Capital Accumulation, Vintage and Productivity:
The Japanese Experience
Taiji Hagiwara
Graduate School of Economics
Kobe University
Yoichi Matsubayashi
Graduate School of Economics
Kobe University
Abstract
We empirically examine the relationship between capital accumulation and vintage aswell as the productivity of industries in Japan from 1980 to 2007. Based on the empiricalanalyses, we confirmed that vintage exerted a significant influence on the productivity
during the period of economic expansion, particularly during the economic upturn thatstarted in 2000, where strong vintage effects were observed in all industries.
The rejuvenation of capital equipment during this period clearly resulted from a strong
productivity effect. In contrast, during the bubble period of the late 1980s, vintage
exerted no observable effects on productivity despite significant increases in investment.
This finding shows that increase of capital stock during this period was not necessarily
Productive and was likely to produce a merely temporary boom. From this view, wereconfirm that the relationship between vintage and productivity changed in subtle ways
in response to the phases of business cycles.
JEL Classification Number: F32, F41
Keywords: Vintage, productivity, Business cycle
Correspondence to:
Yoichi Matsubayashi
Graduate School of Economics, Kobe University
Rokkodai, Nada-ku, Kobe, 657-8501, Japan
TEL +81-78-803-6852
E-mail myoichi@econ.kobe-u.ac.jp

1

1 Introduction
Productivity is an indispensable factor for understanding the mid-and long-term
characteristics of a macroeconomy. A value-added level of the macroeconomy depends on
the labor force and capital stock. However, other factors may increase the value added.
For example, more value can be added from the same level of input through various typesof technological progress, referred to as an increase in productivity. Therefore, examining
the factors that influence technological progress, or productivity, is important. We candivide productivity into two categories. The first category is new product development
through the progress of science and technology. Imagine a case where new IT productsof high value are developed by promoting basic research on semiconductors or a newpharmaceutical is developed from life science research. These exogenous factors, such as
basic and applied scientific research, lead to increase in productivity. The second
category is new investments endogenously determining productivity. It is highly
probable that newly installed equipment include various types of technological progressin production. Depending on the circumstances, strong demand in investments andrejuvenation of equipment can promote innovation in technology and increase
productivity. Various factors simultaneously influence the real economy, and productivity
is no exception. Therefore, it is well worth investigating the mechanism of productivity
growth using Japanese firm-micro data since 1980s.
The reminder of this paper is organized as follows. Section 2 introduces theconcept of capital vintage and provides a detailed overview of prior studies regarding
capital vintage and productivity growth. Section 3 presents a theoretical model which
explicitly considers the relationship between capital vintage and productivity. Section 4
describes the data. Section 5 provides the various estimation results. The final section
summarizes conclusions obtained in this analysis.

2 Overview
The study of capital accumulation and growth in a country’s economy dates back to
the research of Harrod and Domar, and scholars still study their findings as critical andfundamental themes in macroeconomics. Capital accumulation and increased
investment in equipment generate economic growth through expansion in production
capacity while increasing effective demand through a multiplier process. However, therelationship among capital accumulation, technological progress and economic growth2has not been examined explicitly in the discussion of Harrod and Domar.
In contrast, economists such as Solow and Swan (1956) began to actively research
growth theories in the 1950. The ‘neoclassical growth theory’ flourished in this era. These
theories, under a full employment economy, explicitly discussed the role of technologicalprogress and the types of technology, but considered these factors exogenous.
Neoclassical growth theory developed as the optimal growth theory during and after the
1960s, but in the form of an endogenously assumed savings rate later on. However, thisperiod featured interesting perspectives about the impact of endogenous technologicalprogress on economic growth. Arrow (1962) asserted that the accumulation of experiencein economic agents, particularly in firms, induces productivity, that is technologicalprogress. According to Arrow (1962), the introduction of new machinery and equipment,
which represents new investment in equipment, provides learning opportunities forlaborers involved in production. Higher productivity through their learning manifests astechnological progress that accelerates economic growth.
Solow (1960) investigated the role of investment from an aspect different to thatof Arrow (1962).

He considered new machinery and equipment to include novel

technology, and he discussed whether the introduction of unconventional equipment
improves productivity more than conventional technology. Arrow emphasized workers’
improved adaptability following the introduction of new equipment, whereas Solow
focused on new technology as embodied in the new equipment itself., which came to be
known as ‘the embodiment hypothesis’. Under the embodiment hypothesis, the year inwhich capital equipment is installed indicates the level of technological standard.
Therefore, by calling the age of the equipment its ‘vintage’, Solow theoretically clarified
the relationship among capital accumulation, technological progress and economic
growth. Solow (1960) also attempted a quantitative analysis in which he established andestimated a production function with real capital embodying technological progress as
the production factor and calculated the rate of embodied technological progress. Nelson(1964), following Solow (1960), improved the quantitative analysis and concluded thatthe embodiment hypothesis was probably established in the American economy from
1929 to 1960. Phelps (1962) also sought to measure the embodied technological progress.
The study of technological progress embodied in capital have been continuing toundergo extensive analyses in the same direction as that of productivity fluctuations inan actual macroeconomy. Since the 1970s, productivity has been declining in major
developed countries such as the United States. In view of this circumstances, Kendrick(1980) and Clark (1979) employed growth accounting analysis to calculate the rate oftechnological progress embodied in capital. In particular, Clark (1979) noted that of the3

