DPRIETI Discussion Paper Series 21-E-015

In Search of Lost Time: Firm Vintage and Macroeconomic Dynamics

HAMANO, Masashige
Waseda University

OKUBO, Toshihiro
Keio University

The Research Institute of Economy, Trade and Industry

https://www.rieti.go.jp/en/

RIETI Discussion Paper Series 21-E-015
March 2021

In search of lost time: firm vintage and macroeconomic dynamics*
Masashige Hamano
Waseda University
Toshihiro Okubo
Keio University
Abstract

This paper attempts to reproduce the past landscape of the economy with the help of evidence and structuralmodels. For that purpose, we built a theoretical model consisting of endogenous firm entry and firm
selection. Given the distribution of firm age and firm sales that we see today, we simulated age-specifictechnologies and fixed costs for operation. With these simulated parameters, we then reestablished themacroeconomic dynamics of each historical firm. With Japanese data from over 126 years, despite themassive presence of firms created after the Second World War until the oil crisis in the 1970s, we foundthat these historical firms show relatively low productivity. Old historical firms are subject to high fixed
costs and high productivity. Finally, we demonstrated that our counterfactual fixed costs dramaticallychange the landscape of historical firms, as well as their characteristics.
Keywords: Heterogeneity, fixed cost, business cycles.
JEL classification: D24, E23, E32, L11, L60.
The RIETI Discussion Paper Series aims at widely disseminating research results in the form of professional
papers, with the goal of stimulating lively discussion. The views expressed in the papers are solely those of
the author(s), and neither represent those of the organization(s) to which the author(s) belong(s) nor the
Research Institute of Economy, Trade and Industry.

*

This study is conducted as a part of the Project “East Asian Industrial Productivity” undertaken at the ResearchInstitute of Economy, Trade and Industry (RIETI). This study utilizes the micro data of the questionnaire
information based on “the Basic Survey of Japanese Business Structure and Activities” which is conducted by the
Ministry of Economy, Trade and Industry (METI). The author is grateful for helpful comments and suggestions by
Discussion Paper seminar participants at RIETI.
1And suddenly the memory revealed itself. by Proust, “A la recherche du temps perdu”

1Introduction

What does the past look like? Given the economic landscape that we see today, is there
any way to trace back history, not only for the entire economy but also for individual
firms? If the crumbs of a madeleine are enough to reveal one’s childhood memories, as
Proust wrote, then other pieces of evidence may reestablish history in every tiny detail.
In search of lost time, we attempt to build a macroeconomic model with vintage firms
and attempt to reveal the history of each firm with the help of limited data.
The first two panels in Figure 1 provide the distribution of vintage Japanese firms andtheir sales, as reported in a 2013 survey. We define “vintage” as the firm’s age since its
foundation. For the distribution of vintage firm shares and their relative sales, we use the
Basic Survey of Japanese Business Structure and Activities (BSJBSA), as provided by
the Ministry of Economy, Trade and Industry of Japan (METI). The data covers firms
from 1887 to 2012.1 It is noticeable that the share of firms created in the middle ranges ofthe study period spanning 126 years is relatively high, while these firms show lower sales
compared to their counterparts. Sales tended to be higher for old vintage firms in the initial time periods, which lasted until approximately the time of the 1929 Great Depression,i.e., roughly the time corresponding to the Meiji (1868-1912) and Taisho (1912-1926) era.
We intentionally employ the word “vintage” rather than “age” because vintage refers toconditions that are specific to birth years and crucial for the later performance of firm.
We use the distribution of vintage firms and their sales, as well as the business cycleof real GDP (shown in the third panel in the figure), as pieces of evidence with which
we reestablish the history of each vintage firm.2 In the theoretical model, there is aninteraction between the vintage of firms and the macroeconomic aggregate. Each vintage firm constitutes aggregate dynamics in the economy, while the aggregate outcome
1
2

See Appendix A for the description of the data.
The
historicalJapanese
real
GDP

data

is

https://www.rug.nl/ggdc/historicaldevelopment/maddison/?lang=en

2

taken

from

Maddison:

Figure 1: Distribution of vintage firms and their sales in the 2013 survey

The first panel shows the distribution of vintage firms in the 2013 survey. The second panel shows the
distribution of the sales of these vintage firms in the 2013 survey. The third panel shows the cyclicalcomponent of the real GDP for Japan. To detrend the real GDP, we use an HP filter with thesmoothing parameter λ = 100.

influences the sales, production, and employment of each vintage firm. The theoreticalmodel allows us to explore the history of each vintage firm. Given the cyclical componentof the historical GDP and the landscape of today’s economy, namely, the distribution of
vintage firms and their sales, as shown in Figure 1, we simulate two important structuralparameters, namely, vintage-specific technologies and fixed operational costs. Once weobtain the value of these structural parameters, we are able to reestablish other vintagespecific distributions, such as productivity and employment, as well as the dynamics foreach vintage firm.
Our simulated distribution of the productivity and employment of vintage firms shows
remarkably similar patterns to those based on estimation and data. Our simulation results

3are summarized as follows. First, old vintage firms, i.e., firms created in the early part ofthe study time period up until the approximate time of the 1929 Great Depression, i.e.,roughly the time period corresponding to the Meiji and Taisho era, are subject to higher
fixed costs yet are more productive compared to other vintage firms. Second, vintage firms
created near the onset of the Second World War up until approximately the time of the
Plaza Accord in 1985 (this cohort has the largest share in the distribution of vintage firms
in the 2013 survey) have low productivity and low employment, although they benefitted
from low fixed costs when they were founded. Third, vintage firms born in the most recent
time period, i.e., after circa 1985, show low productivity and low employments, and they
have slightly higher specific fixed costs compared to the average.
Next, to see the history of vintage firms in a compact way, we provide “snapshots” atparticular moments in history. These snapshots are the result of our simulation given theabovementioned aggregates, as well as the dynamics of each vintage firm. In particular,
we discuss a snapshot for 1923 and 1996. In our snapshot of 1923, which corresponds
to the boom period after the First World War, the share of vintage producers from 1914
and 1919 is found to be high. However, the sales, productivity, and employment of thesefirms are not particularly high. Importantly, our simulated snapshots provide similarlandscapes that enable comparisons with the actual snapshots taken at these historicalmoments.
Finally, we perform a counterfactual analysis. With a counterfactual distributionof vintage-specific fixed costs that shows the opposite pattern compared to that in our
simulation, we show the share of recent vintage firms has increased significantly, while thenumber of vintage firms created in the post war boom, 1950 to 1980, was reduced. At
the same time, the sales, productivity and employment of these postwar vintage firms aresubstantially high. Our counterfactual fixed costs thus dramatically change the landscapeof vintage firms, as well as their characteristics.
Our paper is related to the literature that discusses firm entry and exit in a realbusiness cycle model, such as Ghironi and Melitz (2005), Bilbiie et al. (2012), Hamano
and Zanetti (2017). Different from these preceding papers, our theoretical model explicitly

