Are multi-plant firms more or less profitable?
Evidence from Swedish electricity firms
+Aili Tang and Zuzana Macuchova*
+Örebro University, SE-701 82 Örebro, Sweden.
*Dalarna University, SE- 791 88 Falun, Sweden.
Abstract:
Using Swedish firm-level panel data, this paper shows that, depending on reaching ‘steady
state’ with only random fluctuations around a fixed firm size, multi-plant firms on average have
a 1% point lower return on total capital than their single-plant counterparts. One potential
reason for this could be some degree of loss of control occurs aggregately across hierarchical
levels within multi-plant firms because of reproduction distortion. If, in addition, objectives
differ among managers across hierarchical levels because of the agent problem, the loss in
control can be more extensive. Given the scenarios above, multi-plant firms which have reached
a ‘steady state’ should be more likely to have lower profit than single-plant firms.
Keywords: Firm performance; return on assets; steady state; random coefficient model;
electricity sector.
JEL codes: D22; L11; L25; L26
0
1.
Introduction
The multi-plant structure is one of the most typical organizational forms of firms. The objective
of such a firm structure is to link together the production plans of several plants which are part
of a vertically integrated firm and achieve near optimal results on performance measures, like
total cost, manufacturing lead time etc., for the entire organization (Bhatnagar et al, 1993).
On the one hand, cost efficiency in multi-plant firms arise since those firms need only make a
single investment, in R&D, for example, while two or more independent firms must each make
the investment; multi-plant firms can also shift resources within the firm in response to adverse
shocks (Bernard, 2007). On the other hand, there seems to be an optimal size for multi-plant
firms, only below that level firm size is important (Markusen, 1995). This means to achieve a
consistently high performance, a large vertically integrated firm that has a complex hierarchy
of production plants with production decisions at these plants must take effective coordination
into consideration, because of the uncertainties and capacity constraints in production process
at each plant.
The existing theoretical and empirical literatures are largely silent on the issue of firm
performance regarding the peculiarities of multi-plant firms, whether horizontal or vertical
integrated (Coad, 2008), although industries characterized by scale economies and imperfect
competition are often dominated by multi-plant firms1. Given the prevalence of both singleand multi-plant firms in the Swedish electricity industry and the market condition of the
industry where imperfect competition still leaves relatively large margin of profit, the present
paper seeks to investigate firm profitability relating to a multi-plant firm structure in Swedish
electricity sector. We ask whether the existence of other plants within the electricity firm affects
the probability; are multi-plant electricity firms more or less likely to achieve higher profit than
single-plant electricity firms?
1
The multi-plant structure of firms has traditionally been associated with the desire of firms to reduce volatility of
their operations. An early empirical study by Scherer and colleagues reports that “some (of the respondents) viewed
the hedge multiple plants afford against ... disasters as one of the most important benefits of multi-plant operation”
(Scherer et al., 1975, p. 278). Relatedly, Wahlroos (1981) presents a theoretical model where firms choose the
number of plants they operate as a trade-off between scale economies and relative stability.
1
To this end, we use data on 2,185 firms active within the Swedish electricity sector during the
period 1997-2011. This unbalanced data set consists of 18,137 firm-year observations,
including 1,564 multi-plant firms and 621 single-plant firms.
The empirical strategy of this paper starts with identification of firms with a multi-plant
structure in the dataset, i.e., firms with a headquarter and at least one additional production
plant, both having local managers. In such firms, there is at least two management levels and
two managers with some discretion regarding plant level costs and thus the profits of the firm
as a whole. Under the assumptions made above, multi-plant firms that have reached capacity
constraints are more likely suffer from some degree of loss of control aggregately, and thus may
have lower profits once compared to single-plant firms with less complex hierarchical
management structure, all else equal.
The second empirical strategy lies on the identification of firms that have reached a ‘steady
state’ firm size in terms of capacity constraints. Since the multi-plant structure is a complex
multi-stage production system, controlling for the ‘steady state’ firm size is important when the
operations of multi-plant firms are considered under tight capacity constraints. This
identification is done by using a method developed by Tang (2014), which enables to identify
which firms are in their ‘steady state’ and which are not. We interpret the ‘steady state’ as the
equilibrium where firm size oscillates randomly around a fixed size.
Lastly, the identification strategy is also dependent on us being able to control for all important
confounders. Thus, we also control for the potential confounders used in previous studies of
firm performance and profits. These include firm-specific factors, such as size of the firm,
salaries, and growth of firm in previous period. Another two groups of factors we control for
are characteristics of the industry in which firms operates and regional characteristics.
The empirical results show that multi-plant firms will, in ‘steady state’ equilibrium, have on
average 1% lower return on assets compared to single-plant firms, after controlling for size
adjustment costs and other confounders. We suggest an important role that is linked to firm
structure, i.e., the overall composition of the firm’s activities matters for firm profit; the lower
profit for multi-plant electricity firms in ‘steady-state’ may due to the aggregated loss of control,
coming from the reproduction distortion and the risk of non-profit maximizing behaviour by at
least one manager in the firm increases with the number of managers.
2
The paper begins with a discussion of loss of control of a multi-plant firm with a more
complexed hierarchical structure and utility maximizations as the objective of firms and
hypothesis to be tested, in section 2. In Section 3, the data and descriptive statistics is presented
and the estimation methods used in this paper is outlined. In Section 4, the empirical results are
presented, while Section 5 concludes the paper.
2.
Conceptual framework and the hypothesis to be tested
2.1 Loss of control from reproduction distortion
Since the multi-plant structure is a complex multi-stage hierarchy production system, the
identification of ‘steady state’ is important when the production of firm is considered under
tight capacity constraints. The problem is even more complicated by the interdependence of
different plants within a firm. Two distinct issues need to be addressed. First, all individual
plants within a firm needs to be represented by a system which captures the salient features of
all plants under capacity constraints. As Evans (1984) notes, control loss across two hierarchical
levels (i.e. superior/subordinate) is defined as the extent to which the subordinate fails to carry
out the intentions of the superior. Therefore, the problem of reproduction distortion, i.e., passing
information and implementing objectives through a hierarchy is one potential cause of loss of
control. Second, even though the information passing through a hierarchical structure up and
down are fully absorbed, inconsistency of firm objective could still occur if managers across
hierarchical levels had objectives other than profit maximization. In this scenario, the
aggregated loss of control across all organizational levels, further represents a measure of the
managerial inefficiency of multi-plant firms with more complex hierarchical structures.
