1# RECORD 7e996f814b72e80b4de3f1e836fe30324b1e29122# TITLE: Hedonic Valuation with Translating Amenities: Mountain Pine Beetles and Host Trees in the Colorado Front Range3# YEAR: 2014.0 VENUE: Environmental and Resource Economics DOI: 10.1007/s10640-014-9856-y4# AUTHORS: J. Cohen; C. Blinn; K. Boyle; T. Holmes; K. Moeltner5# PAGES: 30 CANDIDATE TABLE PAGES (1-based): [17, 20, 21, 26, 27]6# ABSTRACT: In hedonic valuation studies the policy-relevant environmental quality attribute of interest is often costly to measure, especially under pronounced spatial and temporal variability. However, in many cases this attribute affects home prices and consumer preferences solely through its impact on a readily observable, spatially delineated, and time-invariant feature of the physical landscape. We label such a feature a “translating amenity.” We show that under certain conditions changes in the marginal effect of such amenities on home values over time can be used to draw inference on the implicit price of the unobserved environmental quality of interest. We illustrate this approach in the context of a repeat-sales model and the recently intensified outbreak of the Mountain Pine Beetle in the Colorado Front Range.789===== PAGE 1 (score 9, numeric-paren 0, table-words 0, var-words 9) =====1011Environ Resource Econ (2016) 63:613–64212DOI 10.1007/s10640-014-9856-y13Hedonic Valuation with Translating Amenities: Mountain14Pine Beetles and Host Trees in the Colorado Front Range15Jed Cohen · Christine E. Blinn · Kevin J. Boyle ·16Thomas P. Holmes · Klaus Moeltner17Accepted: 15 December 2014 / Published online: 31 December 201418© Springer Science+Business Media Dordrecht 201419Abstract In hedonic valuation studies the policy-relevant environmental quality attribute of20interest is often costly to measure, especially under pronounced spatial and temporal vari-21ability. However, in many cases this attribute affects home prices and consumer preferences22solely through its impact on a readily observable, spatially delineated, and time-invariant23feature of the physical landscape. We label such a feature a “translating amenity.” We show24that under certain conditions changes in the marginal effect of such amenities on home values25over time can be used to draw inference on the implicit price of the unobserved environmental26quality of interest. We illustrate this approach in the context of a repeat-sales model and the27recently intensified outbreak of the Mountain Pine Beetle in the Colorado Front Range.28Keywords29Forest pests · Property values · Repeat-sales model · Wildland–urban interface30We thank seminar participants at the 2013 Meetings of the W3133 Western Regional Science Project (Coeur31d’ Alene, ID, Feb. 27–March 2), and the US Airforce Academy, Colorado Springs (March 15, 2013), for32insightful and stimulating comments. Funding provided by the Southern Research Station, USDA Forest33Service, is gratefully acknowledged.34J. Cohen · K. J. Boyle · K. Moeltner (B)35Department of Agricultural and Applied Economics, Virginia Tech, 208 Hutcheson Hall,36Blacksburg, VA 24061, USA37e-mail: moeltner@vt.edu38J. Cohen39e-mail: jedcohen@vt.edu40K. J. Boyle41e-mail: kjboyle@vt.edu42C. E. Blinn43Department of Forest Resources and Environmental Conservation, Virginia Tech, Blacksburg, USA44e-mail: cblinn@vt.edu45T. P. Holmes46USDA Forest Service, Southern Research Station, Research Triangle Park, NC, USA47e-mail: tholmes@fs.fed.us48123495051===== PAGE 17 (score 32, numeric-paren 15, table-words 4, var-words 4) =====5253Mountain Pine Beetles and Host Trees in the Colorado Front Range5462955Table 6 Estimation results for56HT and fire effects57Est. estimate, (SE) standard error58*, (**), (***) significant at 10%,59(5%), (1%) level60Larimer61Boulder62Est.63(SE)64Est.65(SE)661998 (Larimer baseline)670.062680.019***69−70–71199972−0.067730.040*74−75–76200077−0.074780.037**79−80–81200182−0.024830.04484−85–862002 (Boulder