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2. Disclaimer This document was prepared as an account of work sponsored by the United States Government. While this document is believed to contain correct information, neither the United States Government nor any agency thereof, nor The Regents of the University of California, nor any of their employees, makes any warranty, express or implied, or assumes any legal responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, pro cess, or service by its trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof, or The Regents of the University of Cali fornia. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof, The Regents of the University of California, the Federal Reserve Bank of Kansas City, or the Federal Reserve System. Ernest Orlando Lawrence Berkeley National Laboratory is an equal opportunity employer. i
4. Acknowledgements This work was supported by the Office of Energy Efficiency and Renewable Energy (Solar E nergy Technologies Office ) of the U.S. Department of Energy (DOE) SunShot Initiative under Contract No. DE  AC02  05CH11231. For funding and supporting this work, we especially thank Minh Le, Kelly Knutsen, Elaine Ulrich, Christina Nichols, and Ammar Qusaibaty (DOE). For providing the data that were central to the analysis contained herein, we thank J oshua Tretter and Debra Sinclair (CoreLogic Inc.) as well as the many individuals involved in providing us address data , especially James Loewen of the C alifornia Publi c Utilit ies Commission . Additionally we thank Cassandra May of SUNY Ulster in New York for her help in exploring pool prevalence among PV homes. Finally, we would like to thank the many external reviewers for providing valuable comments on an earlier draft version of the report , including Matt Brost (SunPower), Lisa Desmarais ( Peak to Peak Appraising, LLC ), Mari Hernandez (SolarCity), Robert Dietz (National Association of Homebuilders), Timothy Treadwell (California Center for Sustainable Energy ), Laura Reedy Stukel (Elevate Energy), Greg Lampman (New York State Energy Research and Development Authority) , and Le  Quyen Nguyen (California Energy Comm ission) . Of course, any remaining errors or omissions are our own. iii
3. LBNL  6942E S ELLING I NTO T HE S UN : P RICE P REMIUM A NALYSIS OF A M U LT I  S TAT E D ATASET OF S OLAR H OMES Prepared for the Office of Energy Efficiency and Renewable Energy Solar Energy Technologies Office U.S. Department of Energy Principal Authors: Ben Hoen † & Ryan Wiser Lawrence Berkeley National Laboratory 1 Cyclotron Road, MS 90R4000, Berkeley, CA 94720  8136 Sandra Adomatis , SRA Adomatis Appraisal Services P.O. Box 511355 Punta Gorda, FL 33951 Thomas Jackson , AICP, MAI, CRE, FRICS Real Property Analytics, Inc. Texas A&M University 341D Wehner Building, 4218 TAMU College Station, TX 77843  4218 Joshua Graff  Zivin University of California at San Diego 9500 Gilman Dr. 0519 La Jolla, CA 92093 Mark Thayer San Diego State University 5500 Campanile Dr. San Diego, CA 92182  4485 Geoffrey T. Klise Sandia National Laboratories PO Box 5800, MS 1137 Albuquerque, NM 87185 January 13 , 2015 This work was supported by the Office of Energy Efficiency and Renewable Energy (Solar Energy Technologies Office) of the U.S. Department of Energy under Contract No. DE  AC02  05CH11231. † Corresponding author: Phone: 845  758  1896; Email: bhoen@lbl.gov ; Mailing address: 20 Sawmill Road, Milan, NY 12571. ii
5. Abstract Capturing the value that solar photovoltaic ( PV ) systems may add to home sales transactions is increasingly important. Our study enhances the PV  home  valuation literature by more than doubling the number of PV home sales analyzed (22,822 homes in total, 3,951 of which are PV) and examining transactions in eight states that span the years 2002 – 2013. We find that home buyers are consistently willing to pay PV home premiums acro ss various states, housing and PV markets, and home types ; average premiums across the full sample equate to approximately $4/ W or $15,000 for an average  sized 3.6  kW PV system . Only a small and non  statistically significant difference exists between PV pr emiums for new and existing homes , though some evidence exists of new home PV system discounting . A PV green cachet might exist , i.e., home buyers might pay a certain amount for any size of PV system and some increment more depending on system size. The market appears to depreciate the value of PV systems in their first 10 years at a rate exceeding th e rate of PV efficiency losses and the rate of straight  line depreciation over the asset’s useful life . Net cost estimates — which account for government a nd utility PV incentives — may be the best proxy for market premiums , but income  based estimates may perform equally well if they accurately account for the complicated retail rate structures that exist in some states . Although this study focuses only on hos t  owned PV systems, future analysis should focus on homes with third  party  owned PV systems. Key words: photovoltaic, PV, solar, homes, residential, property value, selling price, premium, hedonic, California, new homes, existing homes, host  owned iv
10. It is important to clarify that this research focuses on only host  owned PV systems and therefore excludes third  pa rty  owned systems, which, we recommend, should be the focus of future research. The remainder of this report is organized as follows: Section 2 discuss es our methodological approach ; Section 3 details the data used for the analysis ; and Section 4 presents the results, followed by a discussion of the results in Section 5 and conclusions in Section 6 . An appendix detailing cost estimate preparation follows the references. 3
25. newly built homes have PV systems that are also new. Table 9 contains the results for the full set of existing homes and the four other quartile models . E ach of the four quartile models uses a different set of PV homes and a set of non  mutually exclusive CEM matched non  PV homes, to which the PV homes are compared. 32 The coefficients for each progressively older subset of PV systems are monotonically ordered , going from 0.0123 for the systems 0.5 – 2.4 years old to 0.0055 for systems 5.9 – 14 years old. These translate into premiums of $5.90 / W for the newest systems and $2.60 / W for the oldest systems, with relatively stable 95% confidence intervals of approximately $1.40/ W and somewhat decreasing cost and income e stimates. Clearly home buyers and sellers place greater value on newer sys tems than on older systems , all else being equal . Although not shown here, additional models were estimated with additional older age group s (e.g., 10 – 14 years) , but the confidence intervals around those estimates increased such that the results were not a ny more revealing than what is presented here . In none of the models, however , did we find an estimate close to zero. This seems to indicate that , as systems age, their value flatten s out, but additional analysis in future years is needed to understand thi s trend better . 33 Finally, it appears that the premiums, as systems age, start well above what would be predicted by the net cost estimates for young systems and then fall well below what would be predicted by the net cost estimates for older systems. This is an artifact of how the net cost estimates are calculated. As discussed in Section 3.2 the cost estimates are prepared without any depreciation and therefore are estimates of a new system. Of course new systems likely would not have the same value as otherwise identical older systems, but knowing the correct amount of depreciation to apply to these estimates is beyond the scope of this work. 32 As described above, because the characteristics on which the PV homes are matched to the non  PV homes are exclusive o f PV system age, the set of non  PV homes (and the block groups in which they are located) are not mutually exclusive across the models, but the same rules apply to these subsets in that for each block group that contains a PV home at least one matched non  PV home is present. 33 Additionally, we calculated a linear estimate of age of PV interacted with PV system size, which was, not surprisingly, negative and highly statistically significant. Although this reaffirms that increasing age of PV systems is highly correlated with lower premiums, by its very nature it implies that PV systems lose 100% of their value at some point in time. This was calculated to be about 13 years, but it is at the end of our dataset and is not borne out in other tests (e.g., bins sho wn above, polynomial interactions, and additional binning for older systems). Therefore, we conclude that older systems are of lower value, but not of no value, at least given the age distribution of 0 to 14 years contained in the sample. 18
31. Are PV home premiums outside of California similar to those within California? As shown in Table 8 and Figure 1 , premiums for PV h omes are estimated , on average, to be $1.10/W larger in California than out side of California . However, this difference, given the relatively large margin of error around the Rest of U . S . estimate, is not statistically significant. That notwithstanding, the apparent difference seems to echo decreases in each of the three othe r contributory value estimates we derived. For example, the g ross and net cost s in California are $1.30/ W and $1.07/ W higher than outside of California. Similarly, the PV Value income estimate is $ 0.80 / W lower outside of California. In any case, t hese find ings should give stakeholders outside of California greater confidence th at PV adds value to homes in the ir market s . How do PV home premiums compare to contributory values estimated using the cost and income methods? The market premiums estimated f r o m our suite of models seem to follow , at least to some degree, the contributory  value net cost e stimates and, to a lesser degree , the PV Value estimates using the income approach , but not the gross cost estimates . For example, as shown in F igure 1 , both the California and Rest of U . S . estimates are within a few pennies of the net cost estimates, but they are more than $2.50 /W less than the gross cost e stimates. Si milarly, the Year of Sale Model results show PV premiums that are not statistically different in any period from the net cost estimates ( Table 10 and Figure 2 ) despite widely changing gross cost estimates and u nderlying housing mark et tumult . Therefore , the net cost estimates — which account for the federal, state , and local incentives available at the time of sale — seem reasonably related to the value added (PV premiums) at least among average PV systems in our sample. Since the data i ndicate that, for the average systems in our sample, the PV premium is similar to the net cost estimate, it is reasonable to conclude the incentives are offsetting the influence of depreciation for those systems . At the same ti me and as discussed in furthe r detail later, net cost estimates diverge from the calculate d market premiums for those PV systems that are considerably newer or considerably older at the time of home sale. D epreciation in PV premiums is therefore apparent when other PV system ages are considered. As such, adjustments to net cost estimates may be required to account for market  derived depreciation. In this instance, it may be necessary for appraisers to estimate physical de terioration and functional obsolescence in situations where replacement costs exceed the contributory market value of older systems . 24
18. in . 21 We distinguish between the two because the ability of the homeowner to benefit from the incentives de pends somewhat on their tax obligations. For example, the federal incentive for PV comes in the form of a reduc ed federal tax obligation (formally known as the Internal Revenue Code Section 25D: Residential Energy Efficient Property Credit ) . I f a home owner expects to pay very little in taxes (e.g., because they have a mortgage and very little taxable income) , then the federal tax incentive might not be realized immediately (it can be carried over year to year). A similar scenario exists if state tax in centives are present . More generally, incentive availability changes with time, so home buyers may have some uncertainty about what incentives might be available, and their value. B ecause of these different scenarios, it is not immediately clear if the mar ket would fully capitalize the incentives calculated as part of the net cost , thus net cost can serve as the low cost estimate for our purposes . Similarly, we expect that buyers would not be willing to pay more than the gross cost , which thereby serve s as the high cost estimate . Finally, i n previous analys es, we prepared cost estimates depre ciated using a straight  line 20  year depreciation schedule , assuming this would be roughly equivalent to the usable life of a PV system ( Hoen et al., 2011 ; 2013a ; 2013b ) . For the present analysis we use, instead, the un  depreciated a mount. In doing so , we do not presuppose how the market depreciates PV systems and/or the replacement costs of those systems ; rather , we allow the market to dictate how best to depreciate their values, if at all. This i s the customary approach of appraiser s ( Adomatis, 2014 ) . 