NCEE Working Paper
Property values and water quality:
A nationwide meta-analysis and the
implications for benefit transfer
Dennis Guignet, Matthew T. Heberling, Michael
Papenfus, Olivia Griot and Ben Holland
Working Paper 19-05
June, 2019
U.S. Environmental Protection Agency	/!f
National Center for Environmental Economics	fw
https://www.epa.aov/environmental-economics	envIronmental^conomics

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Property values and water quality:
A nationwide meta-analysis and the implications for benefit transfer
Dennis Guignet, Matthew T. Heberling, Michael Papenfus,
Olivia Griot and Ben Holland
ABSTRACT: We conduct a meta-analysis using a comprehensive review of studies that examine
the effects of water quality improvements on waterfront and non-waterfront housing values. Rather
than conducting the meta-analysis using dollar values, this study estimates mean elasticity
responses. We identify 36 studies that result in 656 unique observations. Mean property price
elasticities with respect to numerous water quality measures are calculated (e.g., chlorophyll-a,
fecal coliform, nitrogen, and phosphorous) for purposes of value transfer. In the context of water
clarity, function transfers can be performed. We estimate numerous meta-regressions, and compare
transfer performance across models using an out-of-sample transfer error exercise. The results
suggest value transfers often perform just as well as more complicated function transfers. In our
context, however, a simple function transfer that accounts for baseline water clarity performs best.
We discuss the implications of these results for benefit transfer, and outline key limitations in the
literature.
KEYWORDS: benefit transfer; hedonic; meta-analysis; property value; water pollution; water
quality
JEL CODES: Q51 (Valuation of Environmental Effects); Q53 (Air Pollution; Water Pollution;
Noise; Hazardous Waste; Solid Waste; Recycling)
DISCLAIMER
The views expressed in this article are those of the authors and do not necessarily reflect the views or policies of the
U.S. EPA or Abt Associates. The research described in this article has been funded wholly or in part by the U.S. EPA
under contract EP-C-13-039 to Abt Associates. Any mention of trade names, products, or services does not imply an
endorsement by the U.S. Government or the U.S. EPA. No official Agency endorsement should be inferred.