The law of diminishing return (Downs (1966), p. 109) is one of the earliest theories that sheds
light on the loss of control in a hierarchy. It states: “The larger any organization becomes, the
weaker is the control over its actions exercised by those at the top.” Since the decision makers
in each hierarchical layers have a limited capacity to absorb and process data, the loss of control
is accumulated at the top of hierarchical layers in a large organization.
Williamson (1967) attributes this loss in control with a model in which the information given
by the managers are distorted by a fixed amount as they pass through each succeeding level in
the hierarchy. It is claimed that only some fraction of a manager’s orders and directions can be
3
successfully implemented by his subordinates. Williamson assumes the output of any
productive worker to be directly governed by the cumulative loss of control through the chain
of supervision. Assuming constant span of control and wage differential, Williamson shows the
loss of control by the managers in large firms with a hierarchical structure limits the size of an
optimal firm.
In resorting to profitability, various arguments built on the notion of loss of control have been
developed. As John Williamson puts it: “There is no more reason to expect profitability to
decline with size than there is evidence to suggest that it does. This raises the question as to
what does limit the size of firm. The answer is that there are important costs entailed in
expanding the size of a firm, and these expansion costs tend to increase with the firm’s growth
rate.” (Williamson, 1966, p. 1)
In line with Williamson (1967), Mueller (1972) focuses on the importance of penetrating
uncertainty to create profit. Given the assumption that firms with more information have more
advantage in cost in doing this, the ability to process information becomes a key determinant
of the direction and size of diversification and expansion. In his paper, Mueller puts an emphasis
on the obstacle of flow occurs in the firms with a hierarchical structure, especially when
dynamic factor is taking into account. The more uncertainty there is, the greater the need for
information. Any deterioration in the information flow to the top decision-makers reduces longrun profitability. This also corresponds to the stochastic equilibrium ‘steady state’ explained in
Williamson (1967) in the sense that firms are required to adapt to circumstances which are
predictable as they occur with stochastic regularity, however, precise advanced knowledge of
them is unavailable.
Calvo and Wellisz (1978) constructed a related model based on the idea that control across
hierarchical levels depends crucially on the nature of the supervision process. If employees are
not aware of the times at which they are not being monitored sufficiently, they will shrink their
responsibilities. Hence, the profitability of a firm depends on the number of productive workers,
the number of layers in a hierarchical structure and the wage for every layers to maximize the
profit.
Similarly, Beckmann (1977) analyses a model in which the productivity of a worker depends
partly on the amount supervision the worker receives. In turn, the productivity of supervisors
4
also depends on the amount of supervision supervisors receive. Beckmann finally concludes
that the average cost of managing increases with the size of hierarchical structure.
Qian (1994) follows the hierarchical design technique developed by Keren and Levhari (1983)
to analyse the model where managers in a hierarchical structure engage both in monitoring and
in productions. He proves the profit of a firm to be a concave increasing function of firm size
and implies a greater loss of control for a bigger hierarchy than the optimal size.
To sum up, what causes the loss of control of a hierarchical structure explained so far is
following: First, the deterioration of information flow seems to occur when it is passed up and
down within a hierarchical structure. Second, not only workers but also managers in each
hierarchical layers may shirk on the job or divert their effort to their own interests when effort
is not observed by their superiors. To mitigate such a problem, the superior spends time in
monitoring the effort exerted by his immediate subordinates. Therefore the managing cost
increases when the hierarchical structure within a firm is more complex. The final output of the
hierarchy is determined by a production function which is cumulative in the efforts of workers
and managers at all levels. The economic trade-offs are rather complex, but the basic idea that
the benefit of having fewer hierarchical tiers is to decrease the reproduction distortion so that
there is a smaller cumulative loss across hierarchical levels and also fewer managers to pay
(Qian, 1994).
2.2 Loss of control in terms of alternative objectives of managers
Except from reproduction distortion that can result in loss of control when firms reach their
capacity constraints, another problem of inconsistent objectives among managers across
hierarchical levels is also worth attention. As Ladd (1969) emphasized, many economists
disagree with the view of profit maximization being the main objective of firms, in particular
in industries characterized with less than perfect competition. In other words, loss of control
could also be triggered in terms of alternative objectives of managers in the firms with a
hierarchical structure.
Agent theory represents one of the fundamental critics to this assumption of profit maximization
as the main objective of firm. The theory hypothesizes that managerial discretion, i.e. the
5
latitude of manager’s action regarding to firm policy, is related negatively to firm performance
in the situations when managers use their discretion to serve their own objectives. Hence,
managerial discretion allows managers to serve their own rather than shareholders’ objectives
and therefore is likely to be associated negatively with firm performance (Jensen and Meckling
1976, Fama 1980, Fama and Jensen 1983a, 1983b, Jensen and Ruback 1983). Furthermore, it
is possible for managers to exploit the fact that shareholders do not observe manager’s daily
behavior. Presumably, such behavior would tend to lead to poor firm performance. This is
essentially the principal–agent problem (Geetik et al., 2009, p. 50), where managers are
maximizing their own utility given a minimum level of profits adequate to keep shareholders
satisfied. If the minimum profit level is not achieved, this sort of behavior would threaten the
managers’ job security (Mahajan, 2008).
Because of the above discussed agent problem, the neo-classical modelling approach to the firm
based on maximizing profit has been thereby gradually extended to non-competitive
agents/managers pursuing different objectives. This is the modelling approach adopted by
Baumol (1959), by Marris (1964), and Williamson (1963a, 1963b). Following Williamson’s
managerial path, one of the most distinctive features of managerial theories of the firm is the
assumption that utility maximization rather than profit maximization is the objective of the
firm’s managers (Tewari and Singh, 2003). Researchers in favour of utility maximization have
proposed a utility function of managers incorporating the effects of a number of variables, such
as pride, prestige, feeling of accomplishment, material consumption, etc. As one of the
arguments against the profit maximization model, the managerial approach has drawn a lot of
attention as striving for “realism in process”, in contrast to approaches aiming at more “realism
in motivation” (Williamson, 1964).