3.3 Income E stimates U sing the PV Value Algorithm As with cost estimates, a ppraisal theory posits that income estimates — a discounted stream of income derived from an asset over time, such as rent — are likely important price signals in the marketplace . For example, an a partment seller might not be willing to sell a property for significantly less than the present value of rent (minus costs) it receives for that property. Similarly, the buyer and seller of a home with a PV system might use the discounted value of the syst em’s energy cost savings as a key factor in determining any PV premium. F or each of the PV homes in our sample, we prepared data to estimate the present value of energy bill savings ( income e stimates ) using the size and age of the system , the zip code of the home, and the estimated tilt and azimuth of the system. 22 These inputs were fed through the PV Value algorithm ( Klise et a l., 2013 ) to produce estimates for utility bill savings for a similarly sized system as of the time of sale . 23 The algorithm is outlined by Klise and Johnson (2012) , and the inputs for our current research effort are based on the following: the expected energy out put of the PV system after the sale date and assuming a life span not greater than the warranty life of the panels (usually 25 years); an electricity retail rate at the time of sale and an escalation of the rate similar to the historical escalation over th e previous years; discount rates as of the time of sale, which , for the purposes of this study, are equivalent to 100 basis points above the 30  year, fixed mortgage, 60  day Fannie Mae lock  in rate at the time of sale; a system 21 Other incentives exist, such as state renewable energy credits, feed  in tariffs, and performance  based incentives, but these are rare throughout the analysis dataset and therefore are not considered. Understanding how to value them appropriately should be the subject of future research, however, because their value can be significant in certain circumstances. 22 Because tilt and azimuth were not available for all PV systems (the data were not provided during the TTS data  collection effort), they were estima ted via a cascading approach, based on systems with those data in the same census block group if available, then, if not available, census tract or, finally, county when needed. 23 The estimation procedure produces a set of low, average, and high estimates of the present value of the expected energy output, based on a risk premium of 50, 100, and 200 basis points, respectively. O nly the average value was used for this analysis . 11
34. cannot be claimed by new home builders but instead only by the buyer of the home. 37 Therefore, the new home buyer not only r eceives the PV system on the home, but will also be able to receive a tax credit. Correspondingly, the net cost of the builder should not include this federal ITC reduction and , therefore , should be approximately $1.26 /W higher and should affect the premiu m the buyer paid . T his is interesting because we do not see a premium that refle cts this incentive. If we did, the premium would be approximately $ 1.26 / W higher or $4.84 / W; instead we find a premium of $3.58/ W . 38 Understanding the exact reasons for this discounting is beyond the scope of this work, but several plausible explanations exist: home builder discounting — the builder discount s the home for other reasons, for example to sell the home more rapidly (e.g., Dakin et al., 2008 ; SunPower, 2008 ) , which has the effect of obscuring the premium related to the f ederal ITC; buyer discounting — the buyer is not willing to pay the full cost of the tax credit because it cannot be claimed until the following year when taxes are filed and might not be able to be claimed fully because of a lack of tax appetite by the homeowner; and lack of market clarity — because tax rules related to the federal ITC only recently were clarified ( US IRS, 2 013 ) , both the home builder and buyer might not have consistently known if the ITC could be claimed. Is there evidence of a “ green cachet ” for PV homes above the amount paid for each additional watt added? R esults from the Size of PV System Model suggest that the systems with the highest marginal premiums , in terms of dollars per watt , were the smallest systems, and as system size increased the dollar  per  watt premium decreased ( Table 11 ). This decreasing slope is estimated in Figure 4 for PV systems from 1 to 10 kW , w hich shows both the decreasing dollar  per  w att val u e of each additional kilowatt added (left axis) and the total PV system premium (right axis) . This indicates, potentially , that there is a fixed component of PV home premiums that occurs regardless of system size . This might indicate that a green cachet exist s for PV homes in our sample . In other words, buyers might be willing to pay something for having any size of PV system on their home s and then some increment more depending on the size of the system. These finding s echo those found previously ( Dastrup et al., 2012 ) . How does the age of the PV system influence the size of the PV premium? The results from the Age of PV System Models, which explore how premiums change as PV systems age, are shown in Table 9 and Figure 5 . For systems installed on homes just before they were resold, larger premiums were garnered , with premiums falling by almost 60% in the oldest age group compared with the newest group. 39 This indicates that the market quickly depreciates PV systems in their first 10 years at a rate exceeding an average rate of PV efficiency losses, e.g., 0.5%/yea r ( Dobos, 2014 ) , and also exceeding the depreciation expected were straight  line depreciation applied over the asset’s life ; this might indicat e functional obsolescence setting in . Because the mean age for the oldest quartile (5.9 – 14 years) is only 7.8 years ( Figure 5 ), however, we cannot describe PV system values as they age into their second decade. Does their value level out and decrease at the rate of system degradation? Or do they lose 100% of their value before that? Those questions are recommended for future analyses. 37 In this instance we are referring to the federal ITC under Title 26 Section 25D of the Internal Revenue code (see: http://www.dsireusa.org/incentives/incentive.cfm?Incentive_Code=US37F ). 38 The portion of the difference between net and gross cost attributable to the federal ITC ranges from approximately $0.80/W to as high as $1.84/W, with a mean of $1.26/W. 39 Although not shown here, the average size of PV systems was very similar in all fou r age bins, at approximately 4.2 kW. We hypothesize that this larger premium for nearly new systems is related to additional nearly new features installed coincidently or the homeowner not fully taking advantage of tax incentives if they had planned on sel ling the home soon after the installation. 27
17. had not yet been installed as of this previous sale. These “repeat sales” were used in the Repeat PV Home M odel described in Section 2.4.2 . Ideally, for each PV home transaction , we would have a set of identical (i.e., all else being equal ) non  PV home transactions for comparison . This theory underlies the comparable  sales method used by appraisers and other valuation professionals ( Adomatis, 2014 ) , where c omparable homes are chosen that are as similar as possible , and then adjustments are made to account for the observable differen ces. To emulate the comparable  sales method , we employed the Coarsened Exact Matching (CEM) process ( King et al., 2010 ) , which finds a matched sample of PV and non  PV homes that are statistically equal on their covariates. 18 The covariates include being within the same block group , s elling in the same year, and having similar values for size of the home, age of the home, size of t he parcel, and ratio of assessed value of land to total assessed value . 19 This procedure results in a reduced sample of homes to analyze, but biases related to the selection of PV and non  PV homes are minimized. 20 The unmatched dataset has 173,982 non  PV hom e s and 5,373 PV homes, while the matched dataset — the one used for the analysis — has 18,871 non  PV homes and 3,951 PV homes. V arious models , as described above, use subsets of the PV homes and the refore will need matching non  PV homes. For most of the subset s this is straightforward , because we divide the PV and non  PV homes along the same lines used for the CEM matching, such as whether the homes are located in C alifornia or the rest of the U nited States , or if they are newly built homes or existing. For the Age of PV Systems models, though, there is not an intuitive division for the non  PV homes, because age of the PV s ystem was not used for matching. Therefore, for these models the CEM process was employed again for each set of PV homes. The resulting match ed non  PV homes were not necessarily mutually exclusive between the sets of PV homes, but most importantly each block group contained at least one PV home and one non  PV home. 3.2 Cost Estimates In this analysis, as in previous studies ( Hoen et al., 2011 ; 2013a ; 2013b ) , we compare the market premiums we find using our Base Model and alternative m odels to cost and income contributory  value estimates to illuminate how the market might be reacting to various signals . A cost estimate refers to the cost to replace an asset with a new equivalent. A ppraisal theory posits that cost estimates are likely important price signal s in the marketplace , and mar ket values normally should not exceed the replacement cost of an asset . This might mean, fo r example, that a buyer of a PV system already installed on a home is not willing to pay more for it than the cost of a new system (i.e., its replacement cost). For this analysis , we prepared two sets of c ost estimates: gross cost s and net cost s , the detailed preparation of which is described in Appendix A . In this context “net” implies a cost after fede ral and state tax incentives and state rebates are factored in , while “gross” estimates do not factor the se incentives 18 The proced ure used, as described in the referenced paper, is CEM in Stata, available at: http://ideas.repec.org/c/boc/bocode/s457127.html . Because this matching process excludes non  PV homes that are w ithout a statistically similar PV match (and vice versa), a large percentage of homes (approximately 90% of non  PV and 33% of PV) are not included in the resulting dataset. Pre  matching Multivariate Distance (0.95) compares favorably to post  matching Dista nce (0.82). 19 The assessed value of land to total value ratio is expected to capture the unexplained within  block group locational variation that often is present, for example, due to being on a quiet road, abutting a park, or being on the waterfront. Asse ssed values, it is assumed, are consistently applied within the block group. 20 Although the preferred model is one with a matched dataset, the Base Model was also estimated using the unmatched dataset, which results in a slightly higher estimated premium. We attribute this change to the heterogeneity of the unmatched PV and non  PV homes and the fact that the unmatched non  PV homes have lower  valued unobserved characteristics. 10
8. 1. Introduction As of the second quarter (Q2) of 2014, solar photovoltaic (PV) energy systems have been installed on more than a half million homes in the United States ; more than 42,000 systems were installed in Q2 alone , roughly four times the number installed in the same quarter in 2010 ( SEIA & GTM, 2014 ) . This growth is in part related to the dramatic decrease in installed PV cos ts over the last 10 years ( Barbose et al., 2014 ) as well as the incr ease in financing options for property owners installing PV, such as leased PV systems and other zero  money  down purchase options ( SEIA & GTM, 2014 ) . As PV installations have proliferated, so has the number of transactions involving homes with PV ( Hoen et al., 2013b ) . Because of this , the real estate sales and valuation communities have been working t o enable a better understanding of the valuation of PV systems and green features more generally ( Adomatis, 2014 ) . For example, c ourses on the marketing and valuation of green features are available through the Appraisal Institute and the NATIONAL ASSOCIATION OF REALTORS® (NAR) 1 ; gree n attributes for a multiple listing services data dictionary have been recommended by a working group of the NAR ( 2014 ) ; the Appraisal Institute has developed a “ Residential Green & Energy Efficient Addendum ” to capture green attributes during an appraisal 2 ; PV Value ®, a web  based tool specifically designed for the valuation of PV systems , has been developed ( Klise et al., 2013 ) ; the National Home Performance Council and CNT Energy developed a bluepri nt to make energy improvements more visible in the real estate market ( CNT Energy & NHPC, 2014 ) ; Fannie Mae, in its updated standards for conforming loans it will repurchase, now mentions homes with solar panels and the need to “adjust” the appraised value of the home if the market warrants it ( Fannie Mae, 2014 ) ; and , finally, the Federal Housing Administration has proposed requirements for valuing “Special Energy Related Building Components” in its Draft Single Family Housing H andbook , which governs conforming loans for homes with PV systems ( FHA, 2014 ) . Despite th e activity around valuing (and marketing) PV homes , little research documen ts the premiums for these homes . Farhar and Coburn (2008) first documented the apparent increase in values for 15 PV homes inside a San Diego subdivision. This was later corroborated by strong empirical evidence from greater San Diego and Sacramento ( Dastrup et al., 2012 ) and from a relatively large dataset of approximately 1,900 California PV homes ( Hoen et al., 2011 ; 2013 a ; 2013b ) ; these studies employed hedonic pricing models to e stimate premiums . Finally, a case study of 30 PV homes tha t sold in the Denver metro area found evidence of premiums ( Desmarais, 2013 ) . Because the evidence that PV homes garner a premium has focused on a relatively small number of California homes and a f ew in Colorado, there is need for further evidence of premiums outside of California and even inside California . There is also a need to analyze transactions that occurred after the recent housing bubble, the period from whi ch most previous data had been c ollected and analyzed ( Hoen et al., 2011 ; 2013a ; 2013b ) . In most local markets, few PV home sales occur , thus appraisers and other r eal estate professionals ( real estate agent s, lenders , underwriters, etc.) often cannot compare similar PV and non  PV home sales to derive a PV premium. Because of this, valuation professio nals often use other methods to value PV systems, including the income and cost methods ( Adomatis, 2014 ; FH A, 2014 ) . Hoen et al. (2013 b) used hedonic (regression) model ing , employ ing similar methods as the sales  comparison approach , a nd found pr emiums larger than the contributory values generated with the cost and income approaches — a counterintuitive result. Possible reasons for this result includ e issues with the underlying dataset, which 1 See, e.g., http://www.appraisalinstitute.org/education/education  resources/green  building  resources/ and http: //www.greenresourcecouncil.org/ . 2 See http://www.appraisalinstitute.org/professional  practice/professi onal  practice  documents/new  residential  green  energy  efficient  addendum/ . 1