1.17% productivity decrease from 1965-1973 to 1973-1978, only 0.1% is accounted for by
a decline in the progress of embodied technology.
Analysis of the embodiment hypothesis was pursued vigorously in the 1990s,
probably because U.S. productivity rose notably during the late 1990s. In the U.S., thegrowth rate of equipment investment, centering on IT, accelerated from an average of
3.2% in the 1980s to 5.9% in the 1990s. IT investment collectively refers to investment
in various technologies, with personal computers dominating budgets. It also includes
communication devices such as mobile phones and the equipment used to develop andmanufacture these products. In IT-related investment, new technology is embodied athigh speeds, as represented by Moore’s Law, suggesting a clear relationship between
capital vintage and productivity. Recognizing this possibility, academia revived theembodiment hypothesis. Wolff (1991, 1996) applied Nelson’s (1964) method to examine
the G7 countries at the industry level. Both analyses demonstrated that technologicalprogress embodied in capital is significant and cannot be ignored. Hulten (1992),
Greenwood et al. (1997), Gittleman et al. (2006) and Hobjin (2001) also measured
productivity at the industry level. In particular, Hulten (1992) analyzed the embodimenthypothesis within the long-term time series of 1949-1983 using capital goods prices
adjusted by quality. According to Hulten, approximately 20% of the growth rate of totalfactor productivity (TFP) of U.S. manufacturing was embodied in capital during thisperiod. He also concluded that when the sample period is divided into 1949-1973 and1974-1983, the difference in the rate of contribution of the embodied technologicalprogress between the two periods is negligible. Gittleman et al. (2006) conducted adetailed analysis wherein they recalculated TFP considering the economic obsolescence
rate associated with capital vintage and the depreciation rate of capital stock based ondata from 1947 to 1997 from U.S. Bureau of Economic Analysis. Their analysis foundthat the rate of technological progress embodied in capital is approximately 5% of the
TFP growth rate. Sakallearis (2001) utilized Nelson’s (1964) framework in analyzing thedata of American manufacturing from 1974 to 1988 (three-digit SIC category) andindicated that the rate of technological progress embodied in capital is approximately
10% of the TFP growth rate.
Investigations based on firm-level micro data have recently been pursed
vigorously. Bahk and Gort (1993) attempted to estimate the production function withlabor, human capital, physical capital and capital vintage as production factors when
considering the learning process in production activities. Their investigation used panel
data from 2,150 plants. Power’s (1998) analysis used micro data from approximately
14,000 U.S. manufacturing plants between 1972 to 1988. He separated capital stock into4

facilities and machinery and calculated the vintage of capital goods, concluding thatfacilities and machinery have different impacts on TFP. Sakallearis and Wilson (2004)
utilized Nelson’s (1964) framework in analyzing the micro data of 24,000 U.S.
manufacturing plants between 1972 to 1996. Their findings demonstrated that the rateof technological progress embodied in capital accounts for 8-17% of the TFP growth rate.
The embodiment hypothesis has enjoyed long-standing interest in Japan. Using
Nelson’s (1964) method, Watanabe and Egaitsu (1967) quantitatively confirmed that theembodiment hypothesis was established during the Japanese economy’s high growth
period which is from 1952 to 1962. However, when Japan entered its low growth period
during and after the late 1970s, the increasing age of capital, associated with declining
capital investment, and resulting stagnation of productivity posed serious issues. The
Development Bank of Japan (1979) conducted a pioneering attempt that estimated thevintage series in Japan. This estimate was followed by a more sophisticated vintage
calculation by the Development Bank of Japan (1981, 1983, and 1984), Kuninori and
Takahashi (1984) and Suzuki and Miyagawa (1986). After the stagnation of ‘the lost ten
years’, productivity and economic growth were discussed actively in Japan in the 2000s.
Hayashi and Prescott (2003) initiated the discussion. The studies of Miyagawa andHamagata (2006) and Tokui, Inui, and Ochiai (2008) are fascinating attempts in thisdirection that have comprehensively analyzed the relationship among capital
accumulation, capital age and productivity in the context of Japan’s long-term recession
since 1990s.
Miyagawa and Hamagata (2006) captured the qualitative improvement inequipment renewal and capital from the twin aspects of capital age (vintage) and therenewal cycle of equipment (echo effect) to examine the protraction of renewal
investment under long-term stagnation. Tokui, Inui, and Ochiai (2008) examined thevalidity of the embodiment hypothesis in the Japanese economy in the late 1980s from
two aspects: the consideration of capital vintage and the introduction of new technology
for implementing large-scale equipment investment (investment spike). Their intriguingconclusions are that new technological progress will probably be introduced along withlarge-scale investment and will be embodied in capital goods of young vintage.
Unlike the quantitative analyses, the Development Bank of Japan (2005) sought
detailed data about Japanese equipment investment through a questionnaire survey ofindividual firms. This survey investigated interesting topics, uniquely allowed forawareness surveys, such as the level of awareness of ageing equipment, thedisadvantages of ageing equipment and prospects for future equipment age. Based on
this survey, the Development Bank of Japan (2005) indicated that Japanese firms are5inclined to make investments based on maintaining equipment at a certain age level.
This paper study has three major characteristics not found in earlier studies.
First, it uses micro data to perform a substitutive calculation of capital stock and tomeasure the capital vintage series using an approach consistent with the calculation ofcapital stock. The traditional calculation of capital stock used accounting methods on
disposal amounts via the declining balance method and the straight-line method to
calculate capital stock. However, this assumption is strictly based on an accounting
concept and does not reflect actual physical depreciation. Hence this study calculated
gross capital stock on the basis of acquisition cost and successfully measured capital
vintage in a manner consistent with this calculation.
The second notable characteristic is that we calculated the firm-level capital
vintage and productivity time series which cover more than twenty years. Our researchdatabase is the Development Bank of Japan Corporate Finance Data Bank which is themost comprehensive and reliable firm-level accounting data in Japan and we can get
more than 3,000 companies’ information since 1980 to 2007. With this database, we madea detailed calculation of the capital vintage and TFP which have fruitful information
both time series and cross section dimension. Such attempt has been never done inearlier studies.
The third illuminating point is that we succeeded in the examination of the timevarying effects of vintage on productivity. Basically, the older the capital vintage is, thelower the productivity becomes. It is interesting topic that this relationship between
vintage and productivity may vary in the state of economic conditions. For example,
during the late 1980s, which is so called ‘bubble period’ in Japan, despite of rapid
increase in equipment investment, it is widely known that productivity growth was notnecessary dramatic. We can get a deep understanding for the above phenomena with ourpanel dataset which has relatively long time series.

3 ModelIn this section, we present the theoretical model which explicitly considers therelationship between capital vintage and productivity1). Firstly, the capital accumulation
process is described in detail. Various firms accumulate capital stock in the form ofEquation (1).
 =  + 

(1)
6

In this situation,  represents real gross capital stock at the end of period t, and 

represents real gross investment during period t. As Equation (1) is a simplified version,
the capital depreciation rate is assumed to be 0. If initial capital stock was assumed tobe 0, capital stock derived from Equation (1) would be the sum of the gross business
investment of each period, from period 1 to period t-1, which can be represented in theform of Equation (2).
 = ∑ (2)Currently (period t), firms determine the production level (  ) on the basis of thelabor input level of period t (  ) and capital stock at the end of t-1 ( ). In this situation,
the production level represented byis based on the capital equipment ( ) of periods(v = s ≤ t − 1). By using the Cobb-Douglas production function structure, the productionlevel can be represented by Equation (3).
  =   

In this setting,(3)represents the number of employees during period t who operate

capital equipment installed during period s (s ≤ t − 1), and  represents the technology

level during period t of capital equipment installed during period s.

