1# RECORD 02b5387f9679dc6d340d34b2c07dc617e35c96d32# TITLE: Property Values, Water Quality, and Benefit Transfer: A Nationwide Meta-analysis3# YEAR: 2021.0 VENUE: Land Economics DOI: 10.3368/le.98.2.050120-0062r14# AUTHORS: D. Guignet; M. Heberling; M. Papenfus; O. Griot5# PAGES: 28 CANDIDATE TABLE PAGES (1-based): [7, 11, 14, 17]6# ABSTRACT: We construct a comprehensive, publicly available meta-dataset based on 36 hedonic studies that examine the effects of water quality on housing values in the United States. The meta-dataset includes 656 unique estimates and entails a cluster structure that accounts for price effects at different distances. Focusing on water clarity, we estimate reduced-form meta-regressions that account for within-market dependence, statistical precision, housing market and waterbody heterogeneity, publication bias, and methodological practices. Although we find evidence of systematic heterogeneity, the out-of-sample transfer errors are large. We discuss the implications for benefit transfer and future work to improve transfer performance.789===== PAGE 1 (score 10, numeric-paren 0, table-words 0, var-words 10) =====1011Land Economics • May 2022 • 98 (2): 191–21812DOI:10.3368/le.98.2.050120-0062R113ISSN 0023-7639; E-ISSN 1543-832514© 2022 by the Board of Regents of the15University of Wisconsin System16O This open access article is distributed under the terms of the CC-BY-NC-ND license (http://creativecommons. 17org/licenses/by-nc-nd/4.0) and is freely available online at: http://le.uwpress.org 18S Appendix materials are freely available at http://le.uwpress.org and via the links in the electronic version of 19this article.2019121Property Values, Water Quality, and Benefit Transfer: 22A Nationwide Meta-analysis O S23Dennis Guignet Assistant Professor, Department of Economics, Appalachian State University, Boone, 24North Carolina; guignetdb@appstate.edu25Matthew T. Heberling Research Economist, Office of Research and Development, U.S. Environmental 26Protection Agency, Cincinnati, Ohio; Heberling.Matt@epa.gov27Michael Papenfus Environmental Economist, Office of Research and Development, U.S. Environmental 28Protection Agency, Corvallis, Oregon; Papenfus.Michael@epa.gov29Olivia Griot Senior Analyst, Abt Associates, Inc., Cambridge, Massachusetts; olivia_griot@abtassoc.com30ABSTRACT We construct a comprehensive, 31publicly available meta-dataset based on 36 32hedonic studies that examine the effects of 33water quality on housing values in the United 34States. The meta-dataset includes 656 unique 35estimates and entails a cluster structure that 36accounts for price effects at different dis37tances. Focusing on water clarity, we estimate 38reduced-form meta-regressions that account 39for within-market dependence, statistical 40precision, housing market and waterbody 41heterogeneity, publication bias, and method42ological practices. Although we find evidence 43of systematic heterogeneity, the out-of-sample 44transfer errors are large. We discuss the im45plications for benefit transfer and future work 46to improve transfer performance. (JEL Q51, 47Q53)481. Introduction49The hedonic literature examining the effects 50of surface water quality on residential prop51erty values began over 50 years ago with 52David’s (1968) report. Since then, the litera53ture has evolved significantly. To assess this 54literature’s suitability to support manage55ment decisions related to water quality, we 56use meta-analytic methods to synthesize and 57draw key conclusions from 36 unique studies 58in the United States. There are several exist59ing meta-analyses of hedonic property value 60studies, including applications to air quality 61(Smith and Huang 1993, 1995), contaminated 62sites (Messer et al. 2006; Kiel and Williams 632007; Schütt 2021), open space (Mazzotta, 64Besedin, and Speers 2014), and noise (Nelson 652004). To our knowledge, this study is the first 66comprehensive and rigorous meta-analysis of 67the hedonic literature examining surface wa68ter quality.169The results from meta-analyses can help 70make predictions for benefit transfer—where 71an analyst uses the predicted outcomes to in72fer ex ante or ex post effects of some policy 73action, in lieu of conducting a new original 74study. Analyses of public policies often rely 75on benefit transfer because original studies 76require a lot of time and money or are infeasi77ble because of data constraints. In fact, benefit 78transfer is one of the most common approaches 79used to complete benefit-cost analyses at the 80U.S. Environmental Protection Agency (U.S. 81EPA 2010; Newbold et al. 2018a). Improving 82benefit transfer, as well as combining limited 83but heterogeneous information for surface 84water quality changes, remains a priority for 85policy makers (Newbold et al. 2018a).86Several meta-analyses of stated preference 87studies on water