WPS7857
Policy Research Working Paper 7857
Capital Adjustment and the Optimal Fuel Choice
Marie Hyland
Jevgenijs Steinbuks
Development Research Group
Environment and Energy Team
October 2016
Policy Research Working Paper 7857
Abstract
This paper analyzes the important, yet often ignored, link different fuel-using technologies. For all the technolo-
between capital adjustment and the choice of fuels used gies, significant costs to capital adjustment are found. The
by manufacturing firms. A novel econometric framework, costs are much larger compared with earlier estimates
which explicitly incorporates heterogeneous fuel-using of adjustment costs based on lagged values of output
capital stocks in the estimation of optimal fuel choice, is and fuel prices. The findings imply that the path to full
applied to a large panel of Irish manufacturing firms. The adjustment of capital stocks in response to changing fuel
econometric estimates show a significant variation in the prices may be much longer than was previously thought.
optimal response of capital to changing fuel prices across
This paper is a product of the Environment and Energy Team, Development Research Group. It is part of a larger effort by
the World Bank to provide open access to its research and make a contribution to development policy discussions around
the world. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The authors may be
contacted at jsteinbuks@worldbank.org.
The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development
issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the
names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those
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Produced by the Research Support Team
Capital Adjustment and the Optimal Fuel Choice∗
Marie Hyland† Jevgenijs Steinbuks‡
Keywords: capital adjustment, fuel choice
JEL: D22, D24, Q41
∗ This work makes use of data from the Central Statistics Oﬃce (CSO). The possibility for controlled access to
the conﬁdential micro-dataset on the premises of the CSO is provided for in the Statistics Act 1993. The use of
CSO data in this work does not imply the endorsement of the CSO in relation to the interpretation or analysis of
the data. This work uses a research dataset which may not exactly reproduce statistical aggregates published by
the CSO. We thank Gerard Doolan of the CSO for support with the data and clearance. A signiﬁcant amount of
data preparation work was previously carried out by Stefanie Haller and we are very grateful to have been able
to use these previously prepared data. We also thank Nolan Ritter, Mike Toman, and the participants of EMEE
2016 workshop for helpful suggestions and comments. Hyland gratefully acknowledges ﬁnancial support from the
ESRI Energy Policy Research Centre. The views expressed in this paper are those of the authors and do not
represent the views of the World Bank, its board of directors or the countries they represent.
† Economic and Social Research Institute and Trinity College Dublin, Ireland. Email: hylandm1@tcd.ie
‡ Development Research Group, The World Bank, United States. Email: jsteinbuks@worldbank.org
1 Introduction
This research aims to bring new insights into the issue of interfuel substitution by revisiting
the important and largely overlooked relationship between the dynamics of capital stocks and
the optimal fuel choice. The ability of ﬁrms to switch between fuel sources has important
implications for economic growth, particularly in the context of economic adjustment to oil price
shocks and climate policies (as highlighted by Hall (1986) Acemoglu et al. (2012), Stern (2012)
and Papageorgiou et al. (2016), among others), and there is a large body of economic literature
that looks at the issue of fuel substitution. However, few of these studies explicitly model the
choice of fuels and corresponding fuel-using capital stocks. Earlier empirical studies of interfuel
substitution, such as Fuss (1977) and Pindyck (1979), employed a two-stage approach that, in the
ﬁrst stage, estimates the degree of substitutability between diﬀerent fuels and, in the second stage,
estimates the relationship between the energy aggregate and other factors of production. More
recent studies (for example, Jones (1995); Bjørner and Jensen (2002); Urga and Walters (2003);
Serletis and Shahmoradi (2008); Serletis et al. (2010)) have followed the same approach and
mainly focused on methodological innovations of the ﬁrst stage, introducing dynamic functional
forms for estimating demand for diﬀerent fuels. The validity of such approaches hinges on the
assumption that energy and other factors are weakly separable in the production process. This
assumption rules out the possibility that ﬁrms determine jointly their fuel mix and capital stock,
nor does it allow for the possibility that there may be capital adjustment costs associated with
a change in the energy inputs used.1
A similar approach has been used to address inter-fuel substitution in large scale energy
and environmental computational models, in particular, computable general equilibrium (CGE)
models and integrated assessment models. For example, in the energy-environment extension of a
well known GTAP CGE model, the GTAP-E model (Burniaux and Truong, 2002), the production
function is modeled using a technology tree, based on a nested CES production function. This
structure assumes that primary and intermediate factors of production are weakly separable. In
the ﬁrst nest of the production function, the energy aggregate is calculated based on substitution
between diﬀerent fuel types. In the second nest, this energy aggregate is combined with capital
inputs to form a capital-energy composite. In the following nest, capital and energy are combined
with labor and material inputs to produce output. This approach has been largely adopted in
a variety of other climate-economy integrated assessment models (see, e.g., Paltsev et al., 2005;
ateau, 2008).
Burniaux and Chˆ
We argue that this approach, adopted in both econometric and economic modeling studies
of energy and environment, has several important limitations. The ﬁrst limitation relates to
the choice of the nesting structure used by these models. The assumption that the choice of
fuels used in the aggregate energy mix is separable from decisions related to the optimal choice
1 A recent study by Papageorgiou et al. (2016) is the only known attempt to simultaneously model capital
and energy choices, however their analysis is static and limited to choice between “clean” and “dirty” energy
aggregates.
2
of capital ignores the short-run complementarity between energy and capital inputs for a given
production technology. In reality, capital stocks tend to be highly idiosyncratic, and very few
types of energy-using technologies can utilize multiple fuels (Steinbuks, 2012).2 That is, the
relationship between capital technologies and corresponding fuels is ﬁxed, at least in the short
term. This implies that ﬁrms do not pick a particular fuel, but rather a particular technology
bundle that combines capital with a speciﬁc type of energy input.
