This paper investigates the impact of lumpy capital adjustment on productivity at the firm level using data on Japanese manufacturing industries. We estimate stochastic production frontiers, taking firm heterogeneity into account. We find that investment spikes are negatively related to technical efficiency. Furtermore, we find a negative relationship between machinery capital age and measured efficiency.

Keiichi Shima

English

Research Papers in Economics

     
 
 
  
  
Volume 30, Issue 4 
  
Lumpy capital adjustment and technical efficiency 
  
 
 
Keiichi Shima  
Hirosaki University 
Abstract 
This paper investigates the impact of lumpy capital adjustment on productivity at the firm level using data on Japanese 
manufacturing industries. We estimate stochastic production frontiers, taking firm heterogeneity into account. We find 
that investment spikes are negatively related to technical efficiency. Furtermore, we find a negative relationship 
between machinery capital age and measured efficiency.
I would like to thank an anonymous referee and the editor, John P. Conley, for their useful comments. 
Citation: Keiichi Shima, (2010) ''Lumpy capital adjustment and technical efficiency'', Economics Bulletin, Vol. 30 no.4 pp. 2817-2824. 
Submitted: Sep 20 2010.   Published: October 28, 2010. 
 
     1 Introduction
In recent years, a number of empirical studies have attempted to establish the rela-
tionship between technology, investment and productivity. Power (1998) examined the
link between investment and productivity and found virtually no evidence of a positive
correlation between productivity and high levels of investment using pooled regressions
at the U.S. plant level. Huggett and Ospina (2001) investigated the eﬀect of technol-
ogy adoption on productivity growth. They calculated total factor productivity (TFP)
growth at the plant level using Colombian data. They regressed TFP growth on current
and past values of technology adoption measures. They found evidence that productiv-
ity growth falls when a plant undertakes a large equipment purchase and that the eﬀect
of the large investment on productivity growth continues to be negative for subsequent
years. Sakellaris (2004) also used the U.S. plants data and obtained similar results.
These ﬁndings indicate that lumpy investment episodes result in the costly adoption of
new technology embodied in new capital.
These authors employ a two-stage approach to assess the impact of investment spikes
on productivity or productivity growth. In the ﬁrst stage, they construct productivity
variables such as labor productivity, TFP or TFP growth. In the second stage, they
regress productivity variables on current and past investment spike dummies. In con-
trast, our alternative approach is based on estimating a stochastic frontier production
function. Our methodology incorporates the technical eﬃciency eﬀects induced by large
investment episodes that embody new technology and involve costly adoption.
2 Linking Productivity and Investment Spike
We obtain ﬁrm-level TFP measures by estimating a log-linear Cobb-Douglass production
function for each industry. Individual ﬁrms are indexed i, and industries are indexed by
j, for each year t in the sample:
lnyit = lnajt + αj lnkit + βj lnlit + γj lnmit + ϵit (1)
where yit is gross output. Since coeﬃcients on the log capital kit, labor lit and material
inputs mit can vary by industry, this speciﬁcation allows for diﬀerent factor intensities
in diﬀerent industries. An additional speciﬁcation is
lnajt =
∑
t
fyt +
∑
j
indj (2)
where fyt is a year dummy and indj is an industry dummy. Industries are classiﬁed at
the two-digit SIC level.
Consider the stochastic frontier production function for ﬁrm data. We postulate that
the error term in equation (1) is composed of two diﬀerent types of disturbances:
ϵit = uit + vit (3)
1where uit is a non-negative random variable associated with technical eﬃciency of pro-
duction, and vit is assumed to be i.i.d. with N (0,σ2
v). The term uit is assumed to
be distributed independently of vit. Following Battese and Coelli (1993), the technical
eﬃciency eﬀect in the stochastic frontier model is speciﬁed by
uit = zitδ + wit (4)
where zit is a vector of explanatory variables associated with ﬁrm speciﬁc technical
eﬃciency, δ is the corresponding vector of parameters, and wit is a random error. The
term wit is assumed to follow a N (0,σ2) distribution truncated from below at  zitδ,
which is consistent with uit being a non-negative truncation of N (zitδ,σ2).
In this paper, zitδ is assumed to be deﬁned by
zitδ = δage;jageit +
4 ∑
=0
δspk;spikeit  + δtrd;jt (5)
where ageit is machinery age for individual ﬁrms, spikeit is an investment spike dummy
and thus spikeit  is a dummy based on the length of time since the last investment
spike, τ. A time trend is also included in the explanatory variables. Since coeﬃcients
for the machinery age and time trend variables can vary by industry, this speciﬁcation
allows for industry diﬀerences.
The parameters of the stochastic production frontier and the model for the technical
eﬃciency eﬀect are estimated simultaneously using the maximum likelihood method.
Following the suggested parameterization by Battese and Coelli (1993), we let σ2
s 
σ2 + σ2
v and λ  σ2/σ2
s. From the distributional assumptions on uit and vit, the log
likelihood function can be written as
lnL =  
nT
2
log2π   nT lnσs  
1
2σ2
s
n ∑
i=1
T ∑
t=1
(ϵit   zitδ)
+
n ∑
i=1
T ∑
t=1
lnΦ
(
(λϵit + (1   λ)zitδ)/
√
λ(1   λ)σ2
s
)
 
