Economic Integration and the Markups of European Electricity Firms

Economic Integration and the Markups
of European Electricity Firms
Ziga Zarnic
Katholieke Universiteit Leuven and LICOS
March 22, 2009
(The …rst version May 16, 2008)
Abstract
This paper uses EU …rm-level panel data to estimate the impact of energy reforms on the
markups of European electricity …rms. Empirical results reveal that reforms have gradually
reduced the markups, which is consistent with the internal market principle that competition
would develop as a result of the economic integration. But the existing markup premium of
incumbent …rms is on average larger than theoretical models would predict under e¤ective
economic integration. Considering the heterogeneity along the …rms’ allocation of assets
and scale economies, we …nd that better market access and cross-border arbitrage discipline
the markups, but do not lead to competitive market outcomes due to prevailing market
concentration and insu¢ cient unbundling of transmission and distribution channels.
JEL no. F10, L11, L51, L94
Keywords: Energy market reforms; competition; …rm data; price-cost margins; regulation
Remark: I am thankful to Werner Roeger for his suggestions and discussion of the methodology used in
this paper and Hylke Vandenbussche for her constructive comments. I also thank Jo Van Biesebroeck, Joep
Konings, Jo Swinnen, Aida Caldera and Ilke Van Beveren for valuable discussions and comments given at di¤erent
stages of the paper. A special thanks goes to the sta¤ of CORE Department of Mahematical Engineering for
providing insights into the functioning of European electricity sector. This paper has bene…ted from the ETSG
conference in Warsaw and seminars at LICOS - KU Leuven, UC Louvain and Center for Operations Research
and Econometrics. The …nancial support by LICOS, Katholieke Universiteit Leuven is gratefully acknowledged.
Please address correspondence to Ziga Zarnic, LICOS - KU Leuven, Deberiotstraat 34, 3000 Leuven, Belgium;
E-mail: ziga.zarnic@econ.kuleuven.be

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1
Introduction
The competitiveness of the electricity sector is high on the EU agenda aimed at providing com-
petitive, but reliable and safe supply of electricity (EC 2008). The restructuring of European
electricity sector is meant to integrate the national electricity systems into a single European
electricity market to mitigate the market power of incumbent …rms (e.g. Smeers 1997, 2005).
The electricity sector is the key non-manufacturing utility sector and its competitiveness largely
determines the competitiveness of other services and manufacturing sectors, because the exis-
tence of market power in this sector is easily leveraged into downstream sectors, as motivated
by Arnold et al. (2006, 2008). Providing systematic evidence on the responsiveness of electric-
ity …rms’markups towards regulatory changes has thus important implications for an accurate
assessment of the e¤ectiveness of reforms.
This paper estimates the impact of European energy reforms on the price-cost margins of
electricity …rms. In line with the internal market principle we expect that competition would
develop as a result of the economic integration, which would be re‡ected by lower markups.
The underlying economic mechanism is guided by the previous theoretical literature in sup-
port of our econometric analysis (in particular, La¤ont and Tirole 1993, Wolak 1994, Borenstein
et al. 2002). In the neoclassical pro…t-maximization models …rms charge high prices to obtain
high markups, but economic integration facilitates pro-competitive e¤ects re‡ected by lower
markups. Also the agency asymmetric pricing models suggest that deregulation gives incentives
for markup adjustments to the level of competitive rivals. In a simple theoretical model following
Bushnell et al. (2008), we demonstrate that restructuring towards greater integration leads to
more competitive outcomes. In particular, a decline in the average markup is linked to increased
competition from restructured electricity systems that facilitates trading activity to arbitrage
between di¤erent markets.
The econometric model builds upon the Roeger (1995) approach, which main advantage
is that it does not su¤er from endogeneity issues when estimating …rm-speci…c markups. We
construct carefully the measures of regulatory changes to consider complementarity and sequenc-
ing of reforms, as suggested by Dewatripont and Roland (1992, 1995). Our empirical analysis
con…rms the theoretical predictions above as we …nd that reforms have gradually reduced the
markups.
A further decomposition of the markup change shows that better market access and cross-
border arbitrage lead to lower markups, while greater market concentration and bundling of
transmission and distribution channels have the opposite e¤ect. Overall, the existing markup
premium is on average found to be larger than theoretical models would predict under e¤ective
economic integration. These results are consistent with the studies by Wolfram (1999), Jamasb
and Pollitt (2005) and Roeller et al. (2007), which argue that imperfectly competitive outcomes
are largely due to insu¢ cient unbundling, rigid …nancial contracts and limited cross-border
arbitrage of electricity constrained by poor investments into the interconnection grid. Our
results are robust to alternative speci…cations and controlled for the …rm-speci…c attributes
inherent to the electricity sector.
The characteristics of the electricity sector makes it a rather speci…c utility sector because
of its attributes that allow …rms to exercise market power even at relatively low levels of market
1