4examines vintage firms and shows how each vintage firm constitutes aggregate dynamics.
Many previous studies have argued the presence of link between firm size distribution
and firm age in the context of firm growth theory. Cabral and Mata (2003) found thatthe skewness of the distribution comes from financial constraints, which are conditionalon firm age. Arkolakis (2016) and Arkolakis et al. (2018)) and Luttemer (2007, 2011)
explained the size and age distribution using firm growth theory. In a recent study, Pugsley
et al. (2018) emphasized ex-ante firm heterogeneity in the birth period to characterize
the firm’s size distribution and age profile in a theoretical model based on Hopenhayn(1992), Hopenhayn and Rogerson (1993) and Melitz (2003). As in these papers, ourtheoretical model embeds heterogeneous firms. Different from them, however, we place
more emphasis on vintage-specific characteristics rather than those characteristics that are
specific to individual firms that may or may not evolve overtime. In our model, vintagespecific technologies and fixed costs allow us to reestablish firm size distribution and age
distribution both in the past and in the current time period. Finally, Cacciatore and Fiori(2016), Bilbiie et al. (2019), Hamano and Vermeulen (2019) argued the important role
played by fixed costs and induced market regulation to shape the equilibrium outcome as
ours.
The remainder of the paper is organized as follows. Section 2 presents the model.
Section 3 discusses our benchmark calibration and estimation. Section 4 simulates thetheoretical model with Japanese data and provides the simulated vintage-specific technologies and fixed costs. Based on these parameters, we then reestablish the macroeconomic
dynamics of each vintage firm and perform a counterfactual analysis. Section 5 concludes
the paper.

2

The Model

In this section, we present the theoretical model using vintage firms. The model embeds
endogenous firm entry and selection based on heterogeneous firms. Further, we explicitly
model vintage firms and their products. Consumption at time t is composed from dif-5

ferentiated product varieties produced by vintage firms created in previous time periods,v < t. Entrants incur a sunk cost to enter the market and upon entry, they draw vintagespecific technology ϕv from vintage-specific distribution G (ϕv ). Firms are also required
to pay vintage-specific operational fixed costs fv to engage in production, which may startfrom the next time period of entry. This operational cost is assumed to be specific toeach vintage firm. The aggregate dynamics in the current time period are reestablishedby aggregating those at each vintage level.

2.1

Households

During each time period t, the representative household maximizes the following expectedutility:


Et



1
1+ ψ
L
β i−t ln Ct − χ t 1  ,
i=t
1+ ψ

X∞

(1)

where Ct is consumption, Lt is labor supply, 0 < β < 1 is the discount factor, χ > 0 is thedegree of disutility in supplying labor and ψ is the Frisch elasticity of the labor supply.
Consumption at time t is composed from different “vintage” of baskets as follows:

Ct =

t−1
X

1− σ1

! 11

1− σ

Cv,t

v=0

where Cv,t stands for the consumption of a vintage product produced by firms created attime v. Furthermore, product varieties within a particular vintage v are differentiated asfollows:
Z
Cv,t =

cv,t (ω)

1− σ1

 11
dω

1− σ

,

ω∈Ωv

where cv,t (ω) represents the demand for each product variety ω of a vintage v; σ > 1 isthe elasticity of substitution among product varieties. We keep the model as simple aspossible by assuming the same elasticity of substitution across vintage firms and within
the product varieties.

6

The optimal demand for each product variety ω of a vintage v at time t is found tobe as follows:
cv,t (ω) =pv,t (ω)
Pv,t

−σCv,t ,(2)

where pv,t (ω) denotes the price of the product variety ω of a vintage v. The price index
of a basket of vintage v at time t is as follows:Z
Pv,t =

1−σ(pv,t (ω))

1
 1−σ

dω

,

ω∈Ωt

The optimal demand for a basket of a certain vintage v is found to be as follows:
Cv,t =

Pv,t
Pt

−σ
Ct

(3)

where Pt is the price index of aggregate basket Ct . Finally, the aggregate price index Pt
which we choose as numeraire is found to be as follows:

Pt =

t−1
X

1
! 1−σ

1−σ
Pv,t

v=0

2.2

Production, Pricing and Producing Decision

Upon entry, each entrant draws a productivity level, ϕv , from a cumulative distribution,
G (ϕv ), with support on [ϕmin , ∞). Production requires labor as input. It also requires a
fixed operational cost of fv /Zt in effective labor units, where Zt stands for the aggregate
productivity level. We assume that fv is specific to each vintage firm. The total labordemand at time t for a vintage firm with productivity level ϕv is thus given by thefollowing:
lv,t (ϕv ) =yv,t (ϕv ) fv
+ ,
Zt ϕv
Zt

(4)

where yv,t (ϕv ) stands for the production scale of a vintage firm with productivity levelϕv .
The demand addressed to a vintage firm with productivity level ϕv is characterizedby equation (2). Profit maximization yields the following optimal price of a vintage firm7

with productivity level ϕv at time t:
ρv,t (ϕv ) =wt
σ,
σ − 1 Zt ϕv(5)where wt is the real wage.
Depending on the level of firm-vintage-specific productivity, ϕv , firms may or may not
produce. Thus, using equation (4), (5) and (3), if production materializes, the following
real operational profits are generated as follows:
dv,t (ϕv ) =1
fv
ρv,t (ϕv )1−σ Ct − wt .
σ
Zt

(6)

Only vintage firms with dv,t (ϕv ) > 0 produce at time t by covering the operational fixed
cost. We thus determine the cutoff productivity level for a particular vintage v at time t,
ϕv,t , with the following:

dv,t (ϕv,t ) = 0.

2.3

Average within Vintage

Given the distribution of the productivity level, Gv (ϕv ), the mass of firms, Nv,t , is definedover the productivity levels [zmin , ∞). Among these firms, a subset of firms engage inproduction. The number of vintage producers is determined by Sv,t = [1 − Gv (ϕv,t )] Nv,t .
Following Melitz (2003) and Ghironi and Melitz (2005), we refer to the average with ∼and define the average productivity of vintage producers ϕ̃v,t as follows:"1
ϕ̃v,t ≡
1 − Gv (ϕv,t )

Z ∞

1
# σ−1

ϕσ−1
dGv (ϕv )
v

.

