 Original article
 Open Access
Factor substitution in Swiss manufacturing: empirical evidence using micro panel data
 Sebastian M. Deininger^{1},
 Lukas Mohler^{2}Email author and
 Daniel Mueller^{3}
https://doi.org/10.1186/s4193701700165
© The Author(s) 2018
 Received: 15 November 2017
 Accepted: 10 December 2017
 Published: 20 February 2018
Abstract
This paper analyzes the relationship between factor substitutability and the energy intensity of manufacturing firms. Specifically, we compare the degree of substitutability between the input factors capital, labor, energy, and material for firms with low, medium, and high energy cost shares using a panel of Swiss manufacturing companies covering the period from 1997 to 2008. Our findings indicate substitutability between almost all production factors with one notable exception. Energy and capital are complements in the energyintensive firm sample: A 1% increase in energy prices decreases capital use by 0.09%. We show that this complementarity is gradually increasing in the energy intensity of firms and draft important policy implications.
Keywords
 Substitution elasticities
 Complementarity
 Swiss manufacturing
 Micro panel data
 Linear logit
 Translog
JEL Classification
 C33
 D24
 Q41
Background
As many other European countries, Switzerland has revised its environmental and energy policy strategies in order to comply with GHG emission reduction goals and foster the transition from fossil fuels to renewable energy^{1}. Specifically, Switzerland has decided to reduce GHG emissions by 20% by 2020 compared with 1990 levels. In 2008, a carbon tax was introduced at 12 Swiss francs per metric ton of CO_{2}. The tax was raised to 84 Swiss francs in 2016, and a further increase is possible if emissions are above target. Large emitters are exempted from the carbon tax and instead participate in a cap and trade system. Moreover, small and mediumsize companies can also be exempted from the tax provided they commit to legally binding CO_{2} reduction goals.
Policy makers are confronted with the challenge of achieving the environmental targets without negatively affecting the overall economy and the competitiveness of firms. To evaluate the economic impact of such policies, a better understanding of substitution possibilities at the level of individual firms is needed. In this contribution, we analyze the relationship between factor substitutability and the energy intensity of Swiss manufacturing firms^{2}. Our panel dataset comprises approximately 7400 observations at the firm level from 1997 to 2008. Using this micro panel data, we estimate substitution elasticities between capital, labor, energy, and material inputs using the linear logit as well as the translog cost function.
Our work is related to the few existing studies that estimate substitution elasticities using firmlevel data. Woodland (1993) is the first study to use micro data to analyze substitution between capital, labor, and four energy types in Australia. Nguyen and Streitwieser (1999) examine whether plant size in US manufacturing has an impact on the degree of factor substitution. Arnberg and Bjorner (2007) apply crosssection and panel data techniques to a dataset of Danish firms, and Tamminen and Tuomaala (2012) estimate substitution elasticities for 71 sectors employing a large panel of service and manufacturing firms from Finland. Similar to the last two studies, we employ a panel of manufacturing firms and estimate substitution elasticities controlling for timeinvariant unobserved heterogeneity. As a novel contribution to this literature, our focus lies on the relationship between factor substitutability and the energy intensity of manufacturing firms.
To perform our analysis, we classify the firms into three subsets according to their energy intensity and estimate elasticities for these subsets. We stress three main results:
First, we find evidence for substitutability between energy and the input factors capital and labor for firms with lowenergy intensity, implying that upon an energy price increase, factor use of labor and capital will increase in order to optimally compensate for the decreasing energy use. In contrast, capital and energy are estimated to be complements for the energyintensive subset. Specifically, these energyintensive firms substitute the decreasing energy (− 1.03%) and capital (− 0.09%) use upon an energy price increase of 1% with a higher input of material (+ 0.11%) and, to a lesser extent, labor (+ 0.03%).
Second, by gradually excluding the firms with the lowest energy cost shares from the energyintensive subset, we are able to show that the higher the mean energy cost share of the remaining firms is, the stronger the complementarity between energy and capital becomes. This result indicates that it is important to account for the heterogeneity of firms when estimating substitution elasticities: Even when using micro panel data, estimating the elasticities over a broad range of firms with heterogeneous characteristics seems to average out the specific substitution behavior of firms at the margin—in our case, the most energyintensive firms.
Third, these results bear strong policy implications: If energy and capital are complements, higher energy prices lead to lower capital levels, i.e., a reduction in investment. Energy taxes can thus be harmful and negatively affect competitiveness and overall economic performance. As is argued by Tovar and Iglesias (2013), in such a case, it would be beneficial to encourage technological innovation instead of increasing energy prices to achieve reductions in emissions or energy use. Our result thus lends support to policies that exempt certain firms from energy taxes in favor of implementing efficiency measures. In Switzerland, most firms have the choice between paying the carbon tax and committing to reduction goals. There is initial evidence in Oberauner (2010) that, in fact, the higher a firm’s energy intensity is, the more likely it will make use of this possibility. Hence, this may be a policy strategy to prevent the aforementioned harmful effects for energyintensive firms from realizing. Such a strategy may also be eligible in other countries if evidence for complementarity between energy and capital is identified. As another consequence from a policy perspective, our results hint at possible issues using computable general equilibrium (CGE) models for policy evaluation, since these models often do not take into account the possibility of this kind of complementarity.