32. Figure 2 : Year of Sale Model Results Curiously, the PV Value income estimates are consistently lower than the premiums found in the m arket, while theory holds that cost savings should be a strong price signal . One reason for this disparity, which is especially evident in the California subset , might be related to the PV Value inputs that we used in this study , which were based on the av erage retail electricity rate. In California, tiered volumetric rates , which are based on the customer’s consumption, are normal for most of the state’s residential PV customers ( CPUC, 2013 ) . If customers consume more than the average retail customer, then they will be moved into higher  priced tiers. These tiers can be dramatic , with a doubling or even tripling of rates, depending on which tier the consumer falls into ( CPUC, 2013 ) . PV customers tend to be larger consumers of electricity than the average retail customer in California, thus they often pay more than the aver age ( Darghouth et al., 2011 ; CPUC, 2013 ) and , with a PV system, may avoid higher  cost tiers altogether, increasing the value of the avoided costs . We cannot de termine t he exact level of this increase for the specific PV home s in our sample , but e ven a $0.05 /kWh increase in the rate, which is well within the range proposed by others for PV customers ( CPUC, 2013 ) , would result in a substantial increase in the income estimate. The mean default electricity rate we entered into PV Value for the California portion of our sample is $ 0.15 43/kWh. If that rate increased by $0.05/kWh, it would increase the PV Value estimate from $2.93 /W to almost $4/ W , within the margin of error of our premium estimate. Therefore, it seems possible that buyers and sellers might be using the cost savings as an important price signal, but they are estimating those savings at a slightly higher rate than the tool’s default average retail rate. I t is recommended that , when ti ered rates are present that deviate substantially from the default average rate and normal consumption for a particular home would put the homeowner in higher tiers, users of the PV Value tool should input a custom rate that is more appropriate. 36 How did the size of the premium change over the study period, as gross PV system prices decreased and during housing market swings ? W hile gross cost s decreased dramatically over the study period, dropping 40% from $8.97 /W in the 2002 – 2007 period to $5.45 /W in the 2012 – 2013 period, PV premiums remained fairly consistent around 36 For example, for California customers where tiered rates are common, weighting based on the tiers and the usage within each tier for particular PV homes might result in a more appropriate input rate. $ $1.00 $2.00 $3.00 $4.00 $5.00 $6.00 $7.00 $8.00 $9.00 $10.00 20022007 20082009 20102011 20122013 $ Per Watt (DC) Installed of PV Year of Sale Error bars represent 95% confidence interval PV Premium ($/watt) PV Value  Income ($/watt) Net Cost ($/watt) Gross Cost ($/watt) 25
14. 2.4 Robustness Models We also explore the robustness of our results with two alternative model specifications. 2.4.1 PV Only Model It has been well documented that PV homes often have a suite of additional energy  efficiency ( EE ) features (CPUC, 2010 ; Hee et al., 2013 ; Langheim et al., 2014 ) . Further , it has been theori zed that PV home owners, who have the financial resources to install a PV system, might also make other (non  EE) upgrades , such as a new kitchen or bathroom , or may alternatively replace their roof contemporaneous ly with PV system installation . Therefore, the premium estimated from Equation (1) could also include effects of EE and other features and therefore overestim ate the e ffect related to PV alone . To test this , PV homes are compared to other PV homes based on system size . Wh ile the Base Model estimates a difference in sales prices between PV and non  PV homes , all else being equal , the PV Only Model compares the difference between PV homes and PV homes based on differences in their PV system size , all else being equal . Assuming all PV homes have the same frequency of EE and other features among them, an effect free of those influences can be estimated and then com pared to the results in Equation (1) . 10 O ne complication of this model concerns possible collinearities of the block group fixed effects and PV when a single or small number of PV homes exist within a single block group . While in the Base Model the use of the block group fixed effect is appropriate , because each contains at least one PV and one non  PV home, in the PV Only Model collinearities might exist for bl ock groups with only one or a few PV home s , or those that might have only similarly sized PV systems . In those block groups , the fixed effect might absorb the contributory effect of the PV variable . Therefore , this model uses the county as the fixed effect and is restricted to counties that have two or more PV homes, to allow more heterogeneity between the PV homes with in the fixed effect delineation and therefore less collinearity b etween them and the PV variable ; o therwise the model is identical to Equation (1) . 11 2.4.2 Repeat PV Home Model A common concern with hedonic model ing , such as the Base Model , is that a suite of home and site characteristics are not c ontrolled for , which could be driving the results. These omitted variables could include any manner of home features , such as granite countertops, a newly renovated basement, and Jacuzzi , as well as neighborhood features , such as locat ion on a cul  d e  sac, a scenic vista, or l ocat ion next to a major road . T hese variables could be present for PV and non  PV homes. Although t he assumption is that these unobserved features are randomly distributed among PV and non  PV homes, and therefore are not correlated with the presence of PV, this might not be the case. T his can be tested using the Repeat PV Home Model. The Base Model estimates a difference in sales prices between PV and non  PV homes all else being equal , but the Repeat PV Home Model compares sales prices of homes before they had PV installed to prices of the same home s after they had PV installed. Because many of the characteristics controlled for 10 It is at least conceivable that EE and other features are correlated with PV system size, with a larger PV system correlated with more EE and other features. We expect, however, that this would likely be more correlated with the size of the home, which is controlled for in this and the Base Model. 11 Although not shown here, using county fixed effects in the Base Model in place of block group fixed effects has no apparent effect on the premium estimate, and therefore this PV Only Model can be compared directly to the Base Model results. Also, this model assumes a tradeoff with being able to compare PV homes to PV homes, and therefore controlling for the unobservables associated with PV, versus controlling for the unobservables associated with the localized neighborhood effects that the block group fixed effect controls for. 7
23. Table 7 : Base Model Results Variable C o e ffic ie nt Standard Erro r t Statis tic p value  95% CI + 95% CI intercept 12.498 0.016 758.00 0.000 12.465 12.530 pv*size 0.0091 0.0007 13.12 0.000 0.0078 0.0105 sfla1000 0.213 0.004 51.70 0.000 0.205 0.221 lt1acre 0.386 0.028 13.73 0.000 0.331 0.441 gt1acre 0.029 0.006 5.08 0.000 0.018 0.040 age 0.007 0.001 7.86 0.000 0.008 0.005 agesq1000 0.056 0.009 6.63 0.000 0.040 0.073 syq 20021 0.441 0.034 13.100 0.000 0.507 0.375 20022 0.379 0.038 10.060 0.000 0.453 0.305 20023 0.375 0.036 10.480 0.000 0.446 0.305 20024 0.306 0.073 4.220 0.000 0.448 0.164 20031 0.087 0.056 1.560 0.118 0.196 0.022 20032 0.077 0.037 2.050 0.040 0.150 0.004 20033 0.025 0.038 0.670 0.505 0.100 0.049 20034 0.035 0.037 0.950 0.343 0.108 0.037 20041 0.001 0.031 0.040 0.972 0.060 0.062 20042 0.095 0.021 4.430 0.000 0.053 0.137 20043 0.121 0.024 5.120 0.000 0.075 0.168 20044 0.124 0.028 4.340 0.000 0.068 0.179 20051 0.137 0.047 2.910 0.004 0.045 0.230 20052 0.204 0.039 5.170 0.000 0.127 0.281 20053 0.164 0.062 2.640 0.008 0.042 0.285 20054 0.202 0.038 5.340 0.000 0.128 0.276 20061 0.159 0.021 7.710 0.000 0.119 0.200 20062 0.163 0.021 7.900 0.000 0.123 0.204 20063 0.160 0.022 7.300 0.000 0.117 0.203 20064 0.071 0.022 3.240 0.001 0.028 0.114 20071 0.162 0.017 9.700 0.000 0.129 0.195 20072 0.124 0.020 6.170 0.000 0.085 0.163 20073 0.074 0.016 4.580 0.000 0.042 0.106 20074 0.002 0.018 0.100 0.919 0.034 0.038 20081 0.022 0.016 1.360 0.175 0.010 0.054 20082 0.005 0.013 0.380 0.707 0.031 0.021 20083 0.050 0.014 3.690 0.000 0.077 0.023 20084 0.066 0.014 4.630 0.000 0.094 0.038 20091 0.113 0.014 8.070 0.000 0.141 0.086 20092 0.116 0.012 9.800 0.000 0.139 0.092 20093 0.124 0.012 10.610 0.000 0.147 0.101 20094 0.120 0.012 9.700 0.000 0.144 0.096 20101 0.121 0.013 9.030 0.000 0.147 0.095 20102 0.124 0.012 10.750 0.000 0.147 0.102 20103 0.144 0.012 11.660 0.000 0.168 0.120 20104 0.171 0.012 14.070 0.000 0.194 0.147 20111 0.173 0.011 15.170 0.000 0.196 0.151 20112 0.189 0.011 17.360 0.000 0.211 0.168 20113 0.190 0.011 17.040 0.000 0.212 0.168 20114 0.205 0.011 18.360 0.000 0.227 0.183 20121 0.212 0.011 19.000 0.000 0.234 0.190 20122 0.176 0.012 15.180 0.000 0.199 0.153 20123 0.154 0.011 13.660 0.000 0.176 0.132 20124 0.123 0.012 10.220 0.000 0.147 0.099 20131 0.090 0.010 9.480 0.000 0.109 0.072 20132 0.038 0.009 4.150 0.000 0.056 0.020 20133 0.009 0.009 1.000 0.317 0.027 0.009 20134  omitted  16
30. 5. Discussion of Research Questions This section explores in more detail the seven research questions listed in Table 1 , building on the full set of results described above. Are PV home premiums evident for a broader group of PV homes than has been studied previously both inside and outside of California and through 2013? PV home premiums have been found by previous research of transactions of 15 PV homes in one California subdivision from 2001 – 2006 ( Farhar and Coburn, 2008 ) , of 594 PV homes in the San Diego and Sacramento metro areas between 1997 – 2010 ( Dastrup et al., 2012 ) , o f approximately 1 ,9 00 PV homes in 31 California counties between 1999 – 2009 ( Hoe n et al., 2011 ; 2013a ) , and of 30 PV homes in the Denver metro area between 2011 – 2013 ( Desmarais, 2013 ) . This analysis more than doubles the number of transactions analyzed , with data on almo st 4,000 PV home transactions across 102 different counties in eight different states, including California , Connecticut , Florida , Massachusetts , Maryland , North Carolina, New York, and Pennsylvania . Th e data span the period from 2002 to 2013, with more th an a third from 2012 and 2013 alone. The Base Model and Location Models ( Table 8 and Figure 1 ) show a consistent difference in PV home prices compared to matched non  PV homes across the dataset, with premiums rang ing from a bit more than $4/ W in California to approximately $3/ W outside of California , both of which are highly statistically significant. 35 Moreover, this premium , as shown in the Year of Sale Models ( Table 10 and Figure 2 ), survived both the dramatic decrease in installed costs over the study period as well as the market tumult which was the housing bubble, subsequent crash , and recovery. Clearly buyers of homes with PV are willing to pay a premium for PV , and this trend has continued despite dramatic changes in both the PV and housing markets. Finally, similarly sized premiums are found for the two robustness models — the PV Only Model and the Repeat PV Home Model — which further validates these results . Figure 1 : Base and Location Model Results 35 The standard error for the Base Model of 0.0007 is 35% of the standard error found in the previo us analysis of California PV homes of 0.0018 (Hoen et al. 2011; 2013a), indicating the increased precision of this estimate. $ $1.00 $2.00 $3.00 $4.00 $5.00 $6.00 $7.00 $8.00 All Homes California Rest of US $ Per Watt (DC) Installed of PV Error bars represent 95% confidence intervals PV Premium ($/watt) PV Value  Income ($/watt) Net Cost ($/watt) Gross Cost ($/watt) 23