(7)

ϕv,t

The term, ϕ̃v,t thus contains all the information about the distribution of productivity.
By aggregating across productivity levels and substituting equation (7) into equation (5),the average real price of vintage producers is found to be as follows:
ρv,t (ϕ̃v,t ) =σwt.
σ − 1 Zt ϕ̃v,t8

Similarly, by plugging in the optimal demands, the average real profits of vintage
producers can be expressed as follows:
dv,t (ϕ̃v,t ) =

2.4

fv
1
ρv,t (ϕ̃v,t )1−σ Ct − wt .
σ
Zt

Average across Firms in different Vintages

Furthermore, it is convenient to define the average across firms in different vintages at timet. By notation, we represent “the average of averages” of different vintage firms with Xṽ,t .
There is Nt number of firms at time t that are composed of all vintage products, while
only a subset number of St firms produce and are operating. Note that, by construction,
the Nt number of firms at time t that are composed of all vintage products is definedPt−1
as Nt =
v=0 Nv,t = tNṽ,t and a subset number of St producers are aggregated from
Pt−1
St = v=0 Sv,t = tSṽ,t . The average number of producers across different vintage firms
is given by Sṽ,t = [1 − G (ϕṽ,t )] Nṽ,t or equivalently by St = [1 − G (ϕṽ,t )] Nt , where ϕṽ,tstands for the average cutoff level of productivity across different vintage firms. This
cutoff level ϕṽ,t is determined with the following ZCP condition: dṽ,t (ϕṽ,t ) = 0. Given
this cutoff level, we define the average productivity of producers across different vintages
as follows:"1
ϕ̃ṽ,t ≡1 − G (ϕṽ,t )

Z ∞

1
# σ−1

ϕσ−1
dG (ϕv )
v

.

ϕṽ,t

Based on the above cutoff level, the average real price of producers at time t is expressed as follows:
ρṽ,t (ϕ̃ṽ,t ) =σwt,
σ − 1 Zt ϕ̃ṽ,tThe average real price is also expressed as shown in the footnote.3
1

ρṽ,t (ϕ̃ṽ,t ) = Stσ−1 .
Given the above average real price, the average dividends of producing firms at time
t are expressed as follows:3

ρṽ,t (ϕ̃ṽ,t ) =pṽ,t (ϕ̃ṽ,t )=Pt

pṽ,t (ϕ̃ṽ,t )1
Pt−1 1−σ
Pv,t ) 1−σ
( v=0

=

pṽ,t (ϕ̃ṽ,t )1P1−σpṽ,t (ϕ̃ṽ,t )( t−1
v=0 Sṽ,t )91= Stσ−1dṽ,t (ϕ̃ṽ,t ) =1 Ct
f− wt .
σ St
Ztwhere f represents the amount of effective labor that vintage firms employ on average.
Finally, we define the average dividends of all firms at time t as follows:
dt ≡St
dṽ,t (ϕ̃ṽ,t ) .
Nt

Note that dt is equivalent to the sum of the dividends of all existing vintage firms as
Pt−1 Sv,tdt = v=0d (ϕ̃v,t ).
Nv,t v,t

2.5

Firm Entry and Exit

In each period, NE,t number of entrants enters the market. Prior to entry, these new firms
are identical and face a sunk entry cost of fE in effective labor units. The entry cost istherefore equal to wt fE units of consumption goods, where wt stands for the real wage.
We assume that firms that enter at time t only start producing at time t + 1. The value ofa firm is expressed with a stream of their expected profits {di }∞i=t+1 . Using the stochastic
discount factor of households adjusted by exogenous exit-inducing shock δ, we obtain thefollowing:
vt = Et∞X

i−t[β (1 − δ)]

i=t+1



Ci
Ct

−1
di .

(8)

Firm entry occurs until the expected product value (8) is equal to the entry cost, whichleads to the following free entry condition:
vt = wt

fE.
Zt

The timing of entry and production implies that the number of products evolves
according to the law of motion:
Nt = (1 − δ) (Nt−1 + NE,t−1 ) .
Finally, given the above motion of firms the number of firms of a particular vintage is
as follows:
Nv,t = (1 − δ)t−v NE,v .
10

(9)

2.6

Parametrization of Productivity Draw

To solve the model, we must assume a distribution of productivity levels, ϕv . Thus, we
assume the following vintage-specific Pareto distribution:κϕmin vGv (ϕv,t ) = 1 −,ϕvwhere ϕmin is the minimum productivity level and κv determines the shape of the distribution at vintage v. The parameter κv indexes the dispersion of productivity across the
products of a particular vintage v. The dispersion decreases as κv increases and is skewed
towards the lower bound ϕmin . When κv = ∞, all products are located at ϕmin , and the
products become homogeneous within vintage. To ensure the variance of the productivity
distribution is finite, we assume that κv > σ − 1. With the above Pareto distribution, we
can express the average productivity of producers ϕ̃v,t in equation (7) as follows:
ϕ̃v,t = ϕv,tκv
κv − (σ − 1)

1
 σ−1

,

(10)

and the number of vintage producers is given by the following:
κv

 σ−1
κv
Sv,t
κv
v
ϕ̃−κ
= ϕminv,t .
Nv,tκv − (σ − 1)(11)

In addition, substituting equation (10) into the product’s real profits (6) yields anequation that determines the cutoff productivity level:4
dv,t (ϕ̃v,t ) =σ−1
w t fv
κv − (σ − 1) Zt

Similarly, at the average across vintages, we get the following:
ϕ̃ṽ,t = ϕṽ,tκκ − (σ − 1)

1
 σ−1

,

κṽ

 σ−1
St
κ
κ
= ϕminϕ̃−κṽ,t ,Ntκ − (σ − 1)

1−σ

1−σ

fv
fv
Ct − wt Z, dv,t (ϕv,t ) = σ1 ρv,t (ϕv,t )Ct − wt Z= 0 and with pricing
t
t 

1−σ
1−σ
fv
wt
wt
1
σ
1
σ
equations, we have dv,t (ϕ̃v,t ) = σ σ−1 Zt ϕ̃ṽ,tCt − wt Zt and dv,t (ϕv,t ) = σ σ−1
Ct −Zt ϕv,t


1−σ
ϕv,t
fv
fv
wt Z
= 0. Combining these two equations, we get dv,t (ϕ̃v,t ) =− 1 wt Z. With ϕ̃ṽ,t =ϕ̃ṽ,t
t
t
1
h
i σ−1
κ
ϕṽ,t κ−(σ−1), we get (16).
4

dv,t (ϕ̃v,t ) = σ1 ρv,t (ϕ̃v,t )

11

and

dṽ,t (ϕ̃ṽ,t ) =σ − 1 wt f.
κ − (σ − 1) Zt

In the above average expressions, κ stands for the parameter that shapes the Pareto
distribution for all the vintage firms.