The remainder of the paper is organized as follows: the “Related literature” section gives a brief overview and discussion of previous micro data studies in the field of factor substitution. After introducing the applied methodology in the “Methods” section, the empirical analysis is provided in the “Empirical analysis” section. In the “Interpretation of the complementarity result” section, the results are interpreted and policy implications are derived. The paper concludes with the “Conclusions” section.
Related literature
Research on substitution possibilities between energy and other production factors emerged after the first oil crisis in the 1970s. Earlier studies predominantly estimated substitution elasticities using time series or crosssection data for specific industrial sectors or aggregate manufacturing. Enhanced data availability as well as more sophisticated estimation methods have increased the interest in micro data studies. The empirical literature has shown that elasticity estimates vary substantially and depend on the level of sector aggregation, the geographical region, the time period, and the applied model specification (Koetse et al. 2008).
The majority of studies find that production factors are substitutes in the production process. However, there is an ongoing controversy on whether the factors energy and capital are substitutes or complements. Crosssection studies tend to detect substitutability, while in time series studies, these factors are predominantly found to be complementary (Apostolakis 1990). It is argued that the former measure longrun elasticities, whereas time series capture shortrun effects. More recently, such discrepancies have also been observed between crosssection studies and panel studies based on micro panel data. Arnberg and Bjorner (2007) argue that endogeneity problems with labor and energy prices in crosssection studies might cause the differences.
A general issue of studies using aggregated industry data is the difficulty to distinguish between factor substitution and concurrent effects. For instance, Solow (1987) demonstrates convincingly that compositional changes in output can lead to incorrect substitution estimates in studies using aggregate data. He concludes that “[f]actor substitution is a microeconomic phenomenon, and is best examined by looking at microeconomic data” (p. 612). However, only a few micro data studies estimate factor substitution between energy and nonenergy factors. The main reason is that energy expenses are rarely available for individual firms. Below, we summarize the results of previous micro data studies in the field of factor substitution.
The first micro data study on substitution between energy and nonenergy factors was conducted by Woodland (1993). He used repeated crosssectional data of approximately 10,000 manufacturing firms in New South Wales, Australia, covering the period from 1977 to 1985. Woodland focused on different types of fuels (coal, oil, gas, and electricity) as well as labor and capital. He found that the demand for energy fuels is priceelastic (with the exception of coal), whereas the demand for capital and labor is priceinelastic. Moreover, he shows that substitution between fuels and the nonenergy factors appears to be much stronger than substitution between different types of fuels.
Nguyen and Streitwieser (1999) investigate whether differences exist in factor substitution between small and large production firms. They use crosssectional data comprising 10,412 US industrial companies in 1991 to estimate the standard KLEM (capital, labor, energy, and material) model applying the translog function. Nguyen and Streitwieserfind that the demand of all four factors is priceelastic, with energy having the highest value and capital the lowest. Furthermore, when considering the AllenUzawa elasticity of substitution (AES) and the crossprice elasticity (CPE) as a measure of substitution, they find that the factors capital and energy are either substitutes or complements depending on the size of employment.
Arnberg and Bjorner (2007) apply crosssection and panel data techniques to a dataset of 903 Danish industrial firms for 1993 and the period from 1995 to 1997. They estimate substitution elasticities between the factors electricity, other energy, labor and (machine) capital using the translog and the linear logit function. Their main finding is that, in the fixedeffects model, electricity and capital as well as other energy and capital are complements, whereas they are substitutes in the crosssection model. They point out that the results of the crosssection model might suffer from biased estimates due to endogeneity problems with the price of labor and energy. They argue that firm fixed effects can control for unobservable quality differences among employees, as well as for differences of energy fuels. Similar to other studies, Arnberg and Bjorner find lower values for interfuel substitution elasticities than for the elasticities between energy and nonenergy factors.
Finally, Tamminen and Tuomaala (2012) employ panel data from 2000 to 2009 comprising 230,000 manufacturing and service companies operating in Finland. They estimate substitution elasticities for the factors labor, capital, outside services, electricity, and other energy forms for 71 sectors. Their results show that the factors labor and capital are relatively priceinelastic. In contrast, material and energy inputs are pricesensitive. Furthermore, as substitution elasticities significantly differ across the 71 sectors, they recommend using sectorspecific estimates in CGE models.
Methods
Modeling approach
The translog (TL) function introduced by Christensen et al. (1973) is the preferred production function used in the literature because of its functional flexibility and the relatively low data requirements. While the majority of empirical studies make use of the TL function, more recent work also considers the linear logit (LL) function as developed in Considine and Mount (1984) as a functional specification. While the LL function is as flexible as the TL function, it has the advantage that it is wellbehaved for a broader range of factor prices and shares. The LL model is especially suitable if some cost shares are small (Considine 1989) and if there is relatively large variation between firms in the cost shares (Arnberg and Bjorner 2007). For these reasons, elasticities are estimated from both the LL and the TL model in order to analyze the substitution possibilities of Swiss manufacturing firms. One contribution of our paper is a direct comparison of results from the LL and the TL models, also checking the concavity constraints in both model types.
The linear logit function
for i and j = { K,L,E}. The remaining parameter values can be derived by using the imposed symmetry and homogeneity restrictions.
The translog function
where i and j denote the four considered factor inputs capital, labor, energy, and material, while n and t stand for the firm and the time index, respectively, and p denotes the factor price. In the righthand side of the equation, β_{ in } captures input and firmspecific effects which are considered to be constant over time when using panel data. Furthermore, the log of output (y) of firm n at time t is included to control for different production levels. Finally, an error term denoted by ε_{ in,t } is added to the equation.