The second potential limitation of the approach is that the capital adjustment process is
not properly accounted for. The economic and econometric models of interfuel substitution are
either static, where capital adjustment is ignored, or recursive dynamic, where capital adjustment
costs are implicitly estimated using lagged values of output or prices as a proxy for capital. This
implicit estimation largely ignores asymmetries in capital adjustment due to irreversibilities of
capital, and is prone to measurement error as non-capital inputs to production tend to adjust
faster. Failing to account for the capital adjustment process and its associated costs contradicts
the economic literature that ﬁnds these costs non-trivial; see, for example, Caballero (1999),
Caballero and Engel (1999), and Caballero and Engel (2003). Furthermore, the more speciﬁc
role of adjustment costs in the transition to low-carbon and energy-eﬃcient technologies has been
highlighted by Jacoby and Wing (1999), Wing (2008), and Steinbuks and Neuhoﬀ (2014).
Our paper proposes a novel approach to analyze interfuel substitution that explicitly incor-
porates heterogeneous energy-using capital stocks in the estimation of optimal fuel choice. We
model the capital and energy use decisions jointly, implying that ﬁrms choose capital and energy
inputs concurrently. The fundamental choice that ﬁrms make is among diﬀerent competing fuel-
using technologies; this contrasts with the two-step approach in which ﬁrms ﬁrst choose which
fuels to use and then choose the other factor inputs.
Our analysis draws on two previous studies; one that is concerned with energy and capital
utilization (Atkeson and Kehoe, 1999), and another that deals with the adjustment dynamics of
heterogeneous capital goods (Goolsbee and Gross, 2000). Following Atkeson and Kehoe (1999),
we assume that energy inputs and capital stocks are complements in the short run as, for a given
level of capital stocks, a ﬁxed quantity of energy inputs is needed. In the long run capital and
energy will be substitutable as ﬁrms can respond to rising energy prices by investing in new,
presumably less energy-intensive, capital stocks. We incorporate this “putty-clay” structure of
Atkeson and Kehoe (1999) in the modeling framework of Goolsbee and Gross (2000) to estimate
the form of adjustment costs for heterogeneous capital stocks. Speciﬁcally, we develop a structural
model of the demand for diﬀerent types of fuel-using technologies, which we estimate in two
stages. In our model, the “types” of energy-using capital refer to the speciﬁc fuels used to run
the capital stocks. In the ﬁrst stage, we estimate the frictionless stock of each type of capital
for ﬁrms in our data. The frictionless stock of capital is the optimal amount of each type of
capital that ﬁrms would employ in the absence of any adjustment costs. In the second stage
we estimate non-parametrically the relationship between frictionless and actual capital stocks to
2 One example of such technologies is a combined cycle turbine for electricity generation.
3
reveal information on the nature of the adjustment costs faced by ﬁrms.
Our results suggest that the costs of adjusting capital stocks in response to changing fuel
prices are large for all types of capital. These costs are an order of magnitude higher than
in studies where capital adjustment costs are implicitly estimated. Furthermore, we ﬁnd that
investment in fuel-using capital stocks may be irreversible; this is indicative of prohibitively
large adjustment costs associated with divestment of assets. This implies that the path to full
capital-stock adjustment in response to changing fuel prices may be much longer than previously
thought.
These ﬁndings have important implications for both econometric and economic modeling
studies of interfuel substitution. Failure to incorporate proper heterogeneous fuel-using capital
adjustment dynamics in econometric studies will likely result in the downward biased long run
elasticities of optimal fuel choice. Similarly, considering more appropriate nesting structure of
capital energy interaction and revising the magnitude of fuel-using capital adjustment costs
would yield an improvement in robustness of dynamic forward looking energy-environmental
CGE models.
Our paper proceeds as follows: in section 2 we explain our theoretical model and outline our
estimation strategy. In section 3 we present the data used in our analysis. Section 4 outlines the
results of our model. Finally, in section 5 we brieﬂy draw some concluding remarks.
2 Methods
2.1 Theoretical model
The conceptual framework for estimating fuel choice is based on the putty-clay model of energy
use described by Atkeson and Kehoe (1999), extended to account for heterogeneous fuels. In our
model there is a continuum of energy-using capital technologies (Vt ) which are combined with
energy fuels (Et ) in ﬁxed proportions to yield a given amount of capital services (Zt ). Thus, in
the short run, energy and capital are complements for a given technology choice. In the long
run the technologies will be substitutable as ﬁrms can adjust their capital stocks by investing in
machinery and equipment that utilizes other fuels.
Following Atkeson and Kehoe (1999) we assume that, in the short run, a unit of capital of
fuel using technology V provides capital services in combination with a ﬁxed quantity, 1/V , of
fuel E . Combining K units of capital of technology V with E units of fuel yields capital services
(Z ) as determined by:
Z = min(K/V, E )f (V ) (1)
The intuition behind this is that if E > K/V the fuel in excess of K/V is wasted, but if E < K/V
there is capital stock left idle. In our model, ﬁrms’ ﬁnal output would be produced by combining
capital services (a function of capital stocks and fuel use) with labor and materials, which are
assumed separable from the capital-energy composite: Y = f (Zt |Lt , Mt ), and are therefore
4
ignored in this analysis.
Once we account for the putty-clay nature of fuel demand we can formulate ﬁrms’ production,
capital demand, and capital adjustment choices. These choices are based on the heterogeneous
capital goods adjustment model of Goolsbee and Gross (2000), who estimate capital adjustment
costs for the US airline industry using a two-step semi-structural approach. In the ﬁrst step the
f
authors derive the frictionless stock of capital, Ki , i.e., the stock of each type of capital, i, that
a ﬁrm would have in the absence of adjustment costs. The diﬀerence between a ﬁrm’s current
f
capital stock and its frictionless capital stock (Ki /Ki ) captures the ﬁrm’s desired investment. In
the second step Goolsbee and Gross (2000) estimate a ﬁrm’s investment response as a function of
its desired investment to reveal information about the form of adjustment costs facing the ﬁrm.