2.7Household Budget Constraint and Intertemporal Problems

The household budget constraint is given by the following:
Ct + xt+1 vt (Nt + NE,t ) = Lt wt + xt Nt (vt + dt ) .

(12)

During each period t, the representative household chooses its consumption, Ct , shareholding, xt+1 , and labor supply, Lt , to maximize the expected utility function (1) subject
to the budget constraint (12). The first-order conditions with respect to consumption andlabor supply yield the standard labor supply equation as follows:1χ (Lt ) ψ = wt Ct−1 .
The first-order condition with respect to shareholdings yields the following:
−1

Ct+1
vt = β (1 − δ) Et(vt+1 + dt+1 ) ,Ctwhich, once iterated forward, shows the share price as (8).

2.8Model Equilibrium and Solution

In equilibrium, the aggregate labor supply, Lt , is employed in either the production of
consumption goods (intensive margins, i.e., the production scale) or the creation of new
firms (extensive margins):5

Lt = St lṽ,t (ϕ̃ṽ,t ) + NE,t5

Using the notation of vintages, this is equivalent to Lt =

12

vt
,
wt

Pt−1

vt
v=0 Sv,t lv,t (ϕ̃v,t ) + NE,t wt .

where lṽ,t (ϕ̃ṽ,t ) = (σ − 1)

dṽ,t (ϕ̃ṽ,t )+ σ Zft , which represents the labor demand required forwt

the production on average.
As auxiliary variables, we also define real GDP Yt and real average sales yṽ,t (ϕ̃ṽ,t ) withρṽ,t (ϕ̃ṽ,t )Yt ≡ Lt wt + St dṽ,t (ϕ̃ṽ,t ) and dṽ,t (ϕ̃ṽ,t ) =yṽ,t (ϕ̃ṽ,t ) − wZttf , respectively. Finally, we
σassume that the aggregate productivity follows an AR(1) process as ln(Zt ) = ρ ln(Zt−1 ) +εt , where εt is a normally distributed innovation with a zero mean and a variance equal tos2Z . The model at the aggregate average level consists of 14 equations and 14 endogenous
variables. Table 1 summarizes the system of equations.
Table 1: Summary of the benchmark model
Average pricingσwt
ρṽ,t (ϕ̃ṽ,t ) = σ−1
Zt ϕ̃ṽ,tReal priceρṽ,t (ϕ̃ṽ,t ) = Stσ−1

Average profitsdṽ,t (ϕ̃ṽ,t ) = σ1 ρṽ,t (ϕ̃ṽ,t )1−σ Ct − wt Zftfσdṽ,t (ϕ̃ṽ,t ) + wt Ztyṽ,t (ϕ̃ṽ,t ) = ρ ϕ̃ṽ,t ( ṽ,t )1

Average sales
Average profits

dt = NStt dṽ,t (ϕ̃ṽ,t )ZCP
Surviving rate

σ−1 wt f
dṽ,t (ϕ̃ṽ,t ) = κ−(σ−1)
Zt
κ
h
i σ−1
κ
St
κ
=
ϕ
ϕ̃−κ
min κ−(σ−1)
ṽ,tNtFree entry conditionvt =Motion of products
Euler equation

Nt+1 = (1 − δ) (Nt + NE,t )
−1

Ct+1
(vt+1 + dt+1 )vt = β (1 − δ) Et Ct

Optimal labor supplyχ (Lt ) ψ = wt Ct−1

Labor market clearing
Average employment

Lt = St lṽ,t (ϕ̃ṽ,t ) + NE,t wvtt
dṽ,t (ϕ̃ṽ,t )lṽ,t (ϕ̃ṽ,t ) = (σ − 1) wt+ σ Zft

Real GDP

Yt ≡ Lt wt + St dṽ,t (ϕ̃ṽ,t )Productivity processln(Zt ) = ρ ln(Zt−1 ) + εt

wt fE,tAt

1

The variables for each vintage firm are characterized by the system of equations presented in Table 2. Given the number of new entrants in each period NE,v , the aggregatedconsumption Ct , the wages wt and the productivity level Zt , the vintage-specific variables
are derived from these equations. The equilibrium conditions do not have an analytical13

Table 2: Summary of the benchmark model (for a vintage)
Average pricing

wt
σ
ρv,t (ϕ̃v,t ) = σ−1
Zt ϕ̃v,tAverage survivor’s profits
Average sales

dv,t (ϕ̃v,t ) = σ1 ρv,t (ϕ̃v,t )1−σ Ct − wt Zfvt
yv,t (ϕ̃v,t ) = ρv,t (σϕ̃v,t ) dv,t (ϕ̃v,t ) + wZt ft v

Average employment

lv,t (ϕ̃v,t ) = (σ − 1) dv,tw(ϕ̃t v,t ) + σ Zfvt

ZCP

wt fv
σ−1
dv,t (ϕ̃v,t ) = κv −(σ−1)
t
κv
h
iZσ−1
Sv,t
κv
κv
v
=
ϕ
ϕ̃−κ
v,t
min κv −(σ−1)
Nv,tSurviving rate

Nv,t = (1 − δ)t−v NE,vsolution. Consequently, we approximate the system with the perturbation method aroundthe stationary steady state.

3

Benchmark Calibration and Estimation

We calibrate the theoretical model with benchmark values of the parameters, as shownin Table 3. The annual discount factor is set to 0.96, under which the steady state realinterest rate is 4 %. The value of the Frish elasticity of labor supply ψ is 2.15, which istaken from Sugo and Ueda (2008), who estimate the elasticity using Japanese data fromthe postwar period. The elasticity of substitution among varieties and the parameter thatshapes the Pareto distribution across vintages are set to 3.8 and 3.4, respectively, following
Ghironi and Melitz (2005). With σ = 3.8, this gives a markup of 35 %. Note that thelatter value satisfies the restriction on these parameters such that κ > σ − 1. The valueof firm deprecation rate δ and fixed operational cost fṽ are chosen following Hamano andOikawa (2021); thus, these values match the average firm creation and operation rate inJapan, as observed in the current production survey. Specifically, we set δ = 0.0223 and
f = 0.013855, under which the steady state firm entry NE /N and operation rate S/N are
0.00571 and 0.987, respectively.6 The minimum idiosyncratic productivity level ϕmin and
6

The data covers from 2001Q to 2017Q. Note at the steady state, N = (1 − δ) (N + NE ). Then, we

have δ = (NE /N ) / (1 + NE /N ).