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Property values and water quality:
A nationwide meta-analysis and the implications for benefit transfer1
Dennis Guigneta, Matthew T. Heberlingb, Michael Papenfusb,
Olivia Griot0 and Ben Holland0
1. INTRODUCTION
The hedonic property value method is a popular nonmarket valuation technique to estimate how
residents value local amenities and disamenities, including water quality and related ecosystem
services. The basic notion is that a house and its location comprise a bundle of characteristics.
Hedonic modeling allows analysts to estimate how each of those various characteristics contribute
to the overall price of a home. Empirical applications of hedonic methods to property values date
back to Hass (1922), who examined how agricultural land prices vary with distance to the city
center. But it was not until Rosen's (1974) seminal paper that hedonic modeling was formally
linked to welfare analysis. Since then there have been numerous empirical studies examining how
local environmental commodities affect residential property prices.
Dating back to David's (1968) report, the hedonic literature examining the impacts of surface water
quality on residential property values is fairly well-established. Our comprehensive literature
review identified 36 unique studies in the published and grey literature. Many studies focus
primarily on the price impacts of water quality among waterfront homes (Young 1984, Michael et
al. 1996, Boyle et al. 1999, Leggett and Bockstael 2000), but recent studies have found price effects
as far away as about one mile from a waterbody (Walsh et al. 201 la, Netusil et al. 2014, Liu et al.
2017, Klemick et al. 2018).
In order to generalize key conclusions from any literature, economists often turn to meta-analysis,
which is a quantitative synthesis of multiple primary studies (Nelson, 2013). Nelson and Kennedy
(2009) identified 140 meta-analyses in the environmental and resource economics field, about half
of which were published since 2004. Although there are several meta-analyses of hedonic property
value studies, including applications to air quality (Smith and Huang, 1993, 1995), contaminated
1 The authors thank Elena Besedin, Matthew Ranson, and Patrick Walsh for helpful feedback early in the
development of this project. We also thank Charles Griffiths. James Price. Brenda Rashleigh. Stephen Swallow,
Hale Thurston, and participants at the 10th Annual Conference of the Society for Benefit-Cost Analysis and the
USD A Workshop "Applications and Potential of Ecosystem Services Valuation within USD A - Advancing the
Science" for helpful comments.
a Corresponding author: Department of Economics, Appalachian State University, 416 Howard Street, ASU Box
32051, Boone, NC. Email: guienetdb@appstate.edu.
b Office of Research and Development, U.S. Environmental Protection Agency.
0 Abt Associates, Inc.
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sites (Messer et al., 2006; Kiel and Williams, 2007), open space (Mazzotta et al., 2014), and noise
(Nelson, 2004), to our knowledge we conduct the first comprehensive meta-analysis of the hedonic
literature examining surface water quality.2
The results from meta-analyses can help make predictions for benefit transfer - where an analyst
uses the predicted outcomes to infer ex ante or ex post impacts of some policy action, in lieu of
conducting a new study. In practice, benefit analyses of public policies often rely on benefit
transfer because original studies require a lot of time and money, or are infeasible due to data
constraints. In fact, benefit transfer is one of the most common approaches used to complete
benefit-cost analyses at the US Environmental Protection Agency (US EPA, 2010, Newbold et al.
2018). Improving benefit transfer, as well as combining limited, but heterogeneous, information
for surface water quality changes, remains a priority for policy-makers (Newbold et al. 2018).
Our obj ective is to synthesize the vast literature examining how water quality impacts home values,
and estimate unit values and value-transfer functions. Our study aggregates this literature and
systematically calculates comparable within- and cross-study elasticity estimates by accounting
for differences in functional forms, assumed price-distance gradients, and baseline conditions. We
convert the primary study coefficient estimates to common elasticity and semi-elasticity measures
for both waterfront and near-waterfront homes, and then use Monte Carlo simulations to estimate
the corresponding standard errors. Each study can yield numerous meta-observations due to
multiple study areas, water quality metrics, and model specifications. Our meta-dataset contains
n=665 unique observations, and for 656 of these observations sufficient information was reported
to calculate the corresponding elasticity and/or semi-elasticity estimates.
We find considerable differences across the studies in the meta-dataset in terms of how studies
quantified water quality, the type of waterbody studied, and the region of the US the study
examined. We often find it difficult to convert the disparate water quality measures to a common
metric. Therefore, we conduct a separate meta-analysis for each water quality measure. In most
cases this is limited to calculating mean elasticities with respect to each water quality measure. We
calculate these unit values separately for waterfront and non-waterfront homes using a variety of
different weighting schemes. Most notably, we propose a novel cluster-adjusted Random Effect
Size (RES) weighting scheme that simultaneously gives more influence to more statistically
precise primary study estimates and accounts for the cluster- (or panel-) nature of the meta-dataset.
In the context of water clarity specifically, a sufficient number of meta-observations (n=260)
allows us to conduct a meta-regression analysis. In the absence of clear guidance on the most
appropriate estimation approach and specification for these meta-regressions, a variety of
specifications are estimated using different techniques, including Random Effects (RE) Panel
models and the Mundlak (1978) regression model that was recently suggested by Boyle and
Wooldridge (2018) as a possible alternative when estimating meta-regressions for purposes of
benefit transfer.
2 There are, however, two notable unpublished studies. In her Master's thesis, Fath (2011) conducts a limited meta-
analysis of 13 hedonic studies. Abt Associates (2015) estimates the capitalization effects of large-scale changes in
water clarity of lakes based on a simple weighted-average across nine hedonic studies.
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We then statistically test the appropriateness of pooling estimates from different regions and types
of waterbodies, and discuss the implications for benefit transfer. Benefit transfer performance
across the different models for value function transfers are compared to each other, and to a simpler
value transfer. This assessment entails an out-of-sample transfer error exercise. Although value
transfers generally perform on par with more complicated function transfers, and sometimes even
perform better, we do find that a transfer function accounting for baseline water clarity levels
yields the lowest transfer error.
Along with recommendations to practitioners conducting benefit transfer, we provide some brief
guidance on combining our results with available data to assess local, regional, and national
policies affecting water quality. A key contribution of this study is in highlighting gaps in the
literature regarding the types of waterbodies and regions covered, and the disconnect between the
water quality metrics used by economists versus those currently examined by water quality
modelers and policy makers.
The remainder of the paper is organized as follows. First, we describe the meta-dataset, including
how we identified studies and our approach to format comparable elasticity estimates. Section 3
introduces the methodology for weighting and clustering meta-observations, and presents the
meta-regression models used to predict values related to water clarity. We then present the results
for the mean unit value and meta-regression models, including a comparison to determine which
is more accurate for benefit transfer. We end with a discussion of the limitations and future
research.
2. META-DATASET
2.1 Identifying Candidate Studies and Inclusion Criteria
Our search protocol included both peer-reviewed and grey literature sources. We focused on
hedonic studies utilizing surface water quality measures or indices in the US, but we left criteria
such as year published open under different combinations of keywords to capture the largest
selection of studies. The search began with reviewing reports unrelated to this research effort (e.g.,
US EPA 2016; Van Houtven et al. 2008) or other literature reviews and meta-analyses on related
topics (e.g., Abt Associates, 2015; Alvarez & Asci, 2014; Braden et al., 2011; Crompton, 2004;
Fath, 2011). The next step was to search a variety of databases and working paper series which
included Google Scholar, Environmental Valuation Reference Inventory, JSTOR, AgEcon Search,
EPA's National Center for Environmental Economics Working Paper Series, Resources for the
Future (RFF) Working Paper Series, Social Science Research Network (SSRN), and ScienceDirect
among many others. Keywords when searching these databases included all combinations of the
terms: house, home, property, value, price, or hedonic with terms such as water quality, water
clarity, Secchi disk, pH, aquatic, and sediment. Requests also were submitted to ResEcon and
Land and Resource Economics Network on October 24, 2014 and January 21, 2016. Seven studies
were provided from the 2014 request and one publication was added from the 2016 request. After
this lengthy process, we attempted one final literature search through the US EPA's internal library
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system. This last step identified two studies that were not identified previously. Although it was
published after the construction of the meta-dataset, the list of identified studies was compared to
an extensive literature review by Nicholls and Crompton (2018). This provided additional
reassurance that the identified set of studies fitting the outlined criteria is fairly comprehensive.
In total we identify 65 studies in the published and grey literature that are potentially relevant. To
facilitate linkages between water quality models and economic valuation, and ultimately to
perform more defensible benefit transfers to US policies, focus is drawn to the 36 unique primary
studies that examined surface water quality in the US using objective water quality measures. More
specifically, 29 studies are dropped after further screening because an objective water quality
measure was not used, the study area was outside of the US, a working paper or other grey literature
became redundant with a later peer-reviewed publication that is in the meta-dataset, or the research
was not a primary study (e.g., a literature review). The remaining 36 studies are selected for
inclusion in the final meta-dataset.
2.2 Meta-dataset Structure and Details
From the selected 36 studies, 26 are published studies in peer-reviewed academic journals, three
are working papers, three are Master's level or PhD theses, two are government reports, one is a
presentation, and one is a book chapter. The year of publication or study release ranges from 1979-
2017. The majority of primary studies examine freshwater lakes (24 studies), followed by estuaries
(6 studies), rivers (2 studies) and small rivers and streams (3 studies). One study examines both
lakes and rivers. As shown in Figure 1, spatial coverage is limited in the southwest and midwest
regions of the US, while the eastern and southern regions have the most studies. Some states even
have as many as four (Maine, Maryland, Ohio), and even five studies (Florida).
[Insert Figure 1 about here.]
The meta-dataset consists of a panel or cluster structure, where each study can contribute multiple
unique observations.3 Individual studies may analyze multiple study areas, water quality metrics,
and model specifications. Additionally, a unique dimension in the current context is that the
primary hedonic studies sometimes examine how the property value effects of interest vary with
distance from the waterbody. Distance is thus an important factor and should be accounted for
when transferring water quality benefits to a new policy region. A novel contribution of this study
is that the meta-dataset explicitly incorporates price effect estimates corresponding to different
distances from the waterbody. This implies that even a single coefficient estimate from a primary
study may be used to infer price effects for homes at different distances, each of which is
represented as a separate observation in the meta-dataset.
3 In the context of meta-analysis, Boyle and Wooldridge (2018) specify the distinction between a cluster versus a
panel structure. The structures are similar, but with a cluster structure there is no natural ordering to the observations
within a cluster, as is the case in this meta-analysis. We therefore continue with the cluster structure nomenclature,
but believe making the connection to panel data analysis is useful given its prominence in econometrics
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Across the 36 primary studies, there are 30 different measures of water quality examined. To be
fully transparent and provide the most information for practitioners to choose from when
conducting benefit transfers, the meta-dataset includes all water quality measures. The price effect
estimates with respect to different water quality measures, however, are examined separately in
the meta-analysis. The pooling of estimates across different water quality measures is not
appropriate. Even when converted to elasticities, a one-percent change in Secchi disk depth means
something very different than a one-percent change in fecal coliform counts, pH levels, or nitrogen
concentrations, for example. That said, when a valid approach could be found, the primary study
estimates are converted to a common water quality measure. Such a conversion is only undertaken
for two hedonic studies examining light attenuation (a measure of water clarity) in the Chesapeake
Bay (Guignet et al., 2017; Walsh et al., 2017), where an appropriate conversion factor was
available in the literature. In these cases, the meta-dataset includes unique observations
corresponding to the inferred water quality measure (Secchi disk depth), as well as the original
measure (light attenuation). To our knowledge, valid conversion factors or other approaches are
not currently available for other water quality measures and primary study areas included in the
meta-dataset.
2.3 Formatting Comparable Elasticity and Semi-elasticity Estimates
A key challenge in constructing any meta-dataset is to ensure that all the outcomes of interest are
comparable across studies (Nelson and Kennedy, 2009). By focusing on a single methodology,
hedonic property value methods, the outcome of interest itself is always the same - i.e.,
capitalization effects on residential property values. And as just discussed, elasticity estimates with
respect to different water quality measures are never pooled and examined in a single meta-
analysis, thus making the estimates that are examined together even more comparable. Two other
sources deterring comparability of results across primary studies must still be accounted for, and
both pertain to functional form assumptions in the original hedonic specifications.
The first form of cross-study differences is a common obstacle for meta-analysts. Differences in
functional form lead to coefficient estimates that have slightly different interpretations across
studies. In the hedonic literature, some studies estimate specifications like semi-log, double-log,
and even linear models. Other primary studies include interaction terms between the water quality
measure and various attributes of the waterbody (such as lake area) to model heterogeneity. To
address these differences we convert the coefficient estimates from the primary studies to common
elasticity and semi-elasticity estimates based on study specific model-by-model derivations, which
are carefully detailed in Appendix A. These derivations also sometimes include the mean
transaction price and mean values of observed covariates, as reported in the primary study. Such
variables enter into the elasticity calculations due to interaction terms or other functional form
assumptions in the primary study.
The second form of cross-study differences involves how (and if) the home price impacts of water
quality are allowed to vary with distance to the waterbody. In a recent meta-analysis of stated
preference studies on water quality, Johnston et al. (2019) point out that no published meta-
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regression studies in the valuation literature include a mechanism to account for the relationship