It also has to be noted that the managerial theories of the firm are mainly applicable to limited
liability firms where there is a clear separation between ownership and management (Ahuja,
2009). In principle, utility maximization of managers can be expected instead of profit
maximization mostly in modern limited liability firms because of the separation of ownership
and control. Koplin (1963) suggests profit maximization can be achieved only if ownership and
control are not separated. Ladd (1969) argues that even if the separation of ownership and
control is considered, utility maximization is sufficient for firm survival in the market, and
hence rejects profit maximization as a necessary condition for the existence of long-run market
6
equilibrium. Olsen (1973) further emphasizes that, in industries where competition has wiped
out any excess profit, utility maximization and profit maximization occur simultaneously.
Meanwhile, in situations where excess profits exist, Olsen (1973) reaffirms the conclusion of
Scitovsky (1943) that profit maximization occurs only as a special case.
Assuming the probability of profit maximization as the objective of the firm as a whole will
then be decreasing in the number of managers hired, it is reasonable to draw the conclusion that
managers’ utility maximization is more common as an overall aggregated objective in multiplant firms with a more complex hierarchical structure as a product of loss of control in terms
of profit maximization objective of shareholders, since in these settings several self-interested
managers can maximize their own utility rather than profits2.
As a contrast to the phenomenon of loss of control in a hierarchical management structure, a
number of studies finds that firm profitability is positively related to the extent of ownership
control. In a panel study on S&P 500 firms, Anderson and Reeb (2003a) find that family firms
perform better than non-family firms, both in terms of market and accounting measures. Their
results point in the same direction as findings by McConaughy et al. (1998). Sraer and Thesmar
(2007) show that for a sample of French stock-market listed companies, family firms
outperform widely-held corporations. Pesämaa et al. (2013) finds that number of commitments
among board members is significant for firm performance. These results generally suggest that,
as management’s equity ownership increases, their interests coincide more closely with those
of outside shareholders and consequently agency problems are resolved. However, it is
important to note that the studies referred to above provide evidence on very different capital
market environments with different institutional settings, on different samples, and sample
periods. Empirical papers examining the influence of ownership concentration on firm
performance shown opposite evidence are also founded (Andres, 2008).
2.3 The hypothesis to be tested based on the loss of control of multi-plant structure
2
Assume that a manager in a firm is utility maximizing rather than profit maximizing. The manager in the model
have two variables in his/her utility function, discretionary profit and staff expenditure. The discretionary profit
could for example be one determinant of the level of a manager bonus package, and staff expenditure could include
expenditures that directly benefits the manager. If some managers maximize utility rather than profit, when firms
reach a ‘steady state’ size at an equilibrium, the level of firm profits will not be maximized since staff expenditure
exceeds the profit maximizing level.
7
The above theoretical insights brings out one critical issue that needs to be addressed when we
attempt to assess profit of firms with different firm structure, i.e., the identification of being in
‘steady-state’. We expect that the degree of loss of control is higher in the multi-plant scenario
by the assumption of more complex hierarchical structure in multi-plant firms. If, in addition,
objectives differ among managers across hierarchical levels because of the agent problem, the
loss in control can be more extensive. Given the assumptions above, under the ‘steady state’
equilibrium where firm growth keep random variation around a fixed size, multi-plant firms
should be more likely to be exposed to the problem of loss of control. Hence, the following
hypothesis will be tested in this paper:
Hypothesis: Multi-plant firms with a more complexed hierarchical structures will in ‘steady
state’ on average be less profitable than their single-plant counterparts, all else equal.
3. Data and empirical strategy
3.1. Data
In this paper, a firm-level data on limited liability firms operating in the Swedish electricity
sector are used. In Sweden, all limited liability firms are legally obliged to submit their annual
financial reports to the Swedish Patent and Registration Office. The financial report data are an
effective source of information related to economic well-being of firms, as they contain
comprehensive information on firm’s economic performance, such as revenues, profit
measures, number of employees and costs. In addition, the firms in the data are classified
according to the main economic activity using EU’s 5-digit NACE standards and the
geographical location of the firm is also stored in the data.
In the empirical analysis we use data on 2,185 firms being active within the Swedish energy
sector between the years 1997 and 2011. From the total number of 2,185 firms, 1,564 firms are
single-plant firms, while 621 firms are multi-plant firms and consist of a headquarter office and
at least one additional production unit. The unbalanced data set consists of 18,137 firm-years,
12,329 firm-years for the single-plant firms, and 5,808 firm-years for the multi-plant firms.
Firm- and industry-specific variables are retrieved from the financial reports data and for the
purpose of the empirical analysis, some of them are lagged one year, in order to attenuate a
8
possible reversed causality problem. In addition, some of the firm- and industry-specific
variables, along with population size are used in log form, in order to reduce the impact of
outliers in the data. Municipality-specific variables, such as population size and population
density, are obtained from Statistics Sweden. We also consider the fact that consumers can buy
their electricity from any Swedish energy firm after the deregulation of the Swedish energy
market in 1996, and many Swedish energy firms compete at the national level through
television advertising and telephone marketing. Hence, we consider the geographical market
for a Swedish energy firm to be the country as a whole, and thus, all industry-specific variables
are measured at national level.3 Meanwhile, the municipality-specific variables are measured at
municipality level, adopting the Swedish administrative division from year 2000 with 289
municipalities. Table 1 presents the descriptive statistics for the data set, along with variable
descriptions and sources of the data. Most prominent features from the descriptive are that
multi-plant firms are larger, growing faster and older compare to single-plant firms, suggesting
that competition is fiercer between larger multi-plant firms than smaller single-plant firms4. The
variables are discussed more thoroughly in Section 3.3.
3.2. Estimation of steady-state
In the first step of the analysis, we identify in the dataset, which Swedish electricity firms have
reached ‘steady state’ equilibrium, i.e. their size oscillates randomly around a fixed size. For
this identification, we use a method developed by Tang (2014), enabling to identify empirically
whether a firm reached a ‘steady state’, which we interpret as firms have reached their capacity
constraint.