Equation (4) can be derived from the maximum profits of the firm and with optimallabor input.
 =  (4)



Where  the sales is price and  is the nominal wage. Optimal production level isderived as Equation (5) after substituting Equation (4) into Equation (3).


 = 











(5)

At this point, capital stock at the end of period t-1 is considered and the optimal
production level of the current period (t) can be edited to be similar to Equation (6), where! represents the proportion of investment of period s at the time of establishment.

7
 = "∑ 






 ! #  

(6)! = % = ∑%
$

&

$

'( $'

Total factor productivity (TFP) can be defined using Equation (7).
ln+,- . = /0+  . − 1/0+  . − +1 − 1./0+ .

(7)

Substitution Equation (6) into Equation (7) yields Equation (8)
ln+,- . = +1 − 1./0 2∑   ! 3(8)

In this model, technological progress is set according to the exponential form as
Equation (9).
 = 4567+89 + :;.

(9)

B > 0, μ > 0, λ > 0

If s is large, that is, if the data of capital establishment is closer, the level of technologicalprogress is larger. Equation (8) is rewritten as Equation (10) by substituting Equation(9).
ln+,- . = /0+4. + 89 + +1 − 1./0 B∑  ! 567  ; DC(10)At this point, we performed a McLaurin expansion around λ = 0 on the third item on
the right-hand side of Equation (10) and rearranged terms to obtain Equation (11).
ln+,- . = /0+4. + 89 + :E∑  ;! F(11)

Now we set the vintage index to have the same structure as Equation (12).
GH0 = ∑  +9 − ;.!

(12)8

Equation (12) implies that the vintage index depends on two elements: the timeof equipment installation (s) and the proportion (! ) of equipment that accounts forcapital stock of period s at the end of period t-1. Thus, when installation time is recent
and s approaches t, the vintage index decreases, and this value is more noticeable when
the proportion of new equipment increases. Using this vintage index, TFP can be finallyexpressed as Equation (13) by rewriting Equation (11).
ln+,- . = /0+4. + +8 + :.9 − :GH0(13)Equation (13) shows that TFP can be explained by a constant value, time trend

and vintage. For λ ≥ 0 as shown in Equation (9), the coefficient value of the time trend

can be assumed to be positive. In addition, when the vintage index is smaller, that is,when capital equipment is rejuvenated by recent active equipment investment, we canpredict that the value of TFP increases.

4 Data
4.1 Capital
Capital stock
There is a demand for calculating capital stock data using the data on production
capabilities needed to estimating productivity. In accounting, there are two differences
between capital stock in terms of production abilities and of tangible fixed assets.
Tangible fixed assets with depreciation subtracted from the balance sheet are accounted
for as net capital stock, whereas purchasing cost, including accumulated depreciation,
carried on the tangible fixed assets is accounted for as gross capital stock. Capital stockwith production abilities as an index can be measured by the existing amount ofequipment. Therefore, it is preferable to consider gross capital stock2). For accounting
purposes, fixed tangible assets are a nominal value, but because capital stock as an index
of production abilities is represented by the amount of equipment, a real value is needed.
Based on the above consideration, the calculation of real gross capital stock
should be calculated. There are two basic methods for measuring real gross capital stock:
the benchmark method and the perpetual inventory method. Our study adopted the later
method. Firstly, nominal gross capital stock (here after abbreviated as KGN) is obtained
from the current volume of previous investment as Equation (14).
JK = ∑  L+M, 9.K

(14)
9

0 ≤ L+M, 9. ≤ 1, L+M, M. = 1,

NO+ ,.
N

≤ 0, PQR 9 > M

Where ϕ+M, 9. is the proportion of equipment of year t installed in year v, K is thenominal investment installed in year v. Secondly, real gross capital stock (here after
abbreviated as KGR) can be calculated with the investment goods deflator of the various
periods of past investment ( ) as Equation (15).

JU = ∑  L+M, 9.U

U =

(15)

$V'
$'

Where U is the real investment deflated by the investment goods price of the various
periods of past investment ( )In this model, estimates of gross capital stock is estimated by assuming ‘one-hoss
shay decay’3). Equipment, whose accounting value disappears after depreciation,
contributes to production. Although data construction using the age-efficiency profile isdesirable for representing capital stock as production capacity, it is not possible becauseof limited data availability. Therefore, as shown in Equation. (16), we adopt one-hoss
shay decay assumption, wherein efficiency is kept constant immediately before physicalscrapping.
1 M ≤9 ≤M+,
L+M, 9. = W
0 M+, <9(16)

Data from tangible fixed assets schedule are recorded in the annual report that
listed companies are mandated to disclose to the Financial Services Agency. The tangible
fixed assets schedule includes items such as increases in current-period tangible fixed
assets (IN), decreases in current-period tangible fixed assets (SN), the stock of tangible
fixed assets at the end of period (acquired amount base) (KGN), accumulated
depreciation of tangible fixed assets (CDEP), current-period depreciation of tangible
fixed assets (DEP) (according to balance sheets) and tangible fixed assets (net capitalstock: KNN). In these periods, the relationship in Equation (17) and (18) holds.
JK = JK + K − YK(17)KK = JK − Z[\