14

fixed entry cost fE are set to unity in the steady state. The parameter that determines
the disutility of labor supply χ is given so that the value gives the steady state labor
supply of L = 1.

βTable 3: Calibration of the model
Discount factor

0.96

ψ

Frisch elasticity of labor supply

2.15

χ

Disutility of supplying laborσElasticity of substitution among varieties

3.8

κ

Distribution parameter

3.4

δDepreciation ratef

Fixed operational costs

ϕmin0.86091

0.02230.013855

Minimum idiosyncratic productivity level

1

fE

Fixed entry costs

1ρPersistence of aggregate productivity

0.68049sZStandard deviation of productivity shocks

0.014089

For the productivity process, we estimate the standard deviation σZ and persistence ρusing historical real GDP data for Japan (1885 to 2018, taken from Maddison Historical
Statistics) by maximizing the likelihood. For the estimation, we consider an empirically1consistent measure of the theoretical GDP as YR,t ≡ Yt /Stσ−1 following Ghironi and Melitz(2005). The idea is to capture imperfect fluctuations in the number of product varieties in
the official statistics. Additionally, we define empirically consistent consumption CR,t ≡1

1

Ct /Stσ−1 and investment vR,t NE,t ≡ vt NE,t /Stσ−1 accordingly.78
7

To detrend the GDP data, we use an HP filter with a smoothing parameter of λ = 100. Ravn andUhlig (2002) suggests λ = 6.25 for annual data. We find that λ = 100 is sufficiently good to capture thebusiness cycle over 126 years, while λ = 6.25 picks up a higher-frequency business cycle. However, thesimulation result is qualitatively the same with respect to trend of real GDP.
8
In estimation, we introduce the measurement error. The estimation is also performed with theBayesian method using established prior information from the literature. The result is isomorphic to thebenchmark estimation with uniform prior, however. The estimation, as well as the approximation of the15

4

Simulation

4.1

Vintage-specific Technologies and Fixed Costs

To reveal the history of each vintage firm, we simulate the vintage-specific fixed cost fv
and the specific technology that is captured by κv . Our simulation strategy is as follows.
First, we simulate the theoretical model 100,000 times over 126 years with the calibrated
parameters and the estimated productivity process, as shown in Table 3. Second, given thecurrent distribution of vintage firms and their sales in the 2013 survey, as shown in Figure
1, and taking the simulated number of new entrants in each period NE,v , the final datevalues of the simulated consumption Ct , the wages wt and the productivity level Zt , wedetermine the vintage-specific technology κv and the vintage-specific fixed cost fv . Third,
among these simulations, we select the one that gives us the closest dynamics of actual
real GDP, and we choose the corresponding distribution of vintage-specific technology κv
and fixed cost fv as our estimate.9
Figure 2 shows the results of our simulation. Given the end-of-period value of the aggregate consumption, wage, and technology level, as well as the end-of-period distribution
system of nonlinear equations with the perturbation, are conducted with the RISE toolbox developed by
Junior Maih.
9
In the simulation, we match the share of a particular vintage firm in the total number of vintage firms
in the 2013 survey with the theoretical counterpart, Sv,126 /S126 . The data reports manufacturing firmsthat have more than 50 employees and those with more than 30 million yen in capital assets. The total
number of manufacturing firms as of the 2013 survey was 13,426, according to the BSJBSA data. For
the same year, according to the Census of Manufacture by the Ministry of Economy, Trade and Industry(“Kogyo Tokei”, in Japanese) and the converter (KogyoTokei Konbata) prepared by RIETI to sum up
from plant level to firm level, there were 184,485 firms, based on the census of plants that had morethan four employees. Another data source, the Establishment and Enterprise Census of Japan (Ministryof Internal Affairs and Communications), reported the existence of approximately 650,000 publishedestablishments without any restriction regarding the number of employees and any organization. Given
that the average reply rate of the BSJBSA survey is approximately 85% and that there are other vintage
firms that are not captured in the BSJBSA data, the total number of manufacturing firm would be 50
times higher, at most, than the number reported in the 2013 BSJBSA survey. However, our simulation
results are robust with respect to scaling in matching the share.

16

of the relative number of vintage firms and their relative vintage sales (the first and thesecond panel in the figure), we simulate the distribution of vintage-specific technologies
κv and their fixed costs fv (the third and the fourth panel), as well as the implied distribution of vintage-specific relative productivity ϕ̃v,t and relative employment lv,t (the fifth
and the sixth panel).
Vintage-specific technologies κv tend to be high for the initial sample periods andfrom the late 1960s until the beginning of the 1990s. It is noticed the distribution of
vintage-specific fixed costs fv gives an asymmetric wedge-shaped pattern.10 In addition,
the distribution of vintage productivity ϕ̃v,t and employment lv,t (ϕ̃v,t ) show a similar
wedge-shaped pattern.11
From the simulation, the following result emerges. First, old vintage firms (the least
popular cohort in the distribution of firm vintage), i.e., firms created in the initial time
periods up until the approximate time of the 1929 Great Depression, which is roughly thetime corresponding to the Meiji (1868-1912) and Taisho (1912-1926) era, are subject tohigher fixed costs fv , yet they are currently more productive compared to other vintage
firms. Second, vintage firms created near the beginning of the Second World War up
until the approximate time of the Plaza Accord in 1985 (the most popular cohort in
the distribution of vintage firms) show low average productivity ϕ̃v,t and low average
employment lv,t (ϕ̃v,t ), although they benefit from low fixed costs fv . Third, vintage firms
created in the most recent time period after approximately 1985 (the secondly popularcohort in the distribution of vintage firms) show low average productivity ϕ̃v,t and low
average employments lv,t (ϕ̃v,t ) and have slightly higher specific fixed costs fv than the
average.
Noting that vintage-specific fixed costs fv and technologies κv encompass various types
10

The theoretical model cannot compute the vintage-specific technology κv and the fixed cost fv for

1888, 1891 and 1895 because of missing data.
11
Cabral and Mata (2003) argue that time varies the firm size dispersion of firms and found thatthe distribution becomes skewed to the right for young vintage firms. Our results echo their result by
simulating vintage-specific technologies κv that shape the productivity dispersion of firms. Specifically,
our paper replicates a similar pattern of the skewness depending on the sample time period.