As demonstrated by Tang (2014), the identification of firms in steady state can be made using
following random effects, random coefficient model:
𝑖
𝐿𝑛 𝑆𝑡𝑖 = 𝛼0 + 𝛼1 𝐿𝑛 𝑆𝑡−1
+ 𝜃′𝑖𝑘 𝑇𝑡 + 𝛾𝑖𝑡
(1)
3
Note that the period under study precedes the division of the Swedish electricity market into 4 different
regional markets.
4
Boone et al. (2007) measure competition using a firm-specific ‘profit elasticity’ measure, which corresponds to
the elasticity of a firm’s profits with respect to its cost level. They observe that larger firms operate in a more
competitive environment than smaller firms.
9
where 𝑆𝑡𝑖 denotes the size of firm i in the Swedish electricity industry at time period t
(t=1997…2011) measured as total revenues (Daunfeldt et al., 2013a, Macuchova et al., 2014).
Revenues are chosen as our measure of size rather than number of employees since the method
for identifying firms at their steady state will make distributional assumptions more likely to be
fulfilled using a continuous measure of size5. 𝑇𝑡 is a vector of time-specific (yearly) fixed effects
included to capture time-variant heterogeneity in firm growth rates, for example due to eg the
business cycle. Finally, 𝛾𝑖𝑡 is the heterogeneity term, specified as:
𝑖
𝛾𝑖𝑡 = 𝛿𝑖1 + 𝛿𝑖2 𝐿𝑛 𝑆𝑡−1
+ 𝜀𝑖𝑡
(2)
where 𝛿𝑖1 ~ 𝑁(0, 𝜎1) are firm-specific random intercepts and 𝛿𝑖2 ~ 𝑁(0, 𝜎2 ) are firm-specific
random coefficients related to firm size. Substituting (2) into (1), the most general model
estimated can thus be written as:
𝑖
𝐿𝑛 𝑆𝑡𝑖 = (𝛼0 + 𝛿𝑖1 ) + (𝛼1 + 𝛿𝑖2 )𝐿𝑛 𝑆𝑡−1
+ 𝜃′𝑖𝑘 𝑇𝑡 + 𝜀𝑖𝑡
(3)
or
𝑖
𝐿𝑛 𝑆𝑡𝑖 = 𝛽𝑖0 + 𝛽𝑖1 𝐿𝑛 𝑆𝑡−1
+ 𝜃′𝑖𝑘 𝑇𝑡 + 𝜀𝑖𝑡
(4)
𝑖
where 𝛽𝑖0 = 𝛼0 + 𝛿𝑖1 , 𝛽𝑖1 = 𝛼1 + 𝛿𝑖2 .We assume that the covariates 𝐿𝑛 𝑆𝑡−1
and 𝑇𝑡 are
𝑖
𝑖
𝑖
exogenous with 𝐸(𝛿𝑖1 │𝐿𝑛 𝑆𝑡−1
, 𝑇𝑡 ) = 0, 𝐸(𝛿𝑖2 |𝐿𝑛 𝑆𝑡−1
, 𝑇𝑡 ) and E(𝜀𝑖𝑡 │𝐿𝑛 𝑆𝑡−1
, 𝑇𝑡 , 𝛿𝑖1 , 𝛿𝑖2) =
0. Besides that, 𝛿𝑖1 and 𝛿𝑖2 are assumed independent across firms and study period. In the Eq.
(4) above, it is the firm’s specific slope (𝛽𝑖1 ) that plays a special role for the identification of
firms being in the steady state. As shown in Tang (2014), an individual firm with 𝛽𝑖1 equal to
one has reached this steady state, i.e. firm growth or decline is simply a result of a random
deviation around a certain size.
5
The results of the robustness check that uses number of employee as a measure of size to retrieve the variable of
steady state are provided in Table A1 in appendix A, and it shows that the results presented are robust with respect
to the adoption of revenue as a measure of size.
10
This firm’s specific total slope, 𝛽𝑖1, can be estimated by first estimating the parameters a0 and
a1 from Eq. (3) using the method of maximum likelihood. The total residuals, 𝜀̂𝑖𝑡 = 𝐿𝑛 𝑆𝑡𝑖 –
𝑖
̂𝑖𝑘 𝑇𝑡 ) can obtained directly after the estimation. Next, the individual
(𝛼̂0 + 𝛼̂1 𝐿𝑛 𝑆𝑡−1
+ 𝜃′
𝑖
regressions of 𝛿̂𝑖1 and 𝛿̂𝑖2 for both random intercepts and random coefficients on 𝐿𝑛 𝑆𝑡−1
for
each firm are fitted, using the ordinary least squares (OLS) method. Each firm’s total slope is
̂𝑖1 = 𝛼̂1 + 𝛿̂𝑖2 .
then obtained by summing the two estimated parts, i.e. 𝛽
Since the individual firms’ estimated total slopes rarely equal exactly one, we assign a value to
each firm’s total slope to determine whether the growth pattern of each firm in the Swedish
energy industry is in steady state or not. As outlined in Eq. (3) above, a firm’s total slope
consists of two parts, an unbiased estimate of the average effect of firm growth in the industry,
a1 , and a firm-specific random coefficient, 𝛿𝑖2 . We say that a specific firm is in steady state
only if firm’s individual total slope equals one, with random variation around this level during
the period under study.
As outlined in Tang (2014), in order to identify this empirically, we use the estimated index
parameter 𝛼̂1, , obtained in the first step of the estimation, and test the null hypothesis that 𝛼1 +
𝛿𝑖2 = 1. Since testing this hypothesis is equivalent to testing 𝛿𝑖2 = 1 − 𝛼1, using the standard
error of the estimated random coefficient of each firm that comes from the second part of the
estimation, the t-statistic for each firm can easily be calculated. This t-statistic indicates the
probability of the true value of 𝛿𝑖2 equaling the hypothesized value 1 − 𝛼1 . Hence, we say that
a firm reaches a steady state, i.e. its total slope equals one, if its converted p-value from the tstatistic is greater than or equal to 0.05.
3.3. Empirical method and descriptive statistics
In the second step of the analysis, we test empirically if multi-plant firms which are in their
steady state are less profitable than other firms, all else equal. To this end, the following profit
function of Swedish energy firm i being located in municipality m at time t is estimated:
πimt = α0+ αi + β*Xit + δ*Kjt + γ*Rmt + 𝑻𝒕 + 𝜸𝒋 + εimt
(5)
11
where πimt represents the dependent variable, the profit of firm i. The economic literature
suggests several ways how to measure economic performance of firms, in our study we have
opted for using return on assets (ROA) as the profit measure, πimt. We expect the ROA to be the
most accurate measure of the overall economic performance of firms, since it is not affected by
type of financing. As Libby et al. (2011, Chapter 5, p 245.) puts it; "ROA measures how much
the firm earned for each dollar of investment. It is the broadest measure of profitability and
management effectiveness, independent of financing strategy. Firms with higher ROA are
doing a better job of selecting and managing investments, all other things equal. Since it is
independent of the source of financing (debt vs. equity), it can be used to evaluate performance
at any level within the organization". As such, ROA is a more precise profit measure than for
example return on equity (ROE) that will be as affected both by source of financing and by the
performance of the firm. Also, several previous studies have opted for using ROA as the profit
measure when performing economic analysis (Daunfeldt et al. 2006; Daunfeldt et al. 2013b,
2014; Håkansson et al. 2013, 2014, Brandt et al. 2014).
The main parameter of interest in Eq. (5) is related to the indicator variable identifying firms
that are simultaneously in steady state and have a multi-plant structure with one headquarter
and at least one additional production plant. This indicator variable can also be seen as an
interaction variable between two indicators for being in steady state and for being a multi-plant
firm and is thus denoted SteadyStatei * Multiplanti below.
In order to control for important confounders, Eq. (5), contains also other covariates, expected
to influence firm profits, grouped in three vectors: vector Xi represents firm-specific variables,
Kj denotes a vector of industry-specific variables, and Rm denotes a vector of the location
specific variables. Tt is a vector of time-specific fixed effects, β, δ and γ are the corresponding
parameters vectors. Finally, εijmt is a residual term reflecting random optimization errors at the
firm level expected to have zero mean and constant variance. All time variant variables in the
vectors Xit and Kjt are lagged one year to alleviate a potential reversed causality problem.
In addition to the indicator variable SteadyStatei * Multiplanti discussed above, the vector of
firm-specific variables Xit consists of other firm characteristics assumed to affect profits. First,
as the indicator variable SteadyStatei * Multiplanti can be seen as an interaction between two
other indicator variables, these are also included separately in the estimations. Thus, there is an
indicator variable for firms being in steady state (SteadyStatei), and another indicator variable
12
representing multi-plant firms (Multiplanti). The variable SteadyStatei was obtained from the
estimation of a firm’s specific total slope in Eq. (4) for each firm in the data set individually,
and is equal to 1 for all firms being in the steady-state, zero otherwise.
The firm level covariates also include firm growth (Firm growthit-1), firm size (Firm sizeit-1) and
firm age (Firm ageit-1), which have previously been found to affect profits (Håkansson et al.
2014). Firm growth is measured as the log difference of total sales; Firm size is indicated by
the number of employee; Firm age is calculated as the difference between the firm’s start-up
year and time t. The variable Adjustment costs it-1 is included in order to control for costs
associated with changes in firm size, and is calculated as costs for investments (or revenues for
disinvestments) in machinery and buildings. However, since we expect that this variable is
influential only for firms not being in their equilibrium, it is included only for firms not being
in their steady state. Lastly, we expect that profits will be a nonlinear function of staff
expenditure, which we proxy with total salaries. As such, Salary it-1 and Salary2it-1 are also
included in the estimated function.
Firm profits are further expected to be affected by the general characteristics of the particular
industry in which the firms operates, e.g. agglomeration economies, size of the market or market
competition. Considering the nature of Swedish energy markets after the 1996 deregulation,
when energy firms substantially increased the geographical size of their relevant market areas
from the local municipalities to entire Sweden, we opt to measure the industry-specific factors
at the national level, considering Sweden as one single geographic market.
In the vector of industry-specific variables, Kjt, we include minimum efficient scale (MESjt-1),
industry size (Industry sizeijt-1), and a market concentration (Market Concentrationjt-1)
measuring the degree of competition in the market. Following Daunfeldt et al. (2013) and
Håkansson et al. (2013), we measure MES as the average firm size measured by revenue in the
Swedish electricity sector at time t – 1, industry size is measured as the total turnover of the
Swedish electricity industry in period t – 1, and market concentration is measured using
Herfindahl index. The Herfindahl index is the sum of the squared market shares and is defined
on the interval 0-10 000 and has a value of 10 000 if the market is supplied by one firm only; if
all firms in a market have equal sales, then the Herfindahl index is 10 000/number of firms.
13
Finally, firm profits are expected to also be influenced by characteristics of the geographical
environment where the firm is located, and which needn’t be directly linked to the specific
industry in which the firm operates. Frequently mentioned factors in this context are the level
of labour supply and the education level of the labour force. Local differences in the use of the
Swedish Plan and Building Act and differences in land prices are other factors that might affect
the firm’s profits. As such, we control for regional characteristics, including the following
variables in the vector Rmt population size (Population sizemt) and population density
(Population densitymt) are used as proxy variables for land prices, an indicator variable for type
of local government (Local governmentmt) is used as an indicator of how local policy affects
profits, while an indicator variable for the presence of an institution of higher education in the
municipality (Universitymt) and the a share of the population with higher education (Education
levelmt) are used as a measure of the size of a well-educated labour force in the region, all
measured at the municipality level.
Previous studies (Daunfeldt et al., 2013; Håkansson et al., 2014) have shown the importance of
accounting for firm level heterogeneity when studying firm growth and firm profits. However,
since our main variable of interest is time-invariant and measured on the firm level, this cannot
be done using a fixed effects specification. Thus, a firm specific random effect, αi are be used
to control for time-invariant firm specific heterogeneity in profit levels6.
Additionally, a time trend 𝑻𝒕 and 5-digit-industry-specific fixed effects 𝜸𝒋 are incorporated to
capture time-varying and industrial heterogeneity in firm profit within the electricity sector that.
Lastly, 𝜀𝑖𝑡 is a random error term.
6
The result of Hausman test for the model without the time invariant variables confirms the adoption of random
effect.
14
Table 1: Dependent and independent variables; means and standard deviations.
Variable
ROA it-1
Mean
Variable description
All firms
Multi-plant
Single-plant
5.70
(35.2)
5.78
(33.25)
5.58
(36.15)
0.70
(0.46)
0.31
(0.46)
0.24
(0.42)
1.17
(2.82)
1.86
(1.59)
0.07
(0.72)
7,875
(40,046)
1.70+e09
(2.16+e10)
19.97
(22.44)
0.74
(0.44)
1
(0)
0.74
(0.43)
1.19
(2.93)
2.75
(1.77)
0.08
(0.73)
19,668
(66,580)
4.82e+09
(3.70e+10)
25.44
(26.30)
0.68
(0.47)
0
(0)
0
(0)
1.16
(2.77)
1.37
(1.21)
0.06
(0.71)
2,117
(13,087)
1.76e+08
(4.20e+09)
17.90
(20.00)
13,045
(20,054)
1.81e+08
(3.81e+07)
356.2
25.3
15,562
(26,535)
2.81e+08
(4.21e+07)
356.35
(25.31)
12,536
(22,634)
1.51e+08
(3.52e+07)
357.05
(25.37)
Source
Return on assets for firm i and time t
PAR/Own
calculations
Indicator variable of steady state fir firm i
Own calculation
Firm-specific
Steady Statei (D)
Multiplanti (D)
SteadyState*Multiplanti
(D)
Adjustment cost it-1
Firm sizeit-1
Firm growthit-1
Salaryit
Salaryit2
Firm ageit-1
Indicator variable of multi-plant firm
Indicator variable of steady state and multi-plant firm
Adjustment costs for firm i and time t-1
Log value of number of employee for firm i and time t-1
Log difference of total sales for firm i and time t-1 and t-2
Total salaries for firm i and time t-1
Squared value of total salaries for firm i and time t-1
Number of years since firm i registration and time t-1
PAR/Own
calculations
PAR/Own
calculations
PAR/Own
calculations
PAR/Own
calculations
PAR/Own
calculations
PAR/Own
calculations
PAR/Own
calculations
PAR/Own
calculations
Industry-specific
MES-1 (L)
Industry sizeit-1 (L)
Market concentrationit-1
Size of average firm in the industry measured with total sales in the
industry at national level and time t-1
Total sales for the industry at national level in time t-1
Herfindahl index in the industry at national level in time t-1
PAR/Own
calculations
PAR/Own
calculations
PAR/Own
calculations
15
Municipality-specific
151,486
168,538
142,562
Population size in municipality m and time t
(233,394) (286,358)
(206,562)
632.51
649.10
629.68
Population densitymt
Population density in municipality m and time t
(1,239)
(1,214)
(1,230)
Education levelmt
26.77
26.01
26.97
Share of university educated pop. in municipality m and time t
(10.03)
(9.85)
(10.06)
Universitymt (D)
0.40
0.46
0.35
Presence of institution of higher education in municipality m and time t
(0.49)
(0.53)
(0.48)
Local governmentmt (D)
0.28
0.25
0.29
Type of local government in in municipality m and time t
(0.45)
(0.43)
(0.46)
Note: For estimation of the indicator variable Steady State, see Section 3.2; Std. Dev. in parenthesis.
Population sizemt (L)
Statistics Sweden
Statistics Sweden
Statistics Sweden
Statistics Sweden
Statistics Sweden
16
4. Results
First, we identified which Swedish multi-plant electricity firms in the sample that are in ‘steady
state’, which we will interpret as the firm has reached the capacity constraint in terms of firm
size. This is done using the method developed by Tang (2014), identifying whether firms are at
their ‘steady state’ equilibrium or not. To this end, Eq. (4) was estimated for all firms within
the Swedish energy sector in the period 1997-2011. As outlined in Section 3.2, for each firm in
the sample, the firm’s specific total slope is retrieved and the indicator variable for being in
‘steady state’ assigned a value of one when this estimated total slope is not statistically
significant different from one on the 5% significance level.
The results indicate that 71.31 % of all Swedish electricity firms have an assigned value
equalling one when firm size is measured by the firm’s revenues. Meanwhile, if we distinguish
between multi-plant and single-plant firms, then 74.07 % of single-plant firms are at their
‘steady state’, while among multi-plant firms, the share is 70.08 %.
In the next step, we estimated Eq. (5) for firms being active within the Swedish electricity sector
during the years 1997-2011 in order to empirically test if multi-plant firms, have lower profits
than other firms, all else equal.
Table 2 presents the estimated coefficients with their corresponding standard errors for three
different model specifications. Model (1) is the most general specification, including all three
vectors of explanatory variables, along with time-specific fixed effects and firm-specific
random effects. Model (2) and Model (3) are then used to test the sensitivity of our main model
for the exclusion of the region- and industry specific vectors of explanatory variables from the
analysis7.
As has been reported previously when estimating firm profits in Sweden (Håkansson et al.
2014), the estimation results indicate that most variables are insignificantly determined.
However, the main variable of interest in this estimation is the interaction term between the
indicator variable identifying, whether firms have reached the ‘steady state’ or not, and the
indicator variable Multiplanti, which identifies firms with multi-plant firm structure. The
7
In additional estimation, the Model (1), (2) and (3) were run without firm-specific random effects, with results
qualitatively similar. The results of these estimations are available on request from the authors.
17
parameter estimate related to this interaction variable Steady Statei * Multiplanti is negative and
statistically significant at the 1% level in all estimated models. This result suggests that for
multi-plant firms, simultaneously reaching ‘steady state’, the profitability is lower, ceteris
paribus.
The estimation result of Model (1) enables further to analyse the impact of having a multi-plant
firm structure. The estimated effect of being a hierarchical firm or not in relation to firm’s
profitability is given by a combination of the estimated coefficients of Multiplanti (0.658) and
Steady Statei * Multiplanti, (-1.059). Thus, this effect depends on whether a firm i have reached
‘steady-state’ equilibrium. After controlling for the other covariates, having a multi-plant
structure affect firm’s profit positively before the firm reaching ‘steady-state’ equilibrium.
However, after reaching ‘steady state’ equilibrium, the effect of having hierarchical structure
on profitability is negative.