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concentration (Smeers 2005). As emphasized in the previous work (in particular, Joskow 1997,
Joskow 2003, Jamasb and Politt 2005, Wolak 2006 and Roeller et al. 2007), the market for
electricity is typically regionally fragmented with rather inelastic demand elasticity as electricity
consumption relies on a potentially congested transmission network. Companies with very small
market shares can sometimes exert substantial market power in periods of high demand when
generation capacity is tight and their output is required to satisfy demand (Borenstein et al.
2002, Smeers 2005, Bushnell et al. 2008). The electricity has been considered as a rather
homogeneous product for which high …xed costs deter the entry of potential competitors. Joskow
(1997) argues that production of electricity used to rely intensively on public or private monopoly
suppliers, whose strategic behavior has been regulated by governments. On the one hand, the
cost-ine¢ cient storage of electricity, the limited interconnection capacities and availability of
technology have favored large and vertically integrated generation facilities owned by a small
number of …rms. On the other hand, the institutional barriers have hampered competitive gains
that could emerge from unbundled products among which consumers could switch easily.1 The
lack of competition has allowed …rms to price discriminate among consumers and charge high
markups by owing the supply chain from generation to distribution of electricity.
Having said that, we also provide insights into …rm heterogeneity. Our results are in line with
the above literature. In particular, we …nd that specialized …rms active only in the electricity
sector exhibit about 4 percentage points higher markups than the multi-product …rms active
also in other manufacturing and services sectors. The majority of …rms are small and medium
enterprises, which are more responsive to reforms than large …rms. In particular, the …rms with
multiple subsidiaries and vertically integrated …rms exhibit much higher markups than the rest.
Finally, private and foreign-owned …rms appear to have lower markups in concentrated markets
where barriers of entry are high.
The previous literature presented above motivates largely the choice of our econometric model
and the variables used in the analysis. Section 2 describes in more detail European electricity
…rms and regulation of the electricity systems. Section 3 presents a theoretical framework that
guides the empirical analysis. Section 4 develops the empirical strategy to estimate the price-cost
margins of …rms and their casual relationship with the regulatory changes. Section 5 presents
the main results and discusses the robustness checks. Section 6 concludes.
2
European Electricity Firms and Market Regulation
In this section, we provide a selective overview of the European electricity markets and focus on
those elements that motivate our econometric model. We begin with a discussion of the existing
regulation and identify the measures of institutional reforms. We next discuss the regulatory
and economic factors in‡uencing the concentration and markups of …rms. Finally, we provide
descriptive statistics of the …rm-level dataset, documenting discussion points and introducing
our econometric analysis.
1 The environemnt has been evolving and development of new technologies does not exclusively favor large
generation utilities in order to gain from economies of scale and scope. Moreover, electricity is becoming increas-
ingly di¤erentiated product in terms of ecological compliances, reliability and safety of supply (EC 2007, Roeller
et al. 2007).
2

