Feedbacks among electric vehicle adoption, charging, and the cost and installation of rooftop solar photovoltaics

Identifying feedback loops in consumer behaviours is important to develop policies to accentuate desired behaviour. Here, we use Granger causality to provide empirical evidence for feedback loops among four important components of a low-carbon economy. One loop includes the cost of installing rooftop solar (Cost) and the installation of rooftop solar (photovoltaics, PV); this loop is probably generated by learning by doing and reductions in the levelized cost of electricity. The second includes the purchase of electric vehicles (EV) and the installation of rooftop solar that is probably created by environmental complementarity. Finally, we address whether installing charging stations enhances the purchase of electric vehicles and vice versa; there is no evidence for a causal relation in either direction. Together, these results indicate ways to modify existing policy in ways that could trigger the Cost↔PV↔EV feedback loops and accelerate the transition to carbon-free technologies. Feedback loops in consumer behaviour can accelerate desirable phenomena and be used to create effective policy. Kaufmann et al. identify a critical green feedback loop by using Massachusetts data to show bidirectional causality among solar photovoltaic cost, adoption and electric vehicle sales.

K eeping the ongoing rise in global temperature to a socially 'acceptable' 1.5-2.0 °C will require the world to strand large amounts of fossil fuel resources, electrify much of its economic infrastructure and generate most of its electricity from carbon-free fuels 1 . Together, these requirements necessitate a transition to a new ecosystem of technologies and social relations.
So far, analyses of this transition focus on the economic and technical attributes of individual technologies, such as solar photovoltaics and electric vehicles. The economic viability of photovoltaic cells (or other renewable technologies) is often measured by the levelized cost of electricity (LCOE), which is the average revenue per unit of electricity generated that is required to recover the costs of building and operating a solar cell during an assumed financial life and duty cycle. On the basis of this criterion, the penetration of photovoltaic cells depends on its LCOE relative to other technologies. The LCOE generated by photovoltaic cells is declining and is comparable to low cost, combined cycle natural gas generating plants 2,3 .
The adoption of electric vehicles often is examined in relation to internal and external factors: internal factors include the cost of ownership, driving range and charging time, while external factors include fuel prices, charging networks and public visibility/ social norms 4,5 . Marketing studies indicate that the willingness to buy electric vehicles is reduced by their high purchase price [6][7][8] . This obstacle may be lowered by financial incentives [9][10][11][12] , but their efficacy is uncertain 13,14 . Other studies that focus on consumer characteristics suggest that the likelihood a consumer will purchase an electric vehicle increases with education, income, environmental awareness and interest in technology 4,15 .
The use and economics of public charging stations receive considerable attention 16 because many electric vehicles have a driving range (which is the distance that a vehicle can cover using the full charge of its battery) less than the driving range of vehicles powered by an internal combustion engine that burns fossil fuels. This creates range anxiety, which is defined as the fear of depleting the battery before completing a trip 17 . Range anxiety and the long period required to recharge the battery relative to filling a gas tank, are important obstacles to the purchase of electric vehicles 18,19 . As such, the availability of charging stations may reduce range anxiety and ultimately lower barriers to purchasing electric vehicles 17 , but this hypothesis is not supported by empirical evidence 4 .
Here, we go beyond the attributes of individual technologies and focus on whether feedback loops create system dynamics that affect the rate at which technologies penetrate the market 20,21 . We investigate three possible feedback loops. One includes a simultaneous relation between the cost for and capacity of residential solar photovoltaic power, which we term rooftop solar; increased capacity lowers the costs of installing rooftop solar 22 and lower costs spur new investments, which expand capacity. A second includes a simultaneous relation between the installation of rooftop solar and the purchase of electric vehicles; increased installation of rooftop solar increases the purchase of electric vehicles (and vice versa) that is probably created by environmental complementarity and psychological components of decision making. A third includes a simultaneous relation between the purchase of electric vehicles and the installation of public charging stations that is created by their economic complementarity. Causal relations identify two sets of feedback loops: one includes the costs for and the installation of rooftop solar, while the second includes the installation of rooftop solar and the purchase of electric vehicles. Triggering these feedback loops by modifying existing policy may accelerate the transition to these carbon-free technologies. Conversely, we do not find evidence that installing charging stations affects the purchase of electric vehicles or the purchase of electric vehicles affects the installation of charging stations.

Causal relations
To test whether these feedback loops are present in the observational record, we examine (statistical) causal relations among the cost of installing rooftop solar (Cost), the installation of rooftop solar (PV), the purchase of electric vehicles (EV) and the installation of charging stations for electric vehicles (Charge) from 61 monthly observations (January 2014-February 2019) for 571 zip codes in the Commonwealth of Massachusetts. The presence of a feedback loop is evaluated using Granger causality. A finding that variable Feedbacks among electric vehicle adoption, charging, and the cost and installation of rooftop solar photovoltaics

Robert. K. Kaufmann ✉ , Derek Newberry, Chen Xin and Sucharita Gopal
Identifying feedback loops in consumer behaviours is important to develop policies to accentuate desired behaviour. Here, we use Granger causality to provide empirical evidence for feedback loops among four important components of a low-carbon economy. One loop includes the cost of installing rooftop solar (Cost) and the installation of rooftop solar (photovoltaics, PV); this loop is probably generated by learning by doing and reductions in the levelized cost of electricity. The second includes the purchase of electric vehicles (EV) and the installation of rooftop solar that is probably created by environmental complementarity. Finally, we address whether installing charging stations enhances the purchase of electric vehicles and vice versa; there is no evidence for a causal relation in either direction. Together, these results indicate ways to modify existing policy in ways that could trigger the Cost↔PV↔EV feedback loops and accelerate the transition to carbon-free technologies.
X 'Granger causes' variable Y (that is, X→Y) and that variable Y Granger causes variable X (that is, Y→X) indicates a bidirectional causal relation (that is, X↔Y) and is consistent with a feedback loop because a finding of Granger causality goes beyond correlations that are described by previous analyses (Supplementary Note 1). Nonetheless, causality does not necessarily indicate the presence of a physical causal mechanism between variables. Furthermore, findings regarding Granger causality depend on the information in the set of conditioning variables, such as the inclusion of socio-demographic factors (Supplementary Note 1) 23 .
Test statistics reject the null hypothesis of no causal relation at rates much greater than expected by random chance. Of the 240 tests on the 20 panels that are defined by the time series properties of the variables and a minimum sample size (Supplementary Notes 2 and 3 and Supplementary Tables 2-5), 82 reject (P < 0.05) the null hypothesis. This large percentage (roughly 34%) indicates that there are causal relations between variables.
Causal relations are identified by consistent results across the 20 tests of each possible causal relation. A bidirectional causal relation exists between EV and PV; the null hypothesis of no causal relation is rejected in nine and seven of 20 possible tests (Table 1 and Fig. 1 Conversely, none of 60 test statistics reject the null hypothesis that the installation of charging stations does not Granger cause any of the other three variables (Table 1). Similarly, all test statistics fail to reject the null hypothesis that the installation of charging stations is not Granger caused by any of the other variables.

Local learning and lower costs in the Cost↔PV feedback loop
The bidirectional causal relation between Cost and PV goes beyond previous results (Supplementary Note 4 and Supplementary Table  6) and identifies a Cost↔PV feedback loop. The Cost→PV relation is consistent with arguments that cost reductions lower the LCOE, which makes rooftop solar more economically attractive and accelerates deployment (Supplementary Note 4) 2,24 . The causal relation PV→Cost is consistent with the theory that underlies a learning curve 25 , in which installing rooftop solar induces learning, which lower costs 2 .
The price for solar modules, which are the hardware that converts solar insolation to a.c. electricity, can be treated as a commodity [26][27][28] . As a worldwide commodity, the cost of these modules is defined by the balance between global supply and demand, rather than the balance at the local or national level 29 . Because Massachusetts cannot influence the global market in a meaningful fashion, local installations cannot drive (as indicated by Granger causality) the price for a global commodity such as solar modules.
Instead, we postulate that the PV→Cost causal relation is generated by local learning. The price for solar modules accounts for less than a third of their total costs for US residential customers in 2017 30 . About two thirds are associated with the balance of the system (BOS), which includes permitting, inspection, installation and interconnection. BOS costs indicate that the economics of system deployment take place locally and involve downstream components of the PV value chain 28 . Local learning occurs when a standard product platform, which is defined as a collection of common elements, especially the underlying defining technologies 31 , is implemented across a range of products or projects adapted to local conditions 28 . Learning from installing PV exhibits the characteristics of local learning, which include tacit knowledge, shared narratives, user relations and learning in interorganizational networks 32 .
This same local learning-by-doing relation may indirectly generate the EV↔Cost feedback loop. Business models often pair the installation of charging stations with solar cells 33 . Purchases of electric vehicles stimulate local learning by the same workforce that installs rooftop solar and charging stations. Like rooftop solar, local costs for installing charging stations account for 65-70% of the total 34 .

environmental and psychological aspects of the PV↔eV loop
At first glance, a PV↔EV feedback loop seems unlikely. Rooftop solar and electric vehicles are different technologies that provide  different services. On the other hand, both technologies are integral to a new technical ecosystem that is based on renewable/carbon-free technologies. Furthermore, electric vehicles and photovoltaic cells are linked by several technical and economic synergies, such as using the batteries in electric vehicles to balance load on the grid 35 . But these synergies are not implemented widely and therefore probably not responsible for the PV↔EV feedback loop. We postulate that that the PV↔EV feedback loop is generated by environmental complementarity and non-economic aspects of decision making. We postulate that seeing rooftop solar increases the likelihood that an agent will purchase an electric vehicle and that seeing an electric vehicle increases the likelihood that an agent will install rooftop solar. These decisions are driven by their environmental complementarity, which is defined as joint progress toward a desirable environmental outcome 36 . In this case, reducing CO 2 emissions is the desirable environmental outcome; installing rooftop solar can reduce the carbon emitted by charging an electric vehicle while purchasing an electric vehicle can reduce the carbon emitted by a household that has rooftop solar. Consistent with this environmental complementarity, an on-line survey suggests a 433% increase in the use of a charging station if it is powered by renewable energy 37 .
This complementarity is highlighted by their visibility to neighbours. Rooftop solar is easily seen. Electric vehicles in Massachusetts have a special licence plate that distinguishes them from internal combustion engine vehicles. Furthermore, the process of charging an electric vehicle can be highly visible. These visibilities create a 'neighbourhood presence' in zip codes ( Fig. 2; average size in Massachusetts 43.2 km 2 ), which is about the same size as the area of influence (33 km 2 ) assumed by an agent-based model for EV purchases (Supplementary Note 5) 38 .
The neighbourhood presence of rooftop solar and electric vehicles influences the psychological components of decision making, which include peer effects and social norms 39 . Peer effects include interpersonal communication and persuasion 39 . Social norms are based on the hypothesis that people view themselves as members of groups and communities and are influenced by what members of their community think and do 40,41 and the belief that the group can affect important aspects of its environment, which is known as collective efficacy 42 . Although our empirical analysis cannot separate peer effects and social norms, we describe how they influence the decision to purchase an electric vehicle or rooftop solar to illustrate their potential to create the PV↔EV feedback loop.
In California, 'seeing' rooftop solar increases the probably of adoption 43 . Similarly, agent-based models suggest that decisions to purchase an electric vehicle are influenced by a threshold effect, in which individuals consider the purchase of an electric vehicle when their presence exceeds a critical level 38 . Beyond this threshold, simulations of agent-based models assume that the presence of electric vehicles mediate the degree to which external factors, such as the purchase price and battery range, affect the decision to purchase an electric vehicle 38 .
Local exposure to rooftop solar or electric vehicles also gives an agent information about the social norms in their neighbourhood and the potential for collective efficacy. The adoption of electric vehicles is accelerated by descriptive norms, which are typical patterns of behaviour in an agent's socio-cultural group and generally are accompanied by the expectation that people will behave according to the pattern, and/or provincial norms, which are the norms of the those who occupy a comparable setting 40 . Seeing rooftop solar or electric vehicles in their neighbourhood tells agents that their purchase conforms with local norms. Similarly, the presence of other electric vehicles or rooftop solar can frame purchase decisions as a personal contribution to the superordinate collective goal of becoming a more sustainable society 40 .
Empirical analyses provide further evidence that decisions to purchase an electric vehicle or rooftop solar may be influenced by peer effects and social norms. Social norms have information about decisions made by German consumers to purchase an electric vehicle beyond its costs and benefits 40 . Agents are more likely to purchase alternative fuel vehicles when they are purchased by others who live nearby [44][45][46] or are members of their social network 46 . Similarly, peer-to-peer communications affect decisions to purchase rooftop solar in Texas 47 .

Charging stations and electric vehicles stand apart
The absence of causal relations between the installation of charging stations and the purchase of electric vehicles indicates that there is no EV↔Charge feedback loop. This result is surprising. Range anxiety and the availability of charging stations correlate with decisions to purchase an electric vehicle 4,5 and network analysis indicates there is a positive correlation between sales of electric vehicles and deployment of charging stations 48 . Similarly, economic analyses indicate that the economic viability of a charging station is influenced by charging demand, which is related to the number of electric vehicles in a given area 16 . These correlations suggest charging stations and electric vehicles are linked in a feedback loop. Although the literature discusses the difference between factors that correlate with the purchase of electric vehicles and the factors that drive those purchases 40 , our negative results explicitly address the 'chicken and egg' conundrum regarding the presence/absence and direction of causality between the installation of charging stations and the purchase of electric vehicles 4 .
We postulate that the absence of casual relations (and a feedback loop) may be caused by our focus on public charging stations, the spatial resolution of the analysis and the failure to differentiate among types of changing stations. Analyses indicate that most charging occurs at home 17,49 . In the USA, the average automobile trip, 23 miles per day 50 , uses less energy than the battery charge 17 . This balance indicates there is little need for public charging stations, as represented by Charge, near private homes. Under these conditions, we would not expect a causal relation (in either direction) between public charging stations and the purchase of electric vehicles within the driving range of electric vehicles, such as a zip code.
The need for public charging infrastructure, and therefore a causal relation between EV and Charge may vary by housing type. In zip codes dominated by low density housing (that is, detached homes) residents can install home charging stations, which obviates the need for public charging infrastructure. This would depress a Charge→EV relation. But a Charge→EV relation may be present in zip codes dominated by high density housing, where it is difficult and/or illegal for residents to install charging stations. In California, multi-unit dwellings make up about 34% of dwellings, but account for only about 5% of home-based charging 51 .
After homes, workplaces are the next most popular location for charging 17 . These locations suggest causal relations between charging stations and the purchase of electric vehicles in zones defined by commuting and/or vacation patterns. Perhaps installing more public charging stations in Boston's central business district would encourage residents of the greater metropolitan Boston area to purchase electric vehicles. And as purchases increase, this may encourage the installation of more public charging stations in the central business district.
It may also be important to differentiate among stations on the basis of their charging equipment. Here, charging stations include level 1 equipment, which charge at a rate of 2-5 miles per hour, and level 2 equipment, which charge at a rate of 10-20 miles per hour. Future efforts may want to focus on newer fast chargers, which add about 100-800 miles in about an hour 52 . Speed of recharge is important when drivers are away from their home; therefore, fast chargers may have a causal relation with the adoption of electric vehicles in areas defined by commuting or vacation patterns 17 .

Modifying policy on the basis of feedback loops
This study identifies two feedback loops, Cost↔PV and PV↔EV, that can be targeted by policy to accelerate the transition to carbon-free renewable energies. Policy that increases the installation of rooftop solar will reduce the cost of installing rooftop solar and increase the purchase of electric vehicles. Because causal relations run in both directions, reductions in the cost of installing rooftop solar and/or increases in the purchase of electric vehicles feed back on the installation of rooftop solar. These feedback loops indicate that policies to increase the installation of PV, increase the purchase of electric vehicles and/or reduce the cost of installing rooftop solar may be more effective than their direct effects.
These synergisms beg the question, can existing policies aimed at an individual component of the carbon-free technology ecosystem be modified to trigger feedback loops? We argue that existing policy could be modified to be consistent with the spatial scale at which local learning, peer effects, threshold effects, social norms and collective efficacy influence the purchase of electric vehicles and perhaps rooftop solar 53 . We suggest that policy be modified to account for location in ways that increase the number of people exposed to technologies and thereby trigger threshold and peer effects. These changes can be illustrated by modifying existing incentives for purchasing electric vehicles and installing rooftop solar in Massachusetts.
Currently, the US Federal government and the state of Massachusetts offer financial incentives to purchase electric vehicles. The Federal government offers a tax credit for those who purchase an electric vehicle while the state of Massachusetts offers a rebate. At present, these incentives make no reference to space. Instead, Federal incentives are limited to the first 200,000 vehicles that are sold by a manufacturer. As a result, tax credits will 'run out' for various makes and models regardless of where electric vehicles are purchased 54 .
Rather than tying rebates to manufacturers, this analysis indicates that the size and timing of financial incentives could be tied to space. In any given neighbourhood, such as a zip code, the largest rebates should be directed towards the first purchases of an electric vehicle. The first purchases in a zip code increase market penetration towards the threshold at which their presence mediates the internal and external factors that affect decisions to purchase an electric vehicle. This encourages further purchases of electric vehicles and triggers the feedback loop with rooftop solar, but probably at a diminishing rate. As a result, incentives offered for the purchase of an electric vehicle in a zip code could be lowered as cumulative purchases rise in a zip code. These spatial and temporal variations in financial incentives would maximize the number of people exposed to and willing to consider purchasing an electric vehicle. This logic differs from policy designed to support 'learning by doing' , which lowers the incentives needed support a functional market for a single technology over time, as in California, Japan and Germany 55 .
A similar approach could be used to modify the incentives that are used to encourage the installation of rooftop solar in Massachusetts. During much of the sample period, those who install rooftop solar are eligible for Solar Renewable Energy Certificates (SRECs). SRECs can be sold to utilities who purchase SRECs to meet state requirements that mandate a fraction of electricity be generated by renewable resources. Currently, each SREC represents 1 MWh of electricity generated 56 .
Our analysis suggests that the formula that translates rooftop PV generation to an SREC could be modified to account for the date and location of the rooftop PV installation. For early adopters within a zip code, less than 1 MWh of added solar generation might may earn one SREC. This 'discounted' conversion rate might encourage installations in areas where there is little or no rooftop solar. As with electric vehicles, the first installations have the greatest effect on moving the penetration of rooftop solar towards the threshold at which neighbours start to consider the purchase of rooftop solar. As the number of installations within a zip code rises beyond this threshold, their increased presence will encourage more people to install rooftop solar, but probably at a diminishing rate. Consequently, the conversion factor that translates electricity generated into an SREC could increase towards 1 MWh for subsequent installations within the zip code.
With regards to the Cost↔PV feedback loop, policy could be designed to facilitate local learning (town or zip code) associated with the installation of rooftop solar (and perhaps charging stations). This is critical because 'the policy literature has paid limited attention to the role of policy incentives that can foster knowledge and training in localized know-how, enhance craft and practical skills, and support interactive learning and the formation of local knowledge networks' . 32 Efforts to enhance local learning may be especially effective because their effects are amplified by the Cost↔PV feedback loop.
The efficacy of policies that trigger feedback loops is uncertain because they depend on the size of the multiplier effect and the threshold that mediates the importance of external factors. We do not quantify the size of the multiplier effect because it cannot be recovered from the regression parameter(s) used to estimate causal relations (Supplementary Note 6). Future efforts will quantify these relations by estimating cointegrating relations and error correction models from the panel analysed here. Furthermore, we will use logit models to quantify the factors that generate causal relation in zip codes to estimate the aforementioned threshold because it influences the efficacy of our policy suggestion. We include observations for those who purchase a battery electric vehicle and voluntarily request a rebate. Purchasers who do not participate in the MOR-EV programme are known to the Massachusetts Registry of Motor Vehicles, but privacy concerns prevent the Registry from releasing this information. The number of non-participants probably is small because the rebate for battery electric vehicles is large US$2,500, therefore omitting non-participants probably has little effect on our results.

Overview
The location and number of public charging stations are obtained from the Alternative Fuels Data Center Station Locator electric vehicle supply equipment database 58 . We include level 1 and level 2 stations. Installation dates are assigned on the basis of the month and year in which the station opens.
Monthly installations of residential solar photovoltaic, which we term rooftop solar, and the cost of installation are obtained from the Massachusetts Renewable Portfolio Standards Solar Carve-Out II Renewable Generation dataset 59 . These data include solar electric facilities that have a capacity of 6 MW or less, are built after 1 January 2008 and are qualified to generate SRECs. For each installation, data are available on nameplate capacity (kW), total cost of installation (including the cost of solar modules), Cost (US$ per kW), the start date of commercial operation and zip code.
The number of observations varies among zip codes and variables. To test the degree to which results are robust, we compile observations into five unbalanced panels that have a minimum of 20, 30, 40, 50 or 55 observations per zip code for each of the four variables (Fig. 2). The number of zip codes that have at least 20 observations (404) is greater than the number of zip codes that have 55 observations (76). Consistent with the statistical methodology described below, panels with a large minimum number of observations increase the reliability of the test for a causal relation within a zip code (equation (2)). The final test statistic (equation (3)) aggregates results across zip codes for which observations are available, therefore panels with a smaller number of minimum observations increase the number of zip codes that can be analysed and so increase the reliability of the aggregate test statistic.
Statistical methodology. Each of the five panels is analysed using four tests for unit roots to determine whether individual variables are stationary or non-stationary (Supplementary Table 1). One tests the null hypothesis that the time series is stationary 60 , adjusts for heteroscedasticity and is most effective when the number of individuals N and the number of observations per individual T are large. The other three statistics test the null hypothesis that the time series contains a unit root (that is, non-stationary) [61][62][63] . One performs best as ffiffiffiffiffiffi N T p =T ! 0 I , when N lies between 10 and 250 and T lies between 5 and 250 (ref. 63 ). Its performance in small samples is bettered by another statistic 60 . For variables found to have a unit root, we take their first difference: where t is time, because the methodology used to test for causal relations is designed to analyse stationary variables in balanced and unbalanced panels.
The test for causal relations starts with the following general equation 64 : in which x is an array of three variables that may Granger cause a fourth variable y (x→y), i is the zip code, k is the coefficient associated with the lagged (K) value of variable x or y, α, γ, β are regression coefficients and ε is the regression residual. For each set of panels and each specification of y as the dependent variable, the number of lags (K) is chosen using the Akaike information criterion 65 . Because equation (2) is estimated separately for each zip code, the slopes and intercepts can vary across zip codes. Granger causality from x to y is evaluated by testing H O = β i = 0. This null hypothesis, which can be expressed Rθ i = 0, in which θ i ¼ α i ; γ 0 i ; β 0 i I , is tested for each individual (zip code) with a Wald statistic that is calculated as follows: in which θ i is an estimate of the parameter θ that is obtained under the alternative hypothesis, σ 2 i I is the variance of the residuals and R is a (K,2K + 1) matrix with R = [0,I K ] and = [e:Y i :X i ] in which e is a (t,1) unit vector. This test statistic is aggregated across all (N) zip codes as follows: and is distributed as a χ 2 with degrees of freedom equal to the product of the number of lags eliminated and number of individuals (N). The aggregate test statistic (Wald HNC N;T I ) evaluates the null hypothesis of homogeneous non-causality, which assumes that there is no x→y causal relation for any zip code 64 . The alternative hypothesis is heterogeneous non-causality, which assumes that there is an x→y causal relation in at least one and at most N − 1 zip codes. This alternative is less restrictive than the alternative hypothesis in a previous methodology, which postulates that N causal relations are present 66 .

Data availability
Monthly observations for the purchase of electric vehicles are obtained from the MOR-EV programme. The location and number of public charging stations are obtained from the Alternative Fuels Data Center Station Locator electric vehicle supply equipment database 54 . Monthly installations of residential solar photovoltaic, which we term rooftop solar, and the cost of installation are obtained from the Massachusetts Renewable Portfolio Standards Solar Carve-Out II Renewable Generation dataset 55 . These data and the computer code can be obtained are available on OpenBU, which is FAIR compliant and can be accessed through a globally unique and eternally persistent identifier, https://open.bu.edu/ handle/2144/41462. This dataset is distributed under the terms of the Creative Commons Attribution-ShareAlike 4.0 Licence (http://creativecommons.org/ licenses/by-sa/4.0).

Code availability
The code is available on OpenBU, which is FAIR compliant, and can be accessed through a globally unique and eternally persistent identifier, https://hdl.handle. net/2144/40340.