Following Goolsbee and Gross (2000), we assume that in period t a ﬁrm j maximizes its proﬁt
function, Πj,t , given by:
Πj,t = maxΓ (z1,j,t , ..., zn,j,t ; Gj,t ) − pK E
i,t (rt + δ )Ki,j,t − pi,t Ei,j,t , (2)
zi,j,t
where Γ (·) is the ﬁrm’s production function; zi,j,t are the services from the capital technology
utilizing fuel i as deﬁned by equation (1); Gj,t is the composite of all unobservable ﬁxed factors
aﬀecting the ﬁrm’s proﬁtability; pK
i,t is sales price of capital technology utilizing fuel i ; rt is the
interest rate, δ is the capital depreciation rate, and pE
i,t is the input price of fuel i. We assume
that the production function takes the form:
n ρ
Γ (z1,j,t , ..., zn,j,t ; Gj,t ) = α
zi,j,t α
Gβ
j,t (3)
i=1
Applying the putty-clay model of Atkeson and Kehoe (1999), capital and energy are used in
ﬁxed proportions in the short run as determined by technological constraints, thus, Ki,j,t /Vi,j,t =
Ei,j,t . We assume that the eﬃciency of capital stock varies by sector and over time. The eﬃciency
of sector-level capital is calculated, for each type of capital, by dividing the total stock of capital-
type i in each sector by aggregate sectoral output. We assume that the ﬁrm-year variation in the
eﬃciency of capital stock is small enough to be ignored. This implies that Vi,j,t ∼
=V ˜i,j ·V
˜i,j,t = V ˜i,t ,
˜i,j ) + ln(V
˜i,j,t ) = ln(V
so that ln(V ˜i,t , is the time-varying sector-level eﬃciency of fuel-
˜i,t ), where V
using technology i, and Vi,j are the ﬁrm-level technology ﬁxed eﬀects. Under these assumptions
the ﬁrst-order condition for optimal capital using fuel i (in log-linearized form) can be re-written
as:
f 1 pE
i,t
ln(Ki,j,t ) = ln Vi,t + ln Vi,j + ln pK
i,t (rt + δ ) + . (4)
α−1 Vi,j,t
The frictionless stock of capital using fuel i is a function of the price of fuel i, the cost
of capital, and the eﬃciency of capital stock. As noted by Goolsbee and Gross (2000), the
1
estimated coeﬃcient on the cost variable corresponds to −σ = α−1 , i.e., the negative elasticity
of substitution between fuel-using technologies.
5
2.2 Empirical speciﬁcation
2.2.1 Predicting the frictionless stock of capital
For the econometric estimation of equation (4) we include a number of additional control variables
to account for unobservable eﬀects correlated with the choice of energy-using capital. These are
real sectoral output growth rates, Yt , which we include to control for the eﬀect of demand on
capital stocks. We also include a time trend, Tt , that captures exogenous technological progress.
Additionally we wish to account for capacity utilization in our model; ﬁrms may not have the
capital stocks running at full capacity at all times as there may be times at which it is not optimal
for them to do so. Thus, ﬁrms do not maximize proﬁt only with respect to capital stocks, but
rather with respect to capital stocks adjusted for capacity utilization (Ui,j,t ). Therefore, the
proﬁt function becomes:
Πj,t = maxΓ (z1,j,t , ..., zn,j,t ; Gj,t ) − pK E
i,t (rt + δ )Ki,j,t − pi,t Ei,j,t ∗ Ui,j,t , (5)
zi,j,t
And, including the additional control variables, the empirical speciﬁcation we estimate be-
comes:
f 1 pE
i,t ∗ Ui,j,t
ln(Ki,j,t · Ui,j,t ) = Vi,j + γ ln Vi,t + ln pK
i,t (rt + δ ) + + βYt + τ Tt + i,j,t , (6)
α−1 Vi,j,t
Equation 6 is estimated for each type of capital, i. However, it is likely that ﬁrms make
decisions regarding capital stocks and utilization for each technology while simultaneously taking
account of the other types of capital that they use. Thus, we estimate the frictionless stock of
capital for each fuel-using technology within a seemingly-unrelated regression (SUR) model. This
accounts for the fact that the errors may be correlated across the optimization of each technology.
As the majority of ﬁrms in our data utilize no coal-ﬁred capital, including coal-using capital in the
system leads to a much smaller sample size, thus we estimate two separate systems of equations;
one including coal and one without. The ﬁrms utilizing coal are found only in a small number
of energy-intensive sectors.
In the estimation of equation 6 we account for the presence of ﬁxed eﬀects. These ﬁxed
eﬀects are removed by demeaning the data prior to estimation. Finally, following Goolsbee and
Gross (2000), we constrain the coeﬃcients on the cost term to be the same across all fuel-using
technologies, this allows us to present a single estimate for the price elasticity of energy-using
capital.
2.2.2 Estimating the form of adjustment costs
f
The predicted values from equation (5) give us the frictionless stock of each type of capital Ki ,
i.e., the stock of capital that a ﬁrm would hold in the absence of adjustment costs. As outlined
6
by Goolsbee and Gross (2000), the diﬀerence between the predicted and observed capital stock
represents a ﬁrm’s desired investment. Thus, desired investment can be calculated as:
f
Ki,j,t
= θexp(− i,j,t ) (7)
Ki,j,t
f
Where, Ki,j,t and Ki,j,t denote the frictionless and actual stocks of capital i, held by ﬁrm j
in time t, and i,j,t is the error term from equation (5). If the ratio of K f to K is greater than
one, a ﬁrm would, in the absence of any costs of adjustment, invest in additional capital stocks.
Conversely, for values less than one ﬁrms wish to divest some of their assets. The θ term in
equation 7 is what Goolsbee and Gross (2000) refer to as the “scale factor”. This term captures
the fact that frictionless and desired investment may not be identical. For example, in periods of
signiﬁcant sectoral growth, desired investment may exceed actual investment by a factor greater
that what can be represented by adjustment costs. We follow Goolsbee and Gross (2000) and do
not make any assumptions regarding the size of this parameter, instead we set the scale factor to
be equal to one. This will not aﬀect the form of the adjustment costs we estimate, but in level
terms they may be oﬀ by a constant factor.
We use kernel regressions to estimate the relationship between the ﬁrms’ desired investment
and actual investment levels. This approach provides greater ﬂexibility as it allows the rela-
tionship between these values, and thus the adjustment costs, to vary by investment level. The
estimation takes the form:
f
Ii,j,t+1 Ki,j,t
=f + ηi,j,t (8)
Ki,j,t Ki,j,t
Plots of the kernel regression functions will tell us about the form of adjustment costs facing
ﬁrms. Furthermore, the estimated slopes of these functions provide a measure of the size of the
adjustment costs that ﬁrms face.
Equation (8) is estimated using the Nadarya-Watson estimator (which is based on a poly-
nomial of degree zero) to allow for ﬂexible estimation3 ; Goolsbee and Gross (2000) note that
this estimator places almost no restrictions on the shape of the adjustment cost function. The
bandwidth (b) for the kernel estimates is determined using the same formula as Goolsbee and
Gross (2000); b = 2.347 ∗ σ ∗ n−1/5 , where σ is the standard deviation of the X variable, and n
refers to the number of observations.
The slope of the function in equation (8) represents the magnitude of the adjustment costs.
Caballero and Engel (2003) note that, under the quadratic adjustment cost model, the speed of
adjustment, as indicated by the slope of the investment function, conveys information about the
adjustment costs:
3 We also tried estimating the kernel regressions using a polynomial of degree one, but found that this resulted
in over-smoothing of the investment function.
7
f
δKt = λ(Kt − Kt−1 ) (9)
f
Here Kt and Kt represent the actual and optimal levels of capital at time t, while the λ
parameter represents how much of the gap between these values is bridged in each time period.
Lower values of λ imply slower rates of adjustment and, thus, higher adjustment costs. As
adjustment costs may diﬀer for diﬀerent levels of desired investment, Chow tests are conducted
at diﬀerent points along the investment function to test the continuity of its slope for each type
of capital.
3 Data
3.1 Overview
We use a panel of ﬁrm-level data for manufacturing ﬁrms in the Republic of Ireland. These data
are collected by the Irish Central Statistics Oﬃce (CSO) via the annual Census of Industrial
Production (CIP). Response to the CIP is compulsory for ﬁrms operating in the Irish manufac-
turing sector with three or more persons engaged. The census collects data on various accounting
measures such as sector of operation (at the NACE 4 digit level), location, sales, employment,
intermediate inputs, capital acquisitions and trade. While all ﬁrms of three or more employees
are surveyed, larger ﬁrms are asked to complete a more detailed questionnaire which includes,
among other additional information, information on energy expenditure disaggregated by fuel
type (smaller ﬁrms are asked only for aggregate energy expenditure). As we are interested in
adjustment costs of fuel-using capital by type of fuel, we concentrate our analysis on these larger
ﬁrms and for the period from 2004 to 2009, when these more detailed data were collected on an
annual basis. Our ﬁnal dataset contains approximately 8,600 ﬁrm-year observations.
The census does not ask ﬁrms to report a price for capital, therefore, the price of capital
we use in our model is the market cost of capital as estimated for Irish manufacturing ﬁrms by
ˇ
Znuderl and Kearney (2013). This cost is a function of the investment price and the nominal
interest and depreciation rates. Additionally, fuel prices are not recorded in the census and,
as such, a number of external sources are used. The prices of oil and coal are from the ESRI
Databank (ESRI, 2012), while the prices of electricity and natural gas come from Eurostat’s
price series for industrial users.4 The Eurostat price data vary according to the quantity of fuel
used. In Ireland ﬁrms face decreasing block pricing for electricity and gas, whereby prices are
lower at higher consumption levels. However, as we do not observe the quantity used, ﬁrms
are assigned to consumption-based price bands as follows: for each two-digit NACE sector we
calculate the energy intensity of output in that sector by dividing total sectoral electricity and
gas usage (based on aggregate data) by total sectoral output. This gives us an average, sector-
level measure of energy-intensity of output separately for electricity and natural gas. Then, for
4 http://ec.europa.eu/eurostat/web/energy/data/main-tables
8
each ﬁrm we impute the volume of electricity and natural gas that it consumes by multiplying
its output, as recorded in our data, by the average level of energy-intensity of the sector in which
the ﬁrm operates. Based on this inferred consumption, we assign ﬁrms to Eurostat end-user
price bands for electricity and natural gas. For model estimation, all prices are represented as
indices, based on real 2007 values.
Using information in our data set we can account for the level of utilization of fuel-using
capital stocks (Ui,j,t ). For each ﬁrm in the data we observe its fuel inventories at the beginning
and at the end of each year.5 Based on these data we calculate an average annual fuel utilization
rate. This is given by taking the total fuel consumption in that period - which is the sum of the
value of opening stocks plus fuel purchases minus closing stocks, and dividing this by the total
value of fuel available for consumption - the sum of opening stocks plus purchases.
3.2 Calculation and disaggregation of fuel-using capital stocks
The census asks ﬁrms for information on capital acquisitions by type of capital. Capital acquisi-
tions data are disaggregated as follows: acquisitions of computer equipment; computer software;
plant machinery and equipment; motor vehicles; building and construction work; buildings pur-
chased; land purchased; capitalized R&D, and “other”. In our analysis we focus on the plant
machinery and equipment component of capital, where substitution between diﬀerent types of
fuel-using stocks is technologically feasible. Capital stocks are calculated using the perpetual
inventory method and based on capital acquisitions and disposals, as recorded in the data. The
starting stocks are calculated based on the CSO’s industry-level breakdown for the previous year
and then subsequently disaggregated to the ﬁrm level using each ﬁrm’s share of fuel use in total
industry-level fuel use. A detailed description of how this variable is created, including informa-
tion on depreciation rates and assumed assets lives, is provided by Haller (2014) and Haller and
Hyland (2014).
For our analysis, we are interested in the machinery and equipment component of capital
stocks, disaggregated by type of capital - where type refers to the fuel used. To break down
the machinery and equipment component by fuel used we follow Steinbuks (2012) and use data
oir et al., 2012). We calculate ﬁve components of
from the TIMES model for Ireland (Gallach´
equipment based on the TIMES data, they are: those that can only run on electricity (for
example, electrical motors and refrigeration units); those that run on electricity, but where other
fuels can be used (for example high- and low-temperature heating processes)6 ; those that run on
natural gas; those that run on oil; and those that run on coal.7 Average sectoral-level capital
stocks in 2004 (the ﬁrst year of our data) for each of the ﬁve subcomponents are given in Table
1.
5 This
information is available for the sum of all fuels, but not disaggregated by fuel type.
6 These
are referred to as “Electricity (no substitution possible)” and “Electricity (substitution possible)”
respectively in Table 2.
7 For machinery that runs on natural gas, oil or coal, we assume other fuel options are always available for
these processes.
9
Table 1: Average breakdown of machinery by sector and type in 2004 (000s of e2007)
Electricity Electricity Natural gas Oil Coal
(no sub) (sub possible)
Sector manufacturing :
Food & beverages 1,735 2,041 2,019 3,018 821
Textiles & textile products 445 1,694 212 572 -
Wood & wood products 868 - 51 63 2,568
Pulp, paper & publishing 829 2,271 481 547 -
Chemicals & man-made ﬁber 11,979 5,946 6,985 3,585 -
Rubber & plastic products 1,569 847 282 681 -
Other non-metallic minerals 438 596 304 3,566 1,726
Metal products 154 172 1,631 488 -
Machinery & equip. n.e.c. 1,256 5,723 1,745 2,094 -
Electrical & optical equip. 6,171 4,585 11,626 4,444 -
Transport equipment 953 5,049 706 1,412 -
Table 1 shows the relative importance of machinery and equipment driven by electricity. With
only a few exceptions, capital stocks in all sectors are dominated by electricity-using capital. Not
only is the component of capital where only electricity can be used (e.g., for motors and lighting)
large, but processes where it is possible to use other fuels (e.g., drying and separation process)
are frequently dominated by electricity also. After electricity, capital stocks are mostly based on
natural gas or oil, which of these two fuels is the more prominent varies notably from sector to
sector. For example, for the sector producing electrical and optical equipment, natural-gas-ﬁred
capital stocks are signiﬁcantly more important whereas for the sector producing non-metallic
minerals (generally a much more energy-intensive sector), the majority of the machinery and
equipment used runs on oil.
Another important feature of the capital stocks held by ﬁrms in our data, illustrated in Table
1, is the fact that very few sectors hold any coal-ﬁred machinery and equipment. The sectors in
which there is coal-ﬁred equipment in place are those that are generally characterized by higher
levels of energy intensity.
3.3 Descriptive statistics
Table 2 below presents some basic descriptive statistics for ﬁrms in our data. Over the period
from 2004 to 2009, the average ﬁrm employed 120 people, and had an annual turnover of e74
million. Firms are highly heterogeneous in terms of levels of output and size, as illustrated by
the large standard deviations on these variables. Approximately six percent of the ﬁrms in our
data are multi-unit ﬁrms and approximately 26 percent are foreign-owned. At an average rate of
98 percent, the utilization rate of fuel-using capital is very high; this suggests that capital costs
are a much more important component of total operating costs than fuel costs.
As there is a large divergence in the energy prices in terms of their absolute values, all fuel
price indices are normalized by the price of coal in the base year (i.e., 2004). The evolution of
10
Table 2: Descriptive statistics
Mean Std dev Median Mean value in:
2004 2007 2009
Output (000’s real 2007e) 74,422.96 492,579.00 7,847.76 68,301.32 81,417.79 74,830.32
Number of employees 120.95 250.52 49.00 119.55 125.68 112.14
Multi-unit dummy 0.06 0.25 0 0.06 0.07 0.06
Foreign-owned dummy 0.28 0.45 0 0.28 0.27 0.28
Fuel utilization 0.98 0.10 1.00 0.97 0.98 0.98
Sectoral output index (2004 = 100) 1.01 20.21 100.00 100.00 113.58 80.02
Capital expenditure - by type (000’s real 2007e):
Electricity (substitution possible) 2,811.25 17,476.73 421.13 2,512.86 2,823.94 3,067.49
11
Electricity (no subs. possible) 2,913.82 22,198.33 296.46 2,489.22 2,940.55 3,254.56
Gas 3,291.14 38,223.11 329.13 2,733.12 3,347.32 3,647.28
Oil 2,355.98 15,519.58 353.48 2,000.17 2,375.36 2,625.97
Coal 430.99 2,245.60 0.00 375.51 426.95 478.40
Price indices:
(Fuel prices indices are relative to the price of coal)
Capital (2004 = 100) 101.96 11.27 100.00 100.00 102.34 120.90
Electricity 1,071.13 24.77 1,066.18 1,040.19 1,081.49 1,098.12
Gas 348.61 26.34 351.33 303.13 337.79 351.33
Oil 344.15 17.43 346.84 324.95 346.48 323.51
Coal (2004 = 100) 116.63 12.27 119.83 100.00 119.83 120.55
these prices is illustrated in Figure 1. On average over the period studied, the price of electricity
is very high relative to that of the other fuels (and is thus represented on a separate axis). In
2004 the price of electricity per TOE is approximately ten times higher than coal, and three
times greater than natural gas and oil. In general electricity prices in Ireland are expensive
relative to other European countries. This is largely due to high dependency on imported fossil
fuels. Ireland also has high transmission and distribution costs due to the dispersed nature of
the population.
Figure 1: Price indices
450 1120
400
1100
350
300 1080
Price index
250
1060
200
150 1040
100
1020
50
0 1000
2004 2005 2006 2007 2008 2009
Gas Oil Coal Capital costs Electricity
For the majority of fuels, prices are trending upwards until 2008, at which point there is a
relative decline. For ﬁrms in our data, the average oil price declines after 2006 - this is driven
by decreases in the price of the heavy fuel oil component of the oil price (the price of the light
fuel oil component continued to trend upwards until 2008). The price of electricity increases
signiﬁcantly from 2005 to 2008 - this is driven largely by increasing natural gas prices, as the
vast majority of electricity generated in Ireland comes from natural-gas-ﬁred power plants. In
recent years, the need to invest in the network to bring renewable generation sources (generally
located far from load centers) on stream has further added to electricity costs.