(18)
10

The data in the Development Bank of Japan Corporate Finance Data Bank are
categorized as total tangible fixed assets, buildings, structures, machinery, ships,
vehicles and transportation equipment, tools, rental fixed assets, other depreciable
assets, land and construction-in-process accounts. In addition, the database records
increases in current-period tangible fixed assets (IN), decreases in current-period
tangible fixed assets (SN), end-of-period stock of tangible fixed assets (acquired amountbase)(KGN), accumulated depreciation of tangible fixed assets (CDEP), current-period
depreciation of tangible fixed assets (DEP) (according to balance sheets) and tangible
fixed assets (net capital stock: KNN). The database, however, does not record amounts
for current-period depreciation, total and construction-in-process. In addition, increases
in the amount during the current period are small compared with recorded acquisition
costs. Consequently, using on the identity related to stocks (end of period stock= previous
period stock + increased amount－decreased amount) and calculating the gap = end of
period stock－(previous end of period stock + increase amount－decreased amount),
consistency holds by adding to the increased amount when the gap is positive and adding
the absolute value to the decreased amount when the gap is negative.
Depreciable assets are defined by subtracting non-depreciable assets (such as landand construction-in-process account) from the total amount4). Acquisition costs (nominal
gross capital stock: KGN) related to depreciable assets are estimated on the basis of theamount of the current-period increase (nominal investment: IN) and the amount of thecurrent-period depreciation (SN) based on the following procedures in Equation (19)-(22).
Further, the point in time (M ) at 0 or negative in the beginning is determined from theacquisition cost in the most recent period (t = 9 ) when data back to the past andsubtracted from the amount of the current period increase. This calculation follows fromthe logic that current capital stock is organized by the latest investment based on theassumption of first-in/first-out. In other words, the following condition holds.
∑

]

K < JK ≤ ∑



K

(19)

A portion of the oldest amount of the current-period increase (K  ) constitutes

capital stock at the end of the period t. For a portion of the investment of during period(M ):^ =&_V ∑%`' ] $V%$V',

0 < ^ ≤ 1

(20)

11

and after period M + 1, the summation of investment until the aforementioned point intime comprises acquisition costs at the point in time t as Equation (21).
JK = ^ K  + ∑

 a

K

(21)

This approach enables us to determine which investment comprise capital stock
I each period and to create an accurate od real gross capital stock. Using even the oldest
data, acquisition costs fail to reach zero or become negative at point in time v (period9b ).

We proceed with retroactive estimation of the amount of the current-period increase (K ).

If most recent service life is available (!ba = 9b + 1 − Mba), we fix the value and use it,

and then the amount of current-period depreciation (YK ) corresponds to the currentperiod increase amount of (9 − !ba)

Kcd] = YK ,9e ≤ 9 ≤ 9b

(22)

From Equation (22), a retroactive business affiliation of the investment can be obtained
and by using this data, the procedures in the first stage can be determined. Although
this method is the same as the benchmark method, it has the unique characteristic ofprocessing the service life obtained from the recent perpetual inventory method whenrealizing current-period depreciation.
Firstly, firm data from portions of 1956 to March 2008 (FY2007) was gathered.
Among the 74,918 cases in the 1980-2007 data sample, 58,701 cases (78%) of capitalstock data were created The service life of 93% of these cases was not fixed, and by using
the available data for the current-period increase amounts, we created real gross capitalstock data.

4.2 Total Factor Productivity (TFP)
TFP, which is defined by Equation (23), is calculated by using the real value of added(GU ), real gross capital stock of the previous end of period (JU), number of employees(  ) and the average capital distribution rate of industries (α) based on the Cobb=Douglas

production function5).

,- = /0+GU . − 1/0+JU . − +1 − 1./0+  .

(23)

12

GU =   +



(24)

As Defined in Equation (24), real value added is composed by capital income (  ) andlabor income ( ). In this study,   =depreciation + interest and discount expense＋rent+ ordinary income + taxes, and =labor cost+ offices’ bonuses + salaries and allowances+ provision of allowance for houses + welfare expenses + provision of allowance for

employee retirement benefits6). α is obtained from the average value of profit
distribution rate of corresponding industry between 1980 and 20077).
of employees in each company at the end of the period8).

is the number

4.3 Capital vintage
vintage
Based on the Equation (15), the capital vintage is determined by the average ageof existing equipment as Equation (25)9).
GH0 =∑'`(+ .O+ ,.$g'
&_g

(25)

The slight modification of Equation (24) yields the dynamics of capital vintage as
Equation (26).
GH0 =$g

&_g

+ +1 − h.+1 + GH0 .

&_g&_g(26)

Give the initial value of GH0 , capital vintage in each period can be recursively calculated

in Equation (26).

【Figure 1】

Figure 1 summarizes the age-based shares of vintage in the main industries. Thesefigures are categorized into three parts: less than five years, more than five years andless than ten years, and more than ten years. The share of the more than ten-year-old
vintage index has increased in almost every industry since the 1980s. This tendency isparticularly remarkable in the material industries (such as chemical and primary metal),
Electricity, gas and water industries. These heavy industries have large-scale equipment
installed. Since the 1980s, called the period of stable economic growth, such renewal
13

investment grew at a sluggish pace and their share increased gradually. This
characteristics were also observed in the machinery industries. However, the share ofold vintage in these industries is relatively low. For example, in 2007, the average
vintage of more than ten years in the material industries was 54%. In contrast, it was
35 % in machinery industries. In non-manufacturing industries excluding electricity, gas
and water, the aged vintage share was lower than in the material sectors, and theaverage share in 2007 was 34%.
【

Figure 2】

Figure 2 shows changes in the capital vintage index of the various industries.
The subtle differences in trends in different industries can be explained by consideringthat vintage increased during periods of economic recession and decreased during
periods of economic expansion. This is particularly so during the economic bubble of late1980s and the boom after 2000, where vintage decreased steadily. During economic
expansion, capital equipment was rejuvenated because of increase in capital investment,
resulting in decrease in vintage. In contrast, during economic recessions, because theinstallation and renewal of new equipment stagnates and equipment age, the vintage
index also increased. This trend can be observed in the Figure 1, thereby confirming that
Our measurement of the capital index was correct.

