NATIONALEKONOMISKA INSTITUTIONEN Department of Economics
Uppsala University
Bachelor’s Degree Thesis 15 Credits (HP) Subject: Economics
Semester: Autumn 2019 Supervisor: Torsten Santavirta
Authors: Jesper Larsson (950211) & Tobias Ekblom (830301)
The impact of subsidies in the Swedish solar energy market
Uppsala University
Acknowledgement
We would like to express a sincere gratitude to those who made this thesis possible. Firstly, our supervisor Torsten Santavirta, for the continuous support and feedback throughout the work. Lastly, we want to thank Jeffrey Berard at the Swedish Energy Agency for helping us in our research by sharing relevant data.
Tobias Ekblom & Jesper Larsson Uppsala, 18 January 2020
Abstract
Problem - In the light of a world in transition towards sustainability, there is an urge for evaluation of the effect of governmental interference on renewable energy markets. The complexity of doing this, calls for further investigation. This was conducted by examining the Swedish solar cell market.
Approach - The study had a quantitative method approach and was carried out with a sharp discontinuity regression design, in connection to changes of Swedish direct capital subsidy program.
Findings - The results from the study illustrates that the changes in the level of the direct capital subsidy, have affected the demand on the market in short-term. Over time, the Swedish solar cell market have become more mature, which is indicated by a higher price elasticity for private persons.
Further, companies is found to be more sensitive to changes in subsidy than private persons.
Practical implications - A conclusion to the Swedish solar cell market is that a phase out of the direct capital subsidy would have a significant short-term effect. In a long-term perspective, indications are found that the market have become mature enough to keep evolving without the subsidy.
Research contribution - This thesis contributes to the research field of subsidies in renewable energy markets, by reducing the research gap between theory empirical evidence. We are able to decide the effect of an up front direct subsidy, and it would be of value to do the same for other types of subsidies in the future. With respect to additional renewable energy, it is also verified that the direct impact of a subsidy increases as the market becomes more mature. Lastly, the chosen method proved to be successful, and may be used in further studies.
Further research - As stated, this thesis contributes to the empirical work in the complex area of estimating the effects of subsidies, however there is need for further research and development of new methods.
Keywords: Subsidies, Renewable energy, Market maturity, Price elasticity, Solar cells
List of figures & tables
Chapter 2
Figure 2.1 The effect on market price and equilibrium quantity of introducing demand-side subsidies - market 1.
Figure 2.2 The effect on market price and equilibrium quantity of introducing demand-side subsidies - market 2.
Figure 2.3 S-shaped growth model
Figure 2.4 Illustration of commodity maturity from being inelastic to elastic.
Chapter 3
Figure 3.1 Price trend of solar cell module prices on the swedish solar cell market.
Chapter 4
Figure 4.1 Illustration of operationalization.
Figure 4.2 The principle of a discontinuity regression.
Table 4.1 The two investigated changes due to the compensation level in the direct capital subsidy program.
Table 4.2 Descriptive statistics for the time period 1 July 2014 to 30 June 2015.
Table 4.3 Descriptive statistics for the time period 1 July 2017 to 30 June 2018.
Chapter 5
Figure 5.1 Subsidy level change from 35% to 20% made 2015-01-01: Private persons.
Figure 5.2 Subsidy level change from 35% to 30% made 2015-01-01: Companies.
Figure 5.3 Subsidy level change from 20% to 30% made 2018-01-01: Private persons.
Figure 5.4 Subsidy level at 30% not changed 2018-01-01: Companies.
Table 5.1 Sharp discontinuity regression of policy change made 2015-01-01 on installation of solar cells in kW for private persons and companies.
Table 5.2 Sharp discontinuity regression of policy change made 2018-01-01 on installation of solar cells in kW for private persons and companies.
Appendix
Table A Incentives in the Swedish solar cell market.
Table B Changes made in the level of the direct capital subsidy.
Table of contents
1. Introduction 1
2. Theory 3
2.1 Literature review - Externalities, subsidies & the solar cell market 3
2.2 Theoretical framework 6
3. The experience of the Swedish solar cell market 10
4. Method 13
4.1 Methodology 13
4.1.1 Research approach 13
4.1.2 Operationalization 14
4.2 Data 15
4.2.1 Data collection 15
4.2.2 Dependent variable 15
4.2.3 Independent variable 15
4.2.3 Descriptive statistics 17
4.2.2 Weaknesses and limitations of the data 18
4.3 Empirical Methods 19
5. Results 21
5.1 Result for subsidy changes made 2015-01-01 21
5.2 Result of subsidy change made 2018-01-01 24
6. Analysis and findings 27
7. Conclusion 30
7.1 Discussion 30
7.2 Summary 32
8. Reference list 34
Appendix A - Economic conditions on the Swedish solar market 38
Appendix B 44
1. Introduction
In Sweden today, the will and the demand by the Swedish people is now shifting towards a more sustainable lifestyle. This change is not only social and economic but also environmental. The Swedish parliament adopted in 2017 a strategy framework for climate and energy policy. This included new climate goals, a climate law and a board for climate political issues. The intended goal is that Sweden no later than 2045 aims to be a zero net polluter of greenhouse gas emissions to the atmosphere, and thereafter becoming a negative nett polluter. Compared to the level of 1990, the 2045 level should decrease with 85%. (SOU 2017:2, “Sveriges energi- och klimatmål”; Swedish Energy Agency, 2018a). If achieving this goal, it will cause a major change in the Swedish electrical grid, where the share of non-renewable electricity production in 2017 was nearly 43 percent, where nuclear power contributed with 40 percent and energy from fossil fuels for nearly 3 percent (Swedish Energy Agency, 2018a). Noteworthy, solar cells only contributed with approximately 0.1 percent of the total Swedish electricity production in 2017 (Swedish Energy Agency, 2018a).
As a result of this there is a direct capital subsidy program in place, in order to increase the use of solar cells. Evaluations indicates that it has had a big impact on the growth of the Swedish solar cell market. The market shows sign of becoming more mature, and therefore, some of the key players on the market now advocates that the subsidy should be phased out. Whether it should be abolished or not is also a matter of political debate (Ny teknik, 2018). Because of this, it is of interest to investigate how the subsidy affects the market, and how this change through different stages of market maturity.
This is of interest for regulators, in order to compare the perceived benefits with solar cells with the costs of the subsidies that is funded by the taxpayers.