17

Figure 2: Simulation of vintage-specific technologies and fixed costs

The first and second panel in the first row show the distribution of vintage firms and the distribution of
their sales in the 2013 survey, respectively. The first and the second panel in the second row show thesimulated distribution of vintage-specific technologies κv and their fixed costs fv at the end of periods,
respectively. The first and the second panel in the third row show the simulated distribution of
productivity ϕ̃v,t and employment lv,t (ϕ̃v,t ) at the end of the periods, respectively.

in the real world, our results seem consistent with the industrial policies present in postwar
Japan. After the Second World War, the Ministry of International Trade and Industry
implemented several industrial policies (Ito et al., 1988; Komiya et al., 1984). The policy scheme consisted of subsidies for specific industries, tax exemptions, R&D policies,and export promotion policies. The targeted sectors were first the steel and iron industries, followed by heavy industries, and then shifted to machinery sectors and high-techindustries. Government banks also had several lending programs that specialized in infrastructure investment, the development of rural areas, investments for the environment,
and energy-saving technology (e.g., DBJ, 2002, JASME, 2003). The Japan Development
Bank (JDB), which is a government bank housed under the Ministry of Finance, had
18special lending programs that offered lower interest rates to large companies and majorindustries. In contrast to the JDB scheme, the Japan Finance Corporation for Small andMedium Enterprise (JASME) (Chusho Kigyo Kinyu Koko) (1953–2008), which was alsoa government bank, specialized in helping SMEs. The central strategy for several lending
programs consisted of lowering interest rates for investments. 12
To see how our results are comparable with the data, we use the distribution of thenumber of regular employees and the estimated total factor productivity.13 It is striking
to see that our simulated distribution of employment and productivity provides a similar
pattern as that of the distribution of TFP and employment, as shown in Figure 3. The
correlation between the estimated TFP and our simulated productivity amounts to 0.7040,
while the correlation between the employments in data and our simulated employments
is 0.8618.
Finally, we provide the simulation for other sectors in Appendix B. The data forthe light manufacturing, service, public utilities, telecommunication, and transportationand construction sectors are available from the same source, i.e., BSJBSA. While we see
substantial variation across the sectors, it is noticed the share of the firms created in
the middle range of the time period spanning 126 years is relatively high, while thesefirms show lower sales across all sectors. Accordingly, we confirm a similar pattern forthe simulated fixed costs, which produces an asymmetric wedge-shaped pattern, as is thecase for the manufacturing sector.

4.2

Macroeconomic Dynamics of Vintages and Snapshots

Figure 4 shows the macroeconomic dynamics for the major aggregate variables that are
directly required to compute the pass of each vintage firm. The simulated pass of real
GDP captures well the business cycles in the data. Overall, the cyclical properties ofother aggregate variables, including firm entry and exit, are similar to the ones discussed
12

Elliott and Okubo (2016) found that these special lending programs offered lower interest rates thanthe market rates, which promoted abatement investment in Japan.
13
The total factor productivity is estimated following Olley and Pakes (1996). In the calculation of
tangible capital, we use the data of book-to-market value ratio by Hosono et al. (2017).

19

Figure 3: Comparison with estimated TFP and employment data

The first panel shows the simulated distribution of vintage productivity ϕ̃v,t (solid line) and the
distribution of estimated vintage TFP (dashed line) at the end of the periods. The second panel shows
the simulated distribution of vintage employment lv,t (ϕ̃v,t ) (solid line) and the distribution of vintage
employment in the data (dashed line) at the end of the periods, respectively.

in Hamano and Zanetti (2017) and are in line with those discussed in the literature of
real business cycle models.14 Specifically, procyclical investment is a key to generating ahigher number of entrants (NE,v ), which translates into a proportionally higher numberof vintage firms Nv,t , as the equation (9) indicates.
With the simulated distribution of vintage-specific technologies κv and fixed costs fv ,together with the abovementioned aggregate macroeconomic dynamics in hand, we can
14

The standard deviation of GDP in the simulated model is 0.0555, while that in the data is 0.0596.

The simulated consumption is less volatile than GDP (its standard deviation with respect to GDP is
0.4185), while the simulated investments are equally as volatile as GDP (the standard deviation withrespect to GDP is 0.9014).

20

Figure 4: Simulation for aggregate variables

Each entry in the first row shows the percentage-point response in the simulated economy over 126
years. Each entry in the second and third row shows the simulated values expressed in levels over 126
years.

reestablish the history of each vintage firm. Figure 5 provides the simulated number of
producers Sv,t , the percent deviation of the average sales yv,t (ϕ̃v,t ), the average productivity ϕ̃v,t and the average employment lv,t (ϕ̃v,t ) for vintage firms from 1887 to 2012.15
We observe considerable heterogeneity across vintage firms. The number of producers Sv,ttends to be high for the periods that correspond to the boom. It is also noticed the levelsof sales yv,t (ϕ̃v,t ), productivity ϕ̃v,t and employments lv,t (ϕ̃v,t ) fluctuate in a synchronized15

The simulated values of vintage-specific costs κv show substantial heterogeneity across vintage firms(with the highest value of 9159 in 1949 and the smallest value of 3.185 in 1945). While there is no required
restriction per se for its upper end, we find that an unusually high value of κv generates unstable dynamics
at vintage levels, thereby violating the surviving condition such that Sv,t /Nv,t > 1. In generating Figure
5, we exclude the vintage firms that show unstable dynamics.

21

Figure 5: Simulated pass of vintages

Each entry shows the simulated dynamics of the number of producers Sv,t , sales yv,t (ϕ̃v,t ),productivity ϕ̃v,t and employment lv,t (ϕ̃v,t ) for vintage firms over 126 years.

way with each other and with the aggregate dynamics, as shown in Figure 4.
To see the history of vintage firms in a compact way, we provide “snapshots” atparticular moments in history. These snapshots are the result of our simulation given theabovementioned aggregates, as well as vintage-specific dynamics.16 Figure 6 provides asnapshot for 1923. Because of the economic boom during the First World War (“Taisenkeiki” in Japanese), the share of vintage producers from 1914 and 1919 is high (first panelin the figure). At the moment of 1923, these firms are relatively new vintage firms. The
sales, productivity, and employment of these firms born during the war period are notparticularly high. We observe a low entry in 1922 and a rebound in 1923 when the great
Kanto earthquake hit in September.
16

Other snapshots (1914, 1931, 1945, 1960, 1985 and 2009) are given in Appendix C.

22

Figure 6: Snapshot: 1923

The first and the second panel in the first row show the simulated distribution of vintage firms Sv,t andthe distribution of their sales yv,t (ϕ̃v,t ) in 1923, respectively. The first and the second panel in thesecond row show the estimated distribution of vintage-specific technologies κv and their fixed costs fv in
1923, respectively. The first and the second panel in the third row show the simulated distribution of
vintage firm productivity ϕ̃v,t and employment lv,t (ϕ̃v,t ) in 1923, respectively.

To check the relevance of our simulation, we compare our snapshot of the distributionof vintage firms with the Census of Manufacture by the Ministry of Commerce and Agriculture (“Kojyo Tokei Hyo”, in Japanese). The Census of Manufactures in the prewar
period records the number of firms in terms of their founding year. The red dotted line
in Figure 7 shows the distribution of “factory” vintage firms in 1923. It gives a similar
pattern as our simulated distribution of vintage firms in 1923, which is shown by the solid
blue line in the figure. The correlation of these two distributions is 0.8406.
Figure 8 gives a snapshot for 1996 based on our simulated vintage-specific technologies
and fixed costs. It is particularly interesting to have a snapshot for this year since the23Figure 7: Distribution of factories and vintage firms in 1923

The figure shows the simulated distribution of vintage firms Sv,t and the distribution of factory vintage
firms in the data (dashed line) in 1923.

Census of Manufacture provided by the Ministry of Economy, Trade and Industry also has
a snapshot for 1996. While the census covers medium-sized firms (all plants with morethan four employees), our snapshot and the census snapshot provide a similar landscape.17

4.3Counterfactual Analysis

As the last exercise, we explore the consequence of a counterfactual distribution of vintagespecific fixed costs fv . We consider a counterfactual pass of fixed costs fv given thesimulated distribution of vintage-specific technologies κv . Although it is highly stylized
in the theoretical model, the fixed cost for operation ranges from physical costs to legal
17

The correlation between these two snapshots for the distribution of vintage firms, their sales, theirproductivity and their employment rates are 0.2995, 0.3847, 0.2384 and 0.3349, respectively.

24

Figure 8: Snapshot: 1996

The first and second panel in the first row show the simulated distribution of vintage firms Sv,t and the
distribution of their sales yv,t (ϕ̃v,t ) in 1996, respectively. The first and the second panel in the second
row show the estimated distribution of vintage-specific technologies κv and their fixed costs fv in 1996,
respectively. The first and the second panel in the third row show the simulated distribution of vintage
firm productivity ϕ̃v,t and employment lv,t (ϕ̃v,t ) in 1996, respectively.

procedures in the real world. Importantly, we believe that a part of these costs would be
a subject of industrial policy instruments, as mentioned before. This is the reason why
we consider a counterfactual distribution of fixed costs fv rather than a counterfactual
distribution of technologies κv which seems likely to be limited by the condition of thetime.
Our counterfactual distribution of vintage-specific fixed costs fv is shown by the dottedline in Figure 10. To obtain this, we first approximate the simulated distribution of
vintage-specific fixed costs fv with a quadratic function (shown by the smoothed line).
The counterfactual is computed as a flipped symmetric distribution against the horizontal

25

Figure 9: Simulated vs. Census Snapshots in 1996

The solid lines in the figure show the simulated distribution of vintage firms Sv,t , the distribution of
their sales yv,t (ϕ̃v,t ), the distribution of their productivity ϕ̃v,t and the distribution of theiremployment lv,t (ϕ̃v,t ) in 1996, respectively. The dashed lines in the figure show these distributions in
actual data collected in 1996.

axis of the smoothed quadratic distribution. We also set the initial and end values of thesmoothed distribution to coincide with those of the counterfactual distribution. Our
counterfactual distribution shows the opposite pattern as the simulated distribution of
the fixed costs. Specifically, it increases steadily, peaks at approximately 1920, and thendecreases.
The result of our counterfactual simulation is shown in Figure 11. With the counterfactual distribution, it is striking to see that the share of recent vintage firms increases
significantly while dramatically reducing the number of vintage firms created in the postwar boom (the first panel in the figure). At the same time, the sales yv,t (ϕ̃v,t ), productivity
ϕ̃v,t and employment lv,t (ϕ̃v,t ) of these postwar vintage firms become substantially high.
26

Figure 10: Counterfactual fixed-cost distribution (log)The solid blue line shows the simulated vintage-specific fixed costs fv . The smoothed red line shows
the trend of fv estimated with the quadratic function. The dashed line shows the counterfactual
vintage-specific fixed costs fv .

Our counterfactual fixed costs thus dramatically change the landscape of vintage firms, aswell as their characteristics. Our results indirectly point out how powerful the industrial
policies were in supporting these firms in the postwar period.

5

Conclusion

This paper reestablishes the past dynamics of each vintage firm. For that purpose, webuilt a theoretical model based on the entry and selection of these firms. Given the distribution of vintage firms and the distribution of their sales as we see them today, we
simulate vintage-specific technologies and fixed costs required for operation. With thesesimulated parameters and the cyclical component of GDP over 126 years, we reproduce27

Figure 11: Simulation based on the counterfactual fixed costs

The first and the second panel in the first row show the simulated distribution of vintage firms Sv,t andthe distribution of their sales yv,t (ϕ̃v,t ) at the end of periods based on the counterfactual
vintage-specific fixed costs fv , respectively. The first and the second panel in the second row show theestimated distribution of vintage-specific technologies κv and the counterfactual fixed costs fv at the endof periods, respectively. The first and the second panel in the third row show the simulated distributionof vintage firm productivity ϕ̃v,t and employment lv,t (ϕ̃v,t ) at the end of periods, respectively.

the macroeconomic dynamics of each vintage firm. Using Japanese data, the distributionof vintage-specific fixed costs gives an asymmetric wedge-shaped pattern. While the shareof firms created after the Second World War until the oil crisis in the 1970s in the distribution of vintage firms is high in the 2013 survey, these vintage firms have low productivity
and low employments. On the other hand, old vintage firms in the Meiji and Taisho era
have high productivity despite their high fixed costs. Vintage firms created in the recent
time periods after approximately 1985 manifest low productivity and low employments.
Furthermore, given the simulated distribution of vintage-specific technologies and fixed
costs, we reestablish the macroeconomic dynamics of each vintage firm and provide snap28

shots of vintage firm distribution at particular moments in time. Finally, we demonstratethat our counterfactual fixed costs dramatically change the landscape of vintage firms, aswell as their characteristics.
While we choose to keep the theoretical model as parsimonious as possible, for future
research, it would be interesting to incorporate other characteristics of firms, such as capital accumulation within the firm, multiproducts, and economic growth at the firm and/or
aggregate level. In addition, detailing the demand side of the economy by introducing amore elaborated preference may be explored. Finally, our exercise can be useful to shapepolicy debate on a desired allocation of resources and firm dynamics.