quality have been published 881 There are three notable unpublished studies. In her M.A. 89thesis, Fath (2011) conducted a limited meta-analysis of 13 90hedonic studies. Ge et al. (2013) conducted a meta-analysis 91that combined contingent valuation, travel cost, and hedonic 92studies. They estimated one meta-regression using only he93donic studies for comparison (10 studies with 127 observa94tions). Abt Associates (2015) estimated the capitalization 95effects of large-scale changes in water clarity of lakes using 96a simple weighted-average across nine hedonic studies. We 97are aware of one published meta-analysis that focused on 98urban rivers and property values, but it did not examine mea99sures of water quality (Chen et al. 2019).100at BIBL DE L UNIVERSITE LAVAL on October 20, 2026. Copyright 2021101Downloaded from 102103104===== PAGE 7 (score 29, numeric-paren 16, table-words 1, var-words 4) =====10510698(2)107197108Guignet et al.: Property Values and Water Quality109Table 1110Mean Elasticity Estimates of the Three Most Frequently Examined Water Quality Measures111Water Quality Measure112Unweighted 113Mean114(1)115Cluster-Weighted 116Mean117(2)118Variance-Adjusted 119Cluster-Weighted Mean120(3)121RES Cluster-Adjusted 122Weighted Mean123(4)124n125Studies126Clusters (Kd)127Chlorophyll a (mg/L)128Waterfront1290.737*1300.324*131−0.023***132−0.026***13318134 3135 3136[−0.044, 1.517]137[−0.036, 0.684]138[−0.028, −0.019]139[−0.031, −0.021]140Nonwaterfront within 500 m1410.0051420.011430.008***1440.009***14518146 3147 3148[−0.201, 0.211]149[−0.085, 0.105]150[0.005, 0.010]151[0.006, 0.012]152Fecal Coliform (count per 100 mL)153Waterfront154−0.018***155−0.037156−0.028157−1.3E-4***15836159 4160 4161[−0.026, −0.011]162[−0.088, 0.014]163[−0.079, 0.023]164[−1.8E-4, −0.7E-4]165Nonwaterfront within 500 m166−0.020***167−0.058*168−0.061*169−0.052**17020171 3172 3173[−0.034, −0.006]174[−0.127, 0.010]175[−0.129, 0.008]176[−0.096, −0.008]177Water Clarity (Secchi disk depth, m)178Waterfront1790.1581800.2061810.1911820.109***1831771841818566186[−6.099, 6.416]187[−16.575, 16.987]188[−16.590, 16.972]189[0.099, 0.118]190Nonwaterfront within 500 m1910.028***1920.042***1930.041***1940.026***19583196 619719198[0.020, 0.036]199[0.025, 0.059]200[0.024, 0.058]201[0.017, 0.034]202Note: Confidence intervals at the 95% level are displayed in brackets. Only elasticity estimates pertaining to the three most commonly examined water quality measures in the hedonic literature are pre203sented, but the full suite of mean elasticity estimates are presented in Appendix B.2. We present the respective units for each water quality measure in parentheses just as a reference but emphasize that the 204elasticity estimates are unit-less. RES, random effect size.205* p < 0.1; ** p < 0.05; *** p < 0.01.206at BIBL DE L UNIVERSITE LAVAL on October 20, 2026. Copyright 2021207Downloaded from 208209210===== PAGE 8 (score 7, numeric-paren 0, table-words 1, var-words 5) =====211212Land Economics213198214May 2022215same waterbody and housing market, so the 216weight given to those estimates must be re217duced accordingly (Mrozek and Taylor 2002). 218We next present cluster-weighted means, 219where we define each cluster as a unique study 220and housing market combination. Meta-obser221vations estimated from a common transaction 222dataset in terms of the study area, time period, 223and waterbodies are really just different esti224mates of the same underlying “true” elasticity. 225No matter how many estimates are provided 226by a study for a specific location, each cluster 227as a whole is given the same overall weight. 228This holds regardless of whether the estimates 229for different clusters (i.e., housing markets) 230are from the same study or a different study. 231For example, Boyle, Poor, and Taylor (1999) 232estimate the effects of lake clarity on four dif233ferent housing markets in Maine. These esti234mates are each given a weight of one and thus 235are weighted the same as if they were esti236mates for four different housing markets from 237four different studies.12238More formally, let εˆidj denote elasticity es239timate i, at distance d, for cluster j, and dj240k is 241the number of elasticity estimates for distance 242bin d in each cluster j. The cluster-weighted 243mean elasticity for each distance bin d is244{245}246ε247ε248=249=250= ∑251∑252125312541255,256ˆ257d258dj259dj260K261k262idj263k264j265i266d267d268K269 270[1]271where the same ω272= 1273dj274idj275k weight is given to 276each meta-observation in cluster j and for that 277distance bin. The total number of clusters in 278the meta-dataset for distance bin d is Kd.279The cluster-weighted mean elasticities are 280presented in Table 1, column (2). The results 281are generally similar, suggesting a marginally 282significant increase in waterfront home values 283in response to an increase in the concentration 284of chlorophyll a, and again an insignificant 285effect on the value of nonwaterfront homes. 