From 2004 to 2005 there was a small decline in the cost of capital for Irish manufacturing
ﬁrms, which was largely reversed by 2006. This variable then followed a modest upward trend
to 2009 driven by changes in the interest rate and a modest increase in the depreciation rate for
the machinery-and-equipment component of capital.
12
4 Results
4.1 System estimation results
As noted in Section 2, the ﬁrst step of the analysis involves estimating the frictionless stock of
capital for each fuel type. The results of the system estimations are presented in Table 3 below.
Our main estimates are based on a system that does not include coal-using capital stocks; as only
a small proportion of ﬁrms in our data utilize coal-ﬁred capital (approximately one-quarter), the
inclusion of coal in the system leads to a much reduced sample size and inference based on a
small number of unrepresentative ﬁrms.8 However, as a robustness check we also estimate the
system including coal; the results are presented in Table 4 below.
Table 3: Equation (5) - System estimation results
Electricity Natural gas Oil
1
Cost ( 1− α) -0.2359 -0.2359 -0.2359
(0.0166)*** (0.0166)*** (0.0166)***
Eﬃciency(γ ) 0.1337 0.0689 0.0075
(0.0079)*** (0.0043)*** (0.0025)***
Sectoral growth (β ) 0.0011 0.0005 0.0006
(0.0002)*** (0.0002)*** (0.0001)***
Time trend (τ ) 0.0031 0.0238 0.0259
(0.0018)* (0.0017)*** (0.0016)***
N = 8,084. Standard errors in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1.
The results show that there is a negative relationship between the stock and cost of capital, as
would be expected. As noted previously, the estimated coeﬃcient on the cost term corresponds
to the elasticity of substitution across fuel-using capital stocks with respect to their capital costs.
With a estimated coeﬃcient of -0.24, Table 3 illustrates that the demand for fuel-using capital
is highly inelastic with respect to changes in its running costs.
Turning to the other parameters included in the estimation, there are some notable diﬀerences
across fuels in terms of the magnitude of the coeﬃcients, but in all cases, the signs on the
coeﬃcients are the same across fuels and in line with our priors. For all capital types, the
eﬃciency variable, calculated at the sector level, is positive and signiﬁcant. It is to be expected
that capital is more highly valued if it is more eﬃcient. Increases in eﬃciency have the largest
eﬀect on the demand for electricity-driven capital. The sectoral growth term is also positive
and signiﬁcant for all types of capital - indicating higher demand for capital as output increases.
This variable will also reﬂect ﬁrm entry and exit, and thus captures sector composition eﬀects.9
Finally, we note that the time trend variable is always positive and signiﬁcant indicating that
the demand for each type of capital is growing over time.
8 As noted previously, ﬁrms utilizing coal are found only in a small number of energy-intensive sectors.
9 For discussions of the relationship between sectoral activity level, sectoral composition and energy use refer
to, for example, Ang et al. (2015); Su and Ang (2012); Ang and Choi (1997).
13
It should be noted that our both the dependent variable and the independent capital costs
variable in our data may be subject to measurement error.10 Measurement error in the dependent
variable may result in ineﬃcient estimates. However, we are not overly concerned about this as,
even with the possibility of measurement error in the capital stocks, the coeﬃcients on the
explanatory variables remain statistically signiﬁcant. Measurement error in the cost variable
may be a greater cause for concern as measurement error in an independent variable can give
rise to attenuation bias.11 Speciﬁcally, measurement error may bias the estimated coeﬃcients
towards zero; thus the price elasticity estimates of the demand for capital presented in Table 3
may present lower-bound estimates of the true value.
The SUR estimation results for those ﬁrms that, in addition to using electricity, natural gas
and oil, also utilize coal-ﬁred capital equipment are presented in Table 4. The sample size is
much reduced in this system estimation, and only three NACE 2-digit sectors (notably, the three
most energy-intensive of Irish manufacturing) are represented. The results conﬁrm our priors
that these ﬁrms are notably diﬀerent from the full sample. What is particularly striking from the
results is that these ﬁrms show a much lower elasticity of demand for capital stocks in response to
changing running costs. Also notable is that, for these ﬁrms, increased eﬃciency of natural gas,
oil and coal-ﬁred capital leads to a decrease in the demand for these stocks; possibly indicating
that as the stocks become more eﬃcient ﬁrms demand less of them as the same levels of output
can be produced with lower stock levels. For all types of capital however there is a positive
relationship between stocks and the sectoral growth and time trend variables, the coeﬃcients on
these variables are also very similar across the four types of capital.
Table 4: Equation (5) - System estimation results including coal
Electricity Natural gas Oil Coal
1
Cost ( 1− α) -0.0126 -0.0126 -0.0126 -0.0126
(0.0050)** (0.0050)** (0.0050)** (0.0050)**
Eﬃciency(γ ) 0.0234 -0.0057 -0.0060 -0.0019
(0.0031)*** (0.0018)*** (0.0027)** (0.0006)***
Sectoral growth (β ) 0.0012 0.0012 0.0011 0.0012
(0.0004)*** (0.0004)*** (0.0004)*** (0.0004)***
Time trend (τ ) 0.0206 0.0259 0.0237 0.0254
(0.0031)*** (0.0030)*** (0.0030)*** (0.0029)***
N = 2,210. Standard errors in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1.
An indication of the magnitude of the adjustment costs for ﬁrms in our data is given by
looking at the diﬀerences between ﬁrms’ actual stock of capital and the stock predicted by our
model (which represents each ﬁrm’s frictionless stock of capital). Useful metrics for comparing
actual values with model estimates are the symmetric mean and median absolute percentage
error (sMAPE and sMdAPE), which we calculate based on the results presented in Table 3. The
10 A discussion of measurement error in panel data models is provided by Griliches and Hausman (1986).
11 Research discussing measurement error and its eﬀects include Griliches (1974) and Griliches (1986).
14
sMAPE is a commonly-used measure of forecast accuracy, and is based on percentage diﬀerence
between the predicted and actual values, taken on average across values of i. The formula for
calculating the sMAPE is:
1 |Fi − Ai |
sM AP E = (10)
n |Ai | + |Fi |
While sMAPE takes the mean across i, sMdAPE uses the median value.