5 Empirical Evidence
5.1 Estimation results (1)First, we conducted panel estimations for the period 1980-2007. As a preliminary
test, we conducted a specification test (Hausman test) to determine whether we could
choose a fixed effect model or random effect model by industries. As the results ofspecification test vary among industries, we examined the estimation results of bothmodels. Table 1-1 reports the summary of results of the random effects model and Table
1-2 reports the results of the fixed effect model.
【

Table 1－1】【

Table 1－2】

We investigated 13 manufacturing industries, eight non-manufacturing industries
14and all industries. The estimation equation is based on Equation (13) shown in section 3
and we make a little modification of Equation (13) as an estimation form as follows:,-i = 1 + j9R50h + kGH0i + li
Where

(27)

,-i shows the logarithmic value of total factor productivity andtrend represents time trend. GH0i indicates the capital vintage index derived andmeasured in section 4. As the dependent variable is the logarithmic value, the coefficientβ and γ represent semi-elasticity. Coefficient γ is expected to be negative because thesmaller the value of the vintage index, that is, the younger the equipment age of capitalstock, the stronger the effects of productivity improvement.
The following discussions and explanations are based largely on the results ofrandom effects model and, where appropriate, we identify differences to the fixed effectmodel. The vintage coefficient was significant across all industries and recorded a valueof 0.01. This outcome indicates that when the average age of capital increases by one
year, TFP falls to 1%10). By dividing the manufacturing industries into the material

industry (pulp and paper, chemicals, coal and petroleum products, stone, clay and glass,primary metal and fabricated metal) and machinery industry (four types of machines),
we observe that the effect of the vintage coefficient is stronger in the material industry.
This trend is also observed in the fixed effect model. In general, material industry
includes heavy industries, where the setup and installation of capital equipment occurs
infrequently. This outcome implies that despite the comparative lower frequency of therenewal of capital stock in the material industry, it is highly likely that, during renewal,
the new technology introduced is markedly different from the previous technology. For
example, in the petroleum refining and chemical industry, the vintage coefficient values
are relatively higher, highlighting such characteristics. Even in non-manufacturingindustries, slightly different results were obtained in the fixed effect model although thevintage coefficients were significantly negative.
The impact of the trend (β) differs across industries. In the random effect model,
vintage has a significant positive impact on all industries. This result suggests thatbetween 1980 and 2007, certain factors supported the uptrend in TFP on a macro level
level in Japan. However, after examining the details closely, we could not identify thesecharacteristics in the material industry, leaving us to postulate that the factor driving
the uptrend must have been in the non-manufacturing industries.
Finally, we analyze the impact on the constant term. The constant term (α) is
different to the factors behind the trend, as demonstrated by Equation (9) in the15

theoretical model in section 3. The constant term represents a technology improvement
factor. This factor is irrelevant to temporal changes such as business cycle and economic
expansions, but is believed to reflect a range of industry-specific management attitudes
regarding research and development and new products. This factor is significantly
positive across all industries. We confirmed that factors that did not appear to affect
uptrend and vintage actually spurred TFP. These effects may differ slightly acrossindustries, but we observed an overall positive effect.

5.2 Estimation results
results (2)Here, we present estimations by industry. Figure 3 depicts estimations based on
Equation (26) and the results of estimation (rolling regression) conducted on 22
industries on a year-by-year basis. During the estimation period of six years, the initial
Estimation period was between 1980 and 1984, and the last estimation period was
between 2000 and 2007. Upper and lower line in each diagram show the 95% confidence
interval. The shaded zone denotes the period determined by the Cabinet Office as the
economic recession period.
【

Figure 3】

During the economic expansion period in the first half of the 1980s, the vintage
coefficient was significantly negative in all industries. This result indicates that theincrease in new equipment investment backed by economic expansion rejuvenated theage of capital equipment and thereby spurred an improvement in productivity (hereafter
called the ‘vintage effect’). This vintage effect was confirmed during the boom period
beginning in 2002. The effect was particularly distinct in the primary metal and chemicalindustries within the materials industry and in the general machinery and transportmachinery industries within the machinery industry. This growth period lasted longer
than Izamani boom of the 1960s, and it featured brisk investment in equipment acrossall industries. In particular, high demand for semi-finished products and capital goods
in developing countries increased exports of goods from Japan’s material industry, andrenewals and installations of new capital equipment soon followed. This investment
boom prompted adoption of machinery equipment equipped with the latest technology;
thus, the vintage effect was widely evident, even in the material industry.
We now focus on the characteristics of the 1987-1991 expansion. During this period,
the capital equipment boom was larger than the boom period after the 2000s, but the16vintage effect was weaker, as the diagrams in Figure 4 shows. Within the material
industry in particular, few industries exhibited positive vintage coefficient values. Thus,
despite buoyant capital investment during the bubble period, the rejuvenation of the ageof capital equipment did not necessarily cause improvement in productivity.
To explore the reasons for this phenomenon, we conducted two complementary
investigations. First, the rolling estimated coefficients of vintage in Equation (27) wereregressed by the intensity of research and development (R&D intensity) and by the
researcher-employee ratio11). To investigate that regression, we selected two types ofdependent variables: the coefficient of embodied technological progress ( :r = −ks inEquation (27)) and the coefficient of disembodied technological progress (8̂ in Equation(27))12).
【

Table 2】

Table 2 reports the estimation results. Both R&D intensity and the researcheremployee ratio exert positive significant effects on disembodied technological progress(8̂ ). These explanatory variables, however, did not have the correct sign, indicating that
The enforcement of R&D stimulates disembodied technological progress and does notnecessarily correlate with embodied technological progress. In this complementary
estimation, we used industrial level data (16 industries) to investigate the relationshipbetween technological progress and research and development. It is essential that future
research examine this issue using data from individual firms.
As a second complementary investigation, we examined changes in the share of
non-factory buildings (such as dormitories, employee recreation centers) included incapital stock during various periods. Capital equipment in these facilities did notnecessarily feature the latest technology and did not directly spur improvements in
productivity.
【

Table 3】

Table 3 reports the share of buildings, excluding factory facilities, in various
industries (recorded as K share). In addition, we recorded the average values of thecoefficients during this period, which were measured according to a rolling estimation.
Table 3 demonstrates that more than half of the periods that registered the highest K
share occurred during the bubble period. During the same period, we also observe thatvintage coefficient values were remarkably low compared with other periods. In contrast,
17

during the economic boom after 2000, K share was comparatively low whereas vintage
Coefficient values were high across all industries. Hence, even within the same economic
expansion period, the vintage effect does not necessarily present the same situation andrelies strongly on the content of capital equipment. It may be possible to measuretechnological progress using the ratio of buildings in net capital stock at the firm level.
This issue remains for future research.