between households' values for an environmental commodity and distance to the resource.
Johnston et al. account for this relationship by proposing an approach to estimate the mean distance
among the sample in each primary study, and then include that as a control variable in the right-
hand side of their meta-regression models. In our study we are able take a different approach that
explicitly incorporates such spatial heterogeneity into the structure of the meta-dataset itself. We
include unique observations from the same primary study that account for the house price effects
at different distances from the resource. Such an approach is possible due to the relatively fine
spatial resolution associated with hedonic property value methods compared to other non-market
valuation techniques.
In the hedonic literature, different primary studies make different functional form assumptions
when it comes to the price-distance gradient with respect to water quality, including both discrete
distance bins and continuous gradients (e.g., linear, inverse distance, polynomial). The
consideration of how the outcome effects of interest vary with distance adds a unique and novel
dimension to the cluster (or panel) structure of our meta-dataset. Except for internal meta-analyses
by Klemick et al. (2018) and Guignet et al. (2018), our meta-analysis is the first to incorporate this
distance dimension into the meta-dataset. In an internal meta-analysis the researchers estimate the
primary regressions themselves, and so Klemick et al. (2018) and Guignet et al. (2018) had the
luxury of assuming the initial functional forms of their hedonic regressions, and thus ensured that
the distance gradients were specified the same way across all estimates. In the current meta-
analysis we do not have this luxury, and adapting the elasticity estimates to be comparable across
different distance gradient specifications in different studies is a unique challenge.
We make an overarching assumption to limit the meta-dataset and analysis to only housing value
impacts within 500 meters. Although some hedonic studies have found that water quality impacts
home values at farther distances (e.g., Walsh et al. 201 la, Netusil et al. 2014, Klemick et al. 2018,
Kung et al. 2019), 16 of the 36 studies in the literature exclusively analyze price impacts on
waterfront homes. It is unknown whether some primary studies limited the spatial extent of the
analysis because no significant price effects were found or believed to be present at farther
distances, or because of other reasons (perhaps due to stakeholder interest or to keep the analysis
more tractable). The same reasoning applies to why other studies decided to limit the spatial extent
of the analysis at a certain distance. To minimize any potential selection bias of elasticity estimates
corresponding to farther distances, we limit the meta-data and analysis to only price effects within
500 meters.
To standardize the elasticities across different studies with different distance gradient functional
form assumptions, we "discretize" distance into two bins - waterfront homes and non-waterfront
homes within 500 meters. If a primary study only examined waterfront homes, then it only
contributes observations to the meta-dataset corresponding to waterfront homes. But if a study
examined both waterfront and non-waterfront homes, then it contributes separate observations for
each distance bin, even if the observations are derived from the same underlying set of
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coefficients.4 For elasticity estimates corresponding to waterfront homes, when applicable, a
distance of 50 meters is plugged into the study-specific elasticity derivations. This assumed
distance for a "representative" waterfront home is based on observed mean distances among
waterfront homes across the primary studies. For non-waterfront homes within 0-500 meters, the
midpoint of 250 meters is plugged into the study-specific elasticity derivations, when applicable.
Details are provided in Appendix A. Overall, this approach allows us to derive comparable
elasticity estimates across studies based on the form of the distance gradient assumed in each
primary study.
Finally, meta-analysis often requires a measure of statistical precision around the estimates of the
outcome of interest, in our case the inferred elasticity estimates. To obtain the elasticity estimates
of interest and the corresponding standard error of those estimates, we conduct Monte Carlo
simulations consisting of 100,000 iterations. The meta-dataset contains intermediate variables
representing all relevant sample means, coefficient estimates, variances, and covariances from the
primary studies. Often only the variance for the single coefficient entering the study-specific
elasticity calculations is needed for these simulations, and it is fairly standard in the economics
literature to include the coefficient standard errors when reporting results. However, some study-
specific elasticity calculations include multiple coefficients, thus requiring both the variances and
covariances among that set of coefficients. Hedonic studies do not usually report the full variance-
covariance matrix. When needed we contacted the primary study authors to obtain the necessary
covariance estimates required to conduct the Monte Carlo simulations.5 In the case of four studies,
however, we assume the corresponding covariances are zero because the primary study authors
did not respond or could no longer provide the requested information.
Using the primary study coefficient estimates, variances, and covariances, the Monte Carlo
simulations entail 100,000 random draws from the joint normal distributions estimated by the
primary studies. The simulations are carried out separately for each observation in the meta-
dataset. After each draw the inferred elasticity is re-calculated, resulting in an empirical
distribution from which we obtain the inferred elasticity mean and standard deviation for each
observation in the meta-dataset.
2.4 Meta-data Descriptive Statistics
After considering these multiple dimensions, the set of 36 studies provide 665 unique observations
for the meta-dataset. Figure 2 displays the number of observations from each study, which ranges
from just two observations from a single study to over 224 observations. There is sufficient
information to infer 656 unique estimates of the price elasticity and/or semi-elasticity with respect
to a change in an objective water quality measure. The current meta-analysis examines primary
4	In a couple of studies (Poor et al., 2007; Tuttle and Heintzelman, 2015) the distance gradient was essentially
assumed to be flat. In those cases, the resulting elasticity observations for waterfront and non-waterfront homes in
the meta-dataset are identical.
5	We are extremely grateful and thank Okmyung Bin, Allen Klaiber, Tingting Liu, Patrick Walsh, and James Yoo
for providing the variance-covariance estimates needed to complete the Monte Carlo simulations. We also thank
Kevin Boyle for providing details on the functional form assumptions in Michael et al. (2000).
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study estimates of elasticity, which decreases the sample to 607. Nine additional observations are
lost due to insufficient information in the primary study to estimate the standard error of the
elasticity estimates, leaving a final dataset of 598 unique elasticity estimates for analysis.
[Insert Figure 2 about here.]
With 260 unique elasticity estimates, water clarity is by far the most common water quality
measure analyzed in the literature; followed by fecal coliform (56), chlorophyll a (36), nitrogen
(20), pH (19), and phosphorous (12). Several other water quality measures have been examined
by one or two studies in the hedonic literature, and also contribute unique elasticity estimates to
the meta-dataset (see Table B2 in Appendix B for a full list).
The elasticities with respect to different water quality measures are examined separately in the
meta-analysis methodology discussed in the next section. In particular, the meta-regression
analysis focuses on water clarity, where there is currently enough studies and observations to
conduct such an analysis. The 260 unique house price elasticity estimates with respect to water
clarity are estimated from 18 separate studies, and cover 63 different housing markets. About 56%
of these estimates correspond to water clarity in freshwater lakes or reservoirs, while the other
44% correspond to estuaries.
A few additional descriptive statistics of the elasticity observations with respect to water clarity
are provided in Table 1. About 68% of the observed elasticity estimates corresponding to water
clarity are for waterfront homes. The average of the mean clarity levels reported in the primary
studies is a Secchi disk depth of 2.343 meters. Of course, as one may expect this varies by
waterbody type. Estuaries have a mean Secchi disk depth of only 0.635 meters, whereas freshwater
lakes have a mean Secchi disk depth of 3.677 meters. The majority of estimates correspond to the
southern (48.5%) or northeastern (28.8%) quadrants of the US, with the remainder of this set of
elasticity estimates corresponding to the midwest (19.2%) or west (3.5%) US.6 As can be seen by
the "no spatial methods" variable, 38% of the of the elasticity estimates with respect to water
clarity were derived from models that did not utilize econometric methods to account for spatial
dependence (i.e., spatial fixed effects, spatial lag of neighboring house prices, and/or account for
spatial autocorrelation in some fashion). Although admittedly imperfect, this is the only observed
variable that reflects quality of the primary study models, and so it is intended to proxy for
potentially poorer quality studies.
[Insert Table 1 about here.]
Socio-demographics corresponding to the primary study areas and time period were also obtained
from the US Census Bureau by matching each observation to data for the corresponding
jurisdiction and year from the decennial census most closely corresponding to the primary study
time period. Median household income (2017$ USD) is on average $59,080 in the areas examined
by the primary studies. Interestingly, the percent of the population with a college degree is fairly
low (only 13.7%) on average), as is population density, suggesting only 50 households per square
6 Regions of the US are defined following the US Census Bureau's "Census Regions"
(https://www.census.gov/geo/reference/gtc/gtc census divreg.html. accessed 18 Mar. 2019).
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kilometer. These statistics may reflect the fact that homes near lakes and estuaries generally tend
to be in more rural areas.
3. METHODOLOGY
3.1 Mean Unit Values
We next calculate mean elasticity values for each water quality measure examined in the hedonic
literature. These unit values provide a useful summary measure, and can be utilized for benefit
transfer when value transfers are deemed appropriate or are the only transfer approach available.
In fact, although the literature still generally finds function transfer approaches that explicitly
account for various dimensions of heterogeneity preferable (Johnston and Rosenberger, 2010), it
has been found that simpler unit value transfers may perform better in some contexts (Klemick,
2018; Bateman et al., 2011; Johnston and Duke, 2010; Lindhjem andNavrud, 2008; Barton, 2002).
When calculating the mean values in a meta-analysis it is often appropriate to weight each
observation by its inverse variance in order to give more weight to more precise estimates (Nelson,
2013; Borenstein et al., 2010; Nelson and Kennedy, 2009). Two weighting schemes are generally
used. We refer to the first as the Fixed Effect Size (FES) model, in order to avoid confusion with
the frequently used fixed effects models in panel data analysis. Under the FES framework each
meta-observation is considered a draw from the same underlying population distribution (even if
from different studies), and the estimated weighted mean is interpreted as an average of that single
true distribution. In other words, sampling error is the only driver of differences in the observed
estimates across studies. The second weighting scheme is a variant of the above, and is sometimes
referred to as the Random Effects Size (RES) model. The RES model is preferred if the meta-
observations are believed to be estimates of different "true" elasticities from different distributions
(Harris et al. 2008, Borenstein et al. 2010, Nelson 2013). In the RES framework the weighted mean
is interpreted as an estimate of the average of the different average elasticities across the different
distributions.
An additional complication in the current meta-dataset is that primary studies often report multiple
estimates based on the same underlying property transaction data. If such dependence is not
accounted for, some meta-observations would be unduly weighted, counting as a single
observation when they should be discounted appropriately because there are multiple observed
estimates of the same "true" value. We propose the following cluster-adjusted FES and RES
weights to account such dependence in the meta-dataset.
One can think of the clustering (or panel nature) of the meta-data at different levels, such as by
study, or by groups of studies, that rely on the same primary data, researchers, etc., but our
preferred definition of a cluster is by "housing market." Meta-observations estimated from a
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common transaction dataset in terms of study area and time period are grouped together. The
intuition is that these are common estimates of the same underlying elasticity. Under this clustering
scheme, we are agnostic towards who conducted the primary study. Whether from the same study
or not, we are interested in the "true" elasticity in a given area and time period. For example,
consider a primary study that estimated four hedonic regressions and contributed four elasticity
estimates to the meta-dataset. If each elasticity pertained to a different study area (e.g., a different
county in the same state), then these estimates would not be grouped as a cluster. Each observation
in this case is an estimate of the elasticity in a different housing market, and pertaining to a different
waterbody (or set of waterbodies). In contrast, if these four different regressions were just different
functional forms and estimated from the same sample of transactions in the same county, then the
estimates would be grouped as a single cluster. The four meta-observations in that case would
basically just be four different estimates of the same underlying elasticity.
The starting point is the standard Fixed Effect Size (FES) and Random Effects Size (RES)
weighting schemes (Nelson and Kennedy, 2009; Borenstein et al., 2010; and Nelson, 2013), which
are slightly manipulated to account for the distance dimension that is incorporated into the meta-
dataset. For the FES model, the weight for elasticity estimate /, at distance J, in cluster j {sidj) is:
...FES _ _J_	m
Wid j	(1)
J vidj
where vidj is the variance of the estimate iidj from the primary study. We could also add subscripts
denoting estimates from model m of study 5, but these are omitted for notational ease, as are
subscripts denoting different water quality measures. The FES mean elasticity for a given water
quality parameter and distance bin d is thus,
wP
~FES _ yn wid] *	nn
— Z.t=lv« i^FEst-idi	V-)
U=iwidj
where n is the number of observed estimates in the meta-dataset for distance bin d and the water
quality measure of interest.
The RES weights can be calculated in a similar fashion:
...RES _ 1
idJ Vidj+T2
where T2 is the between study variance, and is calculated as:
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T2 =
Q-(n-l)
*a,FES
*-•1=1 id.j '
'^=1
{ 2?=
-Of)
(4)
The numerator of T2 entails the weighted sum of squares of the elasticity estimates around the
FES mean, denoted as Q, minus the available degrees of freedom (i.e., the number or meta-
observations minus one). Q is calculated as:
(r -yFES\2
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We next discount all weights corresponding to elasticity estimates for distance bin d, and within
cluster j, by multiplying it by the inverse of the number of primary estimates in that cluster. This
yields —	„ Wlkd{	, which we must then re-normalize such that the new combined weights sum
k*J
to one. More formally:
i	widj
kdj yKd y kdj
ZJ=1Zi=1™idj
yKd ykdJi _L
Zj/'=lZji=l| fcw;
v id j
dj 2 Kd J
j=i^i=i idjj
This can then be rearranged as:
*dj
vidj
TdT,
-*7=1^1=1
vidj
Kd ^kdj(widj
Kd ykdj
^j=l^i=l id]
y"a y "Ji LU-J
Zj/'=lZji=ll /Cw ;
dj
1
and then after cancelling out the common term ———	, we are left with the normalized
cluster-adjusted weight:
widj
<"&/ =	rh—7	(?)
ld]	y^d ykdj(^id£\	V '
Lj=1Li=1ykdJ j
where h simply denotes the FES or RES weight depending on which was used to calculate widj.
As a result, the cluster-adjusted FES or RES unit value mean elasticities for each distance bin d
are calculated as:
-h _