Estimation approach
The factor shares of the LL and the TL models (Eqs. (2) and (4)) can best be estimated by using a system of equations approach. Specifically, we refer to a pooled regression approach using seemingly unrelated regression (SUR) on transformed data with firm fixed effects. We transform the data as in Cameron and Trivedi (2009) by calculating the variables’ mean over time for every firm and subsequently performing a within transformation.
Considering the symmetry conditions, the system of equations can be estimated by pooled OLS, or, as in this paper, by the SUR approach which accounts for error correlations across the system of equations. The simultaneous estimation of the model, which is also applied in Arnberg and Bjorner (2007), is more efficient compared to the equationbyequation OLS estimation and allows for a straightforward implementation of the various parameter restrictions. Furthermore, SUR accounts for crossequation contemporaneous correlations but assumes crosstime independence of the residual vectors. The SUR estimation considers neither the correlation between individuals (firms) nor the correlation of error terms over time. Consequently, the estimated standard errors are not valid and have to be corrected. We use bootstrap methods to calculate clusterrobust standard errors (Efron 1979).
Measuring factor substitution
We examine the substitutability of the production factors using the crossprice elasticity of demand (CPE) as a commonly used measure in previous studies^{4}.
If η_{ ij }>0, a price increase of input factor j leads to a higher quantity of factor i, with output and all other prices held constant. Firms compensate the price increase of factor j by using a higher amount of factor i instead. Consequently, the input factors are substitutes. If, on the other hand, η_{ ij }<0, a price increase in j decreases the demand for factor i. Thus, firms reduce the amounts of factors i and j in the production process, to maintain a constant output level. In this case, inputs are considered to be complements.
Result and discussion
Empirical analysis
Data description and model selection
Swiss manufacturing data We use firmlevel panel data comprising capital, labor, energy, and material expenditures as input factors for the period from 1997 to 2008. These data as well as the number of employees and the firm’s output are collected in the context of the survey “Production and value added statistics” (WS), conducted by the Swiss Federal Statistical Office (SFSO). The survey levies detailed information on the balance sheets and the income statements of Swiss firms in manufacturing, retail, and services. A total of 10,400 companies were interviewed in 1997/1998, and this number increased to about 20,000 companies in 2008/2009. The response rate is about 90% for large firms, 70% for medium firms, and 60% for small firms. The WS survey has been published since 1997 on an annual basis. The sample used in this study comprises 1965 manufacturing firms (7396 observations) from 22 industry divisions^{6}.
Factor cost shares of an input are obtained by dividing the cost of one input factor by the total costs of all considered factors used in production. While this approach is suitable for labor, energy, and material, obtaining the annual real consumption of capital is a challenging task. Arnberg and Bjorner (2007) use machine capital and include the level of building capital as an explanatory variable in the empirical specification, whereas Woodland (1993) calculates the share of capital as a residual value after subtracting the cost of labor, energy, and material from the firm’s output. In this paper, we follow the second approach.
Firms according to industry sector
Energy cost share  

Sector  Division  Industry description  Obs.  Mean  Q _{0.25}  Q _{0.75} 
1  15, 16  Food products, beverages, and tobacco products  746  2.8  1.0  3.0 
2  17–19  Textiles, wearing apparel, leather, and related products  555  2.1  1.0  2.6 
3  20  Wood, products of wood, and cork  279  1.7  0.8  2.6 
4  21, 22  Paper, paper products, printing, and publishing  914  1.9  0.8  2.0 
5  24  Chemicals, chemical, and pharmaceutical products  392  1.9  0.8  2.0 
6  25  Rubber and plastic products  471  1.7  0.8  1.8 
7  26  Other nonmetallic mineral products  317  2.0  0.9  2.3 
8  27, 28  Basic metals and fabricated metal products  1256  2.2  0.7  2.6 
9  29  Machinery and equipment n.e.c.  790  1.9  0.6  2.2 
10  30–33  Electrical equipment, electronic, and optical products  1152  1.6  0.8  1.7 
11  34, 35  Motor vehicles and other transport equipment  186  1.8  0.8  2.2 
12  36, 37  Furniture and other manufacturing  338  2.2  1.0  2.7 
Given these striking differences between firms with regard to their energy cost shares, we aim to analyze factor substitution possibilities between input factors taking into account different levels of energy needs in the firms’ production processes. Higher energy prices will hit the companies which have high energy shares hardest. However, firms that can easily substitute energy using other production factors are able to mitigate the effects of rising energy prices to a greater extent. One strategy that comes to mind to analyze these possible differences is to split the sample into subsets according to the average energy cost share of the predetermined industry sectors as shown in Table 1. As it turns out, however, the heterogeneity within these sectors regarding the energy cost share is large and at the same time, the heterogeneity between the sectors is relatively small: As the last three columns of the table show, sectors do not differ much regarding the average energy cost share, and in each sector, there are firms with high and with low energy cost shares^{10}. Hence, we cannot follow this strategy in our analysis^{11}.
Mean factor shares of firm subsets
Energy use  All  Low  Medium  High 

Mean capital share  21.4  22.6  20.2  21.5 
Mean labor share  35.5  34.1  36.1  36.3 
Mean energy share  2.0  0.6  1.4  4.0 
Mean material share  41.0  42.7  42.2  38.2 
Observations  7396  2462  2461  2473 
Specification tests and model selection Before discussing the main results using the three subsets and the full sample, we perform different statistical tests in order to motivate our modeling strategy and make sure that important requirements are met. We first check whether the CobbDouglas function would be sufficient to fit the production process of Swiss manufacturing firms. This production function assumes the absence of crosssubstitution possibilities between factors. Tests for the hypothesis that crosssubstitution possibilities can be disregarded and the CobbDouglas function is adequate are rejected for our three subsets^{13}. Thus, we do need the more complex LL or TL models to map the production processes in Swiss manufacturing.
Second, we test whether the cost function is concave at the sample means and at each observation when using the LL or TL model because the concavity condition is not globally satisfied. Concavity violations may indicate a misspecification of the underlying production model and result in biased elasticity estimates (Diewert and Wales 1987). Table 12 in the “Appendix” section displays the eigenvalues of the Hessian matrix at the sample means and the percentage of observations that satisfy concavity for both modeling approaches, all four samples and different parametrizations of the model^{14}. The table indicates that concavity at the sample means is satisfied for all specifications of the LL model and most specifications of the TL model, since all eigenvalues are negative semidefinite. Checking the percentage of concave observations, we find more diverse results. The specification we will use in the empirical analysis for each modeling approach and each of the four samples is shaded in gray: Using the LL model, 100% of the concavity restrictions are met for the full sample as well as the low and medium energyuse subsets. For the high energyuse subset, 90% of all concavity restrictions are met. The TL model achieves 96.5% in the high energyuse sample and hence performs slightly better than the LL model^{15}. Using the other three samples, however, the TL model performs slightly worse than the LL model. Considering the good performance of both modeling approaches with respect to concavity, we present the results from both specifications in the next section.
Main results
In the following, we present the OPEs and CPEs using the LL and the TL modeling approaches. As the elasticity estimates under the two models are in most cases close to each other but the standard errors are usually lower in the LL model, we focus on the LL results in the following discussion and refer to the “Sensitivity of the results” section for a comparison of the results of the two functional specifications. The estimated parameter values from the systems of equations used to derive the elasticities are displayed in Table 13 in the “Appendix” section.
In our description of the results, we focus on the firms’ reaction upon an energy price change. Remember that, by definition, the estimated elasticities describe firms’ optimal adjustments to their production processes under the assumption of constant output quantity. If increased energy prices lead to a decrease in energy use in the production process, one or more of the other factors have to increase to hold the outputs of firms at a constant level. Hence, by construction there will always be at least one of the other factors that is substitutable with energy. The other two factors are substitutes or complements visavis the factor energy.
Ownprice elasticities from the full sample

Crossprice elasticities from the full sample

Ownprice elasticities from the low energyuse firm sample

Crossprice elasticities from the low energyuse firm sample

Medium energyuse firm sample
Ownprice elasticities from the medium energyuse firm sample

Crossprice elasticities from the medium energyuse firm sample

Ownprice elasticities from the high energyuse firm sample

Crossprice elasticities from the high energyuse firm sample

Most CPEs estimated from the high energyuse subset are similar to those shown for firms with low and medium energy use. One exception is the factor pair energy and capital. These input factors are estimated as being complements instead of substitutes in the production process of energyintensive firms (η_{KE}=− 0.09,η_{EK}=− 0.59). The respective elasticities are significantly different from zero at the 10% level using the LL specification (not significant using the TL specification; see the “Sensitivity of the results” and “Sensitivity of the results” sections for a further analysis). If the price of capital increases by 1%, firms reduce the amount of energy by 0.59%. Also, an energy price increase of one percent leads to a decrease in the amount of capital of 0.09%. The magnitude of this effect is about four to five times higher than in the other two subsets and the full sample. Given the still relatively low mean energy cost share of 4.0%, this magnitude is considerable^{16}. Before interpreting the results and formulating policy implications, we perform a sensitivity analysis in the next section, focusing mainly on the complementarity between energy and capital for energyintensive firms, i.e., on the complementarity result.
Sensitivity of the results
A few estimates marked in the figure are worth discussing. First, the negative CPEs between capital and energy in the high energyuse subsets, \(\eta _{EK}^{H}\) and \(\eta _{KE}^{H}\), are of similar magnitude. Second, there are three estimates with opposite signs, namely \(\eta _{EK}^{F}\), \(\eta _{KE}^{F}\), and \(\eta _{EL}^{M}\). However, these estimates are accompanied by large standard errors and are not significantly different from zero under both modeling approaches. Third, we observe that the elasticity estimates using the full sample (depicted as circles) possess less variation than the three subsets—especially regarding the energy elasticities, for example \(\eta _{EK}^{H}\), \(\eta _{KE}^{H}\), \(\eta _{EM}^{H}\), and \(\eta _{EK}^{L}\). This is a first indication that estimating elasticities using data on very heterogeneous firms “averages out” adjustment behavior of the firms at the margin of the distribution. The most striking example of this “averaging out” result is the relationship between the production factors energy and capital: In the low energyuse subset, we find substitutability between the factors energy and capital at the 1% level of significance, and in the high energyuse subset complementarity at the 10% level. Using all firms for the estimation, the relationship becomes insignificant.