15. in the Base Model are held constant in the Repeat PV Home Model, such as block group and size of the home and parcel, they do not need to be controlled for. 12 Therefore, the following greatly simplified model can be estimated: ( ) ( ) ( ) itk 1 i 2 i 3 i i itk a ln(P ) T X PV SIZE αβ β β ε =++ + ⋅+ ∑ ( 3 ) where X i is a vector of age of the home and age squared for transaction i , β 2 is a vector of parameter estimates for age and age squared , β 3 is a parameter estimate for the change in sale price for each additional kilowatt added to a PV system, and all other variables are as defined in Equation (1) . 12 Ideally we would have information on the size of the home as of the first sale and the second sale, but we only have information from the most recent assessment and therefore can only assume that it has not changed between sales. If it has changed, however, it wo uld have likely increased the home’s value, thus the second sale would include the increase in related value. If this were the case, the PV premium would capture this increase. Our results do not exhibit this increase, so it is assumed that the Repeat PV H ome Model results are free of this influence. 8
33. $4/ W (see Figure 2 ). During this same period, the housing market was in upheaval, with a sizable rise, a subsequent crash, and then a recovery. This seems to show , first, that the gross cost is not a strong market signal. Rather, net cost , which over all periods was not statis tically different from the premium, seem s to be the more significant price signal. Moreover, it shows that the PV premium has been reasonably consistent during widely varying housing market conditions. Are premiums for new PV homes similar to existing PV home premiums? The results from the Home Type Model, which explore s differences between new and existing home premiums , are shown in Table 8 and Figure 3 . The average n ew h ome p remiums of $3.58/ W are lower than the e xisting h ome premiums of $4.51/ W , a non  statistically significant difference of $0.93/ W ( p  value = 0.46) . T he net cost estimates for new h omes are also lower (by $0.44/ W ) than those of e xisting homes, potentially explaining some of the difference. P revious analyse s found large , statistically s ignificant differences between n ew and e xisting home premiums ( Hoen et al., 2011 ; 2013a ; 2013b ) . These differences oc curred because e xisting h ome estimates were larger (near $6.50/ W ) and n ew h ome estimates were smaller (near $2.5/ W ) than found in the present analysis. It appears, based on analysis not shown here, that high  priced homes (e.g., over $1 million) , which were included in the past analyses (up to $3.3 million) but excluded from this analysis , might explain a large portion of the differences. Including those homes in our analysis increased the existing home premiums and lowered the new h ome premiums, although no t to the extent found previously. Including these homes also increased the margin of error around the estimates , however, implying that our model s did a poorer job of explaining price differences and that many home and site characteristics for these homes likely are not included in the models . Further, the pre vious analyse s included home transactions only through 2009, but this analysis included transactions through 2013 , with two thirds occurring after 2009 . In summation, this analysis is likely a better r epresentation of the current market for most PV homes because it included many more recent sales, had more sales in total, and excluded high  priced homes (over $1 million) that were difficult to model , but it does not find a statistically significant diffe rence between new and existing homes . Figure 3 : Home Type Model Results One additional nuance to the present finding s involves the new home premium and the net cost estimate. As discussed in Section 3.2, the net cost estimates (e.g., shown in Figure 3 ) represent the gross cost estimates less the appropriate federal and state incentives (and rebate s where appropriate) . T he federal incentive, which normally comes in the form of an investment tax credit (ITC) , is calculated as 30% of the gross cost of a PV system after state and utility incentives are applied. Interestingly, this incentive $ $1.00 $2.00 $3.00 $4.00 $5.00 $6.00 $7.00 $8.00 All Homes New Homes Existing Homes $ per Watt (DC) Installed of PV Error bars represent 95% confidence interval PV Premium ($/watt) PV Value  Income ($/watt) Net Cost ($/watt) Gross Cost ($/watt) 26
19. direct current  to  alternating current derate factor of 0.77% ; a module degradation factor of 0.5% per year; and an expected inverter replacement at 15 years . T iered rates, which are prevalent in California, are not considered here, but instead an average zip  code level rate is used , a s is the default for PV Value . We return to t his issue in Section 5 , wh ere we discuss results from the model estimation in comparison to the income estimates. The description s of th e income estimation procedure are contained elsewhere ( Klise and Johnson, 2012 ; Appendix A in Hoen et al., 2013b ; Klise et al., 2013 ) and therefore are not detailed here . 3.4 Data Summary The final dataset includes 22,822 transactions , consisting of matched PV ( n = 3,951) and non  PV ( n = 18,871) homes. This full matched dataset is comp osed of transactions occurring across eight states ( Table 2 ) from 2002 to 2013 ( Table 3 ) , with the vast majority in California . All PV systems in this dataset are homeowner owned as opposed to third  part y owned (leased or under a power  purchase agreement ). Table 2 : Fr equency Summary of P V and Non  PV Homes b y State Table 3 : Frequency Summary of PV and Non  PV Homes by Sale Year Summary statistics for the PV and non  PV homes are shown, respectively, in Table 4 and Table 5 . The mean sale price ( sp ) of the PV home s in the sample is $47 3, 373 and range s from a min imum of $165,500 to a maximum of $899,500. The average PV home in the sample has 2,334 square feet of living area State NonP V Homes PV Homes Total CA 18,207 3,828 22,035 FL 317 25 342 Mid A tla ntic R e gion: MD , N C , P A 288 77 365 Northeast Region: CT, MA, NY 59 21 80 Total 18,871 3,951 22,822 Sale Year NonP V Homes PV Homes Total 2002 107 18 125 2003 196 31 227 2004 238 53 291 2005 197 56 253 2006 348 64 412 2007 818 242 1,060 2008 1,251 453 1,704 2009 1,762 429 2,191 2010 2,751 504 3,255 2011 3,341 642 3,983 2012 3,928 694 4,622 2013 3,934 765 4,699 Total 18,871 3,951 22,822 12
9. included sales from homes with a very wide range of price s and sales t hat occurr ed largely during the housing boom. In addition to that California  based study, Desmarais (2013) compared the three methods in her analysis of 30 Colorado sales but did not us e statistical tests . Therefore, add itional compa rison of the various methods — using a more recent dataset, statistical methods, and a broader group of transactions — would b e a valuable contribution to the literature. Other considerations are important as well. T he gross installed costs (i.e. , costs before state and federal incentives) of PV systems have declined steadily in recent years , while net cost s (i.e., with incentives included) have remained fairly stable ( Barbose et al., 2014 ) . Examining premium changes over th is period might indicate how the market responds to signals from gross and net costs. Moreover, over the same period, the housing market saw significant swings: the housing bubble, the subsequent crash, and then the recovery. Understanding whether observed PV premiums varied over this period would help illuminate how enduring these premium s might be. T here also has been evidence that the new home market in California heavily discounted PV homes during the housing boom and bust (through 2009) in comparison to the premiums garnered by existing home sellers ( Hoen et al., 2011 ; 2013a ) . 3 Therefore, examining how new hom e PV premiums fared in relation to existing home premiums with in an expanded dataset would be of interest. In a ddition, others have explored the existence of a green cachet , such as the “Prius effect” and other forms of “ c onspicuous ( non ) c onsumption , ” whe re buyers appear to pay more for a “ green ” item than they will save over its life in decreased energy costs ( White, 1978 ; Kahn, 2007 ; Sexton, 2011 ) . Dastrup et al. (2012) find larger PV premiums where more Pri us hybrid vehicles are registered, which they use as a proxy for environmental leanings. T his analysis concentrated on only the San Diego and Sacrame nto areas, thus analysis of a broader dataset is warranted. Finally, previous literature suggests the need for more research o n the market’s depreciation of aging PV systems , especially for systems greater than 6 years old, which have not been well studied because of the immaturity of the PV market ( Hoen et al., 2011 ; 2013a ; 2013b ) . A clearer understanding of how the market depreciates PV systems would likely enhance appraisal techniques. In summary, there are a number of gaps in the literature, each of which the present research seeks to address: 1. Are PV home premiums evident for a broader group of PV homes than has been studied previously both inside and outside of California and through 2013 ? 2. Are PV home premiums outside of California similar to those within California? 3. How do PV home premiums compare to contributory values estimated using cost and income methods? 4. How did the size of the premium change over the study period, as gross PV system prices decreased and during housing market swings ? 5. Are premiums for new PV homes similar to existing PV home premium s ? 6. Is there evidence of a “ green cachet ” for PV homes above the amount paid for each additional watt added? 7. How does the age of the PV system influence the size of the PV premium ? 3 These discounts, it was assumed, were offset by decreased marketing times (i.e., “sales velocity”) for these homes, a priority for home builders as the market for new homes slowed and inventories increased ( Dakin et al., 2008 ; Farhar and Co burn, 2008 ; SunPower, 2008 ) . 2
29. Model where PV homes are compared to non  PV homes. When comparing PV homes to other PV homes, as in the PV Only Model, or the same PV home to itself over multiple transactions, as in the Repeat PV Home Model, we find little evidence to support the claim that the Base Model PV premium estimate is biased . Therefore , there appear s to be no evidence that the PV es timate also c ontains the effects of other omitted features such as EE upgrades. Table 12 : Robustness Model Results PV Pre mium Es timate s All Home s PV Only Repeat PV*Size Coefficient 0.0091 0.0092 0.0087 P V*Size Standard Error 0.0007 0.0028 0.0055 P V *Size p value 0.000 0.001 0.113 Mean Sale Price NonPV ($) 456,377 $ 474,529 $ 528,368 $ PV Premium ($/watt) 4.18 $ 4.37 $ 4.60 $ 95% CI ($/watt) 0.62 $ 2.62 $ 5.69 $ Contributory Value Es timate s PV Value  Income ($/watt) 2.93 $ 2.93 $ 2.15 $ Net Cost ($/watt) 4.14 $ 4.14 $ 3.09 $ Gross Cost ($/watt) 6.90 $ 6.91 $ 5.64 $ M ode l Info Total n 22,822 3,915 1,698 PV n 3,951 3,915 849 NonP V n 18,871  849 Adjusted R 2 0.92 0.68 0.23 Dependent Variable lns p lns p lns p Fixed Effects n 1,830 65 n/a 22
22. Accordingly, at the 95% confidence interval, average price increases are estimated to vary between approximately 0.78% and 1.05% per kilowatt, a relatively precise estimate. T his sample of approximately 4 , 000 PV homes shows a clear premium for each kilowatt of PV installed above the sale prices of comparable non  PV homes. By using the mean sale price (in dollars) for non  PV homes , we can convert this percentage estimate into dollars per watt. 29 Doing so leads to an estimated premium of $4.18/ W , w ith a 95% confidence interval of +/  $0.62/ W , which corresponds to a premium of approximately $15,000 for an average  sized system of 3.6 kW . From Table 4 , we see that , for these PV homes, the mean gross cost estimate is $6.90/ W , while the net cost estimate is $4.14/ W , and the average PV Value ( i ncome) estimate is $2.93 / W . Therefore, the premium in our sample is almost identical to the average net cost for a similarly si zed system as of the time of sale , is approximately $2.70 /W less than the gross cost , and is $1.25 /W higher than the PV Value income estimate. 4.2 Base Model Variations Using Sub s amples As shown in Table 1 , many of the research questions can be investigated using variations of the Base Model that us e subsamples of the data in place of the full sample . The following sections describe those model sets and include: Location Models, for California and the rest of the U nited States ; Home Type Models, for newly built and existing homes; Age of PV System Models; and Year of Sale Models. 4.2.1 Location Model Results Our Location Models estimate premiums for e ither the subset of homes located in California or those located in the rest of the United States; Table 8 shows the results, along with results for the Home Type Mod els (which are discussed in the next subsection). 30 Also shown in the table, for reference purposes, are the results for the Base Model using the full sample. Results shown for each model include the pv*s ize coefficient, standard error, and p  value; the mea n non  PV home sale price; the $/W premium and its 95% confidence i nterval; and estimates for the n et and gross cost s and PV Value income . Finally, for each model, the table shows the total, PV, and non  PV sample sizes; the adjusted R 2 ; and the number of bl ock groups represented by the sample. The coefficient for the variable of interest for the California subsample is 0.0 0 91, which is highly statistically significant and equates to a $4.21/W premium and a 95% confidence interval of +/  $0.64/W. Not surpris ingly, the PV premium is very close to the premium estimated for the full sample, because California PV homes make up 97% of that sample. The PV premi um can be compared to the net, g ross, and PV Value estimates of $4.16/W, $6.94/W, and $2.95/W, respectivel y. For homes outside of California where we have data (in Connecticut, Florida, Massachusetts, Maryland, North Carolina, New York, and Pennsylvania), the PV premium is estimated to be $3.11/W and highly statistically significant ( p  value < 0.01) , but with a 95 % confidence interval of $2.33 . This indicates that, in this broader sample of homes, a premium for PV homes is evident , but that the smaller sample of homes outside California does not allow for a very precise estimate of the effect size . The estimated premium is very similar to the net cost estimate for this subset of $3.09/W , and it is not statistically different from the premium estimated for California homes . 29 The formula for doing so is: $/W premium = ((exp ( pv*size coefficient )  1)* mean sale price in dollars for non  PV homes )/1,000. 30 For brevity, only the variable of interest is shown for the remainder of the report. Results for the controlling variables were similarly signed and leveled across the various models as they are in the Base Model. The full set of results is available upon request. 15
37. of depreciation into the second decade of PV systems’ operation — this is an area for future research. Fig ure 6 : Estimated Premiums Based on an Average  Sized 3.6 kW System This study focuses only on homes with host  owned PV systems, as opposed to those with leased PV systems. Future analysis should focus on leased systems, because t hey are a growing portion of the PV home market and have not been studied . In addition , although our sample indicates that , as PV systems age, the size of the premium diminishes, our data are not robust to systems in their second decade ; such older systems should be the focus of future study , as should the appropriate deprecation to place on PV systems throughout their li ves . A lthough this work allows for a robust analysis of average system premiums across the full dataset, and subsets of the data, the resu lts are not necessarily applicable to individual markets and states that might have unique characteristics. Therefore , any market  specific (“small scale”) analysis, especially one that employ s appraisers and other valuers in those local markets, would be b eneficial. Similarly , collecting and analyzing more data in a wide variety of states individually would be useful. B ecause premium differences related to the availab ility of PV homes are unclear , investigating both buyer’s markets (with many PV homes available) and seller’s markets (with few PV homes available) would add clarity to PV home valuation . Finally, very large PV systems and systems on commercial properties were not represented in our data ; both could have unique v aluation characteristics and are thus areas for further study . $ $5,000 $10,000 $15,000 $20,000 $25,000 All Homes California Rest of US New Homes Existing Homes Premium (in $) Error bars represent 95% confidence interval Premiums are based on an average 3.6 kW sized system 30
36. 6. Conclusion As solar photovoltaic (PV) systems become an increasingly common feature of U.S. homes, the ability to value homes with these systems appropriately will become increasingly important. The U.S. Department of Energy estimates that achieving its SunShot PV system price  reduction targets could result in 108 G W of residential rooftop PV installed by 2050 — equivalent to 30 million American homes with PV ( US DOE, 2012 ) . 40 Conversely, capturing the value of PV to residential properties is important for enabling a robust rooftop PV market. Appraisers, sales agents , and others tasked with property valuation have made strides toward valuing PV homes, and several limited studies suggest the presence of PV home premiums , particularly in California . Our study fills important gaps in this literature and illuminate s various factors that might influence U.S. PV home premiums . The study more than doubles the number of PV home sales previously analyzed, examines transactions in eight different states, and spans the years 2002 – 2013, thus encompassing the recent housing boom, bust, and recovery. Based on our results, we draw the following major conclusions: • Home buyers consistently have been willing to pay more for a property with PV across a variety of states, housing and PV markets, and home types. Average market premiums across the full sample of homes analyzed here are about $4/W or $15,000 for an average  sized 3.6  kW PV system ( Figure 6 ) . • Our findings should provide greater confidence that PV adds value to non  California homes. Premiums for PV homes are $1.10/W larger in California than outs ide of California (respectively equating to $16,000 and $12,700 for an average  sized system – Figure 6) , but this difference is not statistically significant : somewhat lower premiums outside of California are consistent with lower net cost and income estim ates. • Net c ost estimates — which account for government and utility PV incentives — seem to be generally consistent with incremental market value premiums for the average PV home in our sample, but they do not appear to account accurately for market  based depr eciation ( the dif ference between value and cost) . PV Value income estimates — which for this study used the d efault average retail rates — we re consistently lower than the calculated market premiums , which seems to indicate that a higher retail rate would be more appropriate for th at portion of the sample where tiered rates were present . • PV premiums remained fairly consistent even as PV gross cost s decreased dramatically over the study period and the housing market went through upheaval. This suggest s that net cost , rather than gross cost , may be the more dominant market signal . It also suggests that PV premiums are robust to housing market conditions. • In contrast to previous studies, our study found a relatively small and non  sta tistically significant differen ce between PV premiums for new and existing homes ( respectively equating to $12,700 and $16,000 for an average  sized system – Figure 6) , likely because our study includes many more sales and recent sales while excluding very  high  priced homes. That notwith standing , there might be some evidence of either home builder or buyer discounting of new home PV systems. • A green cachet might exist for PV homes; that is, buyers might be willing to pay a certain amount for having any size of PV system on their homes and then some increment more depending on the size of the system. • The market appears to depreciate PV systems in their first 10 years at a rate exceeding the rate of PV efficiency losses and of straight  line depreciation over the asset’s life . Our data do not allow analysis 40 A ssuming the average PV system size of 3.6 kW found for all PV homes in this study. 29
11. 2. Methodological Approach T o examine the questions above, this research relies on a hedo nic pricing model — the “B ase M odel” — against which a series of other models are compared. Those other models use a subset of the data (e.g., new or existing homes ) , an interaction term(s) (e.g., age of the PV system), or other variants to examine the various research questions and test the overall robustness of the results. The basic theory behind the hedonic pricing model starts with the concept that a house can be thought of as a bundle of characteristics. When a price is agreed upon between a buyer and se ller , there is an implicit understanding that those characteristics have value. When data from a number of sales are available, the average marginal contribution to the sales price of each characteristic can be estimated with a hedonic regression model ( Rosen, 1974 ; Freeman, 1979 ; Sirmans et al., 2005 ) . This relat ionship takes the basic form: Sales price = f (home and site, neighborhood, and market characteristics) “Home and site characteristics” might include, but are not limited to, the number of square feet of living area and the presence of a PV system. “Neig hborhood” characteristics might include such variables as the crime rate and the distance to a central business district. Finally, “market characteristics” might include, but are not limited to, temporal effects such as housing market inflation/deflation. 2.1 Base Model Th e “Base Model” to which other models are compared use s a relatively simple set of home and site characteristics : size of the home (i.e., square feet of living area); age of the home at the time of sale (in years); age of the home squared (in y ears); size of the parcel (in acres) up to 1 acre; and any additional acres more than 1 (in acres) . 4 It also includes the presence and size of the PV systems. To control for neighborhood , we include a census block group fixed effect, which, in all cases, includes at least one PV home and one non  PV home. 5 Finally, market characteristics are accounted for by including a dummy variable for the quarter and year (e.g., 2013 Q2, 2009 Q1, etc.) in which the sale occurred. This model fo rm was chosen for its relat ive parsimony, its high adjusted R 2 , and its transparency. 6 It is estimated as follows : ( ) ( ) ( ) ( ) itk 1 i 2 i 3 i 4 i i itk a ln(P ) T K X PV SIZE αβ β β β ε =++ + + ⋅+ ∑ ( 1 ) 4 Acres is entered into the model as a spline function using two variables, up to 1 acre ( acreslt1 ) and any additional acres above 1 ( acresg t1 ), to capture the different values of up to the first and additional acres of parcels in the sample. Therefore acreslt1 = acres if acres ≤ 1 and 1 otherwise, while acresg t1 = acres  1 if acres > 1 and 0 otherwise. Additionally, square feet and age squared are entered into the model in 1,000s to allow for easier i nterpretation of the coefficients. 5 A census block group contains approximately 600 to 3,000 people. By including this fixed effect, and requiring each to contain at least one PV and one non  PV home, the PV estimates are, therefore, essentially a comparis on of those two home types within the block group, while controlling for temporal and characteristic differences between them. 6 Model choice for this work was based on extensive robustness model exploration in previous analysis ( Hoen et al., 2011 ; 2013a ; 2013b ) . Other models were explored but are not presented here. They include adding other home and site parameters such as number of bathrooms, condition of the home, and if a pool is present, all of which further limited the dataset but did not substantively affect the results. Similarly, instead of using a fixed effect fo r sale year and quarter, interacting sale year and, separately, sale quarter, with a geographic variable, such as county, to control for geographic variation in market inflation/deflation was explored with no change to the results. 4
39. Hoen, B., Cappers, P., Wiser, R. and Thayer, M. (2011) An Analysis of the Effec ts of Photovoltaic Energy Systems on Residential Selling Prices in California. Lawrence Berkeley National Laboratory, Berkeley, CA. April, 2011. 46 pages. LBNL  4476E. Hoen, B., Cappers, P., Wiser, R. and Thayer, M. (2013a) Residential Photovoltaic Energy S ystems in California: The Effect on Home Sales Prices. Contemporary Economic Policy. 31(4): 708  718. Hoen, B., Klise, G. T., Graff  Zivin, J., Thayer, M. and Wiser, R. (2013b) Exploring California PV Home Premiums. Lawrence Berkeley National Laboratory, Ber keley, CA. December 2013. 41 pages. LBNL  6484E. Kahn, M. E. (2007) Do Greens Drive Hummers or Hybrids? Environmental Ideology as a Determinant of Consumer Choice. Journal of Environmental Economics and Management. 54(2): 129  145. King, G., Blackwell, M., I acus, S. and Porro, G. (2010) Cem: Coarsened Exact Matching in Stata. Stata Journal. 9(4): 524  546. Klise, G. T. and Johnson, J. L. (2012) PV Value ®  User Manual v. 1.0. Prepared for Sandia National Laboratory, Albuquerque, NM. January 31, 2012. 22 pages . SAND2012  0682P. Klise, G. T., Johnson, J. L. and Adomatis, S. A. (2013) Valuation of Solar Photovoltaic Systems Using a Discounted Cash Flow Approach. Appraisal Journal. Fall 2013: 314  329. Langheim, R., Arreola, G. and Reese, C. (2014) Energy Efficiency Motivations and Actions of California Solar Homeowners. Presented at ACEEE 2014 Summer Study on Energy Efficiency in Buildings, Pacific Grove, CA. August 17  22, 2014. NATIONAL ASSOCIATION OF REALTORS® (NAR) (2014) Green MLS Implementation Guide. Chicago, IL. May 2014. 76 pages. V1.0. Rosen, S. (1974) Hedonic Prices and Implicit Markets: Product Differentiation in Pure Competition. Journal of Political Economy. 82(1): 34  55. Sexton, S. E. (2011) Conspicuous Conservation: The Prius Effect and Willingness to Pay for Environmental Bona Fides. Working Paper . Sirmans, G. S., Lynn, M., Macpherson, D. A. and Zietz, E. N. (2005) The Value of Housing Characteristics: A Meta Analysis. Presented at Mid Year Meeting of the American Real Estate and Urban Economics Associ ation. May 2005. Solar Energy Industries Association (SEIA) and GTM Research (GTM) (2014) U.S. Solar Market Insight Report  Q2 2014. GTM Research (GTM) in Boston MA. Prepared for Solar Energy Industries Association (SEIA), Washington, DC. SunPower (2008) New Homes with Sunpower Solar Systems Are Bright Spot in Market. Ryness Corporation Report. June 24, 2008. [Press Release]. U.S. Internal Revenue Service (US IRS) (2013) Q&A on Tax Credits for Sections 25C and 25D. Washington DC. 12 pages. IRS Notice 2013  70. United States Department of Energy (US DOE) (2012) Sunshot Vision Study. Washington, DC. February, 2012. 320 pages. DOE/GO  102012  3037. White, R. D. (1978) Growth Versus Conservation: A Veblenian Perspective. Journal of Economic Issues : 427  433. 32
16. 3. Data Preparation and Summary This section describes the underlying da ta used for this analysis — including PV h ome and non  PV h ome data , c ost estimates, and i ncome estimates — followed by a data summary . 3.1 PV and Non  PV Home Data F or the Tracking the Sun (TTS) report series ( e.g., Barbose et al., 2013 ) , Lawrence Berkeley National Lab oratory was provided a set of approximately 150,000 host  owned (i.e., not third  party  owned) PV home addresses by various state and utility inc entive providers, along with information on PV system size, date the incentive was applied for , date the system was put into service , and the average tilt and azimuth of the PV system, where available . 13 These data span the years 2002 – 2012 and stretch acros s eight states: California , Connecticut , Florida , Massachusetts , Maryland , North Carolina , New York , and Pennsylvania . 14 T he se PV h ome addresses were matched to addresses maintained by CoreLogic , 15 which CoreLogic aggregate s from county  level assessment and deed recorder offices. Once the addresses were matched, CoreLogic provided , when available, real estate information on each of the PV homes as well as similar information on approximately 200,000 non  PV homes located in the same (census) block group as the PV homes. The data for both of these sets of homes included, but were not limited to: • address (e.g., street, street number, city, state and zip+4 code); • most recent and previous (if applicable) sale date and amount; • home characteristics (e.g., acres, s quare feet of living area, bathrooms, pool, and year built 16 ); • assessed value of land and improvements; • parcel land use (e.g., commercial, residential); • structure type (e.g., single  family residence, condominium, duplex); and, • x/y coordinates. These d ata were clean ed to ensure all data were populated and appropriately valued . 17 Using these data, along with the PV incentive provider data, we determine d if a home sold after a PV system was installed , significantly reducing the usable sample because the ma jority of PV homes have not yet sold . We also culled a subset of these data for which previous sale information was available and for which a PV system 13 For a full discussion of how these data are obtained, cleaned, and prepared, see Barbose et al. (2013) . 14 The TTS dataset also included data on PV homes from other states, including Illinois, New Mexico, New Hampsh ire, Oregon, Texas, and Vermont. However, after matching to the CoreLogic sales transaction dataset and cleaning to ensure all the homes that did sell had data that were fully populated and appropriately signed, no PV home sales existed from these states. 15 More information about this product can be obtained from http://www.corelogic.com/ . 16 Year built, along with previous sales information and a CoreLogic  provided flag on new homes, allowed for a determination of whether the home was newly built or existing at the time of sale. 17 Because the CoreLogic data sometimes are missing or miscoded, the cleaning and preparation of these data were extensive and therefore not detailed here, but the process included the follow ing screens: sale price greater than $165,000 and less than $900,000, size of the home between 1,000 and 5,000 square feet, sale price per square foot between $8 and $800, sale year after 2001, and size of the parcel between 0.05 and 10 acres. 9
26. Table 9 : Age of PV System Model Results 4.2.4 Year of Sa le Model Results Because the dataset spans the peri od from 2002 through 2013 , we can examine how premiums change over time. This is especially interesting given that, in th e same period, the costs for PV modules dropped ( Barbose et al., 2013 ) and housing market prices saw a rapid rise , fall , and recovery . W e break the data into four subsamples roughly consistent with these broad changes ( 2002 – 2007 , 2008 – 2009 , 2010 – 2011 , and 2012 – 2013 ) and estimate the Base Model specification for each subsample. Results from these models are contained in Table 10 . The model results for the full datas et are also contained in Table 10 for reference. In each model , the coefficient of the variable of interest, pv*s ize , is highly statistically significant ( p  value ≤ 0.001), with relatively stable standard errors ranging from 0.002 to 0.001, or a tenth of a percent. Despite varying levels of non  PV homes prices, which range from $512,170 to $440,495, premiums are relatively stable , ranging from $3.41/ W to $4.54/ W , wit h none being statistically different from each other over the various periods. During this period, we see mean gross cost s descend from a high of $8.97/ W in 2002 – 2007 to a low of $5.45/ W in 2012 – 2013 . Net c osts fall much less between these two periods, fro m $5.39 /W to $3.58 /W , while PV Value income estimates remain near , or slightly below, $3/ W . D espite falling gross cost s, and shifts in the overall housing market, premiums remain fairly flat and not statistically different fr om the net cost s in all periods and from the PV Value income estimates in two out of four periods. Exis ting Home s 0.52.4 2.43.8 3.85.9 5.914 PV Pre mium Es timate s PV*Size Coefficient 0.0094 0.0123 0.0113 0.0076 0.0055 P V*Size Standard Error 0.0008 0.0014 0.0014 0.0015 0.0016 P V *Size p value 0.000 0.000 0.000 0.000 0.001 Mean Sale Price NonPV ($) 476,124 $ 477,737 $ 474,560 $ 478,634 $ 474,476 $ PV Premium ($/watt) 4.51 $ 5.90 $ 5.40 $ 3.67 $ 2.60 $ 95% CI ($/watt) 0.71 $ 1.30 $ 1.33 $ 1.37 $ 1.51 $ Contributory Value Es timate s PV Value  Income ($/watt) 2.86 $ 3.06 $ 3.03 $ 2.83 $ 2.52 $ Net Cost ($/watt) 4.29 $ 4.49 $ 4.27 $ 4.24 $ 4.16 $ Gross Cost ($/watt) 6.65 $ 7.08 $ 6.65 $ 6.54 $ 6.34 $ M ode l Info Total n 15,342 4,398 3,865 4,100 3,607 PV n 2,507 633 613 635 626 NonP V n 12,835 3,765 3,252 3,465 2,981 Adjusted R 2 0.91 0.93 0.93 0.92 0.90 Dependent Variable lns p lns p lns p lns p lns p Block Group Fixed Effects n 1,766 574 504 509 540 Age of PV Sys te m Groups 19
20. ( sfla ) , is located on a parcel of 0.45 acres ( acres ) , and was 17 years old ( age ) when it sold in 2010 ( sy ) . 24 It has a 3.6  kW PV system ( size ) , which was installed 2.7 years before the home was sold ( pvage ) . The gross installed cost for a similarly sized PV system in the same county at the time of sale was $6.90 /W ( grosscost ) , while the net cost (after incentives) was $4.14 /W ( netcost ) . The prese nt value of the stream of energy produced by the PV system , as calculated by the PV Value algorithm , is $2.93/ W ( income ) . PV systems in the sample range in size from 0.1 kW to 14.9 kW , with a median of 2.8 kW ( size ) . The age of the PV systems at the time o f sale range s from new to more than 13 years , with a median of 2.2 years ( pvage ) . For the 18,871 non  PV homes , we find a mean sale price of $456,378, which is $16,995 lower than that of the matching PV homes . T he average non  PV home is slightly smaller than the average PV home (2,319 square feet), occup ies a smaller parcel ( 0.4 1 acres ) , and is equivalent in age. The dataset contains 7,480 newly built homes and 15,342 existing homes, of which 1,444 and 2,507, respectively , are PV homes. Table 4 : Summary Statistics for All PV Homes Table 5 : Summary Statistics for All Non  PV Homes 24 Neg ative values for the minimum age of a home (e.g.,  2) apply to newly built homes in the sample and occur when the sale date is prior to the date of home completion, as might occur when a home is purchased on spec. Similarly, for PV system age, a negative m inimum value occurs when the completion date of the PV system occurred before the home sale date, which happens sometimes for new homes. Additionally, although acres is shown in the tables, it is entered in the model as a spline function of up to 1 acre an d any additional acres above 1 (see Section 2.1 ). Finally, age of the home squared is not shown in the tables. variable de s cription N me an sd min me dian max sy year of sale 3951 2010 2 2002 2011 2013 syq year and quarter of sale (yyyyq) 3951 20103 23 20021 20111 20134 sp price of sale (dollars) 3951 473,373 $ 196,451 $ 165,500 $ 433,000 $ 899,500 $ lns p natural log of sale price 3951 12.98 0.43 12.02 12.98 13.71 s f la living area (square feet) 3951 2,334 702 1,006 2,244 4,981 sfla1000 living area (in 1000s of square feet) 3951 2.3 0.7 1.0 2.2 5.0 acres size of parcel (in acres) 3951 0.45 0.95 0.05 0.18 9.99 age age of the home at time of sale (years) 3951 17 21 (2) 7 100 agesq1000 age of the home squared (in 1000s of years) 3951 0.7 1.3 0 0.0 10.0 pv if the home has a P V system (1 if yes) 3951 1  1 1 1 s ize size of the PV system (kilowatts) 3951 3.6 2.0 0.1 2.8 14.9 pvage age of the PV system at time of sale (years) 3951 2.7 2.9 (0.5) 2.2 13.4 income average PV Value estimate ($/watt) 3951 2.93 $ 0.57 $ 1.18 $ 2.92 $ 4.98 $ netcost net cost estimate ($/watt) 3951 4.14 $ 0.93 $ 1.07 $ 4.04 $ 7.95 $ grosscost gross cost estimate ($/watt) 3951 6.90 $ 1.50 $ 3.15 $ 6.92 $ 11.83 $ variable de s cription N me an sd min me dian max sy year of sale 18871 2010 2 2002 2011 2013 syq year and quarter of sale 18871 20103 23 20021 20112 20134 sp price of sale (dollars) 18871 456,378 $ 197,004 $ 165,500 $ 413,000 $ 899,500 $ lns p natural log of sale price 18871 12.94 0.44 12.02 12.93 13.71 s f la living area (square feet) 18871 2,319 714 1,001 2,200 4,990 sfla1000 living area (in 1000s of square feet) 18871 2.3 0.7 1.0 2.2 5.0 acres size of parcel (in acres) 18871 0.41 0.86 0.05 0.18 9.8 age age of the home at time of sale (years) 18871 17 21 (2) 8 100 agesq1000 age of the home squared (in 1000s of years) 18871 0.7 1.3 0 0.1 10.0 pv if the home has a P V system (1 if yes) 18871 0 0 0 0 0 13
24. Table 8 : Location and Home Type Model Results 31 4.2.2 Home Type Model Results Dividing the data by the type of home, specifically whether the home was newly built or existing at the time of sale, allows examination of the differences between these subgroups. In previous analyses, premiums for existing homes were found to be significant ly larger than those for newly built homes, but the sample used was smaller , only for homes in California, only extended through 2009 , and included homes with sales prices up to almost $3 million ( Hoen et al., 2011 ; 2013a ) . The present analysis enables a reexamination of this question by using a sample that is larger, more broadly distributed geographically , has more recent data, and uses homes no more expensive than $900,000 . The results from the Home T ype Models that used the new and existing home subsamples are shown in Table 8 . New h omes have a premium of $3.58/ W , while e xisting h omes have a premium of $4.51/ W , a difference of approximately $1/ W . Both estimates are highly statistically significant ( p  values < 0.001) by themselves , but they are not statistically different from each other (difference in coefficients = 0.001, p  value = 0.46 ; not shown in table) . Therefore, we are unable to uncover a difference in premiums between those subgroups with the larger, more geographically diverse and recent dataset. Nonetheless, the differences between these two sets of estimates mimic the different net cost s, which are higher for existing homes than for newly built homes. 4.2.3 Age of PV System Model Results Dividing the full sample into subsamples consisting of four quartiles based on PV system age (0.5 – 2.4 years , 2.4 – 3.8 years , 3.8 – 5.9 years , and 5.9 – 14 years) allows us to e xplore if the market accounts for PV system age when valuing PV systems. For this set of quartiles, only existing homes are used , because all 31 Here, as in other results tables, the numbers of block groups for subsets of data do not always sum to 1,830. This occurs when the block groups are not mutually exclusive between the subsets, e.g., with new or existing homes. All Home s California R e s t o f US Ne w Home s Exis ting Home s PV Pre mium Es timate s PV*Size Coefficient 0.0091 0.0091 0.0085 0.0084 0.0094 P V*Size Standard Error 0.0007 0.0007 0.0032 0.0012 0.0008 P V *Size p value 0.000 0.000 0.009 0.000 0.000 Mean Sale Price NonPV ($) 456,378 $ 459,366 $ 364,854 $ 422,001 $ 476,124 $ PV Premium ($/watt) 4.18 $ 4.21 $ 3.11 $ 3.58 $ 4.51 $ 95% CI ($/watt) 0.62 $ 0.64 $ 2.33 $ 1.00 $ 0.71 $ Contributory Value Es timate s PV Value  Income ($/watt) 2.93 $ 2.95 $ 2.15 $ 3.04 $ 2.86 $ Net Cost ($/watt) 4.14 $ 4.16 $ 3.09 $ 3.85 $ 4.29 $ Gross Cost ($/watt) 6.90 $ 6.94 $ 5.64 $ 7.34 $ 6.65 $ M ode l Info Total n 22,822 22,035 787 7,480 15,342 PV n 3,951 3,828 123 1,444 2,507 NonP V n 18,871 18,207 664 6,036 12,835 Adjusted R 2 0.92 0.93 0.88 0.97 0.91 Dependent Variable lns p lns p lns p lns p lns p Block Group Fixed Effects n 1,830 1,721 109 155 1,766 Home Type Location 17
21. 4. Results This section presents results , starting with the Base Model, which addresses the first research question : Are PV home premiums evident for a broader group of PV homes than has been studied previously ? This is followed by results for t he vari ous other models, which explore the remainder of the research questions ( Table 1 shows the full set of questions ) , and the two robustness models . 4.1 Base Model Results The Base Model estimates , over the entire dataset , the marginal return to each kilowatt of PV installed on a home as define d in Equation (1) . The model is summarized in Table 6 , with full resu lts shown in Table 7 . 25 Overall the model performs well , with an adjusted R 2 of 0.92, indicating that it captures approximately 92% of the price variation within the 22,822 home sales located in the 1,830 census block groups that make up the sample. Table 6 : Base Model Results Summary The full set of results is shown in Table 7 . The controlling variables that account for size ( sfla 1000 ) and age of the home ( age, agesq 1000 ) and size of the parcel ( lt1a cres , for each acre up to 1 , and gt1acres , for each acre over 1 ) a re all highly statistically significant (i.e., p  value < 0 . 001) . The model indicates that , in our sample, each additional 1 , 000 square feet adds approximately 21% to the selling price, while each acre up to 1 adds 39% and each additional acre beyond 1 adds 3%. 26 Each year a home ages initially takes approximately 0.7 % off its value , but this annual value reduction declines with time, and homes over approximately 60 years in age appreciate in value as they age . 27 Using the fourth quarter of 2013 as the referen ce category, in our sample, prices start approximately 4 4 % lower (Q1 2002) and then increase to approximately 20 % higher (2005 ), befo re falling again to lows in early 2012 and then increas ing to levels present in late 2013. This rise , fall , and eventual re covery are entirely consistent with the national trends in housing prices. 28 Combined , the various controlling characteristics are appropriately signed and leveled based on our expectations, giving us confidence that the model is acting appropriately and ad equately capturing price difference s across the sample. Turning to the variable of interest, pv*s ize , the model estimates that , for each kilowatt of installed PV , sale prices increase by 0.91%, an d this estimate is highly statistically significant ( p  value < 0.001). 25 All models are estimated in Stata using areg , with block groups as the absorbed fixed effect and with robust standard errors. 26 The exact percentage interpretation of coefficients in a semi  log model is as follows: exp(coefficient)  1, but the differences in this context are de minimi s . 27 Approximately 60 years is determined by dividing the age coefficient by the first derivative of the square term’s ( agesq ) coefficient. 28 As noted previously, we also explored interacting the year of sale with the county, to capture regional price trends, with no substantiv e change to the results. 22,822 3,951 18,871 0.92 lns p 1,830 Dependent Variable Block Group Fixed Effects Total n PV n NonP V n Adjusted R 2 14
38. 7. References Adomatis, S. K. (2014) Residential Green Valuation Tools . Appraisal Institute. Chicago, IL. 191 pages. ISBN 978  1  935328  52  0. Barbose, G., Darghouth, N., Weaver , S. and Wiser, R. (2013) Tracking the Sun VI: An Historical Summary of the Installed Price of Photovoltaics in the United States from 1998 to 2012. Lawrence Berkeley National Laboratory, Berkeley, CA. July 2013. 70 pages. Barbose, G., Darghouth, N. and Wi ser, R. (2010) Tracking the Sun III: The Installed Cost of Photovoltaics in the U.S. From 1998  2009. Lawrence Berkeley National Laboratory, Berkeley, CA. December 2010. 54 pages. LBNL  4121E. Barbose, G., Weaver, S. and Darghouth, N. (2014) Tracking the Sun VII: An Historical Summary of the Installed Price of Photovoltaics in the United States from 1998 to 2013. Lawrence Berkeley National Laboratory, Berkeley, CA. September 2014. 66 pages. California Public Utilities Commission (CPUC) (2010) CPUC California Solar Initiative: 2009 Impact Evaluation. Final Report. Prepared by: Itron and KEMA. Prepared for California Public Utilities Commission, Energy Division. June 2010. 632 pages. California Public Utilities Commission (CPUC) (2013) California Net Energy Met ering Ratepayer Impacts Evaluation. Prepared by: Energy and Environmental Economics Inc. Prepared for CPUC, Energy Division. October 28, 2013. 127 pages. CNT Energy & National Home Performance Council (NHPC) (2014) Unlocking the Value of an Energy Efficien t Home: A Blueprint to Make Energy Efficiency Improvements Visible in the Real Estate Market. Washington, DC. November, 2013 (Originally Published August 2013). 38 pages. Dakin, W., Springer, D. and Kelly, B. (2008) Case Study: The Effectiveness of Zero En ergy Home Strategies in the Marketplace. Presented at ACEEE Summer Study on Energy Efficiency in Buildings, Pacific Grove, California. August 17 – 22, 2008. Darghouth, N. R., Barbose, G. and Wiser, R. (2011) The Impact of Rate Design and Net Metering on the Bill Savings from Distributed PV for Residential Customers in California. Energy Policy. 39(9): 5243  5253. Dastrup, S. R., Graff Zivin, J., Costa, D. L. an d Kahn, M. E. (2012) Understanding the Solar Home Price Premium: Electricity Generation and “Green” Social Status. European Economic Review. 56(5): 961  973. Desmarais, L. (2013) The Impact of Photovoltaic Systems on Market Value and Marketability: A Case S tudy of 30 Single ‐ Family Homes in the North and Northwest Denver Metro Area. Prepared for Colorado Energy Office. May 2013. 319 pages. Dobos, A. P. (2014) PVWatts Version 5 Manual. National Renewable Energy Laboratory (NREL), Golden, CO. September 2014. 20 pages. NREL/TP  6A20  62641. Fannie Mae (2014) Selling Guide, Fannie Mae Single Family. Washington, DC. December 16, 2014. 1382 pages. Farhar, B. and Coburn, T. (2008) A New Market Paradigm for Zero  Energy Homes: A Comparative Case Study. Environment: Scien ce and Policy for Sustainable Development. 50(1): 18  32. Federal Housing Authority (FHA) (2014) FHA Single Family Housing Policy Handbook: Section IV  Appraiser and Property Requirements for Title II Forward and Reverse Mortgages. 83 pages. Draft Released for Review September 11, 2014. Freeman, A. M. (1979) Hedonic Prices, Property Values and Measuring Environmental Benefits: A Survey of the Issues. Scandinavian Journal of Economics. 81(2): 154  173. Hee, C. A., Wedding, C. and Urlaub, I. (2013) Motivations and Behaviors of Solar PV and Geothermal System Owners in North Carolina. Prepared for North Carolina Sustainable Energy Association, Raleigh, NC. December 17, 2013. 18 pages. 31
7. List of Tables Table 1: Summary of Research Questions, Models, and Sample Sets ................................ ....................... 6 Table 2: Frequency Summary of PV and Non  PV Homes by State ................................ ......................... 12 Table 3: Frequency Summary of PV and Non  PV Homes by Sale Year ................................ ................. 12 Table 4: Summary Statistics for Al l PV Homes ................................ ................................ ...................... 13 Table 5: Summary Statistics for All Non  PV Homes ................................ ................................ .............. 13 Table 6: Base Model Results Summary ................................ ................................ ................................ .. 14 Table 7: Base Model Results ................................ ................................ ................................ ................. 16 Table 8: Location and Home Type Model Results ................................ ................................ .................. 17 Table 9: Age of PV System Model Results ................................ ................................ ............................ 19 Table 10: Year of Sale Model Results ................................ ................................ ................................ .... 20 Table 11: Size of PV System Model Results ................................ ................................ .......................... 21 Table 12: Robustness Model Results ................................ ................................ ................................ ...... 22 List of Figures Figure 1: Base and Location Model Results ................................ ................................ ........................... 23 Figure 2: Year of Sale Model Results ................................ ................................ ................................ .... 25 Figure 3: Home Type Model Results ................................ ................................ ................................ ..... 26 Figure 4: Estimated Dollar Per Watt Premium for Increasingly Larger PV Systems ............................... 28 Figure 5: Age of PV System Model Results ................................ ................................ ........................... 28 Figure 6: Estimated Premiums Based o n an Average  Sized 3.6 kW System ................................ ........... 30 vi
27. Table 10 : Year of Sale Model Results 4.3 Size of PV System Model To examine if larger PV systems garner an equal , lower, or higher marginal price premium than smaller systems, we estimate a polynomial model as described in Equation (2) with parameters for pv*size and pv*s ize 2 . Abbreviated results from this model are shown in Table 11 . C oefficients for the first  and second  order polynomials are high ly statistically significant ( p  value < 0.02) and indicat e decreasing marginal returns to increasing PV system size . The pv*size coefficient equates to a premium of $5.86/ W, while the pv*size 2 coefficient corresponds to a decrease in value of $0.53/ W . Therefore, t he model estimates that , up to approximately 10 kW, each increase in PV system size adds value to a home, but progressively less value for each addition. Beyond 10 kW , premium increases with increasing system size seem to flatten out, but we are less confident of the results because of the relatively few o bservations in this size range . 34 34 We also estimat ed models using subsets of data, each containing progressively larger systems, and find a similar pattern, with decreasing $/W premiums for increasing sizes. All Home s 2002 2007 2008 2009 2010 2011 2012 2013 PV Pre mium Es timate s PV*Size Coefficient 0.0091 0.0066 0.0103 0.0083 0.0093 P V*Size Standard Error 0.0007 0.0020 0.0016 0.0011 0.0010 P V *Size p value 0.000 0.001 0.000 0.000 0.000 Mean Sale Price NonPV ($) 456,378 $ 512,170 $ 440,495 $ 448,976 $ 453,988 $ PV Premium ($/watt) 4.18 $ 3.41 $ 4.54 $ 3.73 $ 4.23 $ 95% CI ($/watt) 0.62 $ 2.03 $ 1.34 $ 0.97 $ 0.88 $ Contributory Value Es timate s PV Value  Income ($/watt) 2.93 $ 2.79 $ 2.73 $ 3.00 $ 3.02 $ Net Cost ($/watt) 4.14 $ 5.39 $ 4.56 $ 4.00 $ 3.58 $ Gross Cost ($/watt) 6.90 $ 8.97 $ 8.25 $ 6.88 $ 5.45 $ M ode l Info Total n 22,822 2,368 3,895 7,238 9,321 PV n 3,951 464 882 1,146 1,459 NonP V n 18,871 1,904 3,013 6,092 7,862 Adjusted R 2 0.92 0.96 0.96 0.95 0.91 Dependent Variable lns p lns p lns p lns p lns p Block Group Fixed Effects n 1,830 259 313 630 1,022 Ye ar o f Sale Gro ups 20
13. 2.2 Base Model Variation : Size of PV System Model Although the Base Model and variations to the subsets of data allow examination of almost all the research questions, the sixth question require s a slightly altered model : the Size of PV System Model. I f the market exhibits a gree n cachet , theoretically a fixed amount might be added to the value of a home with PV regardless of the size of that PV system . Therefore , for smaller systems , a premium expressed in dollars per installed watt would be larger than it would be for larger sys tems , representing a decreasing marginal premium for each watt added to a PV system. To examine decreasing marginal returns , a second  order polynomial is added , and therefore we estimate the following model: ( ) ( ) ( ) ( ) ( ) 2 itk 1 i 2 i 3 i 4 i i 5 i i itk a ln(P ) T K X PV SIZE PV SIZE αβ β β β β ε =++ + + ⋅+ ⋅ + ∑ ( 2 ) where SIZE i 2 i s a continuous variable for the squared size (in kilowatts ) of the PV system installed on the home prior to transaction i , and β 5 is a parameter estimate for the change in sale price for each additional squared kilowatt added to a PV system, and all other variables are as shown in Equation (1) . The parameter estimate s of p rimary interest in this model are β 4 and β 5 . If decreasing marginal returns exist for increasing sizes of PV systems, we would expect the β 4 coefficient to be positive and larger and the β 5 coefficient to be negative and smaller . 2.3 Model Summary Combining t he Base Model, the use of various subsets of data, and the Size of PV System Model allow s examination of the seven research questions listed in Section 1. The full set of research questions, models , and sample sets a re described in Table 1 . Table 1 : Summary of Research Questions, Models , and Sample Sets Research Question Equation M ode l Name Sample Se t(s ) 1. Are P V home premiums evident for a broader group of P V homes than has been studied previously both inside and outside of California and through 2013? Equation (1) Base Model A ll D a ta 2. Are P V home premiums outside of California s imila r to thos e w ithin C a lif or nia ? Equation (1) Location Models CA vs. NonCA Homes 3. How do P V home premiums compare to contributory values estimated using the cost and income methods? Equation (1) Various Models All Data, or Subsets of Data, But Compare Results To Income and Cost Methods 4. How did the size of the premium change over the study period, as gross P V system prices decreased and during housing market swings? Equation (1) Year of Sale Models Subsets of Years in Sample P eriod (e.g., P re'08; 0809, 1011, P ost 11) 5. Are premiums for new P V homes similar to existing P V home premiums? Equation (1) Home Type Models New vs. Existing Homes 6. Is there evidence that there is a "green cachet" for P V homes over and above the amount paid for each additional watt added? Equation (2) Size of P V System Model A ll D a ta 7. How does the age of the P V system influence the size of the P V premium? Equation (1) Age of P V System Models Subsets of PV System Ages (e.g., < 2 years; 24; 56; 714 years) 6