dj
= 1
vidj
Kd s-kdj(widj
y"a y U-JI <-"-J
Zj/'=lZji=l\ few
1dj
Hdj
(8)
We prefer the cluster-adjusted RES weights over the corresponding FES weights. There is no
reason to suspect that the true home price elasticities with respect to water quality are the same at
different waterbodies and housing markets across the US. These waterbodies differ in size,
baseline water quality levels, and the provision of recreational, aesthetic and ecosystem services,
among other things. The housing bundles, and preferences and income of buyers and sellers, likely
vary as well. We estimate the cluster-adjusted FES weights and other weighting schemes mainly
as a sensitivity analysis.
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3.2 Meta-regression Models
Function transfers based on meta-regressions can be a useful approach for benefit transfer (Nelson,
2013). Such an approach involves first estimating a meta-regression model, and then using the
estimated parameters to predict outcome values for a policy site. The approach takes advantage of
the full amount of information provided by the literature, while also accounting for key dimensions
of heterogeneity in the outcome effect of interest. The meta-regression model description below
is kept general, but in the current study we limit the meta-regressions to just water clarity (i.e.,
Secchi disk depth). In our opinion, this is the only water quality measure analyzed frequently
enough in the current literature to allow for a defensible meta-regression analysis.
The dependent variable iidj is elasticity estimate i for distance bin d in cluster (i.e., housing
market) j. The most comprehensive model is:
£idj =Po+ wfidjPi + estuaryj(32 + WQtjp3 + regionjP4 + ztjps + eidj (9)
where wfidj is a dummy variable denoting that the observed elasticity estimate corresponds to the
value of homes on the waterfront, as opposed to non-waterfront homes within 0 to 500 meters of
the waterbody. The dummy variable estuary j equals one if the elasticity estimate corresponds to
water quality in an estuary, as opposed to freshwater lakes (the omitted category).7 In theory,
different waterbody types in the same housing market could be examined, but in the current meta-
dataset this variable is invariant within each cluster, and so the i subscript is omitted. The variable
WQij is the mean baseline water quality level corresponding to the respective waterbody, or
portion of the waterbody, for observation i in cluster (or housing market) j. In the case of water
clarity, WQtj is measured as Secchi disk depth in meters. The next variable denotes the region of
the US from which the estimates in housing market j are located - the northeast, south, midwest,
and west.
The final variable z,y represents study attributes or model assumptions made by the primary study
authors. As described by Boyle and Wooldridge (2018), such variables are helpful because iidj is
merely an estimate of the true elasticity, and that estimate is dependent on modelling assumptions
made in the primary studies. These assumptions could be correlated with other variables in
equation (9), and so inclusion of ztj helps avoid a potential omitted variable bias. Additionally, if
particular values of z,y denote better modelling choices, then such information can be exploited
when predicting values for purposes of benefit-transfer (Boyle and Wooldridge, 2018). For this
meta-analysis z,y is a dummy variable equal to one if elasticity / for housing market j was estimated
7 Initially, a vector of dummy variables denoting different waterbody types was to be included in the meta-
regression. As described in section 2.4, the meta-dataset includes price elasticities corresponding to freshwater
lakes, estuaries, rivers, and small rivers and streams. However, the primary hedonic studies in the current literature
that examine water clarity focus solely on freshwater lakes or estuaries.
13
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from a primary study model that did not account for spatial dependence among housing
observations in the primary data. In other words, if a model did not include spatial fixed effects, a
spatial lag of housing prices, or account for spatial autocorrelation in some fashion, then Zjy = 1;
and Zjy = 0 otherwise. This is meant as a proxy for potentially poorer quality estimates, and so /?4
absorbs potential effects that could otherwise bias the other meta-regression coefficients.8 The
omitted category is thus potentially better-quality estimates from models that did account for
spatial dependence, and so the remaining meta-regression coefficients can be used directly for
benefit-transfer in practice. The parameters to be estimated are /?0,..., /?5, and eidj is an error term
that we discuss in more detail below.9
As was the case when calculating the mean elasticities, when estimating the meta-regressions the
cluster structure of the meta-dataset must be accounted for so that studies reporting multiple
elasticity estimates from the same housing market are not given an unwarranted amount of
influence. When estimating equation (9), the observations are weighted according to the same
cluster-adjusted RES weights described in section 3.1.
An additional complication that arises from the cluster structure of the meta-dataset is that there
may be cluster-specific effects associated with a particular housing market and the waterbodies
examined in that housing market. In equation (9), we assume that this cluster-specific effect Cy is
reflected in the error term, i.e., eidj = Cy + uidj, where uidj is an assumed independent and
normally distributed error term. This implies that the error terms (e;dy) when estimating equation
(9) are correlated for observations pertaining to the same housing market. To account for such
correlation, we estimate equation (9) as a Random Effects (RE) Panel model (see, for example,
Wooldridge, 2002). A RE Panel regression model is recommended when more than one estimate
is taken from a primary study (Nelson and Kennedy, 2009).
An issue with modelling the cluster (or housing market) specific effect in this fashion is that Cy
could be correlated with observed right-hand side variables, which would lead to inconsistent
estimates (Wooldridge, 2002). In the current context, it may very well be the case that the
necessary assumptions for consistent estimates from the RE panel model are violated. Unobserved
variables associated with a particular housing market and waterbody (or set of waterbodies) may
likely be correlated with observed right-hand side variables. In such cases, a fixed effect (FE) panel
model is often estimated. But the FE Panel model is not a viable approach in the current context.
First, the site specific fixed effect would absorb much of the variation of interest because most of
the modifiers in the meta-regression do not vary within a cluster. Even if there is some within-
cluster variation, it is often only seen among a small subset of the observations, and would thus
disregard a lot of observations and variation of interest. Second, out of sample inference for
8	The later meta-regression results are robust if a dummy denoting results from an unpublished study are used
instead.
9	Subsequent regression models are estimated that include characteristics of the population corresponding to housing
market j (i.e., median income, percent of population with a college degree, and population density), but the
coefficients on these variables are found to be statistically insignificant. See Table B1 in Appendix B for details.
14
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purposes of benefit transfer would not be valid because we cannot estimate the corresponding fixed
effects for housing markets and waterbodies that are not in the current meta-dataset.
When benefit transfer is the primary objective, Boyle and Wooldridge (2018) recently suggested
estimating a regression model first proposed by Mundlak (1978), as an alternative to a FE Panel
meta-regression. The Mundlak model estimates the cluster-specific effects by including the cluster
average of the relevant modifier variables in the right-hand side of the meta-regression:
£idj = Po + wftajPi + estuaryjf]2 + WQtJp3 + regionjP4 + z,7/?5
The variables wfj, WQj, and Zj are the cluster-specific means for the waterfront, baseline water
quality, and model attribute variables, respectively. The corresponding cluster-mean for estuaryj
and region j could also be included, in theory, but in the current meta-dataset these variables do
not vary within a cluster.
A portion of the cluster-specific effect that was previously assumed to be random in equation (9)
is now explicitly estimated in equation (10). More formally,
where e-dj = cj + uidj. The coefficients Yi, Ys and y5 capture the portion of the cluster-specific
effects that are correlated with the other right-hand side modifier variables. The remaining portion
of the cluster-specific effect cj is assumed to be uncorrected with the observed right-hand side
variables and can thus be modelled as random.
The Mundlak model in equation (10) does not require the assumption that Cj be uncorrected with
other right-hand side variables, as is the case with a conventional RE Panel model. The model also
has an advantage over a FE Panel model because it does not disregard variation with respect to
cluster-invariant variables, and allows for out-of-sample inference. In this particular context,
however, it is unclear what the gains from the Mundlak model are, or if it is even appropriate, due
to limited within-cluster variation. In this specific application the model hinges primarily on the
dummy variable denoting whether an observed elasticity estimate corresponds to waterfront
(versus non-waterfront) home values. There is within cluster-variation of wfidj among 19 (of the
63 housing markets), this corresponds to 160 observations from six different studies. There is
some within cluster-variation in WQtj, but this is limited to just six housing markets,
corresponding to 95 observations from three different studies. There is also little within-cluster
variation in the model attribute variable Z;y, with only two housing markets, examined by two
+wfjYi + WQjfs + ZjYs + e*idj
(10)
eidj = wfjYi + WQjYs + ZjYs + e*idj
(11)
15
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studies, showing variation in models that do and do not account for spatial dependence (17 and 18
observations, respectively).
A priori, the most appropriate meta-regression estimation approach and model remains unclear. In
the next section we present estimation results for all meta-regression model variants. Then we
conduct an out-of-sample prediction exercise to compare which modelling approach performs best
in terms of benefit transfer.
4. RESULTS
4.1. Mean Unit Value Estimates
We estimate mean elasticities for each water quality measure used in the hedonic literature. When
available, we present separate mean elasticities for waterfront homes and for non-waterfront homes
within 500 meters of a waterbody. The results in Table 2 display the mean values only for water
quality measures that were used in at least three studies (but the full set of mean elasticity estimates
can be found in Table B2 of Appendix B).
[Insert Table 2 about here.]
Our preferred estimates are the cluster-adjusted RES means, which give more weight to more
precise primary study estimates, and also ensure that equal influence is given to each housing
market examined in the literature. The cluster-adjusted RES means in Table 2 generally have the
expected sign, and the relative magnitude is often larger for waterfront versus non-waterfront
homes, as one would expect. For example, a one-percent increase in nitrogen concentrations leads
to a 0.220% decline in waterfront home values, and a 0.136% decline in the value of non-
waterfront homes that are within 500 meters of the waterbody. A one-percent increase in
phosphorous concentrations leads to a 0.107% decrease in waterfront home values, but has a
statistically insignificant impact on non-waterfront homes. A similar insignificant impact on non-
waterfront home values is found in the context of pH, but a one-percent decrease in pH levels (i.e.,
more acidic waters) does lead to a 0.119% decrease in waterfront home values.
As shown in the subsequent columns of Table 2, these results are generally robust across
alternative weighting schemes, including the FES cluster-adjusted counterpart, as well as more
standard approaches - the conventional RES mean (e.g., Borenstein et al., 2010), a cluster
weighted mean that does not account for statistical precision of the primary estimates, and a
completely unweighted average where all observations are given equal weight. The estimated
mean elasticities with respect to water clarity, at least for waterfront homes, do however appear
sensitive to weighting schemes that do not account for statistical precision of the primary estimates
and/or clustering of estimates from the same housing market. This may be at least partly driven
by the fact that just three studies (Walsh et al., 2017; Ara, 2007; and Michael et al., 2000)
contribute 65% of the observed elasticities with respect to water clarity. In any case, we believe
the cluster-adjusted RES means are the most valid for the reasons previously discussed. The other
mean elasticity calculations are presented mainly as a sensitivity analysis.
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There are some examples where the cluster-adjusted RES means yield somewhat counterintuitive
results. For example, although a one-percent increase in chlorophyll-a concentrations suggests a
0.026% decline in waterfront home values, the mean elasticity estimate for non-waterfront home
values suggests a small but statistically significant 0.009% increase in home values. This result is
sensitive to the weighting scheme. In the other mean elasticity calculations, we see no significant
impact of chlorophyll-a on non-waterfront home values, which at least does not run counter to
expectations. The home price effects of increased fecal coliform concentrations are also somewhat
odd. The price impact among non-waterfront homes is larger in magnitude than that for waterfront
homes. At first, we thought that this result might be driven by the fact that the set of studies used
to calculate these averages differ slightly. Leggett and Bockstael's (2000) hedonic analysis of fecal
coliform in the Chesapeake Bay examines only waterfront property prices. However, even if we
omit that study, the cluster-adjusted RES waterfront mean elasticity is -0.003, which is still less in
absolute value than the -0.052 price elasticity corresponding to non-waterfront homes within 500
meters. Although the relative magnitudes of the price elasticities are against expectations, it is
reassuring that both suggest the expected negative effect of increased fecal coliform counts on
nearby home values.
Due to the limited number of studies, and to our knowledge an inability to defensibly convert
elasticities across different water quality parameters to a common measure, it seems that value
transfers are generally the only viable option available if one is interested in using benefit transfer
to estimate the capitalization effects of water quality changes on home values. In the case of water
clarity, however, there are a sufficient number of observations to estimate limited meta-regressions
and pursue a function transfer approach.
4.2. Meta-regression Results
The meta-regression analysis focuses on just a subset of the meta-dataset, only examining the
n=260 observed elasticity estimates with respect to water clarity (i.e., Secchi disk depth
measurements). All meta-regressions utilize the same weights as the preferred cluster-adjusted
RES mean elasticity estimates. This is the preferred weighting scheme for the same reasons
discussed above - it gives more weight to more precise estimates and ensures that no single study
or analyzed housing market unduly influences the results. The clusters are defined according to
the 63 unique housing markets.10
We first estimate a series of RE Panel meta-regression models following equation (9). The results
are presented in Table 3. The first model (1A) includes only a dummy variable equal to one when
the elasticity estimate corresponds to waterfront home values, and zero otherwise. As expected,
and in line with the earlier unit value estimates, the price elasticity with respect to clearer waters
is significantly higher (0.0791) among waterfront homes. The constant term reflects the price
elasticity with respect to non-waterfront homes within 500 meters (the omitted category). And so,
10 Although the unique housing market-based cluster-adjusted RES weights are preferred, the results are generally
robust to simple OLS models where all observations are given equal weight, and to models where estimates from the
same study (instead of housing market) are defined as a cluster (see Tables B3 through B5 in Appendix B).
17
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a one-percent increase in water clarity corresponds to a 0.0257% increase in non-waterfront home
values and a statistically higher 0.1048% (=0.0791+0.0257) increase in the value of waterfront
homes.
[Insert Table 3 about here.]
Model 2A in Table 3 adds a dummy variable denoting elasticity estimates corresponding to clarity
improvements in an estuary; the omitted category is freshwater lakes. The coefficient is negative
and statistically significant, suggesting that water clarity changes in an estuary have a lesser impact
on home values. The results suggest that a one-percent increase in water clarity of a lake leads to
a 0.1211% (=0.0498+0.0713) and 0.0713% appreciation in the value of lakefront and non-
lakefront homes, respectively. In contrast, a one-percent increase in water clarity of an estuary
leads to a respective increase of 0.0665% (=0.0498+0.0713-0.0546) and 0.0167% (=0.0713-
0.0546) in the value of waterfront and non-waterfront homes. One potential explanation for this
difference is that surrounding residents do not generally expect the water to be as clear in estuaries.
Estuaries have brackish waters that are often naturally more opaque. The unweighted mean Secchi
disk depths reported by the primary studies in the meta-dataset is 3.68 meters for lakes, but only
0.64 meters for estuaries.
To examine whether baseline water clarity matters, the RE Panel Model 3A includes the mean
water clarity level (i.e., Secchi disk depth in meters). The results suggest that water clarity
improvements in waterbodies that already have relatively clear waters lead to larger increases in
home values. For example, a one-percent increase in clarity leads to a 0.0921% increase in the
value of waterfront homes around a waterbody that has a Secchi disk depth equal to the unweighted
mean of 2.343 meters. But a one-percent increase in the clarity of a waterbody that has a baseline
Secchi disk depth of 4.311 meters (a one standard deviation increase) suggests a statistically higher
0.1224%) increase in waterfront home values. This result could be evidence of a premium to
maintain or further improve relatively clear waters, which would run counter to the idea of
diminishing marginal utility with respect to water clarity. A more likely explanation is that it may
reflect differences in perceptions and expectations across different waterbodies or types of
waterbodies (i.e., freshwater lakes versus estuaries), as discussed above. Model 4A shows that
when conditional on the waterbody type, the mean clarity coefficient becomes much smaller and
statistically insignificant.
Model 5 A in Table 3 includes dummy variables denoting different regions of the US. The results
suggest that hedonic studies examining waters in the midwest and western US seem to yield
statistically similar results as studies examining waters in the northeast (the omitted category).
This lends some confidence to potentially performing benefit transfers across regions. We do,
however, see that studies examining water clarity in the southern US yield systematically lower
elasticity estimates on average. Model 6A includes all covariates, and although some of the results
are robust, the inclusion of all covariates leads to losses in statistical significance for some
variables. We posit that such a comprehensive model is too taxing on the currently available n=260
observations in the metadata, especially given the correlation across many of the modifier
variables. We see, conditional on region of the US, the mean clarity coefficient actually becomes
negative; which although it is statistically insignificant, this is at least in line with the notion of
18
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diminishing marginal utility. The same holds true in the later Mundlak models, which controls for
such housing market and waterbody specific effects.
We next re-estimate all six of the RE Panel models, but now also add the model attribute variable
no spatial methods, which denotes elasticity estimates that were derived from primary study
models that did not account for spatial dependence of the original housing transaction data. The
omitted category is thus elasticity estimates from models that did account for such spatial
dependence, and that could thus be interpreted as potentially more accurate estimates. The results
from models IB through 4B in Table 4 are similar to the earlier meta-regressions. The statistically
insignificant coefficients corresponding to no spatial methods suggest that modelling assumptions
by the primary study authors did not systematically affect the elasticity estimates.
This finding is not robust however, in models 5B and 6B, where we condition on regions of the
US. The significant -0.1308 and -0.1412 coefficient estimates corresponding to no spatial methods
suggest that studies not utilizing modelling techniques to account for spatial dependence tend to
yield significantly lower elasticity estimates; implying that modelling choices made by the primary
study authors may be important to control for in a benefit-transfer exercise. The results also
suggests that modelling choices are correlated with where a primary study focused. The midwest
coefficient is now statistically significant, at least in model 5B, implying that that after
conditioning on model attributes, the housing price effects in the midwest are systematically lower
compared to price effects in the northeast. Differences between price effects in the south and the