baseline)87−0.079880.042*89−0.127900.029***91200392−0.086930.040**940.082950.05896200497−0.108980.045**990.0361000.0561012005102−0.1441030.045***1040.0151050.0571062006107−0.1331080.048***1090.0271100.0631112007112−0.1731130.052***1140.0861150.0671162008117−0.1401180.059**119−0.0111200.0751212009122−0.2131230.063***1240.0471250.0791262010127−0.2531280.061***1290.0491300.0781312011132−0.3131330.066***134−0.0061350.086136Fire 5year, 5km1370.0171380.013139−0.0421400.011***141we only retain this single indicator in our final specification. This implies that the vector142difference wit′ −wit0 in (12) reduces to a single indicator, taking the value of −1 if a fire143occurred within 5km and 5 years preceding time t0, but not time t′, a value of 0 if such a144fire occurred preceding neither or both points in time, and a value of 1 if such an event took145place preceding time t′ only.146We estimate separate GLS models for Larimer and Boulder. Estimation results for HT147and fire effects are given in Table 6. Results for area-specific intercepts, time trends, and148age-depreciation effects are provided in Tables 12 and 13 in “Appendix 2”. These appendix149tables essentially confirm the basic sample statistics on price development discussed above:150In Larimer, prices increase vis-a-vis the baseline year of 1998 until 2005 or 2006 by up151to 30–35%, then decline for the remainder of our research period, almost back to baseline152levels for some areas. In Boulder, prices decline immediately compared to the 2002 base153year, reaching a low of 12–15% below baseline by 2011. Age-related depreciation amounts154to between 0.5 and 2% per percentage change in time elapsed between sales, i.e. t′ −t0155in our model notation, relative to time t0.16 These results are largely as expected given the156recent economic downturn and collapse of the housing market for wide parts of the western157US. While they are interesting in their own right, they serve here primarily the purpose of158providing a sound and consistent baseline against which MPB effects are to be measured.159Footnote 15 continued160km, but closer in time (within 1 or 3 years of sale) are likely due to small sample size (less than 0.5% of161observations).16216 Area 5 (southern Fort Collins, Loveland) produces a counterintuitive positive effect for age-related depre-163ciation. We attribute this to the many new constructions that occurred in that area during our time span. This164can produce a large value for ai,165t′,t0, even for pairs of sales that are closely positioned in time, with little to166no age-related depreciation. A large enough share of such properties in the data can then produce a positive167estimate for the depreciation coefficient δs.168123169170171===== PAGE 18 (score 10, numeric-paren 0, table-words 4, var-words 2) =====172173630174J. Cohen et al.175We thus turn our attention to the main results in Table 6, which depicts county-specific176coefficient estimates for the HT baseline effect ζ, the year-specific HT effects βt, and the177pre-sale wildfire effect ψ, as modeled in Eq. (12). As is evident from the table, in Larimer178properties within 0.1 km from host trees fetched a premium over other homes in the baseline179year of 1998. However, starting in 1999 this difference reverts and increases in magnitude180and significance up to the end of our time horizon. In other words, homes within near-181proximity of HTs sold at a progressively increasing discount compared to other residences.182By our translating commodity principle, we attribute this relative loss to MPB damage. In183stark contrast, as shown in the last three columns of Table 6, the MPB effect appears to184have been largely capitalized into home values in Boulder by the baseline year of 2002,185as indicated by the significant and negative coefficient estimate for ζ. Relative HT effects186remain insignificant for subsequent years. Fire effects, which are captured in the last row of187the table, are insignificant for Larimer, but have a significant negative effect on sales prices188in Boulder.171894.4 Predicted Price Trajectories190There are three price trajectories of interest for our application. First, we establish the baseline191pricetrendbyestimatingtherelativedifferenceinsalespriceforanyyearcomparedtothebase192year, focusing exclusively on properties outside the 0.1 km HT perimeter. Econometrically,193this effect is given as194m1t = E195 Pit −Pi1196Pi1197|hi = 0198 199= E200 Pit201Pi1202|hi = 0203 204−1205= E206207exp208209ξs + αst + ψ (wit −wi1) + δsai,(t,1) + eis,(t,1)210211−1212= exp213214ξs + αst + ψ (wit −wi1) + δsai,(t,1) + σ 2215−1216(14)217where E is the expectation operator and the addition of 0.5 times the differenced-error218variance 2 ∗σ 2 follows from the relationship between the normal distribution of eis,(t,1)219and the log-normal distribution of exp220221eis,(t,1)222223(see e.g. Evans et al. 2000). This term is224negligibly small for both the Boulder and Larimer application. In implementing (14) we225follow Case et al. (2006) and set the area-specific, non-temporal component of house price226appreciation ξs to zero, as it is not related to any temporal price trajectory. We do the same227for the wildfire indicators wit −wi1 as we want our baseline price index to be untainted by228fire effects. Finally, to abstract from any specific age bracket for a given home, and given the229close-to-zero estimate of the age depreciation effect for all areas, we also exclude depreciation230effects ai,(t,1) from the computation of m1t. This leaves us with m1t = exp231232αst + σ 2233−1.234Next, we compute the same year-versus-baseline effect for homes with nearby host trees,235i.e.236m2t = E237 Pit −Pi1238Pi1239|hi = 1240 241= E242 Pit243Pi1244|hi = 1245 246−1247= exp248249ξs + αst + ζ + βt + ψ (wit −wi1) + δsai,(t,1) + σ 2250−1251(15)252Implementing the same adjustments as above with the addition of setting the time-invariant253host tree effect ζ to zero produces m2t = exp254255αst + βt + σ 2256−1.25717 Specifically, a home that experienced a recent fire within 5km between sales appreciated, on average, by258(exp(−0.042) −1) = 4.1 % less than an otherwise comparable property without a recent fire history.259123260261262===== PAGE 20 (score 146, numeric-paren 115, table-words 2, var-words 1) =====263264632265J. Cohen et al.266Table 7 MPB effects Larimer267no HT/no HT(1998)268HT/HT(1998)269Est.270(SE)271Low272Up273Est.274(SE)275Low276Up277Area 127819992790.072280(0.045)281−0.0122820.1642830.003284(0.036)285−0.0652860.07528720002880.171289(0.047)2900.0842910.266***2920.087293(0.039)2940.0132950.168**29620012970.129298(0.053)2990.0313000.237**3010.102302(0.041)3030.0243040.187**30520023060.306307(0.059)3080.1953090.427***3100.207311(0.047)3120.1193130.303***31420033150.313316(0.059)3170.2033180.433***3190.205320(0.047)3210.1173220.300***32320043240.343325(0.069)3260.2153270.484***3280.205329(0.048)3300.1143310.304***33220053330.345334(0.066)3350.2213360.480***3370.164338(0.046)3390.0773400.259***34120063420.257343(0.067)3440.1323450.396***3460.100347(0.048)3480.0093490.198**35020073510.234352(0.071)3530.1013540.380***3550.038356(0.050)357−0.0553580.13935920083600.294361(0.082)3620.1433630.464***3640.125365(0.055)3660.0223670.239**36820093690.213370(0.084)3710.0603720.389***373−0.019374(0.055)375−0.1213760.09337720103780.281379(0.090)3800.1173810.469***382−0.005383(0.057)384−0.1103850.11138620113870.142388(0.086)389−0.0143900.322391−0.165392(0.052)393−0.261394–0.057***395Area 439619993970.076398(0.039)3990.0034000.155*4010.006402(0.027)403−0.0464040.06140520004060.195407(0.039)4080.1214090.275***4100.110411(0.028)4120.0564130.167***41420014150.213416(0.049)4170.1214180.313***4190.184420(0.035)4210.1174220.256***42320024240.279425(0.051)4260.1844270.382***4280.182429(0.035)4300.1154310.252***43220034330.329434(0.048)4350.2394360.426***4370.219438(0.036)4390.1504400.293***44120044420.368443(0.058)4440.2604450.486***4460.228447(0.038)4480.1564490.305***45020054510.419452(0.060)4530.3064540.543***4550.229456(0.040)4570.1534580.309***45920064600.450461(0.067)4620.3254630.590***4640.269465(0.043)4660.1874670.356***46820074690.422470(0.074)4710.2854720.574***4730.196474(0.044)4750.1124760.286***47720084780.335479(0.078)4800.1904810.497***4820.161483(0.048)4840.0714850.258***48620094870.293488(0.082)4890.1424900.464***4910.045492(0.047)493−0.0444940.14249520104960.413497(0.084)4980.2584990.588***5000.097501(0.052)5020.0005030.202*50420115050.290506(0.082)5070.1405080.460***509−0.057510(0.045)511−0.1425120.035513HT/no HT514Est.515(SE)516Low517Up518All5191999520−0.004521(0.043)522−0.0855230.0835242000525−0.012526(0.036)527−0.0805280.06252920015300.039531(0.043)532−0.0435330.1275342002535−0.017536(0.039)537−0.0895380.0635392003540−0.024541(0.035)542−0.0915430.0485442004545−0.045546(0.037)547−0.1145480.0305492005550−0.078551(0.034)552−0.142553−0.010**5542006555−0.069556(0.036)557−0.1375580.003*5592007560−0.105561(0.037)562−0.175563−0.030***5642008565−0.075566(0.044)567−0.1585680.017*5692009570−0.140571(0.044)572−0.221573−0.049***5742010575−0.174576(0.041)577−0.250578−0.091***5792011580−0.222581(0.043)582−0.302583−0.135***584Est. estimate, (SE) standard error; *, (**), (***) significant at 10%, (5%), (1%) level585123586587588===== PAGE 21 (score 49, numeric-paren 34, table-words 2, var-words 1) =====589590Mountain Pine Beetles and Host Trees in the Colorado Front Range591633592Table 8 MPB effects Boulder593Area 6594no HT/no HT(2002)595HT/HT(2002)596Est.597(SE)598Low599Up600Est.601(SE)602Low603Up6042003605−0.034606(0.036)607−0.1026080.0416090.049610(0.048)611−0.0426120.14861320046140.013615(0.038)616−0.0576170.0906180.050619(0.045)620−0.0356210.14362220056230.057624(0.041)625−0.0206260.1416270.073628(0.048)629−0.0166300.17163120066320.069633(0.045)634−0.0176350.1616360.098637(0.055)638−0.0056390.212*64020076410.038642(0.047)643−0.0516440.1356450.131646(0.060)6470.0196480.255**64920086500.001651(0.051)652−0.0946530.105654−0.009655(0.060)656−0.1196570.1156582009659−0.039660(0.056)661−0.1436620.0776630.007664(0.060)665−0.1046660.1336672010668−0.055669(0.053)670−0.1536710.053672−0.008673(0.062)674−0.1226750.1226762011677−0.113678(0.052)679−0.211680−0.005**681−0.119682(0.061)683−0.2316840.010*685HT/no HT686Est.687(SE)688Low689Up6902003691−0.044692(0.060)693−0.1546940.0816952004696−0.087697(0.051)698−0.1826990.0197002005701−0.106702(0.047)703−0.194704–0.009**7052006706−0.095707(0.051)708−0.1897090.0107102007711−0.040712(0.054)713−0.1407140.0717152008716−0.128717(0.055)718−0.230719−0.015**7202009721−0.077722(0.060)723−0.1877240.0487252010726−0.075727(0.058)728−0.1817290.0457302011731−0.125732(0.059)733−0.234734−0.001**735Est. estimate, (SE) standard error736*, (**), (***) significant at 10%, (5%), (1%) level737over time. By 2011, MPB-induced losses took substantial proportions. We will translate these738percentage differentials into dollar losses per home and for the region as a whole below.197394.5 Robustness Check: Spokane740To guard against the possibility that our estimated trend of increasing relative losses for741HT homes simply reflects changing preferences of home buyers over the years, we repeat742our analysis for a “control area” with similar population size and abundant host trees, but743no documented MPB damage. Specifically, we estimate our model in (12) for the city of744Spokane, Washington. Assuming home owner’s preferences with respect to “trees” and745woody surroundings in Spokane are at least somewhat similar to those for our Front Range746communities, price trends in Spokane for no-HT homes and HT homes should move in747equal or at least parallel fashion in absence of increasing “tree aversion.” In other words, a74819 As is the case with most hedonic studies, our model cannot distinguish between actually experienced749and expected MPB effects on home prices. Our estimated price trajectories and loss estimates include both750components. However, since our time series of home sales starts well before the explosive expansion of the751MPB, we are confident that our estimates captures the full MPB effect, that is actual plus expected.752123753754755===== PAGE 22 (score 12, numeric-paren 0, table-words 5, var-words 2) =====756757634758J. Cohen et al.759homogeneous price trajectory for no-HT and HT properties in Spokane would rule out a760general and widespread shift in preference away from trees and towards open land in the761mountainous west. This, in turn, would lend additional credibility to our interpretation of762no-HT/HT price differentials in Colorado as attributable to MPB damage.763The Spokane data comprises 23,841 observations for 18,428 homes with repeat sales764between 1997 and 2011. We estimate the Spokane RSM using the exact same variables as for765our main analysis. We allow for separate price trends for three different markets, but continue766to specify a common annual series of HT effects. Estimation results for the latter are given767in Appendix Table 14.20 As is evident from the table, starting with the base year of 1997, HT768effects are—at worst—close to zero and insignificant. In fact, homes with nearby host trees769actually fetch a highly significant price premium of 2–3% for several years in our series.770Clearly, there is no indication of a price discount for HT homes, let alone one that is771progressively increasing over time. The Spokane counter-study thus provides strong support772for our interpretation of value losses in the Colorado Front Range as MPB-induced.7734.6 Loss Predictions and Policy Implications774To translate the percentage losses discussed above into 2011 currency for HT homes in areas775one, four, and six, we proceed in three conceptual steps. First, we compute the year-specific776counterfactual price that each home would have received in absence of MPB damage, using777˜Pit =778Pit7791 + m3t780,781(17)782where Pit is the observed price, and m3t is defined in (16). Second, we translate this “HT783purged” value into the price the same home would have sold for in the final year T (2011 in784our case) via785ˆPi,T = ˜Pit7867871 + κs,t,T788789,790(18)791where κs,t,T = exp792793αs,T −αst + σ 2794−1, and the α-terms are the area and year-specific795generic price effects as given in (12). For Boulder, where estimated wildfire effects are796significant, we also control for forest fires that may have occurred (or subsided) between any797year t and 2011 by adding (or subtracting) the wildfire coefficient ψ in the exponent of κs,t,T .798These first two steps yield the predicted sales price in 2011 for all HT-homes in our sample,799purged of any MPB-induced value losses. In step three, we then simply apply the MPB-800induced percentage losses for 2011, as reported in Tables 7 and 8, i.e. −22.2% for Larimer801and −12.5% for Boulder. We implement these three steps for every HT property in our repeat-802sales data, as well as for all remaining single-sale homes located in the HT zone that are not803included in our principal analysis. Importantly, throughout all three steps we carry forward804the standard errors for all coefficients involved to generate accurate uncertainty bounds for805our final predictions. The details for these derivations are given in “Appendix 2”.806Predicted losses per home and aggregate losses for various sub-sets of our data are given807in Table 9. The first row of the table shows the number of properties that are located within8080.1 km from host trees for each county and the entire region. Within each county, the first809column refers to all such homes, including single-sale properties. The second column refers810to all HT homes that were actually included in our RSM (i.e. those with multiple sales during811our research period). On a per-home basis, MPB induced losses amount to $70,000 for the812broader sample in Larimer, and $61,000 for Boulder. However, while the lower confidence813bound for Larimer is still a sizable $41,000, the lower bound for Boulder is near-zero.81420 The full set of results for Spokane are available upon request.815123816817818===== PAGE 26 (score 97, numeric-paren 75, table-words 3, var-words 1) =====819820638821J. Cohen et al.822Table 11 Price statistics by area,823Boulder (2011 dollars, units of824000s)825SD standard deviation; min (max)826minimum (maximum)827Year828Area 6829Area 7830Mean831SD832Min833Max834Mean835SD836Min837Max83820038398628404208414898421,4648434388441898451938461,06184720048486218492418502748511,2848524158532598541198552,79785620058576228582648592168601,4198614168622378631268643,27886520068667308673618682248692,0198704048712328721068732,29687420078757508764938771628783,051879384880238881828823,07888320088847648853548861468872,007888356889208890738912,29389220098936168943028951448961,524897348898200899829003,04590120109025919032739041579051,329906364907219908699092,18991020119116279124369131089142,500915370916231917759182,600919Table 12 Additional estimation results, Larimer920Est.921(SE)922Est.923(SE)924Est.925(SE)926Area 1927Area 2928Area 3929Intercept930−0.088931(0.025)***932−0.041933(0.005)***934−0.008935(0.003) ***93619999370.070938(0.042)*9390.065940(0.013)***9410.047942(0.005)***94320009440.158945(0.040)***9460.128947(0.013)***9480.113949(0.005)***95020019510.122952(0.047)***9530.193954(0.012)***9550.180956(0.005)***95720029580.267959(0.045)***9600.236961(0.012)***9620.213963(0.005)***96420039650.273966(0.045)***9670.255968(0.013)***9690.213970(0.005)***97120049720.295973(0.051)***9740.248975(0.013)***9760.217977(0.005)***97820059790.296980(0.049)***9810.253982(0.013)***9830.212984(0.005)***98520069860.229987(0.054)***9880.237989(0.014)***9900.198991(0.006)***99220079930.210994(0.057)***9950.166996(0.014)***9970.156998(0.006)***999200810000.2581001(0.063)***10020.1241003(0.016)***10040.0891005(0.007)***1006200910070.1931008(0.069)***10090.1151010(0.016)***10110.1031012(0.007)***1013201010140.2481015(0.070)***10160.1161017(0.017)***10180.0931019(0.007)***1020201110210.1331022(0.075)*10230.0731024(0.018)***10250.0771026(0.008)***1027Age depr.10280.0001029(0.007)1030−0.0231031(0.001)***1032−0.0051033(0.001)***1034Area 41035Area 51036Intercept1037−0.0721038(0.024)***10390.0081040(0.004)***1041199910420.0731043(0.036)**10440.0581045(0.007)***1046200010470.1791048(0.033)***10490.1201050(0.007)***1051200110520.1931053(0.040)***10540.1781055(0.008)***1056200210570.2461058(0.039)***10590.2071060(0.008)***1061200310620.2851063(0.036)***10640.1961065(0.008)***1066200410670.3131068(0.042)***10690.1921070(0.008)***1071200510720.3501073(0.042)***10740.1731075(0.008)***1076200610770.3721078(0.047)***10790.1511080(0.009)***1081200710820.3521083(0.052)***10840.0791085(0.010)***1086200810870.2891088(0.059)***1089−0.0131090(0.011)1091200910920.2571093(0.063)***1094−0.0091095(0.011)1096201010970.3451098(0.059)***1099−0.0251100(0.011)**1101201111020.2541103(0.063)***1104−0.0621105(0.012)***1106Age depr.1107−0.0051108(0.005)11090.0031110(0.001)***1111Est. estimate, (SE) standard error, Age. depr age-related depreciation1112*, (**), (***) significant at 10%, (5%), (1%) level1113123111411151116===== PAGE 27 (score 44, numeric-paren 28, table-words 4, var-words 1) =====11171118Mountain Pine Beetles and Host Trees in the Colorado Front Range11196391120Table 13 Additional estimation1121results, Boulder1122Est. estimate, (SE) standard error,1123Age. depr age-related1124depreciation1125*, (**), (***) significant at 10%,1126(5%), (1%) level1127Area 61128Area 71129Est.1130(SE)1131Est.1132(SE)1133Intercept11340.0461135(0.026)*1136−0.0171137(0.005)***113820031139−0.0341140(0.038)1141−0.0281142(0.007)***1143200411440.0131145(0.037)1146−0.0201147(0.007)***1148200511490.0561150(0.039)1151−0.0021152(0.007)1153200611540.0671155(0.042)1156−0.0111157(0.008)1158200711590.0371160(0.046)1161−0.0561162(0.009)***1163200811640.0011165(0.051)1166−0.1111167(0.010)***116820091169−0.0391170(0.058)1171−0.1051172(0.010)***117320101174−0.0571175(0.056)1176−0.1161177(0.011)***117820111179−0.1201180(0.059)**1181−0.1461182(0.012)***1183Age depr.1184−0.0041185(0.005)1186−0.0051187(0.001)***1188Table 14 Estimation results for1189HT effects, Spokane1190Est. estimate, (SE) standard error1191*, (**), (***) significant at 10%,1192(5%), (1%) level1193Est.1194(SE)1195Baseline1196−0.00111970.003119819981199−0.00812000.0091201199912020.00512030.0091204200012050.01512060.009*1207200112080.01312090.0091210200212110.01912120.009**1213200312140.01912150.009**1216200412170.02812180.009***1219200512200.03512210.009***1222200612230.03112240.010***1225200712260.01512270.0111228200812290.01912300.0121231200912320.00712330.012123420101235−0.00412360.0131237201112380.01512390.0141240Appendix 2: Details for Loss Predictions1241In step one we seek the counterfactual price of a home near host trees in absence of any MPB1242effects, for each year of our series. From Eq. (16) we have1243E1244 Pit|hi = 11245Pit|hi = 01246 1247= 1 + m3t = exp (ζ + βt)1248(19)1249For a given home in the HT zone with observed price Pit we then obtain1250˜Pit = E [Pit|hi = 0] =1251Pit12521 + m3t1253=1254Pit1255exp (ζ + βt)1256(20)1257123125812591260===== PAGE 28 (score 6, numeric-paren 0, table-words 0, var-words 6) =====126112626401263J. Cohen et al.1264Next, we compute the pure price differential between the final time period T and year t in1265absence of any MPB disturbance. Following the derivation in (14) we obtain1266κs,t,T = E1267 PiT −Pit1268Pit1269|hi = 01270 1271= E1272 PiT1273Pit1274|hi = 01275 1276−11277= E12781279exp12801281ξs + αsT −αst + ψ (FiT −Fit) + δsai,(T,t) + eis,(T,t)12821283−11284= exp12851286ξs + αsT −αst + ψ (FiT −Fit) + δsai,(T,t) + σ 21287−11288(21)1289Ignoring the time-invariant spatial index, as well as fire and depreciation effects leaves1290κs,t,T = exp12911292αsT −αst + σ 21293−1. The counterfactual price of affected home i in absence1294of any MPB impacts and projected to the final year T can then be computed as1295˜PiT = ˜Pit129612971 + κs,t,T12981299= Pit13001 + κs,t,T13011 + m3t1302= Pitexp13031304αsT −αst −ζ −βt + σ 21305= Pitρs,t,T1306(22)1307We implement these predictive steps via simulation along the lines proposed by Krinsky1308and Robb (1986) as follows: We take 100,000 draws of each contributing coefficient in1309the last line of (22) from their respective finite sample distribution, taking account of all1310involved covariances. For each draw we then compute ρs,t,T as given in the last line of (22)1311and capture the mean, 2.5th, and 97.5th percentile of the resulting empirical distribution. We1312repeat this procedure for every t ̸= T . We then multiply observed price Pit by the appropriate1313year-specific mean conversion factor [term ρs,t,T in the last line of (22)] as well as by the1314confidence bounds for all HT homes in our data. This produces an estimate and confidence1315bounds for the predicted “MPB purged” sales price ˜PiT in 2011.1316In a final step, we then apply the point estimate of MPB loss in 2011 (see Tables 7, 8) to1317each predicted mean price, the lower bound of the MPB loss estimate to each upper bound for1318predicted price, and the upper bound of MPB loss estimate to each lower bound for predicted1319price to derive a point estimate and confidence bounds for predicted MPB losses, in 20111320dollars, for each property.1321References1322Anselin L, Lozano-Gracia N (2008) Errors in variables and spacial effects in hedonic house price models of1323ambient air quality. Empir Econ 34:5–341324Bentz B, Jacques R, Fettig C, Hansen E, Hayes J, Hicke J, Kelsey R, Negrn J, Seybold S (2010) Climate1325change and bark beetles of the Western United States and Canada: direct and indirect effects. 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