The similar results from the LL and the TL models are a first robustness check of the complementarity result: As mentioned, for example, by Considine and Mount (1984) and Arnberg and Bjorner (2007), heterogeneity of the observations regarding the factor shares can be an issue especially when estimating using a translog function. In our case, this does not seem to be a problem.
While the point estimates between the LL and the TL specifications are of similar magnitude, we find that the LL estimates are—as tvalues are higher on average—more precise than the TL counterparts. An inspection of Tables 4, 6, 8, and 10 shows that under the LL specification, a higher percentage of elasticities are estimated to be significantly different from zero. At the significance level of 10%, for example, 83% of all CPEs are significant both in the full sample (TL 75%) and in the low energyuse subset (TL 50%), while 50% in the medium energyuse subset (TL 50%) and 100% in the high energyuse subset (TL 50%). Since both models satisfy concavity restrictions well, we prefer the LL estimates due to the higher precision.
Complementarityconcavity tradeoff In this section, we test whether our finding of complementarity between capital and energy in the production process of energyintensive firms depends on our definition of the high energyuse subset. Specifically, we gradually exclude the least energyintensive firms from the sample and reestimate the two production models with the remaining firms.
Exploring the complementarity result between energy and capital

Excluding the least energyintensive firms and thus reducing the observations available for the estimation comes at a cost: The percentage of observations for which the concavity restriction is satisfied drops gradually, and in some specifications the concavity restriction is not satisfied even at the sample means. Especially in the last two specifications of the LL model (15 and 10%) and the last specification of the TL model (10%), there is ample evidence for model misspecification.
Another interesting observation is revealed by considering the mean factor cost shares. They indicate that the share of capital increases from 21.6 to 24.2% when we exclude the less energyintensive firms from the high energyuse subset. The production of highly energyintensive firms tends to be more capitalintensive and less labor and materialintensive. This link between capital and energy in the production process may be the underlying reason for the complementarity that we find in our analysis.
Complementarity and subset allocation As described in the “Data description and model selection” section, we allocate firms to the three subsets by their mean energy cost share. The energy cost share is endogenous to our modeling approach. It would be preferable to split the firm sample by applying a truly exogenous variable to prevent any endogeneity issues. As argued before, given the available data as well as other restrictions, we are not able to use a completely predetermined variable to split our sample and at the same time analyze substitution possibilities of firms with different energy intensity in their production processes. In this section, we examine the sensitivity of our results using different approaches of sample splitting.
We allocate firms to subsets depending on their energy cost share in the first year we observe them^{17}. The energy cost share for the first year is not completely exogenous to the analysis, since firms’ previous decisions may also play a role in their subsequent behavior. However, the energy cost share for the first year may be seen as being more predetermined to the analysis than in subsequent years. Results are close to those in the original specification. Specifically, η_{ KE } of the high energyuse subset changes from − 0.093 to − 0.098 (TL: − 0.086 to − 0.088) and η_{ EK } from − 0.587 to − 0.628 (TL: − 0.474 to − 0.493), both still being statistically significant at the 10% level (TL: still insignificant). Repeating the exercise performed in the “Sensitivity of the results” section, i.e., gradually excluding the least energyintensive firms from the high energyuse subset, again strengthens the complementarity result: Using the top 20% of energyintensive firms, η_{ KE } increases to − 0.207, η_{ EK } to − 1.034, now statistically significant at the 5% level (TL: − 0.175; − 0.765, now statistically significant at the 10% level). A very similar result is attained if the firms’ last year’s energy cost share is used^{18}. Our interpretation of this sensitivity analysis is that the complementarity result is robust and does not depend on the specifics of the subset allocation mechanism.
Interpretation of the complementarity result
Energyintensive firms react to an energy price increase of one percent by reducing energy use by 1.03%. At the same time, capital use decreases by 0.09%. This adjustment in capital equipment is substantial, given that the mean capital share of energyintensive firms is more than five times larger than the mean energy share. To hold output constant, these firms increase material and labor use by 0.11 and 0.03%, respectively. Thus, energyintensive firms alter their production processes considerably upon energy price increases. As shown in the “Sensitivity of the results” section, this adjustment process will be more pronounced, the higher the energy intensity of firms and thus the stronger the complementarity between energy and capital inputs^{19}.
The analysis of the exact forces that are behind this adjustment process of energyintensive firms in Switzerland is beyond the scope of our contribution. An example may, however, make the interpretation of our results clearer. It is conceivable that energyintensive firms already produce quite energyefficiently, since energy represents an important cost factor. Investments in innovations and new technologies that may be necessary upon further energy price increases may be difficult or expensive to implement. Consequently, production is becoming more labor and materialintensive as various energy and capitalintensive steps in the production process are replaced. In the context of firms that face international competition, as is common in a small open economy like Switzerland, the energy and capitalintensive steps may be relocated abroad. In the context of Switzerland’s climate policy and thus concentrating on emissions that are an important part of firms’ energy use, these firms may be exposed to the risk of carbon leakage—the reallocation of energyintensive production processes to countries with laxer environmental policies^{20}.
Irrespective of the true underlying causes, complementarity between energy and capital means that divestment will take place upon an energy price increase. The cessation of investment will affect the growth rates of energyintensive industries and the overall economy—especially when it is associated with a weakening in the competitiveness of local firms. This argument is in line with Tovar and Iglesias (2013) who warn of the harmful effects of policies that increase energy prices if there is evidence of complementarity between energy and capital. They recommend that, in such a case, instead of applying pricing policies, policy makers should devise policies that promote innovations within these sectors or support energyefficient technologies. In contrast, pricing policies are advisable if substitutability predominates. Higher energy prices then lead to an increase in other inputs and may also spur investment in energyefficient technologies.