northeast are also now much larger in magnitude, as seen by the large negative coefficient
corresponding to south in models 5B and 6B. In contrast to some of the earlier meta-regression
results, this suggests that heterogeneity across regions may be important to account for when
conducting benefit transfers.
[Insert Table 4 about here.]
As an alternative to the RE Panel meta-regression models we next implement the Mundlak (1978)
regression model that was recently suggested by Boyle and Wooldridge (2018) for estimating
meta-regressions. The results are presented in Table 5. First looking at model 1 A, the positive and
significant coefficient on the waterfront dummy reveals a similar finding to earlier models - that
an improvement in clarity leads to a statistically significant increase in waterfront home values,
and that effect is statistically larger than the price impact on non-waterfront homes. More
specifically, the model suggests that a one percent increase in water clarity leads to a 0.1135%
(=0.0640+0.0471+0.0024) increase in waterfront home values, which is very similar to the results
of earlier models. In contrast, however, the Mundlak variant of model 1A suggests a one-percent
increase in clarity leads to a 0.0495% (=0.0471+0.0024) increase in the value of non-waterfront
homes within 500 meters. Based on the overlapping confidence intervals, this effect is likely not
statistically different from that of earlier models, but the point estimate is twice as large.
[Insert Table 5 about here.]
The Mundlak variants of models 2A through 6A in Table 5 reveal somewhat similar results to the
earlier models. As shown in model 2A, the price elasticities with respect to water clarity are still
lesser in the context of estuaries (compared to lakes), although this difference is no longer
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statistically significant. And model 3 A again suggests higher price elasticities with respect to water
clarity when baseline water clarity levels are higher. A baseline clarity level of one additional
meter suggests an additional 0.0325% (=0.0597-0.0273) increase in home values for a one-percent
improvement in clarity, an effect that is statistically significant at conventional levels (p=0.020).u
As before, elasticity estimates corresponding to housing markets and waterbodies in the
southeastern US are systematically lower than those for the northeast (the omitted category). One
difference compared to the RE Panel models is that the Mundlak variants of models 5A and 6A
suggest that the elasticity estimates corresponding to the midwest are also systematically lower.
Finally, in Table 6 we present the same six Mundlak meta-regression models, but now again
include the model attributes variable, no spatial methods. The results are fairly similar to the
previous meta-regressions. The small and insignificant coefficients on no spatial methods suggests
that such modelling choices do not systematically affect the within-cluster variation in the inferred
elasticities. Interpretation of this variable warrants caution in the Mundlak models, however,
because as discussed in section 3.2 there is limited within-cluster variation. Only two studies,
examining water clarity in two different housing markets, estimated hedonic regressions with
different model assumptions regarding spatial dependence (Ara, 2007; Horsch and Lewis, 2009).
Both of these studies examined waters in the Midwest. The corresponding no spatial methods
cluster mean, however, is in agreement with earlier results. Some models, and in particular models
controlling for study region (5A and 6A), suggest that primary studies not accounting for spatial
dependence tend to yield lower elasticity estimates.
[Insert Table 6 about here.]
4.3. Best Performing Model for Benefit Transfer
In this section we attempt to shed light on whether a value or function transfer approach is more
accurate for benefit transfer, at least in this particular context of water clarity and housing values.
Focusing on water clarity, the cluster-adjusted RES means and all meta-regression models are
evaluated by taking the absolute value of the percent difference between the initial elasticities from
the primary studies (iidj) and the predicted elasticities from the corresponding unit value means
or meta-regressions (£jdy)- Note that we distinguish between waterfront and non-waterfront homes
when estimating the mean elasticities and conducting the value transfer. More formally, the
absolute value of the percent transfer error is calculated as:
\%TE\ =
f^idj ®idj\
V hdj J
, x 100
idj
(12)
To examine out-of-sample transfer error, we iteratively leave out observations corresponding to
one of each of the 63 housing markets and then re-estimate the mean values and meta-regressions
using the remaining a sub-sample. The predicted values (ffdy) and \%TE\ are then estimated for
11 The overall marginal effect with respect to mean water clarity levels is calculated by summing the coefficients
corresponding to the baseline water clarity level and the associated cluster mean water clarity level, yielding 0.0325.
The standard error of 0.0139 is estimated via the delta method.
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the excluded observations. This is repeated by excluding each of the housing market clusters one
at a time. After completing all 63 iterations we then calculate the mean \%TE\ to evaluate out-of-
sample transfer performance. We prefer an out-of-sample transfer error exercise like this over a
simpler in-sample comparison that would directly use the full sample results presented in Tables
2-6 because an out-of-sample transfer error comparison is more indicative of how a value or
function transfer would perform in policy settings.
The results in Table 7 suggest that the unit value transfer often performs on par with the more
complicated function transfers. The value transfer even performs better than some of the most
comprehensive models (e.g., 6A and 6B) and many of the more complicated Mundlak models.
In general, the RE Panel estimation procedures seem superior to the Mundlak approach, at least
within the context of property value capitalization effects with respect to water clarity. Only in the
case of model 1A does the Mundlak model perform slightly better. The superior transfer
performance of the RE Panel model should minimize concerns regarding the validity of the
assumption that the cluster-specific effects be uncorrected with observed right-hand side
variables.
[Insert Table 7 about here.]
Of most relevance is the answer to the question - which transfer approach performs best? In all
cases model specification 3, which includes mean water clarity as a right-hand side moderator
yields the lowest transfer error. Accounting for baseline water clarity levels improves transfer
accuracy. And in particular, the RE Panel variant of model 3 A performs the best, yielding a mean
transfer error of 256% (median of 81%). Overall, in the context of water clarity the results suggest
that practitioners perform a function transfer approach based on the RE Panel variant of model
3A.12
Although this model yields the lowest transfer error, it is concerning that the magnitude of the
transfer error is large. This is unfortunately not unheard of given the current state of benefit-
transfer methods, at least in the context of environmental applications. In a recent study evaluating
modeling decisions that affect benefit transfer errors, Kaul et al. (2013) examined 1,071 transfer
errors reported by 31 studies and report that the absolute value of the transfer errors ranged from
0% to 7,496%), with a mean of 172% (median of 39%>). This is similar to the finding by
Rosenberger (2015), who reports median absolute transfer errors between 36%> - 45%>. Notably,
across all of the observations included in both of these studies, there are only three hedonic
property values studies (which appear in Rosenberger (2015)), and none of these hedonic studies
examined surface water quality.
12 One can use the point estimates in Table 3 for purposes of benefit-transfer. The full variance-covariance matrix is
presented in Appendix C. This is needed to derive the corresponding confidence intervals via the delta method
(Greene, 2003, page 70) or Monte Carlo simulations.
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5. DISCUSSION
The primary objective of this study is to help practitioners exploit the fairly large literature of
hedonic property value studies examining surface water quality, and ultimately to facilitate ex ante
and ex post assessments to better inform local, regional, and national policies impacting water
quality. Based on the constructed meta-dataset, limited value transfers can be conducted to assess
policies impacting chlorophyll-a, fecal coliform, nitrogen, phosphorous, water clarity, and pH in
waterbodies. Our findings, at least in the context of water clarity, suggest that simpler value
transfers perform on par with (and sometimes better than) more complicated function transfers.
This is in line with other recent findings in the literature (Klemick, 2018; Bateman et al., 2011;
Johnston and Duke, 2010; Lindhjem and Navrud, 2008; Barton, 2002), and is a promising result
for practitioners. Given the limited number of studies on any one water quality measure, value
transfers are really the only viable option for examining the property capitalization effects from
changes in water quality (with the exception of water clarity, which we discuss further below).
To conduct a unit value transfer, one would need to select the water quality measure that is most
appropriate for the policy site, and/or based on the available water quality data and projection
models. Policies generally result in changes in many water quality measures, but the hedonic
literature often focuses on a single measure within a hedonic regression.13 We recommend
practitioners do the same when transferring results from this literature, and so when conducting
benefit transfers one should not add up the price impacts across changes in multiple water quality
measures. Our mean elasticity estimates can be combined with spatially explicit data of the
relevant surface waterbodies, housing locations and number of homes, and baseline housing
values, in order to project how a water quality policy impacts residential property values. Ideally,
such a benefit transfer exercise can be carried out using detailed, high-resolution data on
waterbodies and individual residential properties from local or state governments. In the absence
of such data, one can combine our estimated elasticities with waterbody location data provided by
the National Hydrography Dataset (MID), along with aggregated data on housing and land cover,
from the US Census Bureau and National Land Cover Dataset (NLCD).14
In the context of water clarity, our results suggest that a function transfer accounting for baseline
water clarity levels can improve transfer performance. In addition to the data needs discussed
above, one would also need to have information on baseline water clarity levels. Such information
is likely needed anyway to quantify the change in water clarity resulting from a policy.
In future work we hope to expand this meta-dataset in two ways to increase its utility in informing
policy. First, for tractability we decided early in the development of the meta-dataset to limit the
13	Of the 598 observations analyzed in this meta-analysis, 444 (74%) are derived from hedonic regressions that
included a single water quality measure. The remaining 156 elasticity observations were estimated from hedonic
regressions that included two or more water quality measures directly on the right-hand of the same hedonic
regression (Ara, 2007; Bin and Czajkowski, 2013; Brashares, 1985; Liao et al., 2016; Liu et al., 2014; Netusil et al.,
2014; and Walsh and Milon, 2016).
14	Website links to these data sources are as follows: National Hydrography Dataset (NHD),
https://www.nsgs.gov/core-science-svsfems/ngp/natiotial-hvdrographv/: US Census Bureau,
https://www.census.gov/: National Land Cover Dataset (NLCD), https://www.nirle.gov/ (accessed 20 Feb. 2019).
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distance bins to waterfront homes and non-waterfront homes within 500-meters of a waterbody.
The hedonic literature has increasingly expanded this focus, however, finding significant impacts
on home prices up to a few kilometers away (e.g., Walsh et al. 201 la, Netusil et al. 2014, Klemick
et al. 2018, Kung et al. 2019). Adding meta-observations that pertain to farther distance bins, even
within the context of the currently included studies, will provide a more comprehensive meta-
analysis in the future (although one must also consider the sample selection concerns discussed in
section 2).
Second, new studies should be periodically added to the meta-dataset as they emerge in the hedonic
literature. When conducting new hedonic studies, we encourage researchers to consider some of
the gaps in the current literature. Our review reveals limitations in the types of waterbodies studied
and the geographic areas covered. More hedonic studies examining surface water quality in the
mountain states in the west, parts of the Midwest, and the south-central portions of the US are
needed; as are hedonic studies examining how property values respond to water quality changes
in estuaries, rivers, and streams. Such primary studies are needed to provide truly nationwide
coverage and ultimately more robust benefit-transfer procedures for assessing policies.
Another disconnect pertains to the types of water quality metrics used by economists versus those
used by water quality modelers and policy-makers. Water clarity is the most common metric used
in the hedonic literature. It is a convenient measure for non-market valuation because households
are able to perceive and understand it. In certain cases, it also can act as a reasonable proxy for
other measures of water quality (e.g., nutrients or sediments), which may be more difficult for
households to observe. With that said, water clarity is not always a good measure of quality across
all contexts (Keeler et al. 2012). For example, waters with low pH levels due to acid rain or mine
drainage may be very clear, but of poor quality. This disconnect between water clarity and quality
is an issue in the non-market valuation literature more broadly (Abt Associates, 2016).
Although the majority of hedonic studies focus on water clarity, water quality models, such as the
Soil and Water Assessment Tool (SWAT), Hydrologic and Water Quality System (HAWQS), and
SPAtially Referenced Regressions On Watershed Attributes (SPARROW), tend to focus on
changes in nutrients, sediments, metals, dissolved oxygen, and organic chemicals (Tetra Tech,
2018). There are some process-based water quality and aquatic ecosystem models that can
calculate Secchi disk depth, but they require waterbody-specific characteristics as an input (Park
and Clough, 2018). There are other studies that estimate relationships or correlations between
water quality parameters and water clarity, but such relationships are also often very location
specific (e.g., Wang et al. 2013; Hoyer et al. 2002). Due to the location or waterbody specific
nature of the existing approaches to project changes in water clarity, such methods generally
cannot be broadly applied without more information.
Further research is necessary to improve the link between water quality and economic models.
Closing this gap can entail one of two things, or some combination of both. First, when choosing
the appropriate water quality metric, economists conducting future hedonic studies should keep
the application of their results for policy analysis in mind. Doing so will allow their results to be
used to monetize the quantified policy changes projected by water quality models. It will also help
facilitate more robust transfer approaches by adding observations to our meta-dataset that focus
23
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on other water quality measures besides clarity. Second, water quality modelers could develop
models that directly project changes in water clarity, or perhaps develop more robust conversion
factors. Such a call is not a new idea. Desvousges et al. (1992, p. 682) recommended that, at the
very least, statistical analyses establish "... the correlation between policy variables and variables
frequently used as indicators of water quality." Developing such conversion factors would be
challenging, and would likely need to be watershed, and perhaps even waterbody, specific.
If relationships between policy-relevant water quality measures and clarity can be made more
often, then such translations could be directly incorporated into the meta-dataset in a similar
fashion to some of the conversions already made when "standardizing" the primary study estimates
(for example, see Walsh et al. (2017) and Guignet et al. (2017) in Appendix A). Instead of
conducting a separate meta-analysis for each water quality measure, as we do in this study, more
primary studies could be combined into a single more robust meta-analysis that focuses on
whatever water quality measure is most relevant for the policy at hand.
6. CONCLUSION
Despite the large literature of the capitalization of local surface water quality in home values, this
literature has not generally been used to inform decision-making in public policy. For example,
hedonic property value studies have yet to be used in regulatory analyses of regional and
nationwide water quality regulations enacted by the US Environmental Protection Agency.
Heterogeneity in local housing markets, the types of waterbodies examined, the model
specifications estimated, and the water quality metrics used, are key reasons why the results of
these local studies have not been applied to broader policies. This meta-analysis overcame these
obstacles through the meticulous development of a detailed and comprehensive meta-dataset. The
existence of this meta-dataset and our subsequent meta-analysis provides a means for practitioners
to conduct benefit transfer, and assess how improvements in water quality from local, regional,
and even national policies are capitalized into housing values.
24
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FIGURES AND TABLES
Figure 1. Number of Water Quality Hedonic Studies in each State.
# of Studies
1
2
3
4
5
25
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Figure 2. Number of Meta-dataset Observations by Study.
250
224
200
150
100
50
60
60
I	24	20	26 27 |	24
18	15
il^l
26
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Table 1. Descriptive Statistics of Elasticity Observations with respect to Water Clarity.	
Variable	Mean	Std. Dev.	Min	Max
waterfront
0.681
0.467
0
1
estuary
0.438
0.497
0
1
mean clarity (Secchi disk depth in meters)
2.343
1.968
0.380
6.450
northeast
0.288
0.454
0
1
midwest
0.192
0.395
0
1
south
0.485
0.501
0
1
west
0.035
0.183
0
1
no spatial methods
0.381
0.183
0
1
median income (2017$ USD)
59,080
14,142
37,865
91,174
college degree (% population)
0.137
0.041
0.077
0.273
population density (households /sq. km.)
49.908
58.378
1.410
227.963
Unweighted descriptive statistics presented for n=260 unique elasticity estimates in meta-dataset pertaining to water clarity.
Estimates based on 18 primary hedonic studies, corresponding to 63 unique housing markets (as defined by the primary studies).
All variables are dummy variables unless indicated otherwise.
27
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Table 2. Unit value mean elasticity estimates.
Water quality measure
Cluster Adjusted
RES Mean
Cluster Adjusted
FES Mean
Standard
RES Mean
Cluster
Weighted Mean
Unweighted
Mean
n Studies
Chlorophyll a (mg/L)
waterfront
non-waterfront w/in 500 m
Fecal coliform (count per 100 mL)
waterfront
non-waterfront w/in 500 m
Nitrogen (mg/L)
waterfront
non-waterfront w/in 500 m
Phosphorous (mg/L)
waterfront
non-waterfront w/in 500 m
Water clarity (Secchi disk depth, meters)
waterfront
non-waterfront w/in 500 m
pH (pH scale, 0 [acidic] to 14 [basic])
waterfront
non-waterfront w/in 500 m
-0.026***
(-0.031, -0.021)
0.009***
(0.006, 0.012)
-1 3E-4***
(-1.8E-4, -0.7E-4)
-0.052***
(-0.096, -0.008)
-0.220***
(-0.244, -0.196)
-0.136***
(-0.156, -0.116)
-0.107***
(-0.122, -0.092)
-0.005
(-0.012,0.003)
0.105***
(0.095,0.114)
0.026***
(0.017, 0.034)
0.779**
(0.019, 1.540)
-0.188
(-1.086,0.711)
-0.027***
(-0.032, -0.021)
-0.001
(-0.003, 0.001)
-2.2E-5***
(-2.8E-5, -1.6E-5)
-0.036***
(-0.046, -0.027)
-0.131***
(-0.149, -0.113)
-0.030***
(-0.036, -0.023)
-0.093***
(-0.106, -0.081)
0.003
(-0.002, 0.008)
0.031***
(0.028, 0.034)
0.012***
(0.010,0.015)
0 4^9***
(0.183,0.654)
-0.188
(-1.086,0.711)
-0.022***
(-0.031, -0.013)
0.001
(-0.006, 0.009)
-0.2E-4
(-0.6E-4, 0.1E-4)
-0.024***
(-0.036, -0.011)
-0.245***
(-0.321, -0.170)
-0.130***
(-0.184, -0.077)
-0 114***
(-0.154, -0.074)
-0.002
(-0.015,0.010)
0.090***
(0.078,0.102)
0.018***
(0.008, 0.028)
0.424
(-0.285, 1.133)
-0.379
(-1.084,0.326)
0.324*
(-0.036, 0.685)
0.010
(-0.085,0.105)
-0.037
(-0.088, 0.014)
-0.059*
(-0.090, -0.005)
-0.242***
(-0.271, -0.215)
-0.184***
(-0.210, -0.157)
-0.107***
(-0.123, -0.092)
-0.019***
(-0.032, -0.005)
0.182
(-17.398, 17.762)
0.042***
(0.025, 0.059)
1.986***
(-.840, 3.133)
0.008
(-1.405, 1.422)
0.737*
(-0.044, 1.517)
0.005
(-0.201,0.211)
-0.018***
(-0.026, -0.011)
-0.020***
(-0.034, -0.006)
-0.292***
(-0.326, -0.257)
-0.221***
(-0.254, -0.187)
-0.115***
(-0.130, -0.100)
-0.016**
(-0.029, -0.003)
0.155
(-6.102,6.413)
0.028***
(0.020, 0.036)
2173***
(1.015, 3.331)
-0.334
(-1.126,0.457)
18
18
36
20
10
10
6
6
177
83
13
6
3
3
4
3
5
5
3
3
18
6
3
1
***p<0.01, ** p<0.05, *p<0.1. Confidence intervals at the 95% level are displayed in parentheses. Observations weighted by cluster-adjusted RES weights, where each cluster defined
at the housing market level as defined in the primary studies. Only elasticity estimates pertaining to water quality measures used in at least 3 studies are presented here, but the full suite
of mean elasticity estimates are presented in Appendix B, Table B2. We present the respective units for each water quality measure in parentheses, but emphasize that the elasticity
estimates presented in the table are unit-less.
28
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Table 3. Random Effects Panel (RE Panel) Meta-regression Results.
VARIABLES (1A)	(2A)	(3A)	(4A)	(5A)	(6A)
waterfront
0.0791***
0.0498**
0.0457**
0.0443**
0.0347
0.0381*