Table 5: Magnitude of adjustment costs
Electricity Natural gas Oil
sMAPE 23% 23% 22%
sMdAPE 19% 19% 19%
Table 5 shows that the average diﬀerence between actual and frictionless stocks of capital for
ﬁrms in our data ranges from 22 percent for coal-ﬁred capital to 23 percent for capital that runs
on electricity and natural gas. The range of median values is approximately 19 percent for all
types of capital. These preliminary comparisons of the actual versus predicted capital stocks are
indicative that, for many ﬁrms in the data, their current stocks of capital are signiﬁcantly diﬀerent
from their frictionless levels, which suggests that capital adjustment costs may be substantial.
4.2 Kernel estimation results
We next turn to the results from our non-parametric, kernel estimation. As outlined in Section 2,
∗
Kit
for each type of capital, i, we generate a variable Kit that represents the gap between frictionless
and current capital stocks at time t, based on the estimates presented in Table 3. Using non-
parametric regression we estimate the function presented in equation (8); the results are displayed
in Figure 2 for electricity, natural gas and oil-ﬁred capital.
Before proceeding to the estimated investment functions, it is important to note the four
possible shapes of the desired investment function outlined by Goolsbee and Gross (2000).12
In the absence of any adjustment costs, the investment function will cross the X axis when
the ratio of the frictionless to the actual capital stock is exactly equal to one, and the slope
of this function will be equal to one. This implies that any gap between actual and desired
investment will be closed immediately. If the adjustment costs are quadratic, the relationship
between actual and desired investment will be linear, but the slope will be less than one, implying
that a constant part of the gap between actual and desired investment will be closed in each
period. If there are large adjustment costs associated with disinvestment, or if investment is
irreversible, this will be indicated by a ﬂat region in the investment function when actual capital
stock exceeds the frictionless level. Finally, Goolsbee and Gross (2000) note that non-convexities
in adjustment costs will manifest themselves as convexities in the investment response function
12 For further details refer to Andrew B. Abel (1994); Dixit and Pindyck (1994).
15
Figure 2: Investment in fuel-using capital
when desired capital is greater than actual capital, indicating that large deviations in the levels
of desired investment lead to proportionately larger changes in actual investment, relative to
small deviations in investment levels.
Figure 2 shows the investment response of fuel-using capital stocks when the current stocks
f
of capital (Kt ) are not equal to their frictionless levels (Kt ). Looking ﬁrst at electricity-using
capital stocks, the adjustment path of electricity-using capital appears to be divided into two
components. In the region of the graph where the frictionless stock of capital is less than the
f
Kt
actual capital, i.e., Kt < 1, ﬁrms would like to divest their capital assets. However, this region
of the investment response function is relatively ﬂat. This suggests irreversibility of investment,
meaning that for increasing costs of electricity-using capital stock ﬁrms will not be able to divest
their assets or that to do so would be prohibitively costly.
f
For values of Kt /Kt greater than one, the slope of the investment response function is
positive, although clearly less than one - indicating that ﬁrms will invest when their capital
stocks are below the desired level, but investment will have associated adjustment costs and thus
the frictionless level of capital stocks will not be reached within a single time period. A Chow test
was carried out to test the equality of the slope of the investment response function before and
16
after the point of inﬂection (0.75), and the null hypothesis of equal slopes was strongly rejected
(Prob>F = 0.000). The average slope of the investment function to the right of the inﬂection
point is 0.034. According to the partial adjustment model, this parameter indicates how much
of the gap between frictionless and actual stocks is reduced within each period, where a value of
one would imply instantaneous adjustment. A value of 0.034 implies a slow adjustment process,
and shows that capital adjustment costs are large.
The estimated kernel function for natural-gas-using capital stocks is somewhat less smooth
than was the case for electricity, but the graph does illustrate a similar path of adjustment. Once
f
Kt
again the investment response function is relatively ﬂat for values of Kt less than one, this region
of inaction again indicating irreversibility of investment. When the frictionless level of capital
is greater than the current level, the investment response is positive but slow, as suggested by
the extremely ﬂat slope of this portion of the response function. In this region of the estimated
polynomial, the slope of the investment response function is only 0.014, indicating a very long
path to full adjustment. Again a Chow test for equality of slopes on either side of the point of
inﬂection strongly rejects the hypothesis that the slopes are equal: Prob>F = 0.000.
Turning next to the path of adjustment for oil-using capital stocks, once again the investment
response function is characterized by a region of inaction where a ﬁrm cannot divest its stocks
despite the fact that it holds more oil-using capital than it desires. Beyond the point of inﬂection
ﬁrms do adjust stocks, but the slope of less than one indicates the presence of adjustment costs.
The slope of the function beyond the inﬂection point is 0.037, again indicating a slow path to
full adjustment.
4.3 Investment response to changing energy prices
We illustrate the eﬀect of the adjustment costs on the investment response for the diﬀerent types
of capital by simulating a 10 percent change (increase or decrease) in the price of each of the fuel
types. Due to the irreversibility of capital investments - as illustrated by the regions of inaction
in Figures 2 above, ﬁrms will not be able to reduce their stock of capital in response to increasing
fuel prices (or rather it would be excessively costly for them to do so). Thus price increases of
10 percent have no eﬀect on capital divestment; ﬁrms must wait for the capital in excess of the
desired amount to depreciate away.
On the other hand, when the price of a particular fuel falls, ﬁrms will respond in order to bring
their current level of capital closer to the new frictionless level. However, due to the presence
of adjustment costs, full adjustment of stocks to the new frictionless level will take a signiﬁcant
amount of time - this is illustrated in Table 6 below.