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Hamano, M. and W. N. Vermeulen (2019, 08). Natural disasters and trade: the mitigating
impact of port substitution. Journal of Economic Geography 20 (3), 809–856.
Hamano, M. and F. Zanetti (2017). Endogenous Turnover and Macroeconomic Dynamics.
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Hopenhayn, H. and R. Rogerson (1993, October). Job turnover and policy evaluation: A
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Hopenhayn, H. A. (1992, September). Entry, exit, and firm dynamics in long run equilibrium. Econometrica 60 (5), 1127–50.
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and Misallocation. Discussion papers 17071, Research Institute of Economy, Trade andIndustry (RIETI).
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A

Data

This paper uses Japanese firm-level data from the Basic Survey of Japanese Business
Structure and Activities (BSJBSA), provided by the Ministry of Economy, Trade andIndustry of Japan (METI). The data contain a wide variety of firm-level variables such as
founding year, number of employees, sales, profit, and tangible capital. The survey covers
all firms with more than 50 employees and with more than 30 million yen of capital asset
and has an approximate 85% reply rate. The survey was conducted in 2013.
In addition, the paper uses Japanese plant-level data from the Census of Manufacture(“Kogyo Tokei” in Japanese), provided by the Ministry of Economy, Trade and Industry.
The data covers all plants with more than 4 employees.

31Figure 12: Simulation of vintage-specific technologies and fixed costs: light manufacturing

The first and the second panel in the first row show the distribution of vintage firms and the
distribution of their sales in the 2013 survey, respectively. The first and the second panel in the second
row show the simulated distribution of vintage-specific technologies κv and fixed costs fv at the end of
periods, respectively. The first and the second panel in the third row show the simulated distribution of
vintage firm productivity ϕ̃v,t and employment lv,t (ϕ̃v,t ) at the end of the periods, respectively. Light
manufacturing includes food, beverage, fertilizer, textile, printing, paper and pulp, furniture, pottery,
fur skins and glass.

B

Sectors

Figures provide simulation results for the light manufacturing, service, public utilities,
telecommunication and transportation and construction sectors. The figures are obtainedusing the same procedure as the case of the manufacturing sector.

C

Snapshots

32

Figure 13: Simulation of vintage-specific technologies and fixed costs: service

The first and the second panel in the first row show the distribution of vintage firms and the
distribution of their sales in the 2013 survey, respectively. The first and the second panel in the second
row show the simulated distribution of vintage-specific technologies κv and fixed costs fv at the end of
periods, respectively. The first and the second panel in the third row show the simulated distribution of
vintage firm productivity ϕ̃v,t and employment lv,t (ϕ̃v,t ) at the end of the periods, respectively. Service
includes wholesales, retail, restaurant and general services except public service, IT, telecommunication,transportation, insurance finance.

33

Figure 14: Simulation of vintage-specific technologies and fixed costs: public utilities,
telecommunication and transportation

The first and the second panel in the first row show the distribution of vintage firms and their sales in
the 2013 survey, respectively. The first and the second panel in the second row show the simulated
distribution of vintage-specific technologies κv and fixed costs fv at the end of periods, respectively.
The first and the second panel in the third row show the simulated distribution of vintage firm
productivity ϕ̃v,t and employment lv,t (ϕ̃v,t ) at the end of the periods, respectively.

34

Figure 15: Simulation of vintage-specific technologies and fixed costs: construction

The first and the second panel in the first row show the distribution of vintage firms and the
distribution of their sales in the 2013 survey, respectively. The first and the second panel in the second
row show the simulated distribution of vintage-specific technologies κv and fixed costs fv at the end of
periods, respectively. The first and the second panel in the third row show the simulated distribution of
vintage firm productivity ϕ̃v,t and employment lv,t (ϕ̃v,t ) at the end of the periods, respectively.

35

Figure 16: Snapshot: 1914

The first and the second panel in the first row show the simulated distribution of firm vintage Sv,t andthe distribution of their sales yv,t (ϕ̃v,t ) in 1914, respectively. The first and the second panel in thesecond row show the estimated distribution of vintage-specific technologies κv and fixed costs fv in
1914, respectively. The first and the second panel in the third row show the simulated distribution of
vintage firm productivity ϕ̃v,t and employment lv,t (ϕ̃v,t ) in 1914, respectively.

36

Figure 17: Snapshot: 1931

The first and the second panel in the first row show the simulated distribution of firm vintage Sv,t andthe distribution of their sales yv,t (ϕ̃v,t ) in 1931, respectively. The first and the second panel in thesecond row show the estimated distribution of vintage-specific technologies κv and fixed costs fv in
1931, respectively. The first and the second panel in the third row show the simulated distribution of
vintage firm productivity ϕ̃v,t and employment lv,t (ϕ̃v,t ) in 1931, respectively.

37

Figure 18: Snapshot: 1945

The first and the second panel in the first row show the simulated distribution of firm vintage Sv,t andthe distribution of their sales yv,t (ϕ̃v,t ) in 1945, respectively. The first and the second panel in thesecond row show the estimated distribution of vintage-specific technologies κv and fixed costs fv in
1945, respectively. The first and the second panel in the third row show the simulated distribution of
vintage firm productivity ϕ̃v,t and employment lv,t (ϕ̃v,t ) in 1945, respectively.

38

Figure 19: Snapshot: 1960

The first and the second panel in the first row show the simulated distribution of firm vintage Sv,t andthe distribution of their sales yv,t (ϕ̃v,t ) in 1960, respectively. The first and the second panel in thesecond row show the estimated distribution of vintage-specific technologies κv and fixed costs fv in
1960, respectively. The first and the second panel in the third row show the simulated distribution of
vintage firm productivity ϕ̃v,t and employment lv,t (ϕ̃v,t ) in 1960, respectively.

39

Figure 20: Snapshot: 1985

The first and the second panel in the first row show the simulated distribution of firm vintage Sv,t andthe distribution of their sales yv,t (ϕ̃v,t ) in 1985, respectively. The first and the second panel in thesecond row show the estimated distribution of vintage-specific technologies κv and fixed costs fv in
1985, respectively. The first and the second panel in the third row show the simulated distribution of
vintage firm productivity ϕ̃v,t and employment lv,t (ϕ̃v,t ) in 1985, respectively.

40

Figure 21: Snapshot: 2009

The first and the second panel in the first row show the simulated distribution of firm vintage Sv,t andthe distribution of their sales yv,t (ϕ̃v,t ) in 2009, respectively. The first and the second panel in thesecond row show the estimated distribution of vintage-specific technologies κv and fixed costs fv in
2009, respectively. The first and the second panel in the third row show the simulated distribution of
vintage firm productivity ϕ̃v,t and employment lv,t (ϕ̃v,t ) in 2009, respectively.

41