6 Conclusions
Using the firm- level financial data in Japan, this study empirically examined therelationship between the vintage of capital and productivity. As the foundation of ourempirical analysis, we conducted a detailed measurement of capital stock. We thenmeasured the vintage index and total factor productivity and completed the preliminary
work for required for our empirical analysis. Subsequently, we reached the following
conclusions based on the estimation results.
First, we confirmed the vintage effect by examining the entire period. The effect
was particularly distinct in the materials, general machinery and transport machineryindustries. Second, we considered time-varying changes in vintage effects and observed
them during periods of economic expansions, particularly during the post-2000 economic
upturn, where they were generally observed in all industries. We reconfirmed that the
rejuvenation of capital equipment during the same period resulted from a strong
productivity effect. In contrast, during the late 1980s, despite significantly increased
investment, the vintage effect exerted an observable effect on productivity. This findingshows that investment during such periods is not necessarily productive and is highly
likely to produce a merely temporary boom.
We made attempts to deeply analyze the factors that determine productivity. In
addition to reconfirming the effect of vintage on productivity, we closely examined thetime-varying effects of vintage during different business cycles. Our analysis indicatesthat sustained economic expansion and recovery requires higher productivity and that
capital accumulation is significant, effective and necessary for improving productivity.
This message must be a valuable lesson to emerging market economies including East
Asian countries.

18

Acknowledgement
This paper is a revision of the paper presented at the workshop of the Graduate School
Of Kobe University on June 17,2009, at the 11th Macroeconomis conference (at Osaka
University) on December 23,2009 and at the workshop of the Austrian Institute of
Economic Research (WIFO) on March 10, 2010. We would like to specially thank Susano
Basu (Boston College), Simon Gilchrist (Boston University), J.S. Metcafe (University ofManchester), Michael Peneder, Thomas Url and Klaus Nowotny (WIFO),. We also thankTomohiko Inui(Cabinet Office), Charles Yuji Horioka and Mototsugu Fukushige (Osaka
University), Etsuro Shioji (Hitotsubashi University), Masaya Sakuragawa (Keio
University), Hiromasa Kubo, Tamotsu Nakamura, Takashi Unayama and Ichiro Tokutsu(Kobe University) for their helpful comments and suggestions.

Footnote1) We constructed the embodied technological model originally developed by Nelson(1964).
2) OECD (2001) is based on the age-efficiency profile, which recommends estimation ofmacro-/industrial-level capital stock, but when handling industrial data, it can be used
only in the concept of aggregating various types of assets such as buildings, construction,
machinery and equipment. Therefore, it states that estimation based on the ageefficiency profile is not advisable.
3) The phrase ‘one-hoss-shay decay’ is derived from the expression that one-hoss shay
had been running for hundred years and suddenly broke down. This phrase is borrowed
from a passage in the poem ‘Deacon’s Masterpiece’ by Oliver Wendell Holmes (1809-1894).
4) Creating data at the individual asset level, such as a building or piece of machinery,
is possible, but coverage of tangible asset increases at that level is roughly 60% of thebalance. Therefore, such a detailed approach has not been adopted.
5) In this study, GDP deflator is used as a real-added-value deflator and is calculated by
dividing the nominal added value by the amount of real output subtracted from real
input value. For example, when we calculate this value in the electric industry (1990=1),
19

it is 87.9 in 1970, 1.92 in 1980 and 0.53 in 1998, and these values change dramatically.
Therefore, the deflator is assumed to be common in all industries and this study uses
GDP deflator.
6) The definition of personal expenses follows that given in the personal expenses
element of corporate statistics by the Ministry of Finance. In many cases, employee
benefit costs and provisions for severance pay allowances are recorded together andcannot be separated. Therefore, provisions for severance pay allowances are recorded
and included in personal expenses.
7) It is possible to vary α by industry. In such a case, however, it is difficult to calculate

TFP for different values of α and compare TFP across industries. In addition, we cannot
establish panel dataset.

8) The reason why we use value-added and not aggregate products is that the share ofintermediate input differs among industries, indicating that it may be dangerous toassume the same proportion between companies producing intermediate inputs andcompanies outputting them. For example, in the electric industry, a less than 10%
proportion of value-added in sales is about 14%,and a more than 30% proportion is 21%.
9) Technically, building, structures and machinery have their own vintages. In general,buildings and structures may have a longer service life than machines. Therefore, thevintage of these assets affects productivity with a time lag and it seems worthwhile toconsider the calculation of a vintage index by assets. Acquisition costs and amounts ofincreases and decreases in buildings, structures and machinery are recorded.in the
Detailed Table of Tangible Assets in financial statements. Hence we can calculate eachvintage based on this information. However, we cannot use current amounts of decreases
by assets, and we can only uses current amounts of increases by industry from 1978
based on financial data by Development bank of japan, which we used in this study.
These problems cause difficulty in calculating the vintage index by assets. This
modification will be a challenge for the future.
10) By considering a simple average of the vintage index in all industries and measuring
absolute change, it is about 0.15 year, implying that the effect of vintage on TFP is nearly
0.15%. Considering the fact that the real growth rate of GDP from 1980 to 2007 was 2.5%,
the effect of vintage on TFP is about 6%.
2011)R&D intensity and the researcher-employee ratio in 16 industries are collected fromthe Report of Survey of Research and Development (Ministry of Internal Affairs andCommunications). The definition of research and development investment was changed
from experiment and research expenses to research and development in 1998, and thetime series of the data was discontinuous. Thus, research data by industry were used inthis study.
12) 8̂ is calculated by subtracting :u from jr.