28. Table 11 : Size of PV System Model Results 4.4 Robustness Models T he various models estimated above, which most ly are based on the Base Model and subsets of the data, compare PV home prices to non  PV home prices . Here we estimate two Robustness Models, which allow us to examine the robustness of the results under alternative specifications : the PV Only Model and the Repeat Sales Model. The PV Only Model compares sellin g prices of only PV homes, while the Repeat Sales Model examines the selling prices of the same home for homes sold once before the PV system was installed and again after it was installed, as described by Equation (3) . These models use both different sets or subsets of the data and different specifications of the model, which allows them to control for possible specification bias es in the Base Model. They, t he refore , s erve as valuable comparisons to and, potentially, validations of the Base Model results. 4.4.1 PV Only Model Results for the PV Only Model are shown in Table 12 . Th e coefficient for pv * s ize is effectively identical to that estimated for the Base Model with the full dataset, and it is highly statistically significant ( p  value ≤ 0.001) . Th e fact that the coefficient is identical to the Base Model coefficient is remarkable given that it is derived from a model that uses county fixed effects, rather than the more geographically precise block group fixed effect used in the Base Model. The estimated premium is $4.37/ W , although the 95% confidence interval is consider ably larger at $2.62/ W vs. the Base Model’s $0.62 /W , indicating considerably less precision in the PV Only M odel estimate. 4.4.2 Repeat PV Home Model Results from the Repeat PV Home Model are also shown in Table 12 . The coefficient for pv*size is very similar to that estimated for the Base Model with the full dataset, but it is not statistically significant ( p  va lue = 0. 1 13 ). The estimated premium is $4.60 / W , which is also v ery similar to that of the Base Model, although the 95% confidence interval , at $5.6 9 / W, is considerably larger than those for the Base and PV Only Models. 4.4.3 Summary of Robustness Checks B ecause of the large margins of error, we cannot say the three estimates are statistically different from each other . Despite this , none of the results appear markedly different from that estimated using the Base P V *Size P V *Size 2 Coefficient 0.0128 0.0006 Standard Error 0.0015 0.0002 p value 0.0000 0.0130 Mean Sale Price NonPV ($) 456,377 $ 456,377 $ PV Premium ($/watt) 5.86 $ (0.53) $ 95% CI ($/watt) 1.35 $ 0.42 $ M ode l Info Total n 22,822 PV n 3,951 NonP V n 18,871 Adjusted R 2 0.92 Dependent Variable lns p Block Group Fixed Effects n 1,830 21
40. 8. Appendix A: Cost Estimate Preparation To calculate both the net and gross cost estimates for each of the PV home transactions at the time of sale, we estimate a two  stage regression as used previously ( Hoen et al., 2011 ; 2013a ; 2013b ) . This procedure starts with the extensive dataset of more than 150,000 PV homes collected for TTS VI and their respective gross installed costs as reported ( Barbose et al., 2013 ) , for which the respective net installed costs (i.e., net of federal and state incentives) are calculated using the procedure outlined in Appendix C of Barbose et al. (2010) . The first stage uses the net costs as the dependent variable and county, year, system size, and home type (new or existing) as the independent variables, in the following model: ( ) ( ) ( ) ( ) 12 3 4 itsc i i i i itsc C TS NC αβ β β β ε =++ + + + ( 4 ) where C itsc is the “net installed cost” of PV system i after state and federal incentives from the full TTS dataset, T i is a vector of variables representing the year t in which the system was installed, S i is a vector of variables representing the size s of the system in rounded kilowatts (e.g., 1 kW, 2 kW, 3 kW...), N i is a fixed  effect variable indicating if the home was newly built when the system was installed, C i is a vector of variables representing the county c in which the system was installed, α is the constant, β 1  4 are coefficients for the parameters, and ε itsc is the error term. The model accounts for the different state incentives and system component prices over the study period (via T i ), econom ies of scale (via S i ), different installed costs between new and existing homes (N i ), and the variety of rate structures, installer competitive prices, and market development (via C i ). Using the predicted coefficients from this model, the data for the set of PV home transactions (county in which the home is located, PV system size, if the home is newly built, and substituting the sale year for the installation year t ) are fed into the model to produce predicted net cost estimates . These represent, as of th e time of sale, the approximate cost to replace a similarly sized system new on the same home. An identical procedure is followed for gross cost estimates, except, for the first stage, C itsc is the “gross inst alled cost” of PV system i before state and fe deral incentives from the full TTS VI datas et. 33
12. where P i tk rep resents t he sale p rice for transaction i , in quarter t , in block group k, α is the constant or intercept across the full sample, T i is the quarter t in which transaction i occurred , K i is the census block group k in which transaction i occurred , X i is a vector of a home and site characteristics for transaction i , PV i is a fixed  effect variable indicating a PV system is installed on the home in transaction i , SIZE i is a continuous variable for the size (in kW) of the PV system installed on the home prior to transa ction i , 7 β 1 is a parameter estimate for the quarter in which transaction i occurred , β 2 is a parameter estimate for the census block group in which transaction i occurred , β 3 is a vector of parameter estimates for home and site characteristics a , β 4 is a parameter estimate for the change in sale price for each kilowatt added to a PV system, and ε i tk is a random disturbance term for transaction i , in quarter t , in block group k . The parameter estimate of primary interest in this model is β 4 , which rep resents approximately the marginal percentage change in sale price over the average sale price of the comparable set of non  PV homes within the same census block group , with the addition of each kilowatt of PV. 8 If differences in selling prices exist betwe en PV and non  PV homes, we would expect the coefficient to be positive and statistically significant. This model allow s an examination of many of the research questions depending on the dataset that is used. I f the full dataset is used, the first question can be answered . I f a subset of the dataset is used , many of the other question s can be answered. For example, if h omes within and outside California are use d , the second question can be explored. Similarly, if the data are restricted to particular subsets of the study perio d (e.g., 2002 – 2007 , 2008 – 2009, 2010 – 2011 , or 2012 – 2013 ) , the fo u rth research question could be examined. T o explore if new or existing homes had similar premiums ( the fifth question ) , the data could be restricted to those subsets. Finall y, if only PV systems of particular ages were used, the seventh question could be answered. Therefore , almost all of the research questions can be answered using subsets of the data, leaving only the sixth question regarding green cachet , which require s a slightly altered model and will be discussed next , and the third question, which can use either the full dataset or subsets of the data but also requires calculations of comparison valuation estimates using the cost or income method . 9 7 All references to the size of PV systems in this paper, unless otherwise noted, are reported in terms of direct  current watts or kilowatts under standard test conditions. A discussion of this convention is offered in Appendix A of Barbose et al. (2014) . 8 To be exact, the conversion to percent is actually EXP( β 4 )  1, but the differ ences are often de minimis . 9 Although the preferred method is to estimate a separate model using a subset of the data, which allows all of the controlling parameters to take different values for each subset, we also explored estimating models with a categorical variable for each of t he subsets interacted with either the variable of interest only or both the variable of interest and the other controlling parameters, with no substantive change in the results. 5
35. Figure 4 : Estimated Dollar Per Watt Premium for Increasingly La rger PV Systems Figure 5 : Age of PV System Model Results $ $5,000 $10,000 $15,000 $20,000 $25,000 $30,000 $35,000 1 2 3 4 5 6 7 8 9 10 $ $1.00 $2.00 $3.00 $4.00 $5.00 $6.00 Total System Value Size of PV System (kilowatts DC) Incremental $ per Watt Premium For Each Additional kW Incremental PV Premium Left Axis Total System Value Right Axis $ $1.00 $2.00 $3.00 $4.00 $5.00 $6.00 $7.00 $8.00 0.5  2.4 χ = 1.6 yrs 2.4  3.8 χ = 3.1 yrs 3.8  5.9 χ = 4.8 yrs 5.9  14 χ = 7.8 yrs $ Per Watt (DC) Installed of PV Age of PV System Quartiles (Years) Error bars represent 95% confidence interval PV Premium ($/watt) PV Value  Income ($/watt) Net Cost ($/watt) Gross Cost ($/watt) 28
6. Table of Contents 1. Introduction ................................ ................................ ................................ ................................ ..... 1 2. Methodological Approach ................................ ................................ ................................ ................ 4 2.1 Base Model ................................ ................................ ................................ .............................. 4 2.2 Base Model Variation: Size of PV System Model ................................ ................................ ..... 6 2.3 Model Summary ................................ ................................ ................................ ....................... 6 2.4 Robustness Models ................................ ................................ ................................ .................. 7 2.4.1 PV Only Model ................................ ................................ ................................ ................ 7 2.4.2 Repe at PV Home Model ................................ ................................ ................................ ... 7 3. Data Preparation and Summary ................................ ................................ ................................ ........ 9 3.1 PV and Non  PV Home Data ................................ ................................ ................................ ..... 9 3.2 Cost Estimates ................................ ................................ ................................ ....................... 10 3.3 Income Estimates Using the PV Value Algorithm ................................ ................................ ... 11 3.4 Data Summary ................................ ................................ ................................ ....................... 12 4. Results ................................ ................................ ................................ ................................ ........... 14 4.1 Base Model Results ................................ ................................ ................................ ................ 14 4.2 Ba se Model Variations Using Subsamples ................................ ................................ .............. 15 4.2.1 Location Model Results ................................ ................................ ................................ .. 15 4.2.2 Home Type Model Results ................................ ................................ ............................. 17 4.2.3 Age of PV System Model Results ................................ ................................ ................... 17 4.2.4 Year of Sale Model Results ................................ ................................ ............................ 19 4.3 Size of PV System Model ................................ ................................ ................................ ....... 20 4.4 Robustness Models ................................ ................................ ................................ ................ 21 4.4.1 PV Only Model ................................ ................................ ................................ .............. 21 4.4.2 Re peat PV Home Model ................................ ................................ ................................ . 21 4.4.3 Summary of Robustness Checks ................................ ................................ ..................... 21 5. Discussion of Research Questions ................................ ................................ ................................ .. 23 6. Conclusion ................................ ................................ ................................ ................................ .... 29 7. References ................................ ................................ ................................ ................................ ..... 31 8. Appendix A: Cost Estimate Preparation ................................ ................................ ......................... 33 v
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