Prior research argues that the use of solar cell can give positive externalities, because of its function, by replacing fossil energy sources seen as negative externalities. This means that governmental interference on the market can be motivated, bringing the equilibrium quantity closer to the social optimal point. This can be done with a subsidy, which will increase the demand of the desired renewable energy source and promote technological development. In the long run, this can be a part of shifting from non-renewable to renewable energy sources. According to the opinion of some researches the governmental interference should end, once the development of the market has taken the desired direction. Thereafter, it proposed to be ended, since it is considered mature enough to work as an ordinary market. (Gruber, 2013; Nordhaus, 2010; Gillingham & Sweeney, 2010; Acemoglu et al., 2012)
However, research shows that it is difficult to estimate the impact of an intervention. This could be a major reason to the difficulties for regulators to decide when and in what pace to phase out an intervention from the market. Further, some researchers claim that governmental interference on the solar cell markets, in general, is disproportional in relation to their benefit, and therefore recommends less intervention. Also, there are different views when choosing which method to use to combat externalities. While some claim that taxes and regulations are the only needed tool, others argues that subsidies in many cases are justified as a complement. When it comes the use of subsidies, there are claims that a up front cash subsidy is more efficient than a subsidy in a form of a tax-deduction.
(Goulder and Mathai, 2000; Benthem et al., 2008; Branker & Pearce, 2010; Matisoff and Johnson, 2017; Gerarden, 2018)
As mentioned, much of the uncertainties regarding renewable energy incentives are linked to problems with estimating their impact. Whereas the knowledge in a theoretical perspective is comprehensive, it lacks in empirical evidence. A major work remains of testing the theory by empirical studies of existing markets. Therefore, this thesis aims to reduce the gap between theory and application. Consequently, our research question is formulated as follows:
What effect do economic subsidies have on emerging markets for sustainable energy sources?
There are reasons to believe that the use of a subsidy will increase the size of a market for sustainable energy sources. Moreover, it is assumed that this quantitative effect will depend on the maturity of the market and differ between actors on the market. Applied to the Swedish market, this result in the following hypothesis:
What effect does the direct capital subsidy program have on the amount of installed solar cells on the Swedish market? Does this effect depend of the maturity on the market and does it differ between actors?
In order to enable our research, secondary data on the direct capital subsidy was collected from the Swedish Energy Agency. To investigate the effect of the subsidy on the installation of solar cells, the changes in the level of the subsidy that was made 1 January 2015 and 1 January 2018 was used. This by applying a sharp discontinuity regression design. By analysing the results of the regressions, we are able to, answer our hypothesis. Our findings will then be discussed in relation to our research question, as a way to contribute to the research gap and promote future studies.
2. Theory
2.1 Literature review - Externalities, subsidies & the solar cell market
When it comes to governmental interference on energy markets, the concept of externalities is central.
An externality occurs whenever the actions of one party makes another party worse or better off, while the first party neither bears the cost, nor receives the benefits of doing so. According to externality theory, an externality can be either positive or negative and caused through production or consumption. Meaning, that there can be a case of 1. underproduction, 2. overproduction , 3.
underconsumption or 4. overconsumption of a good or service. In our case, the focus will be on a positive consumption/production externality, that is associated with the market. It occurs when a consumer's consumption increases the well-being of others but the consumer is not compensated by those others. This could be seen as a type of free rider problem, where actors will underinvest since investment has a personal cost but a common benefit. Applied to the case of solar cells, it means that investors in solar cells, such as private persons and companies, bears a private cost, without being compensated by other people that gains the benefit of renewable energy production. (Gruber, 2013)
A subsidy can be described as a government payment to an individual or a company that lowers the cost of consumption or production. Meaning, that a subsidy would make a consumer to consume more compared to without payment, and increase the quantity on the market of that commodity or service.
This by reimbursing consumption on a market that has underconsumption, causing the externality to become internalized through a shift in the market between alternatives. However, a subsidy does not always need to be used to support positive externalities, but could also be used as a way to create alternatives to reduce negative externalities. For example, subsidizing alternatives of energy such as solar power to the negative externality-producing activity such as fossil fuels. (Nordhaus, 2010)
According to Gerarden (2018) consumer subsidies have two major effects. The first is that subsidies shift out demand and increase equilibrium quantities while holding production costs fixed. The second effect is that subsidies could give companies incentive to innovate and invest in their own production, and therefore reduce their costs and increase profits over time in the product market. Gillingham &
Sweeney (2010) argue that the socially optimal rate of transition from fossil energy to renewable energy can be achieved as a result of decentralized market decisions. With policy goals such as economic efficiency, policy actions can therefore be based on the deviations from perfectly
competitive markets, since it can be used as a benchmark. But also, under the condition that the cost of implementing the policy is less than the benefits from correcting the deviation. Gillingham &
Sweeney (2010)
Acemoglu et al. (2012) concluded that without government intervention, a change towards more sustainable technologies is unlikely, due to the initial cost benefits of old technologies. This is avoidable through the application of different policies, that only need to be in place temporary. Once the technology development is redirected, further governmental intervention is not needed. Acemoglu et al. (2016) discusses energy markets with several competing production techniques and note that producers do not only chose which technology to use, but also in which technology to make an effort in research. For a technology that currently is far less developed, incremental research improvements will not be profitable, since they still are far behind the currently more developed ones. They conclude, that if research development can be supported through subsidies for a certain time, also research in clean technologies eventually becomes self-sustainable. (Acemoglu et al., 2016)
Also, Lööf et al. (2018) in their comprehensive study underlines that incentives to solar technology and own-knowledge stocks have strong and significant positive effects on solar innovations, because of the initially lower marginal costs for already established power production sources. In addition, Timilsina et al. (2011) argue that solar energy, due to both technological improvements resulting in cost reductions, and government policies supportive of renewable energy development, have had a phenomenal growth. Timilsina et al. (2011) continuous and claims that solar energy, benefits from fiscal and regulatory incentives, for example tax credits and feed-in-tariff.
However, Gillingham & Sweeney (2010) like most in their research field, claims that taxes and permits in general are the best solutions to tackle environmental external damages, and subsidies as the second best approach. Mainly because consumers will be motivated to shift their purchases away from damaging goods and services and towards those that are environmentally better. In addition, Lipton & Krauss (2011), argues that subsidization may be much riskier compared to taxation, since subsidizing unknown alternatives may or may not provide a plausible long-run substitute. This since subsidies require government to raise revenues rather than provide revenues. As you raise the government revenue through taxes in general, you will likely reduce economic efficiency (Lipton &
Krauss, 2011).
In contrast, Matisoff and Johnson (2017) illustrates that tax credits may be an inefficient way to finance solar cells due to the large capital costs of solar cells. Cash incentives seemed to be more
effective than a subsidy in the form of a tax-deduction, and the policy tools should therefore focus on the upfront capital costs in a way to be more effective. In conclusion, it is not always easy to know which policy to use and to what degree, when trying to solve an externality. What is indicated by theory and evidence is that multiple market failures often need multiple interventions, where specific intervention matches the specific failure. (Aldy et al., 2009; Goulder and Schneider, 1999).
Several authors (Goulder and Mathai, 2000; Benthem et al., 2008) claims that many solar incentives are above the level justified by the static environmental benefits of adoption. Different considerations such as technical innovation and efficiency learning-by-doing may justify these subsidies in theory, but Gerarden (2018) argues that there is limited empirical evidence to assess and guide the proper intervention policy. This because of the difficulty to assess the correct economical value of investments in solar cells due to uncertainty of all multiple factors (Branker & Pearce, 2010).
Further on, it is stated that decentralized government intervention nationally in a global market is inefficient. Because a subsidy in one country increases long-run solar adoption in other non-equally subsidised countries due to increased investments in innovation by international companies. This spillover of improved technology by international companies illustrates how countries need to coordinate their solar PV support internationally to get the effect that is intended from the specific subsidy, and also to address climate change. (Gerarden, 2018)
2.2 Theoretical framework
In figure 2.1, the effect of introducing a subsidy is illustrated. In the unregulated market, a market price (P*) makes the production (S-curve) and consumption (D-curve) of a good to meet, resulting in the market equilibrium quantity (Q*). If this level of production and consumption is undesirably low, a way to increase the production is to introduce a subsidy to consumers of the good. One such reason could, as earlier discussed, be the presence of positive externalities. A pigouvian subsidy would in this context be a subsidy that equaled the external marginal benefit of consumption. This would make the demand curve shift (D+Subsidy) outwards, representing higher buying power of the consumers. Since the outwards shifted demand curve equals the social demand curve, the subsidized market price (PS) and the corresponding equilibrium quantity (QS) represents a social optimal level. (Austan et al, 2013).
Figure 2.1. The effect on market price and equilibrium quantity of introducing demand-side subsidies. The demand curve is denoted by D, and the supply curve with S.
As seen in Figure 2.1, the introduction of a subsidy results in a wedge between the price paid by consumers (PC) and the payment received by the producers (P S). Put in other words, producers pay a price (PC) and the government is obligated to pay the difference from what the producers receive (PS-PC). The total governmental expenditure is thus given as (P S-PC)QS , whereof (PS-P*)QS is the extra surplus by the subsidy for the producers, and (P*-PC)QS is the extra surplus by the subsidy for the consumers. By this it is clearly seen that a demand-side subsidy does not only benefit the consumers, but also the producers. As a matter of fact, the incidence of a subsidy is independent of whether it technically is directed towards consumers or producers (Austan et al., 2013)
In Figure 2.2. is another example showing the introduction of a subsidy on a free market. The pedagogical point is to illustrate the importance of the functional form of the supply and demand curves, especially with respect to the relative price elasticity between the two, for telling the price- and quantitative equilibrium effect of introducing a subsidy. Price elasticity less than -1 is perceived as elastic. Price elasticity equal to -1 is perceived as unit elastic. Price elasticity between -1 up to 0 is perceived as inelastic. (Austan et al., 2013) The midpoint method for calculating price elasticity of demand is defined as ED = Q + QQ − Q1 2 / , hence it compares the percent change in equilibrium
1 2 P + P1 2 P − P1 2
quantity with the percent change in market price. With the midpoint method for calculating price elasticity you get the same elasticity between two price points regardless if it is a price increase or decrease. (Allen & Lerner, 1934)
Figure 2.2. The effect on market price and equilibrium quantity of introducing demand-side subsidies. The demand curve is denoted by D, and the supply curve with S.
The introduction of a subsidy in Market 2, displayed in Figure 2.2, bears the exact same notations as Market 1, displayed in Figure 2.1. The mechanism in work is also the same, however the outcome differs significantly. In Market 2, compared to Market 1, the elasticity of supply is higher in relation to the elasticity of demand. As a result, the major price fall and welfare gain accrues to the consumers.
This illustrates the importance of relative elasticity between demand and supply, since the more elastic one of the two get a smaller share of the governmental payouts. Another notation is the difference in response of market quantity equilibrium. Given a certain level of subsidy, the market with higher demand and/or supply elasticity will respond with a higher quantitative increase of the consumption of
the good in the market. As explained by Austan et al. (2013), the supply curve in a market with perfectly competitive market, the supply curve is perfectly elastic meaning it can be represented by a horizontal line. (Austan et al., 2013) With a horizontal supply curve, the market price will not be affected by the subsidy. This means the price fall in the perspective of a consumers, is equal to the size of the subsidy. This is a vital assumption when we calculate price elasticity of demand, since we assume that the price change for the consumers on the market equals the introduced subsidy.
In regard to the solar cell market, it has been expected to grow in different speeds through different stages. These stages include its development from a relatively small market with small scale and off grid applications like satellites and telecom to a larger market with large scale and on grid applications like solar home systems and centralised solar cell parks. The large scale applications will take place as the market become more economically viable. By this an exponential growth of the annual market size have been expected, until it reaches the largest scale applications like centralised solar parks.
Thereafter, the growth rate will decline, creating an s-shaped form of the curve for market size, as seen in Figure 2.3. Although confirming these predictions by showing increasing growth, the market has not developed in a steady and orderly manner over the years. This is due do market barriers that adds to the inelasticity of demand for solar cells by increasing costs, which slow down the growth rate of the market. As a way to handle these market barriers and other market distortions, interventions are justified, with the aim to make solar cells more competitive compared to other energy sources. (Oliver
& Jackson, 1999)
Figure 2.3. S-shaped growth model. A hypothetical illustration of the growth of the solar cell market (Oliver & Jackson, 1999)
As already stated, the solar cell market is characterised by an expansion from niche-markets of small lights on buoys to solar cell parks. Some of these markets are economically functioning while other need external assistance, with the aim to become cost effective in the long term and reach mass production. Cost decreases in the solar market will lead to larger market size, which in turn leads to increased production scales resulting in lower production costs. This spiral assumes to continue to the point where solar cells are competitive in regard to other established energy sources on the market.