In order to investigate if our empirical model is sensitive to changes in model specification, we
have run additional estimations of Eq. (5) excluding different vectors of explanatory variables.
Model (2) does not contain region-specific factors, while Model (3) excludes both region- and
industry-specific factors, and the results are presented in columns with corresponding labels in
Table 2. For our main variable of interest, the exclusion of these variables does not affect the
estimated parameter even at the third decimal, although there are slight changes in the estimated
standard error of the parameter. In addition, none of the variables included in all estimations
changes sign or significance level in these additional estimations, although the non-significant
parameter estimates changes somewhat in size. This suggests that the results obtained from our
main model are not sensitive to the model specification chosen.
Finally, we have tested the robustness of our results to various sources of biases and in
consistence (see Appendix A). First, as a point-of- reference, the Model (1), (2) and (3) were
estimated excluding the variable Steady Statei and the interaction variable Steady Statei
*
Multiplanti, the estimation results of Multiplanti, are negative at 5% significance level in all
three models. Second, paying attention to the entry and exit of firms in the electricity sector; as
multi-plant firms may be less likely to close a plant because they can shift resources within the
firm in bad times, or they may be more likely to close a plant since such plant closures do not
also shut down the entire firm. Conducting the estimation on the surviving firms only, we find
the results are qualitatively robust. Third, we consider the number of employee as a measure of
18
firm size to identify firms that are in their ‘steady state’, the results from the estimation of profit
function shows similar statistical significance for the variable of interest, Steady Statei *
Multiplanti , although it is with smaller magnitude.
Could our results be due to some other variable not included in the estimations but correlated
to the indicator variable for simultaneously being at ‘steady state’ and being a firm with a multiplant structure? One obvious candidate that we are not able to control for is the type of
ownership, and some of the electricity firms under study are owned by local municipalities and
even the national government who might not have profit maximization as their main objective.
However, since the liberalisation of the Swedish electricity market 1996, profit-maximizing
firms carry the main responsibility in the new electricity market and many of the municipality
owned electricity firms are also small, one unit operations while others are not (Wollmann et
al., 2016). As such, we do not deem this to be a major concern in our study, although we would
of course have liked to be able to also control for ownership in our estimations.
19
Table 2: Estimation results (Dependent variable: ROA)
Model (1)
Model (2)
Model (3)
Variables
Coefficient Std.errors Coefficient Std.errors Coefficient Std.errors
Firm-specific
Steady Stateit
0.299**
Multiplantit
0.658***
SteadyStatei* Multiplantit -1.059***
0.157
0.242
0.285
0.337**
0.661***
-1.058***
0.161
0.249
0.294
0.339**
0.661***
-1.058***
0.161
0.249
0.249
Firm ageit-1
Firm growthit-1
Salaryit
Salariesit2
Adjustment costit-1
0.016*
0.012
-0.524
0.00004
-5.53e-12
-0.100
0.062
0.018
0.610
0.00002
3.79e-11
0.401
0.017*
0.011
-0.582
6.86e-06
-2.90e-12
-0.006
0.058
0.018
0.610
0.00002
3.8e-11
0.409
0.017*
0.011
-0.582
6.80e-06
-2.90e-12
-0.006
0.060
0.018
0.610
0.00002
3.8e-11
0.409
Industry-specific
MESjt-1
Industry sizejt-1
Market concentrationjt-1
94.23
-80.685
-0.106
104.35
85.877
0.107
84.95
-73.768
-0.096
103.93
85.51
0.106
Municipality-specific
Population sizemt
Population densitymt
Education levelmt
Universitymt
Local governmentmt
-0.208
-0.0011**
-0.011
-1.777
0.008
0.702
0.00052
0.072
1.345
0.878
Firm sizeit-1
Time FE
Yes
Yes
Yes
Industry
Yes
Yes
Yes
Firm RE
Yes
Yes
Yes
No. of obs.
12 755
13 435
13 435
Conditional R2
0.58
0.36
0.35
Note: The variable Adjustment costit-1 is included for firms that are not in ‘steady state’; ***, ** and * denotes
significance at 1%, 5% and 10% levels, respectively.
20
5. Discussion
This paper has examined whether multi-plant firms are more or less profitable than their singleplant counterparts when they both reach capacity constraints indicated by ‘steady state’ firm
size. To control for the capacity constraints for both multi-plant and single-plant firms, we start
by identifying electricity firms which are at a ‘steady state’ size with only random fluctuations
around that level during the period under study. Our results show that multi-plant firms, in
‘steady state’ equilibrium, have on average 1% lower return on assets compared to other firms,
and we interpret this as an indication that loss of control resulting in lower profitability in the
Swedish electricity sector.
How can this result ne explained? First, it is worth considering the nature of multi-plant firms.
We submit that these multi-plant firms are often run by professional managers, who have only
a limited liability for the firm. A main prediction of theoretical insights suggests that firms with
more complex hierarchical structures overall will more likely to suffer loss of control, resulting
from reproduction distortion and inconsistent objectives of managers in each level of hierarchy
within the firms. Although professional managers are likely to have received formal trainings
and presumably will have a relatively high level of managerial skills, incentives such as
remuneration, likelihood of promotion, prestige and also power are linked to the size of the
firm. These factors can be expected to increase both the degree of capacity constrain of multiplant firms. Single-plant firms, on the other hand, are often smaller and run by ‘lifestyler’
managers with little growth ambitions, who see their firms as a means to an independent life
style and source of stable revenue (Hay and Kamshad, 1994).
Second, it could also be related to the feature of Swedish electricity industry of which the rising
productivity has been greatly characterised by a strong technological and structural renewal
(Schön, 2000). In other words, the electricity firms that have recorded high rates of productivity
are often those with rapid rates improvement in best practice technique. Hence, if there were no
newer best-practice techniques that bring forth lower factors prices in production, enable to
expand output, drive down prices and eventually wipe out the surplus from the plants, those
multi-plant firms will remain in such an equilibrium without further capital investment in favor
of technology progress. The equilibrium could also be long-term in the sense if the old capital
equilibrium did not physically deteriorate. Then all operating costs would remain constant so
that there would be never be any incentive to replace or abandon outmoded plants. This
21
complication of multi-plant firm requires more managerial efficiency and it applies to some
plants within the firm that have very little surplus. Therefore, more potential loss can be
expected in multi-plant electricity firms with more complex hierarchical structure.