17
Table 6: Investment response to a 10% fuel price decrease
∗
K1 K2 Years to adjust
Electricity e618,441 e622.1,76 28
Natural gas e393,910 e393,927 72
Oil e393,206 e393,406 26
In period one, the average ﬁrms holds e618,441 worth of electricity-using capital stock. A 10
percent decrease in the price of electricity will mean that a ﬁrm will want to hold approximately
e622,000 worth. Full adjustment to this new level of capital stock will, according to the results of
equation (9), take 28 years. The path to full adjustment is similar for oil-ﬁred capital equipment
while, for natural-gas-using capital the full adjustment process is notably longer. In all cases the
speed of adjustment is slow, indicating signiﬁcant adjustment costs.
Our estimated adjustment costs are an order of magnitude higher than those estimated by
other papers in the literature. For example, Jones (1995), based on results from a dynamic linear
logit model, estimates an adjustment costs parameter of 0.72 - implying that almost 30% of the
adjustment takes place within a single year. This is a much shorter adjustment path than our
estimates suggest, and is similar to other studies that follow a similar approach to estimating
adjustment. For example, Urga and Walters (2003) estimate a partial adjustment parameter
of 0.73, implying that 27% of adjustment to a price change takes place within one year of that
change occurring. A similar annual adjustment parameter is estimated by Cho et al. (2004);
their estimates (λ = 0.79) implies that 21% of adjustment takes place within one year of a
annlund and Lundgren
price change. Looking at adjustment separately according to ﬁrm size, Br¨
(2004) ﬁnd that for the smallest ﬁrms (ﬁrms in the lowest quartile of the fuel-use distribution)
90% of the long run response to a price change occurs within one year; for larger ﬁrms the ﬁgure
is 63%. More recently, Steinbuks (2012) ﬁnds that the adjustment rate diﬀers depending on
the purpose for which the fuels are used; for aggregate energy consumption 74% of the response
occurs within the ﬁrst year, while for thermal heating process adjustment is somewhat slower
with 53% of adjustment occurring within one year.
All these estimates are based on implicit estimation of adjustment costs. They show that the
most common method used in the literature to date, i.e., the inclusion of lagged values of output
or prices, is understating the true costs of full adjustment of capital stocks. These results suggest
that using observed values of capital, as we do in our model, can more accurately capture the
path to the full adjustment, and thus the associated adjustment costs. To illustrate this point
we re-estimate the adjustment costs for aggregate capital stocks by including lagged values of
the dependent variables (i.e., using the standard approach in the literature). This results in an
estimated lambda parameter of 0.877 which implies that approximately 12% of the adjustment
process takes place within the ﬁrst year, compared to an average of 3% based on our results
using observed capital stocks.
18
5 Conclusions
This paper analyzes the important, yet often ignored, link between capital adjustment costs
and the choice of fuels used by manufacturing ﬁrms. We formulate a structural model that
accounts for the short run complementarity between fuel inputs and corresponding fuel-using
capital stocks. Based on this model, we estimate, for each type of fuel-using capital, its frictionless
stock that would be observed in a steady state. The observed deviations between actual and
frictionless capital stocks reveal the level of adjustment costs faced by ﬁrms in our data.
Our econometric estimates show a signiﬁcant variation in the optimal response of capital to
changing fuel prices across diﬀerent fuel-using technologies. For all these technologies, we ﬁnd a
signiﬁcant gap between the frictionless and observed capital stocks, which indicates signiﬁcant
costs to capital adjustment. Furthermore, the shape of the investment response function shows a
region of inaction when capital is above its frictionless level; this suggests there are prohibitively
large costs to capital divestment. Our estimates of capital adjustment costs are an order of mag-
nitude larger compared to earlier studies that rely on implicit estimation based on lagged values
of output and fuel prices. Based on these ﬁndings we conclude that our approach may capture
more realistic dynamics of fuel substitution which are currently missing from both econometric
analysis of fuel substitution and from the energy-environment component of CGE models.
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Appendix
Results using lagged values
To test the robustness of our estimation results and to check for any potential simultaneity
problems in our estimates, we re-run the systems model using lagged value of prices and eﬃciency.
The results are presented in Table 7 below. While the coeﬃcients on some of the variables (most
notably the cost term) diﬀer in terms of their order of magnitude from the main results presented
in Table 3 above, the sign and the signiﬁcance of the results do not change.
Table 7: System estimation using lagged exogenous variables
Electricity Natural gas Oil
1
Cost ( 1− α) -0.1316 -0.1316 -0.1316
(0.0160)*** (0.0160)*** (0.0160)***
Eﬃciency(γ ) 0.0594 0.0341 0.0011
(0.0081)*** (0.0045)*** (0.0027)
Sectoral growth (β ) 0.0007 0.0006 0.0006
(0.0002)*** (0.0002)*** (0.0002)***
Time trend (τ ) 0.0007 0.0118 0.0114
(0.0020) (0.0019)*** (0.0017)***
N = 6,383. Standard errors in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1.
More importantly however, Table 8 shows that recalculating the SMAPE and SMdAPE based
on these estimates results in almost identical values to those presented in Table 5. Furthermore,
re-estimating the kernel regressions does not alter our conclusions regarding the importance of
capital adjustment costs.
Table 8: Magnitude of adjustment costs - results based on lagged exogenous variables
Electricity Natural gas Oil
sMAPE 23% 23% 22%
sMdAPE 18% 19% 19%
The kernel functions based on estimates using lags as instruments are displayed in Figure 3.
22
Figure 3: Investment in fuel-using capital - using lags as instruments
System including coal - estimated polynomials
The kernel regression functions for those ﬁrms that utilize coal in addition to electricity, gas and
oil are displayed below. Figure 4 shows a similar adjustment path for capital as the polynomials
displayed previously for the larger sample of ﬁrms using only three fuels. Again we ﬁnd that there
are signiﬁcant costs to divesting assets - illustrated by the ﬂat “region of inaction”. Furthermore,
the slope, much smaller than one, indicates the presence of signiﬁcant adjustment costs to capital
investment. In this case the conﬁdence bands for larger values of K f /K are much wider, due to
the greatly reduced sample size.
23
Figure 4: Investment in fuel-using capital, ﬁrms that utilise coal
24