n ∑
i=1
T ∑
t=1
lnΦ
(
zitδ/
√
λσ2
s
)
(6)
where Φ() is a distribution function of a standard normal variable.
3 Data
We use annual ﬁrm-level data from the Development Bank of Japan’s Corporate Finance
Databank. The data consist of ﬁnancial statements for publicly traded ﬁrms listed on
either the ﬁrst or second sections of the Tokyo, Osaka or Nagoya stock exchanges. We
2construct a panel dataset of the Japanese manufacturing ﬁrms in eleven industries cov-
ering the period 1980-2004. Industries at the two-digit level are as follows: Chemicals,
Petroleum and Coral, Rubber, Stone Clay and Glass, Iron and Steel, Nonferrous Met-
als, Fabricated Metals, Nonelectrical Machinery, Electrical Machinery, Transportation
Equipment, and Precision Instruments. The resulting sample contains 623 ﬁrms.
We calculate output as ﬁrm sales (total value of shipments) plus changes in inven-
tories of ﬁnished goods and work in process. mit is material expense for intermediate
goods, which includes inputs from contracted work. lit is total employment, and kit is
real capital stock. Real capital stock is calculated separately for buildings, structures,
machinery, equipment, and vehicles using the perpetual inventory method and then ag-
gregated. We calculate investment as the change in book value of capital stock plus
depreciation expense reported by the ﬁrm. The output, material inputs, and investment
are at constant prices. To reduce the impact of potential accounting manipulations of
book values of capital stock, we use the earliest available book value of capital as the
initial value in the DBJ dataset. This starting date occurs before 1971. Depreciation
rates for each type of capital stock are taken from Hayashi and Inoue (1991).
In accordance with the literature, we deﬁne investment spikes only for machinery.
Machinery capital accounts for the largest share of total investment and is often assumed
to embody technological progress. Power (1998) deﬁnes a lumpy investment episode at
the plant level as occurring if the gross investment rate exceeds 0.2. This threshold
is intended to eliminate routine maintenance expenditures. We use ﬁrm level data. A
ﬁrm consists of several plants. Each plant produces diﬀerent products in the ﬁrm’s
range. Investment timing varies across plants. In order to detect an unusual amount
of investment at the ﬁrm aggregation level, we use a large deviation from the normal
investment.
To identify lumpy investment episodes at the ﬁrm level, we construct a standardized
measure of the investment-to-capital ratio. Following Caballero, Engel and Haltiwanger
(1995), we subtract from the original observations the corresponding ﬁrm-level mean and
divide this diﬀerence by the corresponding ﬁrm-level standard deviation. We classify an
observation as a spike if the standardized investment-to-capital ratio exceeds 1.5. In
experiments not shown in this paper, essentially the same results were obtained using
1.75 and 2.0 thresholds.
Machinery age is measured as follows. Under the declining balance depreciating rule,
the book value of machinery and its acquisition value satisﬁes
bt = (1   dt)
n qt
where bt is the book value of capital, qt is the acquisition book value, and dt is the
accounting constant depreciation rate in year t. In this equation, n is assumed to be the
machinery age. The accounting depreciation rate is deﬁned by dt = gt/(bt + gt), where
gt is depreciation expense. Taking the log of both sides of the equation above yields the
3Table I: Estimation results
Coeﬀcient Standard Coeﬀcient Standard
error error
Machinery age: δage;j Time trend: δtrd;j
Chemicals -.104 *** (.012) .025 *** (.005)
Petroleum and Coral -.040 (.055) .075 ** (.038)
Rubber -.241 *** (.049) .013 (.035)
Stone Cray and Glass -.031 * (.016) -.013 (.010)
Iron and Steel -.331 *** (.037) .004 (.025)
Nonﬀerous Metals -.002 (.012) -.072 *** (.012)
Fabricated Metals -.064 *** (.019) -.034 *** (.012)
Nonelectrical Machinery -.144 *** (.012) .019 *** (.005)
Electrical Machinery -.111 *** (.009) .069 *** (.004)
Transportation Equipment -.403 *** (.032) .056 *** (.014)
Precision Instruments -.537 *** (.070) .106 *** (.032)
Investment spike: δspk;
Spiket -.318 *** (.063)
Spiket 1 -.393 *** (.065)
Spiket 2 -.369 *** (.067)
Spiket 3 -.326 *** (.063)
Spiket 4 -.310 *** (.064)
Variance parameters:
σs .645 *** (.013)
λ .979 *** (.001)
Number of observations 12646
Log likelihood 169.28
Signiﬁcance: *** at 1%, ** at 5%, and * at 10% level, respectively.
machinery age measure
ageit =
lnqit   lnbit
ln(bit + git)   lnbit
4 Empirical Results
Our results are presented in Table I. We use machinery age, investment spikes and a
time trend as determinants of technical eﬃciency. The estimated coeﬃcients of the tech-
nical eﬃciency model are highly signiﬁcant. Coeﬃcients on machinery age are negative
across all industries, indicating that older machines are less eﬃcient than younger ones
(coeﬃcients are signiﬁcant in all industries except two). The positive coeﬃcients on the
time trend suggest that production eﬃciency of manufacturing ﬁrms tends to increase
throughout the sample period. This may imply the existence of technology spillover