Our results have implications for future research in a number of areas. An interesting avenue
for future research should be to try to replicate our result in other sectors in the economy as
well. We have after all been able to show that there is at least one industry in which not all firm
managers seem to be acting in the best interest of the firm owners. Additional theoretical and
empirical work is also need to develop a better understanding of the nature of hierarchical
structures in multi-plant firms, especially those maintain their firm size.
22
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25
Appendix A
Table A1: Estimation results for surviving firms (Dependent variable: ROA)
Model (1)
Model (2)
Model (3)
Variables
Coefficient Std.errors Coefficient Std.errors Coefficient Std.errors
Firm-specific
Multiplantit
0.152
0.061
0.003
0.110
0.00004
6.80e-12
0.081
-0.365**
0.016**
0.010**
0.080
0.00004
-9.52e-12
-0.074
0.155
0.062
0.003
0.113
0.00004
6.93e-12
0.083
Industry-specific
MESjt-1
56.531
Industry sizejt-1
-52.563
Market concentrationjt-1 -0.006
125.321
98.554
0.092
52.512
-48.326
-0.006
124.309
97.365
0.101
Municipality-specific
Population sizemt
Population densitymt
Education levelmt
Universitymt
Local governmentmt
0.115
0.0007
0.012
0.225
0.569
Firm sizeit-1
Firm ageit-1
Firm growthit-1
Salaryit
Salariesit2
Adjustment costit-1
-0.337**
0.024*
0.007*
0.101
0.00006
-1.13e-11
-0.063
-0.078
-0.0009
-0.009
0.730**
0.006
-0.365***
0.016**
0.010**
0.080
0.00004
-9.52e-12
-0.074
0.155
0.062
0.003
0.113
0.00004
6.93e-12
0.083
Time FE
Yes
Yes
Yes
Industry FE
Yes
Yes
Yes
Firm RE
Yes
Yes
Yes
No. of obs.
13,563
13,789
13,798
Conditional R2
0.50
0.36
0.36
Note: The variable Adjustment costit-1 is included for firms that are not in ‘steady state’; ***, ** and * denotes
significance at 1%, 5% and 10% levels, respectively.
26
Table A2: Estimation results for surviving firms (Dependent variable: ROA)
Model (1)
Model (2)
Model (3)
Variables
Coefficient Std.errors Coefficient Std.errors Coefficient Std.errors
Firm-specific
Steady Stateit
0.256**
Multiplantit
0.634**
SteadyStatei* Multiplantit -1.086***
Firm sizeit-1
0.018**
Firm ageit-1
0.010
Firm growthit-1
-0.216
Salaryit
0.00004
Salariesit2
-6.89e-12
Adjustment costit-1
-0.123
0.178
0.221
0.276
0.076
0.016
0.537
0.00003
4.84e-11
0.508
0.255**
0.635**
-1.088***
0.018*
0.009
-0.216
7.92e-06
-3.26e-12
-0.007
0.176
0.245
0.275
0.074
0.016
0.538
0.00001
5.2e-11
0.502
Industry-specific
MESjt-1
Industry sizejt-1
Market concentrationjt-1
86.523
-79.526
-0.106
196.372
76.121
0.107
99.123
-79.520
-0.096
108.252
76.123
0.106
Municipality-specific
Population sizemt
Population densitymt
Education levelmt
Universitymt
Local governmentmt
-0.206
-0.0011
-0.011
-1.769
0.007
0.829
0.0008
0.071
1.299
0.856
0.255**
0.636**
-1.088***
0.017*
0.009
-0.216
7.91e-06
-3.26e-12
-0.008
0.161
0.246
0.274
0.075
0.016
0.537
0.00001
5.2e-11
0.501
Time FE
Yes
Yes
Yes
Industry FE
Yes
Yes
Yes
Firm RE
Yes
Yes
Yes
No. of obs.
9,956
10, 235
10, 235
Conditional R2
0.52
0.33
0.33
Note: The variable Adjustment costit-1 is included for firms that are not in ‘steady state’; ***, ** and * denotes
significance at 1%, 5% and 10% levels, respectively.
27
Table A3: Estimation results, where the ‘steady stat’ variable is retrieved form number of
employee as a measure of firm size (Dependent variable: ROA)
Model (1)
Model (2)
Model (3)
Variables
Coefficient Std.errors Coefficient Std.errors Coefficient Std.errors
Firm-specific
Steady Stateit
0.230**
Multiplantit
0.641***
SteadyStatei* Multiplantit -1.002***
Firm sizeit-1
0.015*
Firm ageit-1
0.009
Firm growthit-1
-0.326
Salaryit
0.00003
Salariesit2
-5.48e-12
Adjustment costit-1
-0.103
0.163
0.238
0.236
0.066
0.019
0.590
0.00002
3.86e-11
0.426
0.286**
0.641***
-1.001***
0.018*
0.010
-0.332
6.74e-06
-2.93e-12
-0.009
0.156
0.238
0.256
0.062
0.018
0.590
0.00002
4.2e-11
0.469
Industry-specific
MESjt-1
Industry sizejt-1
Market concentrationjt-1
106.32
-76.26
-0.126
108.26
86.88
0.109
96.97
-75.78
-0.103
102.11
80.23
0.102
Municipality-specific
Population sizemt
Population densitymt
Education levelmt
Universitymt
Local governmentmt
-0.301
-0.009**
-0.010
-1.726
0.010
0.622
0.00048
0.069
1.236
1.26
0.286**
0.640***
-0.998***
0.018
0.011
-0.332
6.73e-06
-2.93e-12
-0.09
0.156
0.237
0.256
0.062
0.018
0.591
0.00002
4.2e-11
0.469
Time FE
Yes
Yes
Yes
Industry
Yes
Yes
Yes
Firm RE
Yes
Yes
Yes
No. of obs.
11,008
11,270
11,270
Conditional R2
0.56
0.31
0.31
Note: The variable Adjustment costit-1 is included for firms that are not in ‘steady state’; ***, ** and * denotes
significance at 1%, 5% and 10% levels, respectively.
28