With these results in mind, the present design of Switzerland’s environmental policy is of interest: With 84 Swiss francs per metric ton, a substantial tax on CO_{2} emissions is effective. However, large emitters are exempted from the tax and instead participate in a carbon emission trading system. These firms receive fewer emission certificates compared to their historical usage and thus have to reduce their emissions or purchase further certificates. Additionally, small and medium firms can avoid being taxed by committing to reduction goals. Oberauner (2010) shows in an empirical contribution that energyintensive firms use this possibility and commit to efficiency measures instead of paying the tax more often than other firms. Our result, which is based on data from a period before the current environmental policy was implemented, may indicate one reason for this behavior: Differences in the ease of substitution for the input factor energy induce energyintensive firms to choose a different policy instrument. Given the possible harmful effects of pricing instruments in the presence of complementarity, our results lend support to policies that exempt certain firms from energy taxes being used in combination with efficiency commitments.
Conclusions
This contribution provides an analysis of factor substitution among capital, labor, energy, and material in Swiss manufacturing using micro panel data at the firm level from 1997 to 2008. We focus on examining the relationship between factor substitutability and the energy intensity of manufacturing firms in Switzerland. To this end, firms are divided into three subsets according to their energy intensity. We find that substitutability between the considered input factors prevails most of the time and that differences between the subsets are not substantial. One notable exception, however, is the complementarity between energy and capital inputs that we find for energyintensive firms. We subject this result to various sensitivity tests and find that it holds under different modeling strategies as well as different definitions of the high energyuse subset. By gradually excluding the least energyintensive firms, we furthermore show that the complementarity result strengthens as the mean energy intensity of the remaining firms increases.
We stress important policy implications, namely that in the presence of complementarity between energy and capital inputs, policy measures to reduce energyuse should not aim at introducing energy price increases. Due to the complementarity, such increases may negatively affect firms’ investment decisions and therefore have harmful effects on the competitiveness of firms and overall economic performance. In view of these problems, the encouragement of technological diffusion or the support of technical innovation may be more promising approaches. However, we stress that these latter policies depend on the specific production processes of the affected firms as well as on the specific implementation of the policies. In order to successfully implement and operate such policies, more information is needed than can be given within the scope of our contribution. The exploration of these alternative possibilities is an area for future research.
In a similar vein, the complementarity result is relevant for CGE models that use elasticity estimates as an important input for forecasting and policy analysis. As CGE models often use combinations of CobbDouglas and constant elasticity of substitution (CES) production functions, the degree of complementarity that these modeling approaches can account for is naturally restricted. Results from CGE models may therefore be biased for certain energyintensive firm clusters or industries, and an evaluation of energy pricing policies using these models may be unduly positive.
In the light of existing policy regimes, our results back policies that exempt certain firms from energy or emissions taxes and instead require them to adopt efficiency measures. A possible implementation of a carbon tax which satisfies these requirements can be found in Switzerland: The Swiss system gives most firms the opportunity to evade the GHG emissions tax and instead commit to legally binding CO_{2} reduction goals or participate in a cap and trade system. There is first evidence which confirms that primarily energyintensive firms make use of this opportunity. Hence, it may be the case that such a flexible system prevents the mentioned possible harmful effects of pricing policies in Switzerland. Moreover, this approach might provide firms with incentives to innovate and reduce emissions, which has been empirically questioned for current policy instruments such as temporary compensation schemes (Antimiani et al. 2016). A flexible system of this kind may also be eligible for other countries. That said, more research is certainly required to identify and analyze the specific mechanisms that are at work. Here, the principle research questions that need to be established are whether a policy that permits exceptions from an emissions tax will suffice to attain reduction targets, to what extent carbon leakage can be prevented, and how energyintensive firms perform in international competition under such a policy regime.
Appendix
Concavity in the translog and the linear logit model

Estimated parameter values from the systems of equations
Cost function  Linear logit  Translog  

Energyuse  All  Low  Medium  High  All  Low  Medium  High 
β _{kk}  \(\underset {(1.0271)}{1.5323}^{}\)  \(\underset {(1.40383)}{\thinspace 0.3261}\)  \(\underset {(1.37144)}{\thinspace 2.8252}^{**}\)  \(\underset {(1.89095)}{\thinspace 1.4632}^{}\)  \(\underset {(0.0253)}{\thinspace 0.0469}^{*}\)  \(\underset {(0.04405)}{\thinspace 0.0146}^{}\)  \(\underset {(0.03973)}{\thinspace 0.0859}^{**}\)  \(\underset {(0.04697)}{\thinspace 0.0325}^{}\) 
β _{kl}  \(\underset {(0.1451)}{0.0361}^{}\)  \(\underset {(0.22205)}{\thinspace 0.1439}^{}\)  \(\underset {(0.24317)}{\thinspace 0.1153}^{}\)  \(\underset {(0.28905)}{ 0.4746}^{*}\)  \(\underset {(0.009)}{0.0144}^{}\)  \(\underset {(0.01667)}{ 0.0115}^{}\)  \(\underset {(0.01671)}{\thinspace 0.0062}^{}\)  \(\underset {(0.02104)}{ 0.0510}^{**}\) 
β _{ke}  \(\underset {(0.9812)}{\thinspace 0.1921}^{}\)  \(\underset {(1.30739)}{ 2.6823}^{**}\)  \(\underset {(1.26284)}{ 0.7123}^{}\)  \(\underset {(1.8406)}{4.1125}^{**}\)  \(\underset {(0.0064)}{\thinspace 0.006}^{}\)  \(\underset {(0.00446)}{ 0.0054}^{}\)  \(\underset {(0.00428)}{ 0.0005}^{}\)  \(\underset {(0.01588)}{\thinspace 0.0278}^{*}\) 
β _{km}  \(\underset {(0.3294)}{0.7777}^{**}\)  \(\underset {(0.53995)}{ 0.2512}^{}\)  \(\underset {(0.4757)}{ 1.4241}^{***}\)  \(\underset {(0.76975)}{ 0.7326}^{}\)  \(\underset {(0.0310)}{0.0385}^{}\)  \(\underset {(0.05161)}{\thinspace 0.0023}^{}\)  \(\underset {(0.04804)}{ 0.0916}^{*}\)  \(\underset {(0.06072)}{ 0.0093}^{}\) 
β _{ll}  \(\underset {(0.2293)}{0.1659}^{}\)  \(\underset {(0.34239)}{\thinspace 0.0876}^{}\)  \(\underset {(0.3597)}{ 0.3397}^{}\)  \(\underset {(0.46448)}{ 0.2412}^{}\)  \(\underset {(0.011)}{0.0129}^{}\)  \(\underset {(0.0183)}{\thinspace 0.0355}^{*}\)  \(\underset {(0.01913)}{ 0.0499}^{***}\)  \(\underset {(0.01845)}{ 0.0209}^{}\) 
β _{le}  \(\underset {(0.2302)}{\thinspace 0.4714}^{**}\)  \(\underset {(0.34582)}{\thinspace 0.3215}^{}\)  \(\underset {(0.35269)}{\thinspace 0.8072}^{**}\)  \(\underset {(0.4639)}{ 0.0108}^{}\)  \(\underset {(0.0021)}{0018}^{}\)  \(\underset {(0.00096)}{\thinspace 0.0019}^{*}\)  \(\underset {(0.00174)}{\thinspace 0.0057}^{***}\)  \(\underset {(0.00629)}{ 0.0072}^{}\) 
β _{lm}  \(\underset {(0.1030)}{\thinspace 0.1507}^{}\)  \(\underset {(0.1605)}{ 0.1518}^{}\)  \(\underset {(0.16274)}{\thinspace 0.2123}^{}\)  \(\underset {(0.20774)}{\thinspace 0.5160}^{**}\)  \(\underset {(0.0161)}{\thinspace 0.0253}^{}\)  \(\underset {(0.02718)}{ 0.0259}^{}\)  \(\underset {(0.02806)}{\thinspace 0.0380}^{}\)  \(\underset {(0.03152)}{\thinspace 0.0791}^{**}\) 
β _{ee}  \(\underset {(0.8534)}{1.8319}^{**}\)  \(\underset {(1.12522)}{25.0307}^{***}\)  \(\underset {(1.09236)}{ 13.6234}^{***}\)  \(\underset {(1.52994)}{\thinspace 1.8234}^{}\)  \(\underset {(0.0054)}{0.0019}^{}\)  \(\underset {(0.00268)}{ 0.0001}^{}\)  \(\underset {(0.00362)}{ 0.0077}^{**}\)  \(\underset {(0.01391)}{\thinspace 0.0071}^{}\) 
β _{em}  \(\underset {(0.4231)}{0.0528}^{}\)  \(\underset {(0.6342)}{\thinspace 1.0517}^{*}\)  \(\underset {(0.53985)}{\thinspace 0.7720}^{}\)  \(\underset {(0.95967)}{ 2.5192}^{***}\)  \(\underset {(0.011)}{0.0059}^{}\)  \(\underset {(0.00699)}{\thinspace 0.0036}^{}\)  \(\underset {(0.00775)}{\thinspace 0.0026}^{}\)  \(\underset {(0.02741)}{ 0.0277}^{}\) 
β _{mm}  \(\underset {(0.5460)}{\thinspace 0.2741}^{}\)  \(\underset {(0.85543)}{\thinspace 0.2413}^{}\)  \(\underset {(0.74858)}{\thinspace 0.4695}^{}\)  \(\underset {(1.2455)}{\thinspace 0.1279}^{}\)  \(\underset {(0.0367)}{\thinspace 0.0188}^{}\)  \(\underset {(0.05867)}{\thinspace 0.0200}^{}\)  \(\underset {(0.05643)}{\thinspace 0.0511}^{}\)  \(\underset {(0.07306)}{ 0.0421}^{}\) 
linear trend  \(\underset {(0.0026)}{\thinspace 0.0087}^{***}\)  \(\underset {(0.00536)}{\thinspace 0.0136}^{**}\)  \(\underset {(1e04)}{\thinspace 0.0004}^{***}\)  \(\underset {(0.00417)}{\thinspace 0.0109}^{***}\)  
quadratic trend  \(\underset {(1e05)}{ 3e05}^{***}\)  
β _{ Ky }  \(\underset {(0.0200)}{\thinspace 0.0912}^{***}\)  \(\underset {(0.0407)}{ 0.0010}^{}\)  \(\underset {(0.02987)}{\thinspace 0.1820}^{***}\)  \(\underset {(0.03257)}{\thinspace 0.0660}^{** }\)  \(\underset {(0.0019)}{0.0122}^{***}\)  \(\underset {(0.00299)}{ 0.0175}^{***}\)  \(\underset {(0.00317)}{ 0.0028}^{}\)  \(\underset {(0.00334)}{ 0.0182}^{***}\) 
β _{ Ly }  \(\underset {(0.0159)}{\thinspace 0.3492}^{***}\)  \(\underset {(0.03541)}{\thinspace 0.3025}^{***}\)  \(\underset {(0.02483)}{\thinspace 0.3755}^{***}\)  \(\underset {(0.02521)}{\thinspace 0.3589}^{***}\)  \(\underset {(0.0019)}{\thinspace 0.0610}^{***}\)  \(\underset {(0.00382)}{\thinspace 0.0550}^{***}\)  \(\underset {(0.00369)}{\thinspace 0.0629}^{***}\)  \(\underset {(0.00327)}{\thinspace 0.0635}^{***}\) 
β _{ Ey }  \(\underset {(0.0224)}{\thinspace 0.2394}^{***}\)  \(\underset {(0.04123)}{\thinspace 0.2746}^{***}\)  \(\underset {(0.02563)}{\thinspace 0.2315}^{***}\)  \(\underset {(0.04538)}{\thinspace 0.2133}^{***}\)  \(\underset {(0.0004)}{\thinspace 0.0004}^{}\)  \(\underset {(0.00021)}{\thinspace 0.001}^{***}\)  \(\underset {(0.00027)}{\thinspace 0.0005}^{*}\)  \(\underset {(0.00116)}{ 0.0002}^{}\) 
N  7396  2462  2461  2473  7396  2462  2461  2473 
See OECD (2015) for an indepth analysis of energy policies in OECD countries and Ekins and Speck (2011) on environmental tax reforms in Europe.
For Switzerland, substitution elasticities have been estimated on a sectoral level (Mohler and Mueller 2012).
An exception is Berndt and Christensen (1973) who estimate the elasticities directly from the production function.
Morishima elasticities of substitution (MES) represent another way of analyzing substitution possibilities. Since they are less commonly used in the literature, we provide a definition of the MES as well as the resulting elasticity estimates in an online appendix.
The standard errors of the estimated elasticities can be calculated by using the Delta method (see e.g., Greene (2000)).
Only observations of firms stating their energy consumption have been considered. Expenditures on energy are not available by energy carriers. The sample is an unbalanced panel due to firms’ entry, exit, and nonresponse to the survey. The survey was continued after 2008; however, from 2009 onwards, no information on energy costs of firms has been collected.
More precisely, we calculate a chain Laspeyres index where the weights are updated annually by using the expenditure shares of the different energy sources as weights. Sectorspecific expenditure shares were computed by using energy prices and physical quantities (measured in TJ) of the major energy sources (electricity, natural gas, light fuel oil, heavy fuel oil, and coal).
We checked for possible endogeneity issues by applying 3SLS estimations on data from 1998 to 2008, using the oneperiod lagged price series. The results are similar to those of the SUR approach.
Note that Arnberg and Bjorner (2007) exclude material, which leads to a higher energy share. Excluding material in our sample results in a mean energy cost share of 3.5%.
At this level of aggregation, industries are defined very broadly. For example, sector 5 consists of chemical companies with highly energyintensive physical production processes and pharmaceutical companies which mainly carry out less energyintensive research activities.
Also, we cannot use interaction terms depending on the energy intensity of firms or a quantile regression approach, since under translog and linear logit cost functions, elasticities are a function of the estimated betas and the cost shares. These approaches might be suitable using simpler modeling techniques such as the CobbDouglas production function, which, however, is not suitable here as we show in “Data description and model selection” section.
Hence, firms do not change subsets over time. Additional subsetspecific descriptive statistics of the factor cost shares are available in an online appendix.
It is common practice to include a linear or a quadratic trend over time to increase the model fit.
Excluding the few observations that violate concavity, and reestimating the two models does not affect our elasticity estimates.
Given the average energy cost share of 4%, an energy price increase of 1% raises the average firms’ costs by 0.04% before firms undertake any adjustments. A consequential change in the use of the factor capital of 0.09% after this moderate cost increase is substantial.
Remember that an unbalanced panel of firms is used. Hence, the first year of observation might differ for certain firms.
Detailed results are available in an online appendix. The similarity of results is due to the fact that energy cost shares of firms are relatively stable over time and thus most firms would be allocated to the same subset in any year they are observed.
If complementarity is stronger between energy and capital, capital use decreases more sharply following an energy price increase and thus, labor and material have to increase at a higher rate to hold output constant.
See Antimiani et al. (2016) for an assessment of the rate of carbon leakage and negative effects on competitiveness in the EU.
Declarations
Acknowledgements
Valuable suggestions from an anonymous referee are gratefully acknowledged. We further thank Dietmar Maringer, Hannes Weigt, Hermione MillerMoser, and the audience at the IAEE 2013 conference in Düsseldorf for the comments. We also thank the SFOE for the financial support (grant 500616). The views expressed in this paper are those of the authors and do not necessarily reflect those of the SFOE, the Swiss Competition Commission or its Secretariat.
Authors’ contributions
All authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
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References
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