(Oliver & Jackson, 1999)
Figure 2.4. Illustration of commodity maturity from being inelastic to elastic (Oliver & Jackson, 1999).
The conceptual idea on how demand side price elasticity changes, as the solar cell market evolves through different stages, is displayed in Figure 2.4, referring to Figge & Butz (1998). In the stage of a niche market with small scale applications, the demand for solar cells is relatively inelastic. As it evolves through the different stages, reaching larger market segments, the demand for solar cells is expected to become more price elastic. Solar cells will likely become elastic in demand when solar cells are competitive with the cost of electricity from traditional energy sources. Meaning, that as long as solar cells are characterised as a niche market, the demand will be inelastic in response to market prices but will become more elastic in demand as the market becomes more mature. (Oliver &
Jackson, 1999)
3. The experience of the Swedish solar cell market
The industry of solar cell production has increased massively in recent years due to changes in supply and demand conditions. During the period 2010-2015, subsidies increased global adoption of solar cells with additional 49%. (Gerarden, 2018) One of the two most common policy mechanisms globally to increase demand on the market for solar cells is to introduce subsidies to solar cell installations, as in the USA, that provides a tax credit of 30% for solar investment costs. The other common policy is to subsidise the electricity generated from solar cells, as in Germany, Japan, China.
The electricity generated subsidy is given in form of feed-in tariffs, set at the time of investment.
Feed-in tariffs are prices paid for solar electricity fed into the electric grid that are independent of the cost of electricity from alternative sources. (Gerarden, 2018) Another characteristic for the solar cell market are falling prices. In Figure 3.1, the falling price trend on solar modules in Sweden during 2009 to 2018 are displayed, which is closely related to global solar cell prices (NSR, 2018). Palm (2014) concludes that subsidies globally have led to the creation of early markets and learning opportunities which have contributed to the reduced costs.
Figure 3.1. Price trend of solar cell module prices on the Swedish solar cell market (NSR, 2018)
Although subsidies towards solar cells globally has substantially increased the market for solar cell installations, local conditions is important when analysing the Swedish market. A limiting factor has been the few numbers of local actors conducting installations in the Swedish market. (Palm, 2014) However, today there are plenty of incentives for choosing renewable production options producers of
electricity on the Swedish electricity market. Among those is the direct capital subsidy program for solar cells (investeringsstödet), is in place to favour the installation of solar cells. It is a payout to solar electricity producers, which is given as a percentage of the total cost for installation of a solar cell facility. It was first introduced in 2005, by then directed towards public buildings. After the programme was abolished in the beginning of 2009, it was reintroduced 2009-07-01 and has since then been available for all type of producers on the market. (NSR, 2018). The solar cell market can be divided into companies and private persons, where companies received 69 percent of the total subsidy payout since then (Swedish Energy Agency 2018c). However, the number of granted applications was dominated by private persons, accounting for 63 percent. The direct subsidy is described by Palm (2014) as the most important financial support for installation of solar cells in Sweden, although concluding that the expected introduction of a tax reduction also would have a major impact. After the report was written, a tax reduction for micro producers were implemented 1 January 2015 (NSR, 2018).
In a report from consulting firm Ångpanneföreningen (ÅF), made on behalf of the Swedish Energy Agency, it was found that the direct capital subsidy has had a major impact on the installation of solar cells in Sweden (ÅF, 2011). Also, The Royal Swedish Academy of Engineering Science (IVA) describes the subsidy as popular, having contributed to an increase in the interest of solar cells.
Because of other coexisting incentives, in form of tax reduction and complementary green energy support systems, the additional gain of solar cell installations is considered as difficult to determine.
(IVA, 2015)
The formation of the market has transformed from dominated off-grid solar cell systems to a large majority of on-grid systems, where the implementation of the investment subsidy in 2005 has been a driving factor (Palm, 2014). An increasing number of those installations are made by so called prosumers, which means that the owners of solar cells both buys and delivers electric energy to the electric grid, depending on their production and consumption of electricity. (Olkkonen et al., 2017) Palm & Tengvard (2011) found that the main driver for people that had installed small scale solar cells facilities at home was due to environmental concerns. Among the households that had not installed solar cells, the financial aspects were one of the important factors, since it was considered an expensive solution. Given this, Palm (2014) concludes that the majority of solar cell purchasers could be characterised as early adopters. Another notation was that the belief among potential actors was that prices of solar cells was higher than they actually were. (Palm, 2014)
The Swedish Energy Agency (2014; 2016; 2018b) has for several years recommended lower levels of the direct capital subsidy, supported by Palm (2014) which also concludes that the structure of the financial subsidy set a cap on the demand on the Swedish market. The first reason behind the proposed decrease of the subsidy is that they consider other incentives, like the tax-decrease system, to be sufficient enough. The second reason for reducing the level of the direct capital subsidy is to reduce the queue for applicants and enable more actors to get the subsidy. (Swedish Energy Agency 2016) The queue for payment of the subsidy has also created extra administration costs, hampering the market formation. Moreover, the Swedish subsidy system is described as being managed in a
“stop-and-go” manner with no transparent long term plan for phase out, giving large uncertainties in the market, making it difficult for the investors to predict and plan long-term, with a clearly disruptive and negative impact on the Swedish solar cell market. (Palm, 2014)
At several times, the level on the direct capital subsidy has been lowered, primarily due to insufficient funds in the budget (IVA 2015), but also due to the falling prices on the solar cell market (Swedish energy agency 2016). In a report from 2018, the Swedish Energy Agency advocates for a graduate decrease of the subsidy, with 15 percent for all actors from 2019, followed by abolishing it in 2021.
Their point of view (demanding a gradual decrease) is shared by Svensk solenergi (2019), a Swedish solar energy business organisation. (Swedish energy agency 2018b). However, in the beginning of 2018 the government decided to keep its level at 30 percent of investment cost for companies and increase it from 20 to 30 percent of investment cost for private persons. An explanation might be that the legitimacy of using solar cells as an energy source is very high among the public and has probably been a crucial driver for political decisions, and is likely strengthened due to the debate of climate change. (Palm, 2014)
4. Method
4.1 Methodology
4.1.1 Research approach
The methodology used in a study can be understood by the concepts of ontology, epistemology and method, each defining different aspects of the methodology. Methodology is defined as a philosophical and theoretical system that structures the way research is conducted. Slevitch (2011)
The first level is ontology, which is the nature of reality or things that form reality. When it comes to perceiving the reality, this study has an approach of realism, rather than idealism. Meaning that this study extracts information as one objective truth of reality, independent of human perception, in our case by collecting data of the subsidy and the amount of installed solar cells. This in contrast to idealism, where several truths can be constructed in the same context. (Slevitch, 2011)
The second level is epistemology, which describes the approach taken when trying to examine the nature of reality and the scope of knowledge. As such, this study adopted a positivistic view instead of an interpretivist view. This means that the investigator and its examined entities are independent from each other without any possibility to influence or being influenced by each other. The positivist epistemology view also describes that values can be separated from facts. This perspective therefore regard truths as matter of validity and to what degree the data reflects the existing reality. (Slevitch, 2011)
The third level is method, which can be described as a set of tools, applied by procedures or strategies as means to create scientific research. As such, our empirical study had a deductive top-down quantitative approach, by hypothesis testing on established theory. The purpose was to measure and analyse causal relationships of our phenomena within a value-free framework with the aim of generalization, compared to a qualitative study that are more context bound. With this approach, a large sample size is important, to ensure better representativeness and generalizability. Quantitative methods are used to prevent the influence of values and biases as a way to minimize threats to validity of the outcome. Compared to a quantitative study though, that focus on the causality between the variables, it bears limitation when it comes to describing the mechanism and in-depth understanding of the phenomenon examined. (Slevitch, 2011)
4.1.2 Operationalization
In this comparative study, dependent and independent variables were used. The intention of using the dependent variable was to illustrate the variation in the character of the study object that this thesis aimed to explain. The use of an independent variable aimed to describe the variation of the dependent variable. It is believed that the independent variable cause variation in the dependent variable. The goal of the operationalisation was to strengthen the validity, by illustrating the representativeness between the theoretical variables and the operational indicators. This to ensure that the study tried to measure what it intended to measure. (Esaiasson et al., 2009) An illustration of the operationalization is displayed in Figure 4.1.
The dependent theoretical variable of this study was defined as the use of sustainable energy sources, represented by the amount of installed solar cells in Sweden as the underlying operational indicator. It was measured in Watt (W), which is the measurement of the size of a solar cell due to its capacity to produce electricity. (Esaiasson et al., 2009)
The independent theoretical variable of this study was defined as a subsidy, represented by the direct capital subsidy as the underlying operational indicator. It was measured in Swedish krona per installed Watt (SEK/W) paid to the consumer on the solar cell market. (Esaiasson et al., 2009)
Figure 4.1. Illustration of operationalization.
4.2 Data
4.2.1 Data collection
The data used is secondary data of the solar cells registered in the direct capital subsidy program. It is initially collected by the Swedish County Administrative Boards (Länsstyrelserna), forwarded to the Swedish National Board of Housing, Building and Planning (Boverket), and thereafter to the Swedish Energy Agency (Energimyndigheten). Since the data is only public from 2016 to 2019, the additional data from prior years was collected through Jeffrey Berard at the Swedish Energy Agency. The time period for the data, including all the observations collected, reaches from the implementation of the subsidy in 1 July 2009 to 22 November 2019. The data contains (for each application): date of application, the amount of installed power (kW), the payout of the subsidy (SEK) and in which region the installation is made. The total number of observations during the time period amounts to 53 640 before delimitation.
4.2.2 Dependent variable
The dependent variable of interest is the amount of solar cells (kW), which was divided into two subcategories: private persons (0 - 15 kW), and companies (15 kW - 255 kW). The division was made due to typical size difference between solar cell installations made by this two groups of solar cell owners. Solar cell installations larger than 255 kW was delimited since other rules apply for them and that these types of installations are not that common, where only 289 installations larger than 255 kW have been granted subsidy during the whole period. (NSR, 2018). Also, in this thesis, the impact by the subsidy program on such large installations is assumed to be reduced, due to the cap on the maximum payment given in the program.
4.2.3 Independent variable
The independent variable of interest is the compensation level of the subsidy given to solar cell installers in the direct capital subsidy program. It is given as a percentage value of the total installation cost, and differs between private persons and companies. The first version of the subsidy was first introduced on 14 April 2005, focusing on improvement of energy efficiency in public buildings, and ended on 31 December 2008. Not until seven month later on 1 July 2009, a new version of the program was launched, now available to all actors on the market.
Several changes of the subsidy level have been made over the years, summarised in Table B in Appendix B. As described in 4.3 Empirical Methods, the analysis of the impact of a level change of subsidy on installation of solar cells, includes a time period ranging from six months before the subsidy change to six months after the change. However, not all changes are suitable to analyse, and the considered time periods was reduced to range from 1 July 2014 to 30 June 2015 ,(change made on 1 January 2015) and from 1 July 2017 to 30 June 2018 (change made on 1 January 2018). The changes are summarised in Table 4.1 below.
Table 4.1. The two investigated changes due to the compensation level in the direct capital subsidy program.
Ordinance describes the name of the ordinance and the date for change it was implemented.
Ordinance Date for
change
Maximum coverage of the installation cost
PRIOR TO CHANGE
Maximum coverage of the installation cost
AFTER CHANGE 2014:1582
amendment of 2009:686
2015-01-01 Companies 35 %
Privates 35 %
Companies 30%
Privates 20 %
2017:1300 amendment of 2009:686 2018-01-01 Companies 30 %
Privates 20 %
Companies 30 %
Privates 30 %
A motivation behind the choice of suitable time periods is included in Appendix B. As a summary, the following characteristics applies to both of the chosen time periods.
1) The changes was announces a very short time before implementation, meaning that the consumers of solar cells had no time to plan for the change.
2) The planned date for the subvention to end, was far ahead of the date for the change of the subsidy level, meaning that the consumers of solar cells were assured (also prior to the change) that the subvention was available a long time ahead.
3) There were no other changes due to regulations in the solar cell market that considerably affected the amount of solar cell installations in the chosen time periods.
4.2.3 Descriptive statistics
In this section, descriptive statistics for the analysed time periods is displayed in Table 4.2 and Table 4.3. It presents the number of observations, installed solar cells in power and the total subsidy payout, distributed on private persons and companies. The difference between number of applicants granted and number of applicants granted and paid is due to the existing queue for receiving the payment. The Number of applications granted refers to the amount of Installed power, hence representing the dependent variable. The Number of applications granted and paid refers to both the Total Subsidy payout for those installations and their Average subsidy payout per installed kW,hence representing the independent variable.
Table 4.2. Descriptive statistics for the time period 1 July 2014 to 30 June 2015.
Private persons Companies
6 months Prior to change
6 months After change
6 months Prior to change
6 months After change
Number of applications granted 727 460 368 387
Total installed power [kW] 5 661 3 787 20 189 20 009
Number of applications granted and paid
725 457 362 383
Total subsidy payout [SEK] 33 936 010 14 740 016 89 040 432 81 406 406 Average subsidy payout
[SEK/kW] 5 995 3 892 4 410 4 068
Table 4.3. Descriptive statistics for the time period 1 July 2017 to 30 June 2018.
Private persons Companies
6 months Prior to change
6 months After change
6 months Prior to change
6 months After change
Number of applications granted 1 837 4 999 1 089 2 063
Total installed power [kW] 16 086 44 509 62 769 107 537
Number of applications granted and paid
1 701 4 006 937 1 571
Total subsidy payout [SEK] 74 369 260 185 197 078 210 101 772 320 767 899 Average subsidy payout
[SEK/kW]
4 623 4 161 3 347 2 983
4.2.2 Weaknesses and limitations of the data
Since the data is chosen without randomization the risk for biased selection increases, by other words a risk that we only examine units that fits our hypothesis. This was especially taken into consideration when choosing time periods to analyse, which was selected as objectively as possible. Regarding selection of data for the chosen time period though, there is no obvious weakness. This since the data enables a census study. Further, we do not suspect systematic errors in the used data set. This since it was handed and quality controlled by official servant Jeffrey Berard from the Swedish Energy Agency, which indicate a high level of certainty of the data without obvious errors. One concern is of course the approximative division of actors into two groups. Some companies with installations smaller than 15 kW will be included as private persons, and some private persons with installation of a size between 15-250 kW will be included as companies. However, we assume this error to not have a major impact, and therefore not in a serious way affect the results. (Esaiasson et al., 2009)
A concern that could be raised, regards the availability of data. Since only data from the period 2016-2019 was available publicly, data for the time period 2009-2015 was handed by official servant Jeffrey Berard. Because of this, it might be difficult for other researches to get access to the same data in the future. As a result, the reliability could be somewhat weakened. (Esaiasson et al., 2009)
The solar cell market is complex, with various regulations, subsidies, taxes and other economic incentives. This imply that the installation of solar cells is affected by various factors, not only the direct capital subsidy program, which raise concerns of potential omitted variables. However, these other regulations have not been changed during the two time periods investigated in our study and are therefore assumed to have had a neglectable impact on our result. One important exception from this assumption can be identified. This is the introduction of a tax credit of 0.60 SEK/MWh initiated 1 January 2015, given to all installers below a certain size. Nevertheless, our belief is that the main effect on the market will be dependent on the subsidy level. Further details on regulations and incentives are provided in Appendix A. (NSR, 2018)
4.3 Empirical Methods
Our study will use a statistical design with a manipulative and selective approach, since a randomized test approach was not possible. Our data is divided on an interval scale, meaning that the distance between all our data points is equal (observation per date). We collected information with a large amount of observations, in order to conduct a controlled comparison of the actors in the market. The two investigated groups are perceived as heterogeneous, since they make decisions in different contexts. Private persons might invest to a higher degree as a lifestyle choice, while companies probably are more motivated in investing due to future expected profit. Meaning, that we do not try to explain omitted or complementary variables to the phenomena examined. (Esaiasson et al., 2009)
To analyse our data, we have used a regression discontinuity estimator design. This approach is relevant to use when the examined objects are affected by a treatment. Its principle is illustrated in Figure 4.2, W in our case would represent the date and Y the amount of solar cells installed per date on the Swedish market. The shift in W=0, would be the estimated effect of the discontinuity treatment, in our case the effect of a change in the subsidy level on installations of solar cells. The time period will range from a period of six months before the change in subsidy level (period 1, W=0), to six month after the change in subsidy level (period 2, W=1). Assuming there is nothing special to the threshold value except its use in mandating the amount of installed power on the market, it is plausible to attribute any skip in outcomes to that threshold, from the change in subsidy level. Meaning, if the only role of the threshold is to mandate the volume of installed solar cells, then the skip in changed power for the next period, is an estimate of the effect of the subsidy level on installed power. (Stock &
Watson, 2015)
To be more precise, this test was conducted by a Sharp regression discontinuity approach, described by the equation below. This approach is possible, since we know the exact date for the change in subsidy level. With this course of action, examined objects by the treatment, is entirely determined by whether the date of a subsidy ( X) exceeds the threshold to a new subsidy level ( W) or not. In our case, the shift in installed power ( Y) at the threshold equals the average treatment effect for the compared to period 2 (when W = 1) compared to the subpopulation with observations in period 1 (when W = 0).
This will be a useful approximation to the average treatment effect in the larger population of interest.
(Stock & Watson, 2015) Since we are interested in the total amount of installation on the market, the data was collapsed to the total amount of installation made per date.
Yi= B0+ B1 iX + B2Wi+ ui
If the regression function is linear in W, with exemption for the induced treatment through discontinuity, the treatment effect can be estimated by B1in the regression. The interpretation of the value of the coefficient will be the amount of extra installation of solar cells made per day in kW, due to the change in subsidy level. The treatment is represented by the difference in subsidy level between period 1 and 2, and is measured in percent (%). However, we want to put a monetary value on this change. The payout of the subsidy is given as a percentage (%) of the installation cost, which means that if the cost of a solar cell installation is 10 SEK/kW, the payout with a 20 % subsidy level is 2 SEK/kW. As we have average costs of solar cell installations available, displayed in Figure 3.1, we can use this approach to put a monetary value on the change in subsidy level. (Stock & Watson, 2015)
In our test, we have used an error term that allows for heteroscedasticity. This is the most common type in standard applied econometrics, including OLS regressions. With heteroscedasticity, the variance of the residuals is assumed to not be constant, and varies to some degree along all values of the explanatory variable. If assuming homoscedasticity when errors are in fact heteroscedastic, it will lead to biased and inconsistent estimates of the standard error, or vice versa. (Stock & Watson, 2015)
From our test, we will in addition measure and discuss the adjusted regression R 2. This value measures the fraction of the variance of Yithat is explained by XiandWi. Since we have more than one explanatory variable, adjusted R2 is considered better to use than the regular R 2. The dependent variable Yican be decomposed as the sum of the predicted value plus the residual. The variance of the dependent variable that can be explained by the independent variables is represented by the adjusted R2value. This implicates that the closer the adjusted R 2is to one, the better is the regressed model at predicting the value of Yi. (Stock & Watson, 2015)
5. Results
This section presents the results for the sharp regression discontinuity, investigating the economic effect of change in subsidy level on installation of solar cells. The examined periods include changes of subsidy levels made 1 January 2015 and 1 January 2018, where its effect on private persons and companies is illustrated separately.
5.1 Result for subsidy changes made 2015-01-01
In Figure 5.1 is a graphic presentation of the effect of the change in subsidy level made for private persons 1 January 2015. The subsidy level was increased from 35% to 20% and, as seen in the diagram, resulted in a negative shift in the installation pace in the Swedish market. In general, the installation pace was increasing during the period. Both the effect of the subsidy change and the general trend line are statistically significant on a 99% level.
Figure 5.1 Subsidy level change from 35% to 20% made 2015-01-01: Private persons
The result of the sharp regression discontinuity for the period 1 July 2014 to 30 June 2015, with day number in relation to when the change of subsidy level was made (1 January 2015). Each dot represents the total power granted for subsidies per date, and the blue regression line represents the sharp regression discontinuity. The effect of the change in subsidy level is illustrated by the discontinuity shift between the different periods in day number 0.
In Figure 5.2 is a graphic presentation of the effect of the change in subsidy level made for companies 1 January 2015. The subsidy level was increased from 35% to 30% and, as seen in the diagram, resulted in a negative shift in the installation pace in the Swedish market. In general, the installation pace was increasing during the period. Both the effect of the subsidy change and the general trend line are statistically significant on a 99% level.
Figure 5.2 Subsidy level change from 35% to 30% made 2015-01-01: Companies
The result of the sharp regression discontinuity for the period 1 July 2014 to 30 June 2015, with day number in relation to when the change of subsidy level was made (1st January 2015). Each dot represents the total power granted for subsidies per date, and the blue regression line represents the sharp regression discontinuity. The effect of the change in subsidy level is illustrated by the discontinuity shift between the different periods in day number 0.
In Table 5.1 is a presentation of the sharp discontinuity regression. It contains more details about the results than the diagrams in Figure 5.1 and Figure 5.2. All regression coefficients are statistically significant on a 99% level. For private persons the subsidy was lowered from 35% to 20%, represented by the sharp regression coefficient denoted policy. Its coefficient indicates that the change resulted in a general 27 kW decrease of installed power of solar cells per day. The Constant coefficient of 46 kW represents the predicted amount of installed power for day zero, if no policy changed had been made. Thus, the policy change gave a 58.7% decrease of amount of solar cell power installed per day. For companies the subsidy was lowered from 35% to 30%, which resulted in a general 98 kW decrease of installed power of solar cells per day. With a prediction of 191 kW for day zero, this corresponds to a 51.3% decrease of amount of solar cell power installed per day. The
variableDay number is the day number in relation to 1 January 2015 and its coefficient indicated the general trend in installation of solar cell power in the market during the period. For private persons the installations of solar cell power increased with 0.089 kW per day and for Companies with 0.540 kW per day.
Since the observations was collapsed to installed power per day, the number of observations decreased from 1187 to 289 for Private persons and from 755 to 238 for Companies. Each observation represents the amount of solar cell power registered for a certain date. The adjusted R-square values gives that our model explains 9.07 % of the variation in installation of solar cells for Private persons and 2.40 % for Companies.
Table 5.1. Sharp discontinuity regression of policy change made 2015-01-01 on installation of solar cells in kW for private persons and companies. Policy denotes the change of subsidy level, Day number the day number in relation to 1 January 2015 and Constant the estimated installation in day number 0. All regression coefficients are given with a 95% confidence interval.
5.2 Result of subsidy change made 2018-01-01
In Figure 5.3 is a graphic presentation of the effect of the change in subsidy level made for private persons 1 January 2018. The subsidy level was increased from 20% to 30% and, as seen in the diagram, resulted in a positive shift in the installation pace in the Swedish market. In general, the installation pace was increasing during the period. Both the effect of the subsidy change and the general trend line are statistically significant on a 99% level.
Figure 5.3 Subsidy level change from 20% to 30% made 2018-01-01: Private persons
The result of the sharp regression discontinuity for the period 1 July 2017 to 30 June 2018, with day number in relation to when the change of subsidy level was made (1 January 2018). Each dot represents the total power granted for subsidies per date, and the blue regression line represents the sharp regression discontinuity. The effect of the change in subsidy level is illustrated by the discontinuity shift between the different periods in day number 0.
In Figure 5.4 is a graphic presentation of the installations in the Swedish market for companies between 1 July 2017 to 30 June 2018. During the period, no change was made, with a subsidy level held constant at 30%. A discontinuity regression design was made for 1 January 2018, but gave no significant shift of the installation pace. In general, the trend of the installation pace was positive, on a 99 % significance level.
Figure 5.4 Subsidy level at 30% not changed 2018-01-01: Companies
The result of the sharp regression discontinuity for the period 1 July 2017 to 30 June 2018, with day number in relation to 1 January 2018. Each dot represents the total power granted for subsidies per date, and the blue regression line represents the sharp regression discontinuity. In the absence of a change in subsidy level in day number 0, no significant discontinuity shift appeared.
In Table 5.2 is a presentation of the sharp discontinuity regression. It contains more details about the results than the diagrams in Figure 5.3 and Figure 5.4. All regression coefficients are statistically significant on a 99% level, with exceptions of policy for companies that have no statistical significance. For private persons the subsidy was raised from 20% to 30%, represented by the sharp regression coefficient denotedpolicy. Its coefficient indicates that the change resulted in a general 102 kW increase of installed power of solar cells per day. The Constant coefficient of 120 kW represents the predicted amount of installed power for day zero, if no policy changed had been made. Thus, the policy change gave a 85% decrease of amount of solar cell power installed per day. For companies the subsidy was kept constant, and no statistically significant change of installed power of solar cells per day occurred. The variable Day number is the day number in relation to 1 January 2018 and its coefficient indicated the general trend in installation of solar cell power in the market during the
period. For private persons the installations of solar cell power increased with 0.300 kW per day and for Companies with 1.376 kW per day.