eﬀects. The exception to this observation is the metals industries, which seem to have
an opposite tendency regarding the time trend.
4The negative estimates for all investment spike dummies indicate that large invest-
ment episodes reduce TFP levels but have persistence eﬀects even after the timing of the
spike. This tendency implies that the adjustment cost of large investment is substantial
and that it is not a one-time loss. Drops in production are likely to be persistent after
the large investment episodes.
Vintage capital models assume that technical progress is embodied in new capital.
Firms invest to reap beneﬁts of technical progress embodied in new capital. As in the
models of Nelson (1964), Hulten (1992) and Wolﬀ (1996), productivity of a ﬁrm should
be associated with its vintage or age distribution of capital stock. Under embodied
technical change, investment spikes should raise productivity.
Several empirical ﬁndings indicate a negative relationship between capital age and
productivity. Previous studies, such as Baily, Hulten and Campbell (1992) and Bahk
and Gort (1993), have found a negative correlation between capital age and productivity
at the plant level. Hulten (1992) using U.S. manufacturing sector data and Wolﬀ (1996)
using six OECD countries data document that the average age of capital stock negatively
aﬀects output growth. On the other hand, productivity may not improve immediately
after the adoption of new capital. Jensen, McGuckin and Stiroh (2001) ﬁnds that new
entrant plants display productivity levels below the industry averages. Sakellaris (2001)
and Huggett and Ospina (2004) also show that productivity growth falls after investment
spikes. The negative relationship between investment spikes and productivity predicts
that ﬁrms face sunk costs. However, vintage capital models can not explain the persistent
reduction in TFP shown in Table 1.
From a diﬀerent perspective, models of learning by doing also link technology and
productivity. In Jovanovic and Nyarko (1996) and Klenow (1998), productivity increases
as ﬁrms learn about the given technology. Once the productivity gains on the given
technology are exhausted, ﬁrms can switch to a better technology. But a switch of
technologies temporarily reduces expertise because technical knowledge is highly speciﬁc
to particular production processes. The model of Klenow (1998) clearly states that
productivity initially falls when ﬁrms adopt new technologies, but gradually rises as the
ﬁrms acquire experience with the new technologies. Jensen, McGuckin and Stiroh (2001)
empirically show that surviving plants improve their relative standing in the productivity
distribution as they age. Power (1998) ﬁnds that productivity tends to monotonically
increase with plant age. The positive correlation between technical eﬃciency and the
time trend and the reduction in technical eﬃciency accompanying investment spikes in
table 1 are both consistent with predictions of learning models as well as the empirical
ﬁndings described above.
5 Conclusion
This paper has considered technical eﬃciency induced by large investment episodes. We
estimate the technical eﬃciency eﬀects in a stochastic frontier production function. With
5ﬁrm-level data from the Japanese manufacturing sector, we ﬁnd a persistent relationship
between investment spikes and production eﬃciency drops thereafter. After controlling
for a time trend, aging capital stock has a negative impact on production eﬃciency,
although the magnitudes diﬀer by industry.
These ﬁndings are summarized as follows. First, reductions of machinery age at ﬁrms
signiﬁcantly increase their productivity. The empirical results of this paper provide sup-
port for the hypothesis that machinery age is a signiﬁcant source of technical eﬃciency.
The replacement of old with new machines exhibits a strong relationship with technical
eﬃciency. Second, drops in production after large investments and productivity growth
over time are both consistent with ﬁrm/plant dynamics models by Jovanovic and Nyarko
(1996) and Klenow (1998).
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7

A stochastic frontier production function incorporating a model for technical ineﬃciency eﬀects” Working

Aggregate production functions and medium-range growth projections”

Decomposing learning by doing in new plants”

Does productivity fall after the adoption of new technology?”

Growth accounting when technical change is embodied in capital”

Learning by doing and the choice of technology”

Learning curves and the cyclical behavior of manufacturing industries”

Plant level adjustment and aggregate investment dynamics”

The impact of vintage and survival on productivity: evidence from cohorts of U.S. manufacturing plants”

The missing link: technology, investment and productivity”

The productivity slowdown: the culprit at last?

The relation between ﬁrm growth and Q with multiple capital goods: theory and evidence from panel data on Japanese ﬁrms”

Lumpy capital adjustment and technical efficiency

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Lumpy capital adjustment and technical efficiency

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