21

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24

Figure 1
Age share of capital vintage 1980-2007
ChemicalLess than 5 years

Between 5 and 10 Years

More than 10Years

Primary Metal

Less than 5 years

Between 5 and 10 Years

More than 10Years

MachineryLess than 5 years

Between 5 and 10 Years

More than 10Years

Electric Machinery

Less than 5 years

Between 5 and 10 Years

25

More than 10Years

Transport Machinery

Less than 5 years

Between 5 and 10 Years

More than 10Years

Precision Machinery

Less than 5 years

Between 5 and 10 Years

More than 10Years

Construction

Less than 5 years

Between 5 and 10 Years

More than 10Years

Electricity,Gas and Water

Less than 5 years

Between 5 and 10 Years

26

More than 10YearsFigure 2
Vintage Index 1980-2007

27

Figure 3
Estimation Results (2)Agriculture, Forestry and Fishery

Mining

.2

.4

.3
.1
.2
.0
.1

.0

-.1

-.1
-.2
-.2
-.3
-.3

-.4
80

81

82

83

84

85

86

87

88

89

90

91

VIN1

92

93

94

VIN1H

95

96

97

98

99

00

01

-.4
02
80

81

82

83

84

85

86

87

88

89

90

91

VIN2

VIN1L

Food

92

93

94

VIN2H

95

96

97

98

99

00

01

02

96

97

98

99

00

01

02

VIN2L

Textile

.02

.04

.02
.00
.00
-.02
-.02

-.04

-.04

-.06
-.06
-.08
-.08
-.10

-.10
80

81

82

83

84

85

86

87

88

89

VIN3

90

91

92

VIN3H

93

94

95

96

97

98

99

00

01

-.12
02
80

81

82

83

84

85

86

87

88

VIN3L

89

90

91

VIN4

Pulp and Paper

92

93

94

VIN4H

95

VIN4L

Chemical
.02

.050

.025

.00

.000
-.02
-.025
-.04
-.050
-.06
-.075
-.08
-.100
-.10

-.125

-.12

-.150
80

81

82

83

84

85

86

87

88

89

90

VIN5

91

92

93

VIN5H

94

95

96

97

98

99

00

01

02 80

81

82

83

84

85

86

87

88

89

90

VIN6

VIN5L

Coal and Petroleum Products

91

92

93

94

VIN6H

95

96

97

98

99

00

01

02

VIN6L

Stone, Clay and Glass

.10

.02
.01

.05
.00
.00
-.01
-.05

-.02

-.10

-.03
-.04

-.15
-.05
-.20
-.06
-.25
80

81

82

83

84

85

86

87

88

89
VIN7

90

91

92

VIN7H

93

94

95

96

97

98

99

00

01

-.07
02 80

VIN7L

81

82

83

84

85

86

87

88

89
VIN8

28

90

91

92

VIN8H

93

94

95

VIN8L

96

97

98

99

00

01

02

Primary Metal

Fabricated Metal

.04

.04

.02
.02

.00
.00

-.02
-.04

-.02

-.06
-.04

-.08
-.06

-.10
-.12

-.08
80

81

82

83

84

85

86

87

88

89

90

VIN9

91

92

93

VIN9H

94

95

96

97

98

99

00

01

02

80

81

82

83

84

85

86

87

VIN9L

88

89

90

VIN10

Machinery

91

92

93

VIN10H

94

95

96

97

98

99

00

01

02

96

97

98

99

00

01

02

96

97

98

99

00

01

02

96

97

98

99

00

01

02

VIN10L

Electric Equipment
.03

.02

.02
.01
.01
.00
.00
-.01

-.01
-.02

-.02

-.03
-.03
-.04
-.04

-.05
-.06

-.05
80

81

82

83

84

85

86

87

88

89

90

VIN11

91

92

93

VIN11H

94

95

96

97

98

99

00

01

80

02

81

82

83

84

85

86

87

88

VIN11L

89

90

VIN12

Transport Equipment

91

92

93

94

VIN12H95
VIN12L

Precision Instrument
.100

.04

.075
.02
.050

.025
.00
.000
-.02

-.025

-.050
-.04
-.075

-.100

-.06
80

81

82

83

84

85

86

87

88

89

90

VIN13

91

92

93

VIN13H

94

95

96

97

98

99

00

01

80

02

81

82

83

84

85

86

87

88

89

90

VIN14

VIN13L

Other Manufacturing

91

92

93

VIN14H

94

95

VIN14L

Construction
.04

.02

.03
.00
.02
-.02
.01
-.04

.00

-.06

-.01
-.02

-.08
-.03
-.10
-.04
-.05

-.12
80

81

82

83

84

85

86

87

88

89

VIN15

90

91

92

VIN15H

93

94

95

96

97

98

99

00

01

02

VIN15L

80

81

82

83

84

85

86

87

88

89

VIN16

29

90

91

92

VIN16H

93

94

95

VIN16LElectricity, Gas and Water

Commerce

.08

.08

.06
.04
.04

.02

.00

.00
-.04
-.02

-.04
-.08
-.06

-.12

-.08
80

81

82

83

84

85

86

87

88

89

90

VIN17

91

92

93

VIN17H

94

95

96

97

98

99

00

01

02

80

81

82

83

84

85

86

87

VIN17L

88

89

90

VIN18

Real Estate

91

92

93

VI N18H

94

95

96

97

98

99

00

01

02

97

98

99

00

01

02

VIN18L

Transport and Communication

.08

.04

.04
.00
.00

-.04

-.04

-.08
-.08

-.12

-.16
-.12
-.20

-.24

-.16
80

81

82

83

84

85

86

87

88

89

90

VIN19

91

92

93

VIN19H

94

95

96

97

98

99

00

01

02

VIN19L

.04

.02

.00

-.02

-.04

-.06

-.08
81

82

83

84

85

86

87

88

89

VIN21

90

91

92

VIN21H

93

94

95

81

82

83

84

85

86

87

88

89

VIN20

Service

80

80

96

97

98

99

00

01

02

VIN21L

30

90

91

92

VIN20H

93

94

95

VIN20L96

Table 1-1 estimation results（1）1980-2007
Fixed Effect Model
Constant

Time trend

Vintage

Group

Obs

All Industry

3.953(8.72)***0.001(4.64)***-0.018(-22.88)****

3074

58286

Agr. F. F.

-2.269(-0.36)

0.004(1.27)

0.001(1.18)

239

Mining39.118(3.76)****-0.017(-3.36)***-0.045(-2.83)***

7

191

Food

0.811(0.54)

0.002(3.41)***-0.031(-11.33)***

144

3171

Textile-2.940(-1.29)

0.004(3.89)***-0.018(-4.91)***

73

1752

Pulp

24.020(7.14)***-0.009(-5.45)***-0.006(-1.07)

37

809

Chemical3.999(3.54)***0.0007(1.31)-0.031(-14.36)***

200

4690

Coal and P.

14.098(1.05)-0.005(-0.76)-0.079(-4.62)***8208

Stone, Clay

7.494(4.51)***-0.0007(-0.83)-0.013(-4.44)***

90

1878

Pri. Metal

2.318(0.97)

0.001(1.45)-0.019(-4.57)***

114

2649

Fab. Metal

4.701(1.79)**0.0008(0.64)-0.021(-4.93)***

88

1901

Machinery5.730(3.49)***0.0002(0.24)-0.009(-3.33)****

245

5511

Elec.

7.859(5.09)***-0.0008(-1.07)-0.013(-4.29)***

258

5182

Trans. Eq.

-7.243(-5.30)***0.006(10.09)***0.004(1.53)

144

3337

Precision

0.530(0.15)

0.002(1.54)-0.001(-0.14)

52

1042

Other Man.

2.782(1.50)

0.001(1.82)**-0.026(-8.46)***

178

3336

Construction-0.900(-0.67)

0.004(6.01)**-0.022(-8.35)***

212

4438

E.G.W.

49.820(13.66)***-0.023(-12.75)***-0.010(-1.75)*

24

607

Commerce

22.515(18.75)-0.008(-14.19)-0.003(-1.91)***

608

9347

Real Estate

16.269(2.63)***-0.006(-2.02)**-0.039(-4.52)***

88

1157

Trans&Com-19.716(-9.07)***0.013(11.97)***-0.024(-5.33)***

147

3144

Service-5.495(-2.38)***0.005(5.17)***-0.008(-2.48)***

355

3897

***, **, and * are significant at 1%, 5% and 10% significance level.

31

Table 1-2 estimation results（2）1980-2007
Random Effect Model
Constant

Time trend

Vintage

Group

Obs

All Industry

6.674(14.58)***-0.0003(-1.63)-0.012(-14.87)***

3074

58286

Agri. F. F.

-14.427(-1.93)**0.010(2.70)***0.0003(0.03)

239

Mining32.141(3.22)***-0.014(-2.80)***-0.061(-3.81)***

7

191

Food

1.263(0.83)

0.002(3.02)***-0.030(-10.57)***

144

3171

Textile-2.211(-0.97)

0.004(3.55)***-0.016(-4.24)***

73

1752

Pulp

26.043(7.69)***-0.010(-6.01)***-0.002(-0.42)

37

809

Chemical

4.916(4.34)***0.0002(0.45)-0.029(-13.16)***

200

4690

Coal and P.

26.536(1.75)*-0.011(-1.51)-0.051(-2.30)***8208

Stone&Clay

7.958(4.70)***-0.0009(-1.09)-0.012(-3.85)***

90

1878

Pri. Metal

4.539(1.86)*

0.0006(0.51)-0.015(-3.37)***

114

2649

Fab. Metal

3.675(1.34)

0.001(0.99)-0.023(-4.92)***

88

1901

Machinery

8.912(5.21)***-0.001(-1.65)*-0.002(-0.89)

245

5511

Elec. Eq.

9.853(6.25)***-0.001(-2.34)***-0.008(-2.75)***

258

5182

Trans. Eq.

-6.052(-4.37)***0.006(9.06)***0.007(2.58)***

144

3337

Precision

2.255(0.60)

0.001(1.03)

0.002(0.29)

52

1042

Other Man.

4.822(2.58)***0.0006(0.66)-0.022(-6.98)***

178

3336

Construction-0.731(-0.54)

0.004(5.83)***-0.021(-7.80)***

212

4438

E.G.W.

52.005(14.42)***-0.024(-13.52)***-0.006(-1.10)

24

607

Commerce

25.065(20.67)***-0.009(-16.21)***0.001(0.73)

608

9347

Real Estate

40.456(6.75)***-0.018(-6.23)***0.002(0.32)

88

1157

Trans& Com-17.100(-7.77)***0.011(10.57)***-0.017(-3.66)***

147

3144

Service-1.719(-0.73)

0.003(3.37)***-0.001(-0.44)

355

3897

32

Table2. Determinants of Rolling Estimated Coefficients of Vintage
2-1 Fixed Effect model
Dependent

R&D intensity

variableλμResearcher-Employee
ratio-0.70206-0.00024(0.005)(0.105)

1.15101

0.00082(0.000)(0.000)2-2 Random Effect model
Dependent

R&D intensity

variableλμResearcher-Employee
ratio-0.43786-0.00002(0.029)(0.841)0.862960.00066(0.000)(0.000)33

Table 3 Vintage Coefficient and Components of Capital Stock

1980-1986

1987-1991
Vintage

Kshare1992-2001
Vintage

Ksharecoefficient

2002-2007
Vintage

Ksharecoefficient

Vintage
Ksharecoefficient

coefficientAgri. F.F.

0.669

-0.038

0.584

0.020

0.663

0.082

0.636

NA

Mining

0.164-0.157

0.384

0.018

0.335

0.028

0.280

-0.042

Food

0.258

-0.0090.274-0.0020.243-0.0270.247-0.065

Textile0.241-0.015

0.269

0.006

0.154

-0.0370.125-0.075

Pulp

0.296

-0.0330.460-0.0100.290-0.0240.235-0.030Chemical

0.283-0.0250.424-0.0050.259-0.0250.248-0.078

Coal & P.

0.376-0.102

0.381

0.002

0.489

-0.0830.519-0.067

Stone, Clay

0.289

-0.0190.329-0.001

0.192-0.021

0.194-0.044Pri. Metal

0.389-0.0170.545-0.0030.339-0.0170.252-0.083

Fab. Metal

0.391-0.014

0.234

0.000

0.233

-0.0190.254-0.035

Machinery

0.153-0.0250.157-0.0120.101-0.0250.111-0.032

Elec. Eq.

0.375

-0.0100.237-0.0120.136-0.0220.123-0.032

Trans. Eq.

0.195-0.020

0.320

0.015

0.158

-0.0120.115-0.002

Precision

0.310-0.004

0.096

0.021

0.066

-0.0190.063-0.003

Other Man.

0.198

-0.0240.182-0.0190.188-0.0570.185-0.088Construction

0.241-0.0030.315-0.0010.178-0.0060.079-0.028

E.G.W

0.704

0.000

0.564

0.030

0.491

-0.0140.452-0.046

Commerce

0.521

0.009

0.564

0.041

0.418

-0.0190.299-0.048

Real Estate

0.992-0.001

0.988-0.0070.983-0.1090.994-0.179Trans& Com

0.553-0.0250.570-0.0120.550-0.031

0.582-0.105Service

0.509-0.004

0.398

0.006

0.285

-0.0250.174-0.053

K share is industry share of building in capital stock (shaded are is the highest share). Vintage coefficient is averageof estimate in Figure 3.

34