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2.1
The Electricity Market and Institutional Reforms
Electricity markets are subject to extensive regulation in European countries. A certain degree
of regulation is required to secure reliable and safe supply of electricity, but currently there is
no single European market for electricity and regulation varies across countries. In the mid-
nineties, the European Commission initiated stepwise directives to enhance the dynamic and
competitive performance of a single European market. The institutional reforms have built upon
the national legislations and invoked several aspects of market design and regulation evolving
particularly around the market power and concentration, cross-border trade and reliability of
supply (EC 2001, EC 2007a, EC 2007b). In Figures 1 to 3, we show duration of the EC Electricity
Directives and systematically overview the main building steps of national legislations. These
…gures consider the implementation dates of key regulatory measures, in particular, they refer
to operative national legislation, wholesale and retail markets.2
[Insert Figures 1 to 3]
The horizontal bars in Figure 1 refer to duration of national legislations and the vertical
lines depict the initiation dates of the EC Electricity Directives. In most EU15 countries, a
de facto operating authority has begun to operate soon after the establishment of national
legal basis, which refers to de jure implementation of the national Electricity Act. In particular,
Figure 1 shows that the centralized approach to market liberalization through the EC Electricity
Directives has maintained the pace of reforms in the EU15 countries. In particular, the EC e¤orts
to move towards a single electricity market have regarded sector restructuring, where the focus
has increasingly been on the access to transmission and distribution networks, and competition
in wholesale markets and retail supply (Jamasb and Politt 2005). Figures 2 and 3 provide
cross-country information on functioning of the wholesale and retail markets. The horizontal
bars in Figure 2 depict operation of the organized market exchange in each country from the
establishment year. Similarly Figure 3 presents the timing of retail market opening referring to
the period during which consumers were able to switch between di¤erent suppliers of electricity.
Figures above show that institutional reforms vary across EU15 countries, which motivates our
econometric analysis to exploit the variation in staging and vintage of institutional changes and
capture their e¤ect on price-cost margins of …rms.
There is large regional fragmentation with several electricity systems in the EU, which are
the UK-Ireland, Scandinavian Nord Pool, Baltic, East European, West and Southeast European,
Spanish, and Italian zonal markets (Roeller et al. 2007). Figures 4 to 7 depict the evolution of
di¤erent market indicators of regulatory changes across these markets.
[Insert Figures 4 to 7]
The plotted lines in Figures 4 to 6 represent the mean value of each indicator with the
vertical bar denoting the variance across these markets. These markets vary largely in strictness
of entry barriers, vertical integration and state ownership. This evidence is in line with Roeller
et al. (2007) and ERGEG (2007 and 2008), which also document large variation in degrees
2 Data Appendix describes in more detail the data used for construction of measures of institutional changes.
3

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of internal competition and note that the Nordic market is the most advanced in terms of
e¤ective international integration, while the Iberian and Italian markets are particularly lagging
behind. Moreover, they emphasize the importance of west European market (including France,
Germany, Switzerland, Netherlands and Belgium), which is the largest regional market and its
position implies that further progress toward an integrated electricity market in the EU will be
dependent on the development of this market. Figures 4-6 show that the entry barriers, share
of vertical integration and state ownership are gradually declining over time and moreover, the
variance across countries is declining as well. Figure 7 shows that the market share of the largest
electricity …rm is declining at lower pace over time and remains considerably large in most of the
countries. This evidence motivates our econometric analysis, where we expect that price-cost
margins will be positively a¤ected by market concentration, but could have gradually declined
over time due to increased competition fostered by weaker regulatory constraints.
2.2
Preliminary Evidence on European Electricity Firms
The …rm-level data are derived from a commercial database Amadeus (2008), collected by the
consultancy Bureau van Dijk. The database consists of company accounts reported to national
statistical o¢ ces for European companies. The advantage of using the company-accounts data
is that prices generally determined by state regulators are based on accounting costs of services
at the …rm level (Fabrizio et al. 2007).3 In Table 1 we present the summary statistics of the
variables retrieved from the company accounts. Data Appendix describes the de…nitions and
measurement issues of the variables we use.
[Insert Table 1]
The sample contains virtually the entire population of medium and large units of …rms in
the electricity sectors of ten European countries over the period 1995-2007. In particular, the
…rm-level data on average account for about 95% of the total employment as compared to the
aggregated data retrieved from Eurostat (2008). The descriptive statistics in Table 1 are divided
in three sub-samples with the last two columns referring to the period before and after the second
EC Electricity Directive. The full sample includes the unbalanced data on about 700 …rms with
rather high capital intensity and market power of 0.42, as measured by the Lerner index bounded
between 0 and 1 with lower values representing higher degrees of competition.
Two key observations emerge from the comparison of two sub-samples reported in the last
two columns of Table 1. First, the …rms have on average exhibited lower price-cost margins of 4
percentage points during the second EC Electricity Directive as compared to the period before
2003. Second, we note that the …rms have on average employed much less capital per employee
at slightly lower levels of employment and similar levels of factor costs during the period of the
second EC Electricity Directive. Moreover, they exhibited higher returns on total assets after
3 We use long-term annual data, which is motivated by the availability of comparable data across countries
and by the recent literature. Smeers (2005) points out that the relevant marginal cost is the long run marginal
cost that is equal to the short run marginal cost when the generation system is optimally dimensioned. However,
considering long-run marginal costs has the advantage that it smoothens the trajectory of short-run variations in
capacities where prices are not su¢ cient to justify new investments (Smeers 2005).
4

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2003, which could imply that restructuring have lead to more e¢ cient use of capital at slightly
lower levels of employment.
The preliminary evidence above motivates further our analysis by implying downward pres-
sure of European liberalization e¤orts on the price-cost margins of electricity …rms. Moreover,
the e¤ect may have been heterogeneous across …rms that could have been on the one hand less
‡exible in adjustments of their sta¤ due to labor market rigidities, but could on the other hand
adjust easier a fraction of their capital to current demand shocks. In what follows, we will look
more formally for the causality between the decline in the EU price-cost margins and restructur-
ing. The choice of variables in the econometric section is motivated by this preliminary evidence.
We will explicitly consider national and …rm-speci…c measures of regulatory changes and try to
account adequately for electricity …rms’attributes such as size, capital intensity, ownership and
vertical integration of their activities. The ultimate objective of the next sections is to inves-
tigate whether the gradual implementation of reforms disciplined the market power of …rms in
European electricity sector.
3
Theoretical Framework
The recent theoretical literature assessing the market power of electricity …rms typically refers to
structural equilibrium models, which are discussed in more detail by Smeers (2005). In principle,
an equilibrium unit commitment model decomposes a period of time into smaller segments at
which the output and market price are assumed to be …xed (Smeers 2005).4 Consumers h 2
f1;:::;Hg have inverted demand function pt(dht) at each period of time and …rms i 2 f1;:::;Ng
maximize their pro…ts by choosing the operation level of each running unit to satisfy the demand
of consumers at minimal cost Cit(qit) = Kit + citqit, which may include both start-up capacity
costs (Kit) and operational variable costs (citqit). In the equilibrium model, demand and supply
N
H
instantaneously meet at every period of time t, so that
The unit commitment model has been among
Pqit=
others used b P dht.
i=1
h=1
y Joskow and Kahn (2002) and
Borenstein et al. (2002), in which marginal costs of electricity generation are simulated for
di¤erent periods of time and compared to the observed prices in these periods. Bushnell et
al. (2008) additionally apply a counterfactual approach to compare the perfectly competitive
outcomes with the outcomes of Cournot type of competition. In this model, …rms exercise market
power, if the simulated price under Cournot competition exceeds the perfectly competitive price.5
We follow directly Bushnell et al. (2008) to provide economic intuition about the link between
integration and the markups of …rms. The model demonstrates that economic integration in
terms of greater integration of wholesale and retail markets imposes downward pressure on
the markups of incumbent …rms that are simultaneously exposed to external competition, for
example, from the electricity supplied through the cross-border imports or by smaller units
operating only at certain periods of time (see Borenstein et al. 2002). The model by Bushnell
4 The backbone of the equilibrium unit commitment models is the optimal dispatch model, which has been
developed by the electrical engineers to solve short-run optimizations of the generation systems to satisfy an
exogenously given demand, as discussed in more detail by Smeers (2005).
5 This framework has been further extended to include other attributes of the electricity sector, such as
electricity transmission and price discrimination between di¤erent types of consumers as discussed by Smeers
(2005).
5

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et al. (2008) is an elegant version of the equilibrium unit commitment model, which considers
Cournot competition at the wholesale and retail levels. Firms thus maximize pro…ts by using
production quantities as the strategic decision variable. The total production of …rm i at time
t is represented by qit and the retail sales are denoted by qr . Following Bushnell et al. (2008),
it
each strategic …rm i at independent period of time t maximizes its pro…ts:
it(qit; qr
it) = pt(qit; q(N
1)t)[qit
qrit] + prt(qrit; qr
)qr
(N
1)t
it
citqit
Kit
(1)
where q(N i)t and qr
are the quantity produced and retail quantity supplied by the other
(N
i)t
(N
i) …rms in Eq. (1) and pt and prt are the wholesale and retail market prices, respectively. In
general, the equilibrium positions of …rms consider both wholesale and retail demand elasticities
as well as production capacity (Kit) and marginal costs (cit). However, in the unit commitment
model both retail quantity and prices are …xed at each unit or segment of time t. Under these
assumptions, Bushnell et al. (2008) develop the Cournot equilibrium as the set of quantities
that simultaneously satisfy the …rst order conditions for each …rm i at time t as:
@ it
@p
= [p
t
t(qit; q
(2)
@q
(N
i)t)
cit(qit)
rit(qit)]
[qrit
qit]
it
@qit
Equation (2) shows that the retail position of …rm i matters for the level of its markup.
As the retail supply increases towards the quantity produced, the marginal revenue approaches
the wholesale price. This implies that the Cournot model with greater economic integration of
wholesale and retail markets leads to the markups, which are closer to a competitive outcome,
where the market price equals marginal revenues of the …rm (see Bushnell et al. 2008). The
di¢ culty of these models arises from identi…cation of the marginal cost curve in the market.
Within a certain period, di¤erent units of …rms may operate at di¤erent segments of marginal
cost curve, depending on the overall utilization of capacity in the market.6 In general, the
marginal costs of …rm i can be de…ned as:
pt(qit; q(N i)t)
cit(qit)
rit(qit)
0
(3)
where the pure markup premium (pt
cit) should exclude the rent of capacity utilization
rit(qit) to assure the investment incentives of …rms in terms of scarcity rents of capacity Kit, as
pointed out by Smeers (2005).7 The wholesale market price is determined from the …rms’residual
demand function (Qit), which equals the market demand (Qm
t ) net of supply from imports
M
P
F
qjt(pt) and the fraction
at the peak levels of deman P qft(pt) of small units f 2 f1; :::; F g that supply electricity only
j=1
f =1
d. Bushnell et al. (2008) model the additional supply as a function
6 For example, the hydro-plants may operate exclusively at the peak-loads in certain periods of time, when
demand for electricity exceeds the capacity of other sources of electricity, while the nuclear plant must operate
permanently due to technical requirements. The short-term demand is rather inelastic and companies with very
small market shares can sometimes exert substantial market power in periods of high demand when generation
capacity is tight and their output is required to satisfy demand (Borenstein et al. 2002, Smeers 2005).
7 Smeers (2005) discusses di¤erent extensions of equilibrium models to account for the investment decision
function of …rms to invest in their capacities. Firms invest in new capacities, if they can sell their output forward
over the long run. In principle, this model under certain assumptions comes close to Bushnell et al. (2008) in
predicting that a forward commitment towards the greater amount produced leads to more competitive outcomes
as the marginal revenue approaches the wholesale price.
6

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of price, thereby providing price responsiveness to Qit as:
M
F
Qit(pt) = Qm
t
Pqjt(pt) Pqft(pt)
(4)
j=1
f =1
The simple model above demonstrates that restructuring towards greater integration leads
to more competitive outcomes. Moreover, a decline in the average markup is linked to increased
competition from restructured electricity systems, which facilitates trading activity to arbitrage
between di¤erent markets.
In what follows, we look for a testable econometric model to estimate the response of electric-
ity …rms’ markups to reforms aimed at integrated European electricity market. The marginal
costs are very di¢ cult to measure directly in the data as pointed out in the previous literature.
Smeers (2005) notes that the relevant cost is the long-run marginal cost, which is equal to the
short-run marginal cost only when the electricity system is optimally dimensioned and prices
are su¢ cient to justify new investments. By contrast, comparing prices with short-run variable
costs may lead to upward biased estimates of markups, re‡ecting the short-run excessive market
power in situations of tight capacities. Borenstein et al. (2008) use unique US data, which allows
them to explicitly model marginal cost curve for a certain fraction of electricity units, but for the
rest of them they …nd it impractical due to data limitations. We take into account the concerns
of both views in the literature and in the following sub-sections formulate testable econometric
model that allows us to directly estimate the average long-term markup for a representative
sample of European electricity …rms.
4
Empirical Methodology
4.1
The Baseline Model with Variable Returns to Scale
We use the Roeger (1995) approach adjusted to variable returns to scale to specify our baseline
econometric model. The main intuition of this method is that the markup term is embodied
in the measurement of the total factor productivity (TFP) growth, which is the output growth
not accounted for by the growth in inputs. Roeger (1995) exploits the earlier empirical …ndings
(e.g. Abbot et al. 1989) that productivity measure can be estimated either as the residual in
the production function or as the residual of the dual cost function. In fact, Roeger (1995)
argues that the dual Solow residual capturing output and production factor prices nests the
same productivity term that will cancel out, if the dual Solow residual is deducted from the
primal Solow residual.8 We hereby outline the baseline model, while the necessary derivation
steps are explained in Appendix.
Consider a log-linear homogeneous production function Qit = G(Kit; Lit; Mit)Eit for output
Qit, where Kit, Lit, and Mit are capital, labor and material inputs (Iit) and Eit is a shift
variable representing changes in productivity e¢ ciency of a …rm i at time t. That is, total factor
productivity (TFP) is a residual between actual and potential output and this consideration is
standard in literature (e.g. Hall 1988, Harrison 1994, Olley and Pakes 1996, Fabrizio et al. 07).
8 Such approach for deriving of the markups under imperfect competition has been further followed by, among
others, Martins et al. (1996), Konings and Vandenbussche (2005), and Vandenbussche and Zarnic (2008).
7

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Roger (1995) circumvents the potential problem coming from the correlation of inputs with the
output by subtracting the price-based from the output-based Solow residual. Decomposition
of the markup and the technology component from the output-based Solow residual SRit and
price-based Solow residual SRPit is a crucial step in the Roeger method and are expressed as:
SRit = it( qit
kit) + ( it
it)eit
(5)
SRPit = it( FKit
pit) + ( it
it)eit
(6)
where the right-hand side is decomposed in the markup and the pure technology component,
where Lerner index for a …rm i at time t is denoted by
it = Pit cit , scale economies are
Pit
denoted by it and small letters refer to the logarithms.9 Similar to Fabrizio et al. (2007), we
hereby implicitly assume that production factors are to a certain degree substitutable only in
the long-run, but …xed in the medium-run.10
The output-based and price-based residuals are respectively the di¤erences between the
growth rates of output
qit and weigthed inputs
Iit
Iit, and alternatively the di¤erences
between the growth rates of output prices
pit and weigthed input prices
Iit
FIit. More
formally, the Solow residuals can be expressed as:
SRit =
qit
P Iit Iit
(7)
I
SRPit = P Iit FIit pit
(8)
I
where the share of inputs (Iit) in total revenues (PitQit) are denoted by Iit = FIitIit with
PitQit
the letters F and P representing input and output prices. To obtain a price-cost margin term
it = Pit cit , which can be directly estimated, one has to subtract the price-based residual SRP
c
it
it
from the output-based residual SRit as:
(4qit + 4pit) P Iit FIit = it[(4qit+4pit) (4kit+4FKit)]
(9)
I
The price-cost margin term ( it) in (9) can be estimated consistently, because the error term
capturing unobserved productivity shocks has canceled out. The baseline econometric model is
thus simply speci…ed as:
yit = ai + 1 xit + "it
(10)
where the left-hand side variable (4Yit) represents the di¤erence between the Solow residuals
and the right-hand side explanatory variable (4Xit) represents the growth rate of output per
value of capital with the white noise error term "it for …rm i at time t.
9 Roeger (1995) shows that the change in the marginal cost (4cit) is a weighted average of the changes in
input prices (FIit) with respect to their relative cost shares in the …rm’s cost function (
), accounting for the
Iit
change in technology (eit), i.e. 4cit = Iit4FIit 4eit.
1 0 This assumption is relaxed in the next sub-section, in which we consider that …rms can adjust a fraction of
their capital to current demand shocks.
8

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4.2
Firms’Allocation of Capital Assets
We now consider that due to restructuring the …rms can adjust a fraction of their capital assets to
current demand shocks by following the approach by Roeger and Warzynski (2004). While …rms
may be less ‡exible in adjustments of labor force, e.g. due to European labor market rigidities,
they can adjust a fraction of capital to current demand shocks. In other words, this extension
allows us to come closer to the estimate of pure markup premium, which is controlled for the
part of scarcity rent of capacity utilization rit in (2) providing incentives for future investments.
Consider a log-linear homogeneous production function Qs = min(
)
Kf
it
LitLit;
KitK v
it
it
with the variable capital input Kv = s
it
itKit where sit measures the degree of variable capital
within the capital stock Kit. Similar to Roeger (1995) with the share of inputs in revenues,
consider now the share of inputs in total costs. The output and price-based Solow residuals are
de…ned as:
SRsit = 4qit ( sKit 4 kit + sLit 4 lit + sMit 4 mit) + 4eit
(11)
SRP s
it =
s
Kit 4 FKit + sLit 4 FLit + sMit 4 FMit
4pit 4eit
(12)
where the shares of input costs in total costs, Cit = FIitIit, are denoted by s
= FKitKit ,
Kit
FIitIit
s
= FLitLit and
s
= FMitMit with the letter F
Lit
F
it denoting input prices and Iit total inputs.
IitIit
M it
FIitIit
The variable capital is not directly observed in the data, so Roeger and Warzynski (2004) suggest
to express its growth rate in terms of revealed productivity growth,
xit, and observable capital
input,
kit. The growth rate of variable capital input is then de…ned as:
kvit = "sx xit + kit
(13)
Consider the output-based and price-based Solow residuals in (11) and (12), which are ad-
justed for the share of inputs in the total costs, and subtract them to obtain the following
expression:
(4q
s
s
it + 4pit)
s
Iit
Iit = (1
sit) sKit[(4qit +4pit) (4kit +4FKit)]+sit Kit"sx 4xit (14)
where
s
s
= s
(
(
(
Iit
Iit
Kit 4kit + 4FKit) + sLit 4lit + 4FLit) + sMit 4mit + 4FMit). The left-
hand side variable represents the subtraction of Solow residuals the right-hand side represents
the growth rate in revenues per capital weighted by the share of capital in total costs considering
productivity of a …rm i at time t. The testable model of the price-cost margins ( it) corrected
for the variable capital is estimated with a system of seemingly unrelated equations, referring
to (10) and (14):
( yit=ai+ 1 xit+"it
(15)
ys = a
+ "
it
i +
1
xsit
it
where the share of variable capital 1 is estimated as a nonlinear logistic function, described
in more detail in Appendix. In this model, the price-cost margin is explicitly controlled for the
variable part of capital of …rm i at time t.
9

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Document Outline

• zzpe 120.pdf
• ZZPE TF 04dec08.pdf

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