Since the observations was collapsed to installed power per day, the number of observations decreased from 6 836 to 353 for Private persons and from 3 152 to 315 for Companies. Each observation represents the amount of solar cell power registered for a certain date. The adjusted R-square values gives that our model explains 32.2 % of the variation in installation of solar cells for Private persons and 6.38 % for Companies.
Table 5.2. Sharp discontinuity regression of policy change made 2018-01-01 on installation of solar cells in kW for private persons and companies. Sharp discontinuity regression of policy change made 1 January 2018 on installation of solar cells in kW for private persons. The same regression is displayed for companies, for which no change was made. Policy denotes the change of subsidy level, Day number the day number in relation to 1 January 2018 and Constant the estimated installation in day number 0.
All regression coefficients are given with a 95% confidence interval.
6. Analysis and findings
1 January 2015 the subsidy level for private persons was lowered from 35% to 20%, which corresponds to 15% points decrease of subsidy level. This means that the consumer of solar cells got 15% points less of the installation cost covered by the subsidy. The typical solar cell price was 7.6 SEK/kW in 2015, according to Figure 3.1, meaning that the subsidy in monetary terms was lowered from 2.66 SEK/kW to 1.52 SEK/kW with a 1.14 SEK/kW less payout to the private person. It means that, given that the market price for solar cells was unaffected by the change, that the price the consumer paid increased from 4.94 SEK/kW to 6.08 SEK/kW. This decrease of subsidy level lead to a decrease from 46 kW to 19 kW, thus a 61% decrease in the size of the solar cell market for private persons for the following 6 months. Given those numbers, the midpoint price elasticity for private persons in 2015 was - 4.02.
1 January 2015 the subsidy level for companies was lowered from 35% to 30%, which corresponds to 5% points decrease of subsidy level. This means that the consumer of solar cells got 5% points less of the installation cost covered by the subsidy. The typical solar cell price was 7.6 SEK/kW in 2015, according to Figure 3.1, meaning that the subsidy in monetary terms was lowered from 2.66 SEK/kW to 2.28 SEK/kW with a 0.38 SEK/kW less payout to the company. It means that, given that the market price for solar cells was unaffected by the change, the price the consumer paid increased from 4.94 SEK/kW to 5.32 SEK/kW. This decrease of subsidy level lead to a 98 kW decrease in the size of the solar cell market for companies. This decrease of subsidy level lead to a decrease from 191 kW to 93 kW, thus a 51% decrease in the size of the solar cell market for companies for the following 6 months.
Given those numbers, the midpoint price elasticity for companies in 2015 was -8.41.
Compared to private persons, it is seen that a smaller decrease of subsidy in SEK/kW for companies, had a larger impact on the size of the market. However, considering that the market for companies is larger, the relative change was somewhat smaller for companies. Nevertheless, it appears that the market for companies were more sensitive to changes in the subsidy level.
The demand curve for both companies and private persons were elastic in 2015. This would indicate that solar cells have transformed from being an inelastic commodity to an elastic commodity, applying what's discussed in connection with the S-shape growth model by Oliver & Jackson (1999) in Figure 2.3 and Figure 2.4. This illustrates that the solar cell market in Sweden has transformed from an immature niche market in early 2000 to a more mature market in 2015. This since a higher degree of
elasticity, according to the theoretical framework, is an indication of a more mature market.
Moreover, it is noted that the elasticity in 2015 between private persons and companies differs.
However, the elasticity is measured in different intervals for the two groups, due to that the change of subsidy level differ, giving elasticity for private persons in the interval 4.94 SEK/kW to 6.08 SEK/kW and for companies in the interval 4.94 SEK/kW to 5.32 SEK/kW. This makes the results for the two groups difficult to compare.
In 2018-01-01 the subsidy level for private persons was increased from 20% to 30%, which corresponds to 10% points increase of subsidy level. This means that the consumer of solar cells got 10% points more of the installation cost covered by the subsidy. The typical solar cell price was 4.50 SEK/kW in 2018, according to Figure 3.1, meaning that the subsidy in monetary terms was increased from 0.90 SEK/kW to 1.35 SEK/kW with a total 0.45 SEK/kW more payout to the private person. It means that, given that the market price for solar cells was unaffected by the change, the price the consumer paid decreased from 3.60 SEK/kW to 3.15 SEK/kW. This increase of subsidy level lead to a increase from 120 kW to 222 kW, thus a 85% increase in the size of the solar cell market for private persons for the following 6 months. Given those numbers, the midpoint price elasticity for private persons in 2018 was -4.47.
Since no subsidy change occurred for companies in 2018, it resulted in no significant changes in the market. Meaning that the supply and demand for companies was the same during the whole period, 1 July 2017 to 30 June 2018. This is a result that strengthen the validity of our approach, since a statistically significant result with no change would have indicated that our model not investigates what it is supposed to investigate. Put in other words, it does not appear to exist any omitted variables in our model that seriously affect the results. One such concern, in beforehand, was that there could be a strong seasonal variation.
Between 2015 and 2018, the price elasticity for private persons had an increase in elasticity from -4.02 to -4.47. Applying the illustration of maturity by Oliver & Jackson (1999) in Figure 2.4, this is expected, since the elasticity of demand in the solar cell market should increase with falling prices on a commodity. This was also the case between 2015 and 2018, according to the global price trend of solar cells displayed in Figure 3.1. In accordance with the S-shape growth model by Oliver & Jackson (1999) in Figure 2.3, the increased elasticity indicates a more mature market. The increase of maturity is in line with the model, that predicts a continuous growth of maturity over time.
Our findings show that the result is in line with the theoretical framework. Meaning that the Swedish solar cell market has become a more mature market over time. This is indicated by higher price elasticity in the market. As predicted by the theory of subsidies in a free competitive market, the direct capital subsidies increase the demand of the market and thereby increasing the installations of solar cells. When the market has become more mature, the effect of the subsidy have increased, which is explained by increased price elasticity. Higher price elasticity means that the demand for solar cells is more sensitive to price changes. In the short-run, changes of the subsidy have large effects, whereas the long-term trend does not seem to be affected. Moreover, a low degree of explanation indicates that the number of installations is affected by various factors not included in our model.