286The negative price elasticity among water287front homes with respect to fecal coliform is 28812 Ara (2007) statistically identified and separately ana289lyzed several submarkets when estimating the housing price 290effects around Lake Erie. These submarkets sometimes 291overlap because of different statistical strategies, and so in 292our meta-analysis we treat all estimates from Ara (2007) as 293being from the same broader housing market.294now insignificant. The mean elasticity with 295respect to fecal coliform counts for nonwa296terfront homes is only marginally significant 297but larger in magnitude, suggesting a 0.06% 298decrease in value due to a 1% increase in fecal 299coliform counts. The cluster-weighted mean 300elasticities with respect to water clarity are 301similar to the unweighted means, suggesting a 302positive but insignificant effect on waterfront 303home prices, and a significant 0.04% increase 304in nonwaterfront home prices due to a 1% in305crease in Secchi disk depth.306We propose an adjustment to the above 307cluster weights that redistributes the weight 308given to each observation within a cluster and 309distance bin. Consider the incorporation of a 310reallocation parameter (ridj) to the above clus311ter weights, as follows:312ω313= 1314,315dj316idj317idj318k r319 320[2]321where 322≤323≤3240325idj326dj327r328k . This is a generalization 329of the above cluster weights, where 330=1331idj332r333. 334This is also a generalization of the approach 335taken by some meta-analysts who select a 336single “preferred” estimate from each clus337ter, in which case 338=339idj340dj341r342k for the preferred 343estimate and zero otherwise. As discussed, 344choosing a single preferred or best estimate 345can be challenging, disregards information, 346and introduces additional subjectivity to the 347meta-analysis.348Instead, we propose an adjustment to the 349cluster weights based on the inverse variance, 350or fixed effect size (FES) weights commonly 351used in the meta-analysis literature (Nelson 352and Kennedy 2009; Borenstein et al. 2010; 353Nelson 2015; Havránek, Horvath, and Zey354nalov 2016; Vesco et al. 2020; Schütt 2021). 355Under the FES framework, each meta-obser356vation is considered a draw from the same 357underlying population distribution, which 358makes sense in the context of multiple esti359mates from the same cluster (i.e., housing 360market). Our proposed variance-adjusted 361cluster (VAC) weights give more weight to 362more precise estimates within a cluster while 363ensuring that equal influence is given to each 364cluster (or housing market) examined in the 365literature. For example, Walsh, Milon, and 366Scrogin (2011) provide six elasticity estimates 367at BIBL DE L UNIVERSITE LAVAL on October 20, 2026. Copyright 2021368Downloaded from 369370371===== PAGE 11 (score 28, numeric-paren 0, table-words 6, var-words 10) =====37237398(2)374201375Guignet et al.: Property Values and Water Quality376were derived from models that did not use 377econometric methods to account for spatial 378dependence (i.e., spatial fixed effects, spatial 379lag of neighboring house prices, or accounting 380for spatial autocorrelation via a formal spatial 381autocorrelation coefficient or cluster-robust 382standard errors). Although the majority of pri383mary studies use in situ Secchi disk measure384ments (12 studies), we do see that 61% of the 385elasticity observations are based on hedonic 386regressions that used clarity measures other 387than in situ measures.14 About 22% of the ob38814 This large proportion is primarily due to Ara (2007) 389and Walsh et al. (2017), who provide 30 and 112 elasticity 390served elasticities with respect to water clarity 391are from hedonic regressions that also con392trol for other measures of water or ecological 393quality. A time trend variable, as reflected by 394the last year of transaction data in the primary 395study, is also included and ranges from 1994 396to 2014. This is converted into an index repre397senting the number of years since 1994, which 398estimates for homes around Lake Erie and the Chesapeake 399Bay, respectively. Those studies, along with Guignet et al. 400(2017), use water clarity values based on spatial interpola401tions. Two other studies use measurements predicted from 402water clarity models (Boyle and Taylor 2001; Liu et al. 4032014), and one study uses satellite data (Horsch and Lewis 4042009).405Table 2406Descriptive Statistics of Observations Pertaining to Water Clarity407Variable408Mean409Std. Dev.410Min.411Max.412Dependent Variable413Elasticity4140.11674150.2543416−0.64784171.7198418Study Area/Commodity Variable419Waterfronta4200.68084210.467142204231424Mean clarity (Secchi disk depth, m)4252.344261.974270.384286.45429Lake or reservoira4300.56154310.497243204331434Estuarya4350.43854360.497243704381439Waterbody sizeb (sq. km)4406.88464415.31564420.000244320.8858444Median income (thousands, 2017$)44559.07844614.14444737.86544891.174449College degree (% population)4500.13664510.04144520.07684530.2734454Population density (households/sq. km)45549.9145658.384571.41458227.96459Mean house price (thousands, nominal $)460211.314461131.34146231.287463675.364464Northeasta4650.28854660.453946704681469Midwesta4700.19234710.394947204731474Southa4750.48464760.500747704781479Westa4800.03464810.183248204831484Methodological Variable485Elasticity variance4861,228.15948718,704.524889.03E-06489301,448.5490Unpublisheda4910.15004920.357849304941495Not in situ measurea4960.61154970.488349804991500Other water quality variablesa5010.21925020.414550305041505Assessed valuesa5060.05385070.226150805091510Study time period (years)51110.275123.82513351424515Time trend (0=1994 to 20=2014)5168.595176.17518051920520No spatial methodsa5210.38085220.486552305241525Double-loga5260.43085270.496152805291530Linear-loga5310.30775320.462453305341535Lineara5360.03855370.192753805391540Log-lineara5410.22315420.417154305441545Note: Unweighted descriptive statistics are presented for n = 260 elasticity estimates in the meta-dataset per546taining to water clarity. Estimates are based on 18 primary hedonic studies, corresponding to 66 study-housing 547market clusters.548aIndependent variables that are dummy variables.549bSize of the waterbody (or waterbodies) examined in the primary studies was only available for n = 79 of the 550260 observations in the meta-dataset pertaining to water clarity. If multiple waterbodies were examined in the 551primary study hedonic regression models, the average waterbody size is reported.552at BIBL DE L UNIVERSITE LAVAL on October 20, 2026. Copyright 2021553Downloaded from 554555556===== PAGE 12 (score 10, numeric-paren 0, table-words 1, var-words 8) =====557558Land Economics559202560May 2022561corresponds to the first study of water clarity 562in the meta-dataset.563We were able to identify and include three 564unpublished hedonic studies examining water 565clarity (15% of the observations), but publi566cation bias is still a concern given our goal 567of obtaining an accurate estimate of the true 568underlying elasticities for purposes of benefit 569transfer. Following recommendations by Stan570ley and Doucouliagos (2012), we examine 571a series of funnel plots and implement more 572formal funnel-asymmetry and precision-effect 573tests. In doing so, we find clear evidence that 574publication bias is a concern with the meta575data collected from this literature (see Appen576dix B.3 for details). In the meta-regression 577models discussed next, we include the inverse 578of the elasticity variances as a right-hand-side 579covariate to minimize such publication bias 580(Stanley and Doucouliagos 2012, 2014).5813. Meta-regression Methodology582Function transfers based on meta-regressions 583can be a useful approach for benefit transfer 584(Nelson 2015). The approach takes advantage 585of the full amount of information provided 586by the literature while accounting for key di587mensions of heterogeneity in the outcome of 588interest. Consider the following reduced-form 589meta-regression model:590ε591β592=593+594+595+596059715982599ˆ600,601idj602idj603e604x605z606β607β608idj609idj610 611[6]612where the parameters to be estimated are β06131614, β , 615and 6162617β . The right-side moderator variables 618include a vector of characteristics of the pri619mary estimate, study area, and corresponding 620waterbody (xidj) and a vector of methodolog621ical variables (zidj), which describe attributes 622of the primary study and model assumptions. 623The error term eidj is assumed to be normally 624distributed and is allowed to be correlated 625within clusters.626The vector xidj includes indicators of 627whether the elasticity estimate corresponds to 628waterfront homes, water quality in an estuary 629(as opposed to freshwater lakes),15 and the 63015 As described in Section 2, the meta-dataset includes 631price elasticities corresponding to freshwater lakes, 632mean baseline water clarity level correspond633ing to the respective waterbody or portion of 634the waterbody. The vector xidj also includes 635characteristics of the study area and housing 636market, such as median income, proportion 637of the population with a college degree, mean 638house prices, and indicators denoting each of 639the four broad U.S. regions: the Northeast, 640Midwest, South, or West.641The vector zidj captures differences in elas642ticities due to estimate quality and method643ological choices made by the primary study 644authors. If particular values of zidj denote best 645practices, then such information can be ex646ploited when predicting values for purposes of 647benefit transfer (Boyle and Wooldridge 2018). 648The vector zidj includes the variance of the 649corresponding elasticity estimate. Under the 650assumption that better-quality estimates have 651a lower variance, Stanley and Doucouliagos 652(2012, 2014) argue that this attribute should 653be set to zero in any subsequent benefit trans654fer exercise.655In addition, zidj includes indicator vari656ables denoting unpublished studies, whether 657a study used assessed values (as opposed to 658actual transaction prices), different functional 659forms, and when the model did not account 660for spatial dependence. If a primary study 661model did not include spatial fixed effects, a 662spatial lag of housing prices, nor account for 663spatial autocorrelation in some fashion, then 664the no spatial methods indicator is set to one, 665and is zero otherwise.666We also include a study year trend vari667able to possibly reflect changes in empirical 668methods, data, tastes and preferences, and 669awareness of water quality over time (Rosen670berger and Johnston 2009). Time trends in 671meta-analyses of stated preference studies are 672typically based on the year the primary study 673survey was conducted, which is different from 674the year of publication (e.g., Van Houtven, 675Powers, and Pattanayak 2007; Rosenberger 676and Johnston 2009; Johnston, Besedin, and 677Holland 2019). For a hedonic meta-analysis, 678the choice is not as clear because the observed 679revealed preference data in a primary study 680estuaries, rivers, and small rivers and streams. However, the 681hedonic studies in the meta-dataset that examine water clar682ity focus solely on lakes and estuaries.683at BIBL DE L UNIVERSITE LAVAL on October 20, 2026. Copyright 2021684Downloaded from 685686687===== PAGE 14 (score 97, numeric-paren 70, table-words 6, var-words 4) =====688689Land Economics690204691May 2022692in water clarity leads to a 0.04% increase in 693the price of nonwaterfront homes within 500 694m of the waterbody. As expected, the price 695elasticity with respect to clearer waters is sig696nificantly higher among waterfront homes (by 6970.1457 percentage points). Together these es698timates suggest that, on average, a 1% increase 699in water clarity leads to a 0.19% increase in 700waterfront home prices. The statistically sig701nificant coefficient corresponding to elasticity 702variance suggests that publication bias is a 703concern, but setting this variable to zero when 704predicting values for function transfers con705trols for such bias (Stanley and Doucouliagos 7062012).707Model 2 in Table 3 includes indicator 708variables denoting the four regions of the 709United States, with the Northeast being the 710omitted category. The negative region coef711ficients suggest that housing price elasticities 712with respect to water clarity in the Midwest, 713South, and West tend to be less than those 714in the Northeast, but such differences in this 715model are only significant in the South. For 716example, a 1% increase in water clarity in the 717Northeast would lead to an average increase 718in value of 0.27% for waterfront homes and 7190.25% for nonwaterfront homes within 500 720m. In the South, the results suggest that a 7211% increase in clarity corresponds to much 722smaller but still significant 0.04% and 0.02% 723increases in price among waterfront and non724waterfront homes. Considering the average 725house price of $211,314, this suggests that a 726Table 3727Variance-Adjusted Cluster-Weighted Least Squares Meta-regression Results728Variable729(1)730(2)731(3)732(4)733(5)734(6)735Waterfronta7360.1457***7370.0170738−0.06777390.1010**740−0.11267410.1251***742(0.046)743(0.023)744(0.052)745(0.039)746(0.086)747(0.042)748Midwesta749−0.1056750−0.1488*751−0.2059752−0.2561***753−0.3156***754(0.087)755(0.082)756(0.132)757(0.096)758(0.116)759Southa760−0.2248***761−0.2797***762−0.3209*763−0.2889***764−0.3945***765(0.076)766(0.084)767(0.171)768(0.108)769(0.131)770Westa771−0.1803772−0.1803773−0.1747774−0.3745**775−0.3772**776(0.120)777(0.121)778(0.147)779(0.180)780(0.174)781Estuarya782−0.0401**783−0.1223***784(0.016)785(0.039)786Waterfront × estuary7870.1274**7880.1721*789(0.055)790(0.088)791Mean clarity 7920.03757930.0799**794(0.030)795(0.035)796Waterfront × mean clarity 797−0.0684**798−0.1061**799(0.029)800(0.050)801Elasticity variance8028.97E-07***8036.26E-07**8046.26E-07**8055.10E-078066.02E-07**8075.02E-07808(1.52E-07)809(2.56E-07)810(2.57E-07)811(3.30E-07)812(2.56E-07)813(3.65E-07)814Time trend8150.0183***8160.0223***817(0.006)818(0.006)819Linear-loga8200.19738210.1987822(0.161)823(0.159)824Lineara8250.2198**8260.1159827(0.086)828(0.083)829Log-lineara830−0.0020831−0.0059832(0.008)833(0.008)834Constant8350.0414*8360.2474***8370.3320***8380.3092*8390.16818400.0493841(0.021)842(0.077)843(0.090)844(0.182)845(0.122)846(0.180)847Observations848260849260850260851260852260853260854Adjusted R-squared8550.0808560.1488570.1488580.1568590.1708600.176861Note: The dependent variable is the home price elasticity with respect to water clarity (Secchi disk depth). Clustered-robust standard errors are 862in parentheses and are clustered according to the K = 66 study-housing market combinations. Weighted least squares regressions are estimated 863using the “regress” routine in Stata 16 and defining analytical weights equal to the variance-adjusted cluster weights (see equation [3]).864aIndependent variables that are dummy variables.865* p < 0.1; ** p < 0.05; *** p < 0.01.866at BIBL DE L UNIVERSITE LAVAL on October 20, 2026. Copyright 2021867Downloaded from 868869870===== PAGE 15 (score 14, numeric-paren 0, table-words 2, var-words 9) =====87187298(2)873205874Guignet et al.: Property Values and Water Quality8751% increase in water clarity (an average of 8762.34 cm or just under 1 in.) would increase 877the value of a waterfront and nonwaterfront 878home in the Northeast by $559 (p = 0.000) 879and $522 (p = 0.001), respectively. This same 880improvement for otherwise similar waterfront 881and nonwaterfront homes in the South would 882be only $84 (p = 0.061) and $48 (p = 0.041).883Models 3 and 4 assess potential hetero884geneity in the housing price effects based 885on characteristics of the environmental com886modity, in this case, the type of waterbody 887and whether the waters are already relatively 888clear. Model 3 includes an indicator denoting 889whether the elasticity estimates correspond to 890an estuary (as opposed to a freshwater lake or 891reservoir) as well as a corresponding interac892tion term with the waterfront indicator. The 893negative and statistically significant coeffi894cient on estuary suggests that an increase in 895water clarity has a smaller effect on the price 896of homes near an estuary, compared with an 897increase in lake water clarity. Such a finding 898seems reasonable given that surrounding res899idents may not generally expect the water to 900be clear in estuaries because brackish waters 901are often naturally opaque. However, the op902posite is found among waterfront homes, as 903suggested by the positive and statistically sig904nificant 0.0873 (p = 0.049) sum of the estuary 905and waterfront × estuary coefficients.906To better illustrate the implications of 907model 3, consider a 1% increase in clarity in 908an estuary in the Northeast. This would lead 909to a 0.35% increase in the value of a bayfront 910home and a 0.29% increase in the value of a 911nonbayfront home that was still within 500 m 912of the estuary. In contrast, the same 1% in913crease in water clarity would lead to a 0.26% 914increase among lakefront homes in the North915east and a larger 0.33% increase among non916lakefront properties that are within 500 m. Al917though it may seem counterintuitive that the 918elasticity among lakefront properties is less, 919this does not necessarily violate the intuition 920that those closest to the resource should hold 921a higher value for an improvement. Baseline 922house values tend to be much larger among 923waterfront homes, so a smaller elasticity does 924not necessarily translate to a smaller marginal 925implicit price. For example, Walsh, Milon, 926and Scrogin (2011) report a mean sale price of 927$452,646 and $199,982 (2002$) among lake928front and nonlakefront homes, respectively. 929Applying these mean values to the aforemen930tioned elasticities suggests an implicit price 931for a 1% increase in clarity of $1,197 for lake932front homes and $664 for nonlakefront homes.933Model 4 explores whether the house price 934elasticity with respect to clearer waters tends 935to be systematically different depending on 936baseline water clarity.18 The model includes 937the mean clarity level corresponding to each 938primary study estimate and an interaction 939term between mean clarity and the waterfront 940indicator. The main effect is statistically in941significant, as is the sum of the main effect 942and the coefficient on the waterfront × mean 943clarity interaction term. This suggests that the 944price elasticity for nonwaterfront and water945front homes, respectively, does not vary with 946baseline water clarity.947In subsequent models not reported here, 948we find little evidence of systematic hetero949geneity with respect to the other study area 950and commodity variables reported in Table 2, 951including household median income, percent 952of population with a college degree, mean 953house prices, and waterbody size. Although 954mean house prices and waterbody charac955teristics are taken from the primary studies, 956the lack of significant findings pertaining to 957household median income, education, and 958other census-derived sociodemographics may 959be partly attributed to the spatial coarseness 960of the county- or state-level variables and the 961resulting measurement error.962Models 5 and 6 build on the previous 963two models by controlling for methodolog964ical characteristics of the primary studies. 965The time trend variable is added, as well as 966indicators denoting the functional form of 967the hedonic price function that was assumed 968by the primary study authors (double-log is 969the omitted category). The positive and sig970nificant time trend suggests that, all else 971constant, the elasticity estimates have been 972increasing over time. The specification indi973cators are largely insignificant, with the ex974ception of linear in model 5. This suggests 97518 Because of collinearity concerns, we do not account for 976both waterbody type and baseline water clarity in the same 977model.978at BIBL DE L UNIVERSITE LAVAL on October 20, 2026. Copyright 2021979Downloaded from 980981982===== PAGE 17 (score 92, numeric-paren 64, table-words 6, var-words 5) =====98398498(2)985207986Guignet et al.: Property Values and Water Quality987proportions across the remaining three speci988fication indicators. More specifically, among 989the remaining 250 observations that used 990one of these specifications to estimate the 991price elasticity with respect to water clarity, 992we see that 45% were based on a double-log 993(the omitted category), 32% on a linear-log, 994and 23% on a log-linear specification. To 995infer an elasticity that is based on the most 996recent methods and data possible, the value 997for the time trend index is set to 20 (which 998(2007), where the meta-analyst identifies the set of all possi999ble combinations of methodological variable values, assigns 1000a probability to each, and then predicts the benefit transfer 1001estimates for each methodological variable combination and 1002takes the average across all combinations.1003corresponds to 2014, the most recent year ob1004served in the metadata).1005This illustrative exercise yields an “av1006erage” elasticity for waterfront homes of 10070.2698, suggesting that a 1% increase in 1008Secchi disk depth (an increase of 2.34cm, on 1009average) leads to an average increase in wa1010terfront home values of 0.27% (p = 0.000). 1011A slightly smaller 0.2564 elasticity is esti1012mated for the “average” nonwaterfront home 1013(p = 0.000). Based on the average home price 1014from Table 2, these results translate to a mean 1015implicit price of $570 (p = 0.000) and $542 1016(p = 0.000) for waterfront and nonwaterfront 1017homes, respectively. Overall, the literature 1018yields plausible and statistically significant 1019Table 41020RES Cluster-Adjusted Weighted Least Squares Meta-regression Results1021Variable1022(1)1023(2)1024(3)1025(4)1026(5)1027(6)1028Waterfronta10290.0828***10300.0374*1031−0.035610320.0715*10330.008010340.0829**1035(0.018)1036(0.022)1037(0.050)1038(0.036)1039(0.044)1040(0.031)1041Midwesta1042−0.02041043−0.04621044−0.04751045−0.1565***1046−0.1476***1047(0.040)1048(0.036)1049(0.048)1050(0.032)1051(0.039)1052Southa1053−0.0833***1054−0.1451***1055−0.10961056−0.2600***1057−0.2495***1058(0.031)1059(0.043)1060(0.081)1061(0.037)1062(0.044)1063Westa1064−0.06071065−0.06071066−0.05951067−0.3200***1068−0.4216***1069(0.097)1070(0.098)1071(0.107)1072(0.111)1073(0.077)1074Estuarya1075−0.01811076−0.0534***1077(0.020)1078(0.020)1079Waterfront × estuary10800.1019*10810.05821082(0.055)1083(0.050)1084Mean clarity 10850.024710860.0601***1087(0.037)1088(0.022)1089Waterfront × mean clarity 1090−0.03321091−0.03171092(0.032)1093(0.024)1094Elasticity variance10952.22E-0510962.05E-0510972.01E-0510982.01E-0510991.91E-0511001.86E-051101(2.18E-05)1102(2.04E-05)1103(2.01E-05)1104(2.01E-05)1105(1.93E-05)1106(1.89E-05)1107Time trend11080.0121***11090.0158***1110(0.002)1111(0.002)1112Linear-loga1113−0.03711114−0.0953*1115(0.040)1116(0.049)1117Lineara11180.080711190.04931120(0.091)1121(0.052)1122Log-lineara1123−0.00231124−0.00011125(0.005)1126(0.005)1127Constant11280.025711290.1025***11300.1755***11310.108611320.1577***11330.00341134(0.016)1135(0.031)1136(0.055)1137(0.098)1138(0.034)1139(0.063)1140Observations1141260114226011432601144260114526011462601147Adjusted R-squared11480.10111490.14611500.15911510.14811520.20111530.2221154Note: The dependent variable is the home price elasticity with respect to water clarity (Secchi disk depth). Clustered-robust standard errors are 1155in parentheses and are clustered according to the K = 66 study-housing market combinations. Weighted least squares regressions are estimated 1156using the “regress” routine in Stata 16 and defining the analytical weights equal to the random effect size (RES) cluster-adjusted weights (see 1157Section 2).1158aIndependent variables that are dummy variables.1159* p < 0.1; ** p < 0.05; *** p < 0.01.1160at BIBL DE L UNIVERSITE LAVAL on October 20, 2026. Copyright 20211161Downloaded from 116211631164===== PAGE 18 (score 15, numeric-paren 0, table-words 6, var-words 3) =====11651166Land Economics11672081168May 20221169estimates of how water clarity is capitalized 1170in surrounding home values, even after empir1171ically controlling for key dimensions of het1172erogeneity, publication bias, and methodolog1173ical assumptions.1174Best-Performing Model for Benefit Transfer1175To examine out-of-sample transfer error and 1176assess the performance of the various models 1177and weighting schemes, we iteratively leave 1178out observations corresponding to the 66 hous1179ing market study clusters, and then reestimate 1180the mean unit values and meta-regression mod1181els using the remaining sample. The predicted 1182elasticities are then estimated for the excluded 1183cluster. This is repeated by excluding the 66 1184clusters one at a time. After completing all 66 1185iterations, we calculate the median absolute 1186transfer error. Similar out-of-sample transfer 1187error exercises have been implemented in the 1188literature (e.g., Lindhjem and Navrud 2008; 1189Stapler and Johnston 2009).1190We conduct this out-of-sample trans1191fer exercise in two ways. In the first ap1192proach, we construct a synthetic observa1193tion for each distance bin d in cluster j and 1194then compare the elasticity value for this 1195synthetic observation to the predicted elas1196ticity from the meta-regression models. The 1197synthetic observation is constructed us1198ing the same VAC weights (i.e., an inverse 1199variance weighted mean across all elastic1200ity estimates for distance bin d in cluster j):1201ε1202ε1203=1204=12051206120712081209=1210121112121213121412151216∑1217∑121811219112201122111222.1223ˆ1224ˆ 1225idj1226dj1227dj1228idj1229v1230k1231s1232idj1233dj1234k1235i1236v1237i1238The corresponding right-hand-side variables 1239for the synthetic observations are calculated 1240in the same fashion. Those variable values 1241are then plugged into the estimated meta-1242regressions to yield a predicted elasticity εˆ1243s1244dj, 1245which is compared to the “actual” elasticity 1246for each synthetic observation εˆs1247dj. A similar 1248exercise is done using the mean unit values, 1249where the waterfront or nonwaterfront means 1250are calculated each iteration, and then used as 1251the unit value prediction εˆ1252s1253dj for the excluded 1254observations. The transfer error is calculated 1255as the absolute value of the percent difference:1256ε1257ε1258ε1259−12601261126212631264=1265×12661267126812691270ˆ1271ˆ1272ˆ1273%1274100 .1275s1276s1277dj1278dj1279s1280dj1281dj1282TE1283 1284[7]1285 1286Our synthetic observation approach for 1287measuring 1288out-of-sample 1289transfer 1290error 1291weights the “actual” observed elasticity es1292timates and the sample used to parameter1293ize the meta-regression models in the same 1294way. When dealing with a panel- or cluster-1295structured meta-dataset, the more common 1296practice of comparing predicted and observed 1297elasticity estimates for all left-out observa1298tions within each iteration (e.g., Londoño and 1299Johnston 2012; Fitzpatrick, Parmeter, and 1300Agar 2017; Subroy et al. 2019) potentially 1301inflates the transfer error. The parameterized 1302meta-regressions, and hence the predicted 1303elasticities εˆidj, would discount less precise 1304estimates, but the excluded elasticity observa1305tions εˆidj that these are compared with in each 1306iteration would all be treated equally when 1307assessing the transfer error. This inconsistent 1308weighting across the predicted and observed 1309elasticities automatically puts the predictive 1310performance of the meta-regression models at 1311a disadvantage. Nonetheless, we carry out our 1312transfer error exercise using this conventional 1313approach and find similar results.1314The median absolute transfer error results 1315for each model and weighting scheme are 1316presented in Table 5. The top panel shows 1317the median transfer errors using our out-of-1318sample synthetic observation approach. The 1319lower panel shows the median transfer errors 1320when all excluded observations are treated 1321equally and used for comparison. The results 1322suggest a median absolute transfer error of 132376%–119% under the synthetic observation 1324comparison versus 83%–131% when compar1325ing all excluded observations.1326Although errors of this size are not un1327heard of, the transfer errors for this study are 1328in the high range. Kaul et al. (2013) examined 13291,071 transfer errors reported by 31 studies 1330and report that the absolute value of the trans1331fer errors ranged from 0% to 7,496%, with a 1332median of 39%. Rosenberger (2015) summa1333rized the results for 38 studies that statistically 1334at BIBL DE L UNIVERSITE LAVAL on October 20, 2026. Copyright 20211335Downloaded from 1336