(0.018)
(0.024)
(0.020)
(0.021)
(0.022)
(0.021)
estuary

-0.0546*

-0.0395

-0.0015


(0.030)

(0.053)

(0.024)
mean clarity


0.0146**
0.0059

-0.0103



(0.007)
(0.013)

(0.019)
midwest




-0.0318
-0.0513





(0.039)
(0.053)
south




-0.0865***
-0.1239*





(0.032)
(0.067)
west




-0.0622
-0.0609





(0.097)
(0.108)
constant
0.0257*
0.0713**
0.0138
0.0538
0.1065***
0.1517

(0.016)
(0.031)
(0.017)
(0.060)
(0.033)
(0.096)
Dependent variable: home price elasticity with respect to water clarity (Secchi disk depth).
***p<0.01, ** p<0.05, *p<0.1. Standard errors in parentheses. Random Effects Panel (RE Panel) regressions
estimated using the "mixed" routine in Stata 14, where the n=260 observations are weighted by the cluster-
adjusted Random Effect Size (RES) weights and the cluster specific effects are defined according to the K=63
unique housing market clusters.
29
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Table 4. RE Panel Meta-regression Results with Model Attributes.
VARIABLES	(IB)	(2B)	(3B)	(4B)	(5B)	(6B)
waterfront
0.0654***
0.0612***
0.0552***
0.0553***
0.0524***
0.0514***

(0.017)
(0.018)
(0.019)
(0.018)
(0.018)
(0.018)
estuary

-0.0788

-0.0535

0.0168


(0.053)

(0.059)

(0.022)
mean clarity


0.0299**
0.0213

0.0077



(0.013)
(0.013)

(0.016)
midwest




-0.0695**
-0.0579





(0.029)
(0.043)
south




-0.2003***
-0.1958***





(0.058)
(0.060)
west




-0.0582
-0.0588





(0.097)
(0.089)
no spatial methods
0.0227
-0.0405
-0.0739
-0.0890
-0.1308**
-0.1412**

(0.025)
(0.051)
(0.050)
(0.057)
(0.054)
(0.066)
constant
0.0252
0.0925*
0.0031
0.0552
0.2156***
0.1904***

