Ct −

∫ ∞ω?t

1

σeφ

(ω?t −∆ut − (1− α)∆wt

σe

)H?dω?t

+(1− η)

∫ ω?t

−∞K?t (ω?t )dω

?t

]+MtDt

[∫ ∞−∞

e1

1−α (ω?t−∆ut−(1−α)∆wt)K?t (ω?t )dω

?t − K?

t

]

+Mt

∫ ∞−∞Qt(ω?t+1)

[(1− δ)

∫ ∞ω?t

1

σωφ

(ω?t+1 − ω?t + ∆ut + (1− α)∆wt

σω

)×K?

t (ω?t )dω?t +

∫ ∞ω?t

1

σωφ

(ω?t+1 − ω?t + ∆ut + (1− α)∆wt

σω

)× 1

σeφ

(ω?t −∆ut − (1− α)∆wt

σe

)H?dω?t

−e1α

(∆zt+1+∆xt+1+∆ut+1+(1−α)∆wt+1)K?t+1(ω?t+1)

]dω?t+1.

47

Note that the Lagrange multipliers44 Qt(ω?t+1) represent the value of a unit

of e1α

(∆zt+1+∆xt+1+∆ut+1+(1−α)∆wt+1)K?t+1(ω?t+1) =

Kt+1(ω?t+1+ut+(1−α)wt)

e1α (zt+xt+ut+(1−α)wt)

denomi-

nated in units of the normalized output Y ?t = Yt

e1α (zt+(1−α)xt+ut+(1−α)wt)

; equiva-

lently, Qt(ω?t+1) is the value of a unit of Kt+1(ωt+1) denominated in units of

(unnormalized) capital goods.

The first-order conditions are as follows:

• Optimal labor:

κ =1

C?t

× α

(K?t

Nt

)1−α

. (15)

The marginal disutility of labor equals the product of the marginal utility

of consumption and the marginal product of labor.

• Plant asset pricing45:

Qt(ω?t+1) = Et

[βe−

1α

(∆zt+1+∆xt+1+∆ut+1+(1−α)∆wt+1)

(C?t+1

C?t

)−1

(16)

×(

(1− α)

(K?t+1

Nt+1

)−αe

11−α(ω?t+1−∆ut+1−(1−α)∆wt+1)

+I(ω?t+1 ≤ ω?t+1)(1− η) + I(ω?t+1 > ω?t+1)(1− δ)

×∫ ∞−∞

1

σωφ

(ω?t+2 − ω?t+1 + ∆ut+1 + (1− α)∆wt+1

σω

)×Qt+1(ω?t+2)dω?t+2

)].

The value of a plant with the idiosyncratic productivity ω?t+1 is the ex-

44The other Lagrange multipliers are straightforward(Mt = 1−β

C?t, Dt = (1 −

α)

(K?t+1

Nt+1

)−α )and are substituted out in the following first-order conditions.

45I(·) is an indicator function.

48

pected discounted value of the following terms: the marginal product of

the plant with ω?t+1, the resale value of capital if the plant exits, and

the transition probability from ω?t+1 to ω?t+2 multiplied by the value of a

plant with ω?t+2 if the plant does not exit.

• Optimal entry:

1 =

∫ ∞−∞

1

σωφ

(ω?t+1 − ω?t + ∆ut + (1− α)∆wt

σω

)(17)

×Qt(ω?t+1)dω?t+1.

The marginal benefit of increasing the entry threshold ω?t is saving the

purchase cost of capital. The marginal cost is giving up the value of new

plant.

• Optimal exit:

1− η = (1− δ)∫ ∞−∞

1

σωφ

(ω?t+1 − ω?t + ∆ut + (1− α)∆wt

σω

)(18)

×Qt(ω?t+1)dω?t+1.

The marginal benefit of increasing the exit threshold ω?t is earning the

resale value of capital. The marginal cost is losing the continuation value

of the plant.

49

Appendix B Competitive Equilibrium and the

Social Planner’s Problem

B.1 Recursive Competitive Equilibrium

The aggregate state of the economy is described by Λt = (Kt(·), H t, zt, xt, ut, wt).

Denote the perceived law of motion for Kt(·) by Γk:

Kt+1(·) = Γk(Λt).

Let Mt,t+1 represent the stochastic discount factor between t and t + 146 and

W (Λt) represent the equilibrium wage rate.

To be well defined, the following problems must be transformed into sta-

tionary ones by appropriately scaling in a similar way to Appendix A. To avoid

an explosion of notation, the problems are stated below without scaling as if

all variables are stationary. A recursive competitive equilibrium is defined by

the following conditions:

• Plants optimally decide how much labor to hire and whether to exit the

market. The plant’s problem is:

46Mt,t+1(Λt,Λt+1) depends on the aggregate state of the economy in the current andnext periods. Its arguments are dropped for notational simplicity.

50

vk(ωt; Λt) = maxn

[ezt+ωtnα −W (Λt)n+ max

{(1− η)e−xt ,

(1− δ)∫ ∞−∞

1

σωφ

(ωt+1 − ωt

σω

)E[Mt,t+1v

k(ωt+1; Λt+1)∣∣∣Λt

]dωt+1

}]

= maxn,ω

[ezt+ωtnα −W (Λt)n+ I(ωt ≤ ω)(1− η)e−xt

+I(ωt > ω)(1− δ)∫ ∞−∞

1

σωφ

(ωt+1 − ωt

σω

)×E

[Mt,t+1v

k(ωt+1; Λt+1)∣∣∣Λt

]dωt+1

].

The policy functions are employment nk(ωt; Λt) and exit threshold ω(Λt),

which satisfy

nk(ωt; Λt) =α

11−α e

11−α (zt+ωt)

W (Λt)1

1−α(19)

(1− η)e−xt = (1− δ)∫ ∞−∞

1

σωφ

(ωt+1 − ω(Λt)

σω

)(20)

×E[Mt,t+1v

k(ωt+1; Λt+1)∣∣∣Λt

]dωt+1.

The resulting value (share price) of the plant is

vk(ωt; Λt) = (1− α)α

α1−α e

11−α (zt+ωt)

W (Λt)α

1−α(21)

+I(ωt ≤ ω(Λt))(1− η)e−xt + I(ωt > ω(Λt))(1− δ)

×∫ ∞−∞

1

σωφ

(ωt+1 − ωt

σω

)E[Mt,t+1v

k(ωt+1; Λt+1)∣∣∣Λt

]dωt+1.

• There are a mass H t of idea owners, who make the following once-and-

51

for-all decision about entry:

vh(ωt; Λt) = max

{0,−e−xt +

∫ ∞−∞

1

σωφ

(ωt+1 − ωt − (1− α)wt

σω

)×E

[Mt,t+1v

k(ωt+1; Λt+1)∣∣∣Λt

]dωt+1

},

where ωt is the idea owner’s productivity before it is shifted by (1−α)wt,

distributed by N(ut, σ2e). Equivalently, we can define the idea owner’s

problem in terms of the productivity after it is shifted by (1− α)wt:47

vh(ωt; Λt) = max

{0,−e−xt +

∫ ∞−∞

1

σωφ

(ωt+1 − ωt

σω

)×E

[Mt,t+1v

k(ωt+1; Λt+1)∣∣∣Λt

]dωt+1

},

where ωt is now distributed by N(ut + (1− α)wt, σ2e).

The policy function is the entry threshold ω(Λt), which satisfies

e−xt =

∫ ∞−∞

1

σωφ

(ωt+1 − ω(Λt)

σω

)(22)

×E[Mt,t+1v

k(ωt+1; Λt+1)∣∣∣Λt

]dωt+1.

The resulting value of the idea is

vh(ωt; Λt) = I(ωt > ω(Λt))

[− e−xt (23)

+

∫ ∞−∞

1

σωφ

(ωt+1 − ωt

σω

)E[Mt,t+1v

k(ωt+1; Λt+1)∣∣∣Λt

]dωt+1

].

47vh(ωt; Λt) = vh(ωt − (1− α)wt; Λt) holds. Also see footnote 41.

52

• Households’ state variables include their share holding of plants Kt(·) in

addition to aggregate state variables Λt. Note that households receive

endowments of ideas H t in each period. They solve:

vc(Kt(·),Λt) = maxc,nc,Kc(·)

(1− β) [log c− κnc] + βE[vc(Kc(·),Λt+1)|Λt],

subject to

c+

∫ ∞−∞

qk(ωt+1; Λt)Kc(ωt+1)dωt+1 = W (Λt)n

c (24)

+

∫ ∞−∞

vk(ωt; Λt)Kt(ωt)dωt

+

∫ ∞−∞

vh(ωt; Λt)1

σeφ

(ωt − ut − (1− α)wt

σe

)H tdωt,

where qk(ωt+1; Λt) is the current period share price of plants that begin

the next period with productivity ωt+1; that is,

qk(ωt+1; Λt) = E[Mt,t+1v

k(ωt+1,Λt+1)|Λt

]. (25)

The policy functions are consumption c(Kt(·),Λt), labor supply nc(Kt(·),Λt),

and shares of plants Kc(ωt+1; Kt(·),Λt), which satisfy

κ =1

c(Kt(·),Λt)W (Λt), (26)

qk(ωt+1; Λt) = E

β(c(Kt+1(·),Λt+1)

c(Kt(·),Λt)

)−1

vk(ωt+1; Λt+1)

∣∣∣∣∣Λt

(27)

• The labor market clears:

nc(Kt(·),Λt) =

∫ ∞−∞

nk(ωt; Λt)Kt(ωt)dωt. (28)

53

• The good market clears:

c(Kt(·),Λt) =

∫ ∞−∞

ezt+ωtnk(ωt; Λt)αKt(ωt)dωt (29)

−e−xt[∫ ∞

ω(Λt)

1

σeφ

(ωt − ut − (1− α)wt

σe

)H tdωt

−(1− η)

∫ ω(Λt)

−∞Kt(ωt)dωt

].

• The asset market clears:

Kc(ωt+1;Kt(·),Λt) = Kt+1(ωt+1) for all ωt+1. (30)

• Rational expectations: the economy indeed evolves as Kt+1(·) = Γk(Λt);

that is, for all ωt+1,

Γk(Λt)(ωt+1) = (1− δ)∫ ∞ω(Λt)

1

σωφ

(ωt+1 − ωt

σω

)Kt(ωt)dωt (31)

+

∫ ∞ω(Λt)

1

σωφ

(ωt+1 − ωt

σω

)1

σeφ

(ωt − ut − (1− α)wt

σe

)H tdωt.

Note that in equilibrium, households’ asset holding is equal to the economy-

wide capital stock:

Kt(·) = Kt(·), (32)

which is imposed in market clearing conditions (28)–(30).

B.2 Comparison

This subsection shows that the solution to the social planner’s problem in

Appendix A satisfies the conditions of recursive competitive equilibrium. Sup-

54

pose that C?t , Nt, ω

?t , ω

?t ,Qt(·) solves the problem (14) and the endogenous

state variable K?t (·) evolves accordingly. Consider the following allocations

and prices from the social planner’s problem:

nk(ωt; Λt) = nt(ω) (33)

ω(Λt) = ω?t + ut−1 + (1− α)wt−1 = ωt (34)

ω(Λt) = ω?t + ut−1 + (1− α)wt−1 = ωt (35)

c(Kt(·),Λt) = C?t e

1α

(zt+(1−α)xt+ut+(1−α)wt) = Ct (36)

nc(Kt(·),Λt) = Nt (37)

Kc(ωt+1;Kt(·),Λt) = K?t+1(ω?t+1)e

1α

(zt+1+xt+1+ut+1+(1−α)wt+1) (38)

= Kt+1(ωt+1)

Mt,t+1 = βe−1α

(∆zt+1+(1−α)∆xt+1+∆ut+1+(1−α)∆wt+1)

(C?t+1

C?t

)−1

(39)

= β

(Ct+1

Ct

)−1

W (Λt) = α

(K?t

Nt

)1−α

e1α

(zt+(1−α)xt+ut+(1−α)wt) (40)

= αezt

(Kt

Nt

)1−α

.

Because the competitive equilibrium conditions are presented with unscaled

variables, it is important to keep the correspondence between scaled and un-

scaled variables. The second, if any, equality in each of the above equations

are in terms of unscaled variables of the original—before being transformed

into a stationary one—social planer’s problem.48

48The second equality in equation (40) comes from

Kt =

∫ ∞−∞

e1

1−αωtKt(ωt)dωt

55

Substituting (34) and (40) into (21), we get:

vk(ωt; Λt) = (1− α)

(K?t

Nt

)−αe

11−α (ω?t−∆ut−(1−α)∆wt)e−xt

+I(ω?t ≤ ω?t )(1− η)e−xt + I(ω?t > ω?t )(1− δ)

×∫ ∞−∞

1

σωφ

(ω?t+1 − ω?t + ∆ut + (1− α)∆wt

σω

)×E

[Mt,t+1v

k(ωt+1; Λt+1)∣∣∣Λt

]dω?t+1.

Therefore, equation (25) implies

qk(ωt+1; Λt) = E[Mt,t+1v

k(ωt+1,Λt+1)|Λt

]= E

[Mt,t+1

((1− α)

(K?t+1

Nt+1

)−αe

11−α(ω?t+1−∆ut+1−(1−α)∆wt+1)e−xt+1

+I(ω?t+1 ≤ ω?t+1)(1− η)e−xt+1 + I(ω?t+1 > ω?t+1)(1− δ)

×∫ ∞−∞

1

σωφ

(ω?t+2 − ω?t+1 + ∆ut+1 + (1− α)∆wt+1

σω

)×qk(ωt+2; Λt+1)dω?t+2

)∣∣∣∣∣Λt

].

By comparing the above with equation (16) using (39), we obtain

qk(ωt+1,Λt) = Qt(ω?t+1)e−xt . (41)

In other words, the values of plants—vk(ωt; Λt), qk(ωt+1; Λt)—that are implied

by the allocations and prices considered in (33)–(40) satisfy equation (41).

Now examine whether these allocations and prices satisfy the conditions of

=

∫ ∞−∞

e1

1−α (ω?t+ut−1+(1−α)wt−1)K?t (ω?t )e

1α (zt+xt+ut+(1−α)wt)dω?t

= K?t e

1α (zt+xt+ 1

1−αut+wt).

56

recursive competitive equilibrium:

• Condition (19) is implied by equations (9), (33), and (40).

• Condition (20) is implied by equations (18), (25), (34), and (41).

• Condition (22) is implied by equations (17), (25), (35), and (41).

• Condition (24) is implied by equations (12) and (13): plugging equations

(21), (23), (25), (32), (34)–(38), and (40) into (24) gives

Ct +

∫ ∞−∞

qk(ωt+1; Λt)Kt+1(ωt+1)dωt+1

= αeztK1−αt Nα

t

+

∫ ∞−∞

[(1− α)ezt

(Kt

Nt

)−αe

11−αωt + I(ωt ≤ ωt)(1− η)e−xt

+I(ωt > ωt)(1− δ)∫ ∞−∞

1

σωφ

(ωt+1 − ωt

σω

)qk(ωt+1; Λt)dωt+1

]Kt(ωt)dωt

+

∫ ∞−∞

I(ωt > ωt)

[− e−xt +

∫ ∞−∞

1

σωφ

(ωt+1 − ωt

σω

)×qk(ωt+1; Λt)dωt+1

]1

σeφ

(ωt − ut − (1− α)wt

σe

)H tdωt

= αeztK1−αt Nα

t + (1− α)ezt

(Kt

Nt

)−α ∫ ∞−∞

e1

1−αωtKt(ωt)dωt

+(1− η)e−xt∫ ωt

−∞Kt(ωt)dωt

+

∫ ∞−∞

qk(ωt+1; Λt)

[(1− δ)

∫ ∞ωt

1

σωφ

(ωt+1 − ωt

σω

)Kt(ωt)dωt

]dωt+1

−e−xt∫ ∞ωt

1

σeφ

(ωt − ut − (1− α)wt

σe

)H tdωt +

∫ ∞−∞

qk(ωt+1; Λt)

×

[∫ ∞ωt

1

σωφ

(ωt+1 − ωt

σω

)1

σeφ

(ωt − ut − (1− α)wt

σe

)H tdωt

]dωt+1

= eztK1−αt Nα

t − e−xt[∫ ∞

ωt

1

σeφ

(ωt − ut − (1− α)wt

σe

)H tdωt

57

−(1− η)

∫ ωt

−∞Kt(ωt)dωt

]

+

∫ ∞−∞

qk(ωt+1; Λt)

[(1− δ)

∫ ∞ωt

1

σωφ

(ωt+1 − ωt

σω

)Kt(ωt)dωt

+

∫ ∞ωt

1

σωφ

(ωt+1 − ωt

σω

)1

σeφ

(ωt − ut − (1− α)wt

σe

)H tdωt

]dωt+1

where equation (11) is applied in the last equality; hence equation (24)

becomes

eztK1−αt Nα

t = Ct + e−xt

[∫ ∞ωt

1

σeφ

(ωt − ut − (1− α)wt

σe

)H tdωt

−(1− η)

∫ ωt

−∞Kt(ωt)dωt

]

+

∫ ∞−∞

qk(ωt+1; Λt)

[Kt(ωt+1)− (1− δ)

∫ ∞ωt

1

σωφ

(ωt+1 − ωt

σω

)Kt(ωt)dωt

−∫ ∞ωt

1

σωφ

(ωt+1 − ωt

σω

)1

σeφ

(ωt − ut − (1− α)wt

σe

)H tdωt

]dωt+1,

which is implied by equations (12) and (13).

• Condition (26) is implied by equations (15), (32), (36), and (40).

• Condition (27) is implied by equations (25), (32), (36), and (39).

• Condition (28) is implied by equations (8), (33), and (37).

• Condition (29) is implied by equations (10), (12), (34), (35), and (36).

• Condition (30) is implied by equation (38).

• Condition (31)—rational expectations—is trivially satisfied because all

agents’ perceived law of motion for Kt(·) is assumed to be the actual law

of motion for Kt(·) from the social planner’s problem.

58

Therefore, all conditions of recursive competitive equilibrium are satisfied

and the solution to the social planner’s problem indeed forms a competitive

equilibrium.

Appendix C Model Implications on Macroe-

conomic Variables

Figure 13 plots the impulse responses of key macroeconomic variables49 in the

model. Note that the responses in the last two panels are identical because

two rival technologies, ut and wt, are isomorphic except for their effects on the

quality-adjusted price of capital and the entry threshold (see Appendix A).

All four shocks lead to an economic expansion, but the initial responses to

shocks other than the first one do not exhibit a typical pattern of comovements.

First, consumption and labor move in opposite directions (bottom three

panels). This negative comovement of consumption and labor on the im-

pact of non-TFP shocks is common in the standard neoclassical growth model

(Barro and King, 1984): consumption and leisure are both normal goods and

therefore, unless shocks affect the relative price (marginal product of labor),

consumption and leisure move in the same direction.

Second, output and labor fall at the outset of the rival technology shocks

(bottom two panels). Innovation to the rival technologies in the model gradu-

ally spreads across the whole economy as a new generation of plants takes over

and thus it represents an anticipated increase in future TFP. The initial fall

of output and labor in response to a news shock is also common in neoclassi-

49Investment here is net investment, representing e−xt[∫∞ωtHt(ωt)dωt − (1− η)

∫ ωt−∞Kt(ωt)dωt

]in equation (3).

59

10 20 30 400

0.5

1

1.5

pe

rce

nt

quarters

Output

10 20 30 400

0.5

1

1.5

pe

rce

nt

quarters

Consumption

10 20 30 400

1

2

3

pe

rce

nt

quarters

Investment

10 20 30 400

0.1

0.2

0.3

0.4

pe

rce

nt

quarters

Labor

10 20 30 400

0.5

1

1.5

pe

rce

nt

quarters

Labor Productivity

10 20 30 400

0.5

1

1.5

pe

rce

nt

quarters

Output

10 20 30 40−0.5

0

0.5

1

1.5

pe

rce

nt

quarters

Consumption

10 20 30 400

2

4

6

8

10

pe

rce

nt

quarters

Investment

10 20 30 400

0.5

1

1.5

pe

rce

nt

quarters

Labor

10 20 30 40−0.5

0

0.5

1

1.5

pe

rce

nt

quarters

Labor Productivity

10 20 30 40−0.5

0

0.5

1

1.5

pe

rce

nt

quarters

Output

10 20 30 400

0.5

1

1.5

pe

rce

nt

quarters

Consumption

10 20 30 40−1

0

1

2

3

pe

rce

nt

quarters

Investment

10 20 30 40−0.2

0

0.2

0.4

pe

rce

nt

quarters

Labor

10 20 30 400

0.5

1

1.5

pe

rce

nt

quarters

Labor Productivity

10 20 30 40−0.5

0

0.5

1

1.5

pe

rce

nt

quarters

Output

10 20 30 400

0.5

1

1.5

pe

rce

nt

quarters

Consumption

10 20 30 40−1

0

1

2

3

pe

rce

nt

quarters

Investment

10 20 30 40−0.2

0

0.2

0.4p

erc

en

t

quarters

Labor

10 20 30 400

0.5

1

1.5

pe

rce

nt

quarters

Labor Productivity

Figure 13: Impulse responses of entry and exit to a 1 percent increase in nonrivalinvestment-neutral technology zt (top panel), nonrival investment-specific technol-ogy (1 − α)xt (second panel), rival investment-neutral technology ut (third panel),and rival investment-specific technology (1− α)wt (bottom panel).

cal environments (e.g., Cochrane, 1994): good news about future productivity

makes households wealthier, thereby reducing labor supply.

Various specifications have been introduced in the literature (e.g., Green-

wood et al., 1988; Justiniano et al., 2010; Jaimovich and Rebelo, 2009; Schmitt-

Grohe and Uribe, 2012) to generate positive comovement in response to investment-

specific technology shocks and news shocks. These specifications include vari-

able capital utilization, preferences with a weak wealth effect on labor supply,

and investment adjustment costs.

60

Appendix D Time to Exit

Figure 14 shows the results when four quarters of time to exit is assumed. The

exit rate initially declines in all four cases: the exit does not respond imme-

diately by the time-to-exit assumption but the entry and the total measure

of plants rise so that the exit rate falls. The exit response appears after the

fourth quarter, displaying a lead-lag pattern between entry and exit rates.

10 20 30 40−8

−6

−4

−2

0x 10

−4

quarters

Entry threshold

10 20 30 40−1

−0.8

−0.6

−0.4

−0.2

0x 10

−3

quarters

Exit threshold

10 20 30 400

0.02

0.04

0.06

0.08

pe

rce

nt

quarters

Entry rate

10 20 30 40−0.03

−0.02

−0.01

0

pe

rce

nt

quarters

Exit rate

10 20 30 40−1

−0.5

0

0.5

1

pe

rce

nt

quarters

Capital price

10 20 30 40−3

−2

−1

0x 10

−3

quarters

Entry threshold

10 20 30 40−3

−2

−1

0x 10

−3

quarters

Exit threshold

10 20 30 400

0.1

0.2

0.3

0.4

pe

rce

nt

quarters

Entry rate

10 20 30 40−0.1

−0.08

−0.06

−0.04

−0.02

0

pe

rce

nt

quarters

Exit rate

10 20 30 40−3

−2

−1

0

pe

rce

nt

quarters

Capital price

10 20 30 400

0.002

0.004

0.006

0.008

0.01

quarters

Entry threshold

10 20 30 400

0.002

0.004

0.006

0.008

0.01

quarters

Exit threshold

10 20 30 400

0.05

0.1

0.15

0.2

pe

rce

nt

quarters

Entry rate

10 20 30 40−0.05

0

0.05

0.1

0.15

pe

rce

nt

quarters

Exit rate

10 20 30 40−1

−0.5

0

0.5

1

pe

rce

nt

quarters

Capital price

10 20 30 40−3

−2

−1

0x 10

−3

quarters

Entry threshold

10 20 30 400

0.002

0.004

0.006

0.008

0.01

quarters

Exit threshold

10 20 30 400

0.05

0.1

0.15

0.2

pe

rce

nt

quarters

Entry rate

10 20 30 40−0.05

0

0.05

0.1

0.15

pe

rce

nt

quarters

Exit rate

10 20 30 40−3

−2

−1

0

pe

rce

nt

quarters

Capital price

Figure 14: Four quarters of time to exit is assumed. Impulse responses of entry andexit to a 1 percent increase in nonrival investment-neutral technology zt (top panel),nonrival investment-specific technology (1 − α)xt (second panel), rival investment-neutral technology ut (third panel), and rival investment-specific technology (1 −α)wt (bottom panel). All deviations are in levels.

61

Appendix E Data Summary Statistics

Figure 15: Data. Shaded areas indicate NBER recessions.

62

Variable Description Mean Std AC(1) AC(4)Corr

with ∆y

∆p log difference of investment price -1.32 0.61 0.46 0.02 -0.43

∆a log difference of labor productivity 0.30 0.70 -0.03 -0.08 0.36

h log of per capita hours -7.66 0.07 0.99 0.93 0.28

∆h log difference of per capita hours -0.08 0.77 0.71 0.27 0.61

enr establishment entry rate 3.22 0.25 0.87 0.78 0.36

exr establishment exit rate 2.94 0.20 0.79 0.57 -0.36

exr + enr establishment turnover rate 6.17 0.34 0.87 0.81 0.04

jcr job creation rate 7.20 0.81 0.92 0.93 0.45

jdr job destruction rate 6.91 0.68 0.94 0.76 -0.04

jcr + jdr job reallocation rate 14.10 1.35 0.96 0.97 0.25

tr1 acquisitions/lagged total assets 0.22 0.09 0.75 0.59 0.23

tr2 sales of PP&E/lagged total PP&E 0.45 0.14 0.87 0.77 0.16

tr1 + tr2 capital turnover rate 0.68 0.21 0.90 0.78 0.20

Table 4: Summary Statistics. Sample period is 1993:II–2014:II. The expressionAC(j) is the jth autocorrelation, ∆y is real per capital GDP growth, and PP&Estands for property, plant, and equipment. All variables are expressed as a percent-age except for log per capita hours h.

Appendix F Job Flow in the Manufacturing

Sector for 1972:I-1993:IV

Figure 16 shows that on impact, job destruction rate falls while job creation

rate slightly rises. As a result, job reallocation rate falls, which confirms the

finding of Michelacci and Lopez-Salido (2007). Note that the investment-

specific technology shock accounts for a small fraction of the job creation and

destruction rates in Figure 17. Not surprisingly, the correlation between the

reallocation shock and the investment-specific technology shock is low in this

sample.

63

5 10 15 20 25 30 35 40

−2

−1.5

−1

−0.5

0

Investment price

perc

ent

quarters5 10 15 20 25 30 35 40

−0.8

−0.7

−0.6

−0.5

−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

Labor productivity

perc

ent

quarters5 10 15 20 25 30 35 40

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Hours

perc

ent

quarters

5 10 15 20 25 30 35 40−0.2

−0.15

−0.1

−0.05

0

0.05

0.1

0.15

Job creation rate

perc

ent

quarters5 10 15 20 25 30 35 40

−0.4

−0.3

−0.2

−0.1

0

0.1

Job destruction rate

perc

ent

quarters5 10 15 20 25 30 35 40

−0.45

−0.4

−0.35

−0.3

−0.25

−0.2

−0.15

−0.1

−0.05

0

0.05

Job reallocation rate

perc

ent

quarters

Figure 16: Impulse responses to an investment-specific technology shock based onjob flow data in the manufacturing sector for 1972:I-1993:IV.

0 10 20 30 400

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Investment price

fra

ctio

n o

f F

EV

quarters0 10 20 30 40

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Labor productivity

fra

ctio

n o

f F

EV

quarters0 10 20 30 40

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Hours

fra

ctio

n o

f F

EV

quarters

0 10 20 30 400

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Job creation rate

fra

ctio

n o

f F

EV

quarters0 10 20 30 40

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Job destruction rate

fra

ctio

n o

f F

EV

quarters0 10 20 30 40

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Job reallocation rate

fra

ctio

n o

f F

EV

quarters

Figure 17: Fraction of forecast error variance (FEV) explained by investment-specific technology shock based on job flow data in the manufacturing sector for1972:I-1993:IV.

64

Appendix G Impulse Responses with 90 Per-

cent Error Bands

5 10 15 20 25 30 35 40

−5

−4

−3

−2

−1

0

Investment price

pe

rce

nt

quarters5 10 15 20 25 30 35 40

0

0.5

1

1.5

2

2.5

3

Labor productivity

pe

rce

nt

quarters5 10 15 20 25 30 35 40

−3

−2

−1

0

1

2

3

4

Hours

pe

rce

nt

quarters

5 10 15 20 25 30 35 40

−0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

Entry rate

pe

rce

nt

quarters5 10 15 20 25 30 35 40

−0.08

−0.06

−0.04

−0.02

0

0.02

0.04

0.06

0.08

Exit rate

pe

rce

nt

quarters5 10 15 20 25 30 35 40

−0.05

0

0.05

0.1

0.15

Turnover rate

pe

rce

nt

quarters

Figure 18: Impulse responses to an investment-specific technology shock based onentry and exit data.

0 10 20 30 400

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Investment price

fra

ctio

n o

f F

EV

quarters0 10 20 30 40

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Labor productivity

fra

ctio

n o

f F

EV

quarters0 10 20 30 40

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Hours

fra

ctio

n o

f F

EV

quarters

0 10 20 30 400

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Entry rate

fra

ctio

n o

f F

EV

quarters0 10 20 30 40

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Exit rate

fra

ctio

n o

f F

EV

quarters0 10 20 30 40

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Turnover rate

fra

ctio

n o

f F

EV

quarters

Figure 19: Fraction of forecast error variance (FEV) explained by investment-specific technology shock based on entry and exit data

65

5 10 15 20 25 30 35 40

−2

−1.5

−1

−0.5

0

Investment price

pe

rce

nt

quarters5 10 15 20 25 30 35 40

−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

Labor productivity

pe

rce

nt

quarters5 10 15 20 25 30 35 40

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Hours

pe

rce

nt

quarters

5 10 15 20 25 30 35 400

0.05

0.1

0.15

0.2

Job creation rate

pe

rce

nt

quarters5 10 15 20 25 30 35 40

−0.15

−0.1

−0.05

0

0.05

0.1

0.15

Job destruction rate

pe

rce

nt

quarters5 10 15 20 25 30 35 40

−0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

Job reallocation rate

pe

rce

nt

quarters

Figure 20: Impulse responses to an investment-specific technology shock based onjob flow data.

0 10 20 30 400

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Investment price

fra

ctio

n o

f F

EV

quarters0 10 20 30 40

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Labor productivity

fra

ctio

n o

f F

EV

quarters0 10 20 30 40

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Hours

fra

ctio

n o

f F

EV

quarters

0 10 20 30 400

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Job creation rate

fra

ctio

n o

f F

EV

quarters0 10 20 30 40

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Job destruction rate

fra

ctio

n o

f F

EV

quarters0 10 20 30 40

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Job reallocation rate

fra

ctio

n o

f F

EV

quarters

Figure 21: Fraction of forecast error variance (FEV) explained by investment-specific technology shock based on job flow data.

66

5 10 15 20 25 30 35 40

−5

−4.5

−4

−3.5

−3

−2.5

−2

−1.5

−1

−0.5

0

Investment price

perc

ent

quarters5 10 15 20 25 30 35 40

0

0.5

1

1.5

2

2.5

3

Labor productivity

perc

ent

quarters5 10 15 20 25 30 35 40

−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5

Hours

perc

ent

quarters

5 10 15 20 25 30 35 40

−0.01

−0.005

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

Acquisitions turnover rate

perc

ent

quarters5 10 15 20 25 30 35 40

−0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

Property sale turnover rate

perc

ent

quarters5 10 15 20 25 30 35 40

−0.02

0

0.02

0.04

0.06

0.08

0.1

Sum of turnover rates

perc

ent

quarters

Figure 22: Impulse responses to an investment-specific technology shock based oncapital reallocation data.

0 10 20 30 400

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Investment price

frac

tion

of F

EV

quarters0 10 20 30 40

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Labor productivity

frac

tion

of F

EV

quarters0 10 20 30 40

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Hours

frac

tion

of F

EV

quarters

0 10 20 30 400

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Acquisitions turnover rate

frac

tion

of F

EV

quarters0 10 20 30 40

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Property sale turnover rate

frac

tion

of F

EV

quarters0 10 20 30 40

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Sum of turnover rates

frac

tion

of F

EV

quarters

Figure 23: Fraction of forecast error variance (FEV) explained by investment-specific technology shock based on capital reallocation data.

67