(0.016)
(0.053)
(0.018)
(0.062)
(0.057)
(0.073)
Dependent variable: home price elasticity with respect to water clarity (Secchi disk depth).
*** p<0.01, ** p<0.05, * p<0.1. Standard errors in parentheses. Random Effects Panel (RE Panel) regressions estimated using
the "mixed" routine in Stata 14, where the n=260 observations are weighted by the cluster-adjusted Random Effect Size (RES)
weights and the cluster specific effects are defined according to the K=63 unique housing market clusters.
30
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Table 5. Mundlak Model Meta-regression Results.
VARIABLES	(1A)	(2A)	(3A)	(4A)	(5A)	(6A)
waterfront
0.0640***
0.0602***
0.0607***
0.0595***
0.0581***
0.0579***

(0.018)
(0.019)
(0.019)
(0.019)
(0.019)
(0.019)
waterfront cluster mean
0.0471
-0.0571
-0.1744
-0.1791
-0.2279*
-0.2566

(0.052)
(0.093)
(0.112)
(0.122)
(0.134)
(0.158)
estuary

-0.0693

-0.0399

0.0183


(0.046)

(0.058)

(0.025)
mean clarity


-0.0273
-0.0305

-0.0378



(0.067)
(0.068)

(0.070)
clarity cluster mean


0.0597
0.0548

0.0469



(0.066)
(0.068)

(0.070)
midwest




-0.0806***
-0.0693*





(0.030)
(0.042)
south




-0.1832***
-0.1781**





(0.070)
(0.075)
west




-0.0622
-0.0633





(0.097)
(0.087)
constant
0.0024
0.1118
0.0856*
0.1282
0.3109**
0.2969**

(0.034)
(0.088)
(0.052)
(0.094)
(0.132)
(0.136)
Dependent variable: home price elasticity with respect to water clarity (Secchi disk depth).
***p<0.01, ** p<0.05, *p<0.1. Standard errors in parentheses. Regressions estimated using n=260 observations.
Observations are weighted by the cluster-adjusted Random Effect Size (RES) weights, where each cluster is defined as one of
the K=63 unique housing markets. Mundlak (1978) regressions estimated by first calculating cluster (primary study) means
for independent variables that vary within each cluster, and then by running the subsequent model via the "mixed" routine in
Stata 14, where the residual cluster-specific effect is maintained.
31
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Table 6. Mundlak Model Meta-regression Results with Model Attributes.
VARIABLES	QB)	(2B)	(3B)	(4B)	(5B)	(6B)
waterfront
0.0637***
0.0613***
0.0621***
0.0609***
0.0598***
0.0596***

(0.018)
(0.019)
(0.019)
(0.019)
(0.019)
(0.019)
waterfront cluster mean
0.0248
0.0531
-0.0828
-0.0385
-0.0146
-0.0526

(0.041)
(0.070)
(0.072)
(0.095)
(0.141)
(0.146)
estuary

-0.0860

-0.0569

0.0281


(0.059)

(0.065)

(0.022)
mean clarity


-0.0243
-0.0280

-0.0363



(0.060)
(0.061)

(0.060)
clarity cluster mean


0.0631
0.0575

0.0550



(0.064)
(0.064)

(0.065)
midwest




-0.0849***
-0.0622





(0.029)
(0.039)
south




-0.2441***
-0.2311***





(0.053)
(0.054)
west




-0.0569
-0.0589





(0.097)
(0.078)
no spatial methods
0.0129
0.0135
0.0124
0.0129
0.0137
0.0135

(0.016)
(0.016)
(0.015)
(0.015)
(0.016)
(0.015)
no spatial methods cluster mean
-0.0005
-0.0890
-0.0879*
-0.1252
-0.1877**
-0.2050**

(0.033)
(0.073)
(0.049)
(0.081)
(0.085)
(0.098)
constant
0.0131
0.0731
0.0370
0.0711
0.2648***
0.2316**

(0.022)
(0.055)
(0.031)
(0.059)
(0.081)
(0.092)
Dependent variable: home price elasticity with respect to water clarity (Secchi disk depth).
***p<0.01, ** p<0.05, *p<0.1. Standard errors in parentheses. Regressions estimated using n=260 observations. Observations are
weighted by the cluster-adjusted Random Effect Size (RES) weights, where each cluster is defined as one of the K=63 unique housing
markets. Mundlak (1978) regressions estimated by first calculating cluster (primary study) means for independent variables that vary
within each cluster, and then by running the subsequent model via the "mixed" routine in Stata 14, where the residual cluster-specific
effect is maintained.
32
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Table 7. Out-of-Sample Transfer Error: Average of the Absolute Value of Percentage Difference
in Predicted Elasticities.
Cluster-
adjusted
RES Mean
Meta-regression Model
286%
Original Models
RE Panel
Mundlak
286%	265% 256% 262% 267%	294%
276%	293% 281% 301% 355%	391%
(1A)	(2A)	(3A)	(4A)	(5A)	(6A)
Models w/
Methodological
Variable
(IB)	(2B)	(3B)	(4B)	(5B)	(6B)
RE Panel
Mundlak
280%	278% 261% 265% 278%	306%
280%	299% 272% 296% 354%	386%
Bold text denotes the model that yields the lowest transfer error, in absolute terms. Absolute value of the percentage transfer error
is calculated as the absolute value of the percentage difference between the predicted elasticity from the corresponding meta-
regression model or mean value and the original elasticity estimate from the primary studies. Observations in all unit value mean
and meta-regression estimates weighted following the cluster-adjusted RES scheme. The out-of-sample absolute transfer error is
calculated by iteratively leaving out each of the K=63 unique housing market clusters, estimating the model with the remaining
clusters, and then calculating the predicted elasticities and resulting transfer error for the excluded cluster.
33
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APPENDICES
Appendix A: Study specific description and meta-dataset details.
This appendix provides a brief summary of each study in the meta-dataset, and provides
examples to illustrate the study-by-study derivations of the common elasticity and semi-elasticity
estimates in the meta-dataset. The below textbox introduces the standardized notation used.
p = sales price (or alternative measure of house value)
WQ= water quality variable of interest. If multiple water quality parameters are included, then
they are denoted using subscripts. Letter subscripts denote differences in units (e.g., meters
(m) versus feet (ft)).
area = surface area of waterbody
X= vector for all other variables not of primary interest
distwF= waterfront dummy variable
dist= continuous variable measuring distance to waterbody
diste-f= distance dummy variable ranging from e to f (e.g., distance buffer between zero and
200 meters would be disto-200)
y= coefficients on X
/?= coefficient on WQ
D= coefficient on WQdummy variable	
Ara (2007)
This study examined water clarity and fecal coliform in Lake Erie. The study used several
clustering algorithms to define submarkets along Lake Erie. This clustering led to eight
submarkets for which hedonic price equations are estimated for secchi depth and fecal coliform.
Equations are estimated for both waterfront and non-waterfront homes. The authors estimated
each model using both OLS and spatial error models. The study contributed 60 observations to
the meta-dataset.
The derivation of our standardized elasticity and semi-elasticity estimates is as follows. All
models have a double-log specification:
In (p) = yX + filn (WQ)	(1)
Taking the partial derivative of equation (1) with respect to WQ yields:
dp _ p v
dWQ r WQ
The formulas for the semi-elasticity equation (2) and elasticity equation (3) follow
dp 1 _ p
dWQp ~ WQ
(2)
41
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-^- = /2	(3)
dWQ p r	v '
The relevant sample means for WQ are then plugged in as needed to calculate the estimated
semi-elasticities.
Bejranonda et al. (1999)
This study examined sediment inflow rates for state park lakes and reservoirs within 4,000 feet
(1219.2 meters) of homes in Ohio. The counties are not identifiable based on the information
provided in the primary study. The hedonic models examined the effect of sedimentation rates
on property values for homes near lakes/reservoirs with regulations limiting boating horse-power
to 10 (Limited HP) versus unlimited horse-power lakes (Unlimited HP). The dependent variable
is the annual rental value which is obtained from a transformation on the total assessed housing
value. The authors excluded homes near lakes that had a water surface area less than 100 acres
(one acre equals 4046.86 square meters). The study estimated two models (one for the Limited
HP lakes and one for the Unlimited HP lakes) each yielding a waterfront and non-waterfront
estimate. Therefore, four observations are included in the meta-dataset.
The derivation of our standardized elasticity and semi-elasticity estimates is as follows.
Consider a simplified representation of model (1) as an example.
In (p) = yX + filn (WQ)	(1)
Taking the partial derivative of equation (1) with respect to WQ yields:
dp _ n v
dWQ ~ " WQ
The formulas for the semi-elasticity equation (2) and elasticity equation (3) follow
dp 1 _ p
dWQ p WQ
dp WQ
dWQ p
(2)
= P	(3)
The relevant sample means for WQ are then plugged in as needed to calculate the estimated
semi-elasticities.
Bin and Czajkowski (2013)
This study examined a variety of water quality variables including visibility, salinity, pH, and
dissolved oxygen (DO) in the St. Lucie River, St. Lucie Estuary, and Indian River Lagoon of
Florida. The study estimated eight hedonic regression models, but only four included an
objective and usable set of water quality parameters (e.g., water visibility, pH, dissolved
oxygen). The four models not included used a subjective location-based grade to measure water
quality. The study contributed a total of 18 observations to the meta-dataset.
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For 12 observations, water quality variables were actual measures. The derivation of our
standardized elasticity and semi-elasticity estimates for these 12 observations is as follows.
Consider a simplified representation of Table 3's Model I as an example.
In (p) = yX + fcWQ + p2WQ2
Rearranging for p,
p = exp(yX + fcWQ + P2WQ2)	(1)
Taking the partial derivative of equation (1) with respect to WQ yields:
dWQ
= exp(yX + 01WQ + faWQ') ¦ (ft + 2(12WQ)
Substituting for inp from equation (1) yields: = p ¦ (/?x + 2(32WQ)
The formulas for the semi-elasticity equation (2) and elasticity equation (3) follow
ap i = (& + 2p2WQ)	(2)
dWQp
dp WQ
dWQ p
= (/?! + 2p2WQ) ¦ WQ	(3)
The relevant sample means for WQ are then plugged in as needed to calculate the estimated
elasticities and semi-elasticities.
Six observations are based on dummy variables for WQ. The dummy variables were equal to
one for water visibility fair, water visibility good, and salinity good.
Consider a simplified representation of Model III in Table 3 of the primary study as an example.
ln(p) = yX + DWQ
Rearranging to isolatep on the left-hand side yields,
p = exp (yX + DWQ)
Let po denote the price when WQ = 0, and pi denote when WQ = 1. These can be written out,
respectively, as:
Po = exp (yX)
px = exp (yX + D)
Because the functional form is log-linear, we use the transformation first outlined by Halvorsen
and Palmquist (1980) for calculating the percent change in price: %Ap = Pl Po.
Po
Plugging in the above equations yields:
n/A„ Pi-Po exp(yX+D)-exp(yX)
%Ap = — =		
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Some rearranging and simplification yields:
n/A„ exp(yZ)exp(D)-exp(yZ)
%ap =		
%Ap = exp(D) — 1
The relevant coefficient estimate for D is then plugged in as needed to calculate the percent
change in price. The percent change in price enters the meta-dataset as a "semi-elasticity"
estimate for observations like this, and the corresponding elasticity variables are not applicable
and are left as null.
Boyle and Taylor (2001)
This study examined water clarity in 34 lakes of Maine that are divided into four groups. The
study estimated four hedonic regression models based on the groupings and each model is
estimated with two different datasets of property characteristics. The first was labeled as town
data and utilized tax-assessor records, and the second used survey responses from buyers and
sellers. Each model contributed a waterfront estimate to the meta-dataset, yielding a total of
eight observations. Waterbody surface area was measured in acres in the original study (one acre
equals 4046.86 square meters).
The derivation of our standardized elasticity and semi-elasticity estimates is as follows.
Consider a simplified representation of Group 1, town data model as an example.
p =yX + /3- areaacres ¦ In(WQ)	(1)
Taking the partial derivative of equation (1) with respect to WQ yields:
dp
— ¦ areaacres ¦
dWQ X	WQ,
The formulas for the semi-elasticity equation (2) and elasticity equation (3) follow
dp 1 _ (.p-dredgeres)
dWQp ~ WQ-p
dp WQ _ {p-dredacres)
dWQ p	p
(2)
(3)
The relevant sample means for WQ, price, and area are then plugged in as needed in order to
calculate the estimated elasticities and semi-elasticities. Because Boyle and Taylor did not
include lake area or the specific lakes that are used for the different groups, we use the 3,515
mean acreage estimate (14,224,713 sq. meters) from Michael et al. (2000), who used a similar,
but not the exact same, data set.
44
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Boyle et al. (1999)
This study examined water clarity (secchi depth) of lakes in four different housing markets in
Maine. The study estimated four hedonic regression models, one for each market, and each
yielding one observation for waterfront homes. Therefore, the study contributed a total of four
observations to the meta-dataset.
The derivation of our standardized elasticity and semi-elasticity estimates is as follows.
Consider a simplified representation of the linear-log model.
p = yX + /? ¦ area ¦ In(WQ)	(1)
Taking the partial derivative of equation (1) with respect to WQ and some rearrangement yields
the semi-elasticity and elasticity calculations, equations (2) and (3) respectively:
dp 0	i
= (5 ¦ area	
dWQ r	WQ
dV 1 _ p . area
i „ ~ P ' Mrn.-r,	v /
dWQ p r WQ-p
dp WQ _ p _ area	^
dWQ p
One complication for the study is only the mean implicit prices (^~~~) are reported, not the
actual regression coefficients /? (see Table 1 in Boyle et al., 1999). Therefore, we back out the
relevant elasticities and semi-elasticities using the available estimates and the implicit price
equation preceding equation (2) above. In addition, the relevant sample means for WQ andp are
plugged in as needed for each of the four study areas in order to calculate the estimated
elasticities and semi-elasticities.
Brashares (1985)
This study examined the effect of turbidity and fecal coliform on lakeshore home values in
southeast Michigan. The study estimated several hedonic price functions each using different
subsets of the data. One model examined homes with lake frontage only, one with lake or canal
frontage, and one with selected homes on lakes with public access. With three different subsets
of the housing data and two water quality variables, this study contributed 6 observations to the
meta-dataset. All the models followed a log-quadratic specification, where the water quality
variables entered as squared values of the mean.
The derivation of our standardized elasticity and semi-elasticity estimates is as follows. All
models have the following log-quadratic specification:
In (p) = yX + (1WQ2	(1)
Taking the partial derivative of equation (1) with respect to WQ yields:
45
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^ = 2PWQ'P
The formulas for the semi-elasticity equation (2) and elasticity equation (3) follow
dp - = 2(3WQ	(2)
dWQ p
dp WQ
dWQ p
= 2 (1WQ2	(3)
Elasticities and semi-elasticities are then computed using the summer mean values for the water
quality variables as reported in table v. 3 of the primary study.
Cho et al. (2011)
This study examined impairment in streams and the river in the Pigeon River Watershed of
North Carolina and Tennessee. The impairment source was identified as a paper mill. The study
estimated six hedonic regression models (four for NC and two for TN), each yielding a
waterfront and non-waterfront estimate for two impairment dummy variables. Therefore, the
study contributed a total of 24 observations to the meta-dataset.
The derivation of our standardized semi-elasticity estimates is as follows. Consider a simplified
representation of the North Carolina Thiessen Polygon (TP) model as an example, where
W Qimpairriver ar|d W Q impair streams are dummy variables denoting that the nearby river and
contributing streams, respectively, are considered impaired.
ln(p) — yX + DiWQimpairriver + D2 impair streams
Rearranging for p,
p — exp (yX + DiWQimpairriver + D2WQimpairstreams)	(1)
Because the functional form is log-linear, we use the Halvorsen and Palmquist (1980) equation
for calculating the percent change in price which can then be expressed as %Ap = Pl v°.
p 0
As an example, the percent change in price due to a river being classified as impaired is
expressed as follows. Let po denote the price when the dummy variable is turned off, and pi
denote when it is turned on. These can be written out, respectively, as:
Po = exp (yX)
px = exp (yX + Dt)
Plugging in the above equations yields:
0/ a _ P1-P0 _ expCyjf+Dj-expCyjQ
Po	exp (yX)
Some rearranging and simplification produces:
46
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n/A„ exp(yZ)exp(D1)-exp(yZ)
%ap =		
%Ap = exp(D1) — 1
The relevant coefficient estimate for Z7?is then plugged in as needed to calculate the percent
change in price. The percent change in price enters the meta-dataset as a "semi-elasticity"
estimate for observations like this, and the corresponding elasticity variables are not applicable
and are left as null.
Epp and Al-Ani (1979)
This study examined pH levels in small rivers and streams in Pennsylvania. The study estimated
four hedonic regression models, but only three included an objective water quality parameter for
waterfront properties. The excluded model focused on a subjective water quality measure based
on property owners' perceptions. Therefore, the study contributed a total of three observations to
the meta-dataset.
The derivation of our standardized elasticity and semi-elasticity estimates is as follows.
Consider a simplified representation of model 1 as an example.
In(p) = yX + fa \n(WQ) + fa[\ n(WQ) popchange]
ln(p) = yX + [fa + fapopchange]\n(WQ)
where popchange denotes the change in population in that area. Rearranging for p,
p _ eYX+[p1+p2popchange]ln(WQ)
Taking the partial derivative of equation (1) with respect to WQ yields:
dv	1
r _ eYx+[Pi+P2Popchange]\n(WQ). [fa + fopopchange]-
dWQ	r u AWQ
Substituting forp from equation (1) yields: = p ¦ [fi1 + /?2p°pchange]-^
The formulas for the semi-elasticity equation (2) and elasticity equation (3) follow
dp - = [fa + fapopchange] —	(2)
dWQp LrL	r	u WQ
dp WQ
dWQ p
= [fa + fapopchange]	(3)
The relevant sample means for pH and population change are then plugged in as needed in order
to calculate the estimated elasticities and semi-elasticities.
47
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Feather et al. (1992)
This study examined the effect of water quality — as proxied by a trophic status index (TSI) — on
the sale of vacant lots on lakes in Orange County, Florida between 1982-84. TSI theoretically
ranges from 0 (good water quality) to 100 (very poor). The study estimated two hedonic
regression models. The first used a linear model specification for waterfront properties only and
the second model, for both waterfront and non-waterfront properties, was log-linear based on
Box-Cox procedures for estimating functional form. Therefore, the study contributed a total of
three observations to the meta-dataset.
The derivation of our standardized elasticity and semi-elasticity estimates is as follows.
Consider a simplified representation of Table V-4 as an example.
p = yX + PWQ	(1)
Taking the partial derivative of equation (1) with respect to WQ yields:
dp
—— = /?
dWQ p
The formulas for the semi-elasticity equation (2) and elasticity equation (3) follow
=	(2)
dWQ p p
JP_WQ=nWQ
dWQ p	p
For the log-linear specification, consider the simplified representation of the model in Table V-8
of the primary study.
In (p) =yX + PWQ	(1)
Rearranging for p,
p = exp (yX + (3WQ)
Taking the partial derivative with respect to WQ yields:
dp
dWQ
= exp (yX + (1WQ) ¦ (3
Substituting in for p yields: = p/?
The semi-elasticity and elasticity are respectively:
T2-- = P	(2)
dWQp r	v '
= pWQ	(3)
dWQ p r v	v '
48
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The relevant sample means for TSI and price are then plugged in as needed in order to calculate
the estimated elasticities and semi-elasticities.
Gibbs et al. (2002)
This study examined water clarity (secchi depth) of lakes in four different housing markets in
New Hampshire. The study estimated four hedonic regression models, one for each market, and
each yielding one observation for waterfront homes. Therefore, the study contributed a total of
four observations to the meta-dataset. The derivation of our standardized elasticity and semi-
elasticity estimates is similar to that reported for Boyle et al. (1999) in this appendix. Consider a
simplified representation of the linear-log model.
p = yX + /? ¦ area ¦ \n(WQ)	(1)
Taking the partial derivative of equation (1) with respect to WQ and some rearrangement yields
the semi-elasticity and elasticity calculations, equations (2) and (3) respectively:
dp „	1
= (5 ¦ area	
dWQ r	WQ
dp 1 _ r, . area
dWQ p ~ " WQ-p	^ '
dp WQ _ _ _ area	. .
dWQ p	p
The relevant sample means for lake area, secchi depth, and price are then plugged in as needed in
order to calculate the estimated elasticities and semi-elasticities.
Guignet et al. (2017)
This study examined water clarity (light attenuation coefficient) in the Chesapeake Bay. The
study estimated several hedonic regression models but only one included a water quality
parameter of interest, yielding a waterfront and non-waterfront observation. Two additional
observations are derived from the same regression results by converting the estimates to
correspond to Secchi disk depth (instead of the light attenuation coefficient). Therefore, the study
contributed a total of four observations to the meta-dataset. The derivation of our standardized
elasticity and semi-elasticity estimates is as follows. Consider a simplified representation of
model 2.C as an example.
In(p) = yX + jff1(ln(WQ/H)) ¦ distWF) + (i2{\n{WQKD) ¦ dist0_200)
+^3(1 ^(WQkd) ' dist2oo-soo)
where distWF is a dummy variable equal to one for waterfront homes, dist0_2o0 is a dummy
variable equal to one for non-waterfront homes within 0-200 meters of the water, and
dist200-500 is a dummy variable equal to one for non-waterfront homes within 200-500 meters
49
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of the water. The above equation can be simplified to:
p _ eYX+{p1distWF+p2dist0.200+p3dist200-Z00)\n(WQKD)
Calculating the elasticities and semi-elasticities with respect to the light attenuation coefficient
(WQkd) is straight forward and follows similar derivation as that below. Here we focus on
converting those estimates to secchi depth in meters (VKQm), using the following inverse
relationship estimated for this particular study area and referenced in the primary study:
WQkd = lASfWQm. Plugging this into the above hedonic regression yields:
(145 \
Wq^J	(1)
To calculate the semi-elasticity and elasticity estimates (equations 2 and 3 below, respectively),
we take the derivative with respect to WQm and then do some slight rearranging:
(145 \
WQ^J
dWQm ~ "
¦ —(Pidistwp + (32dist0_2oo + ^3^^^200-500)(1-45)
QWQrn = ~~ ~WQ^(-P1^S^WF	200 + ^3^^^200-500)
dwQmJj = — vi+ (32dist0_2oo + ^3^^^200-500)	(2)
d WQm = ~(Pldist\VF + P2dist0_200 + ^3^^^200-500)	(3)
After plugging in the appropriate value of zero or one for the corresponding distance bin dummy
variables, the elasticities and semi-elasticities for waterfront homes are simply — /?xand — ,
respectively. For non-waterfront observations, the representative non-waterfront home distance
of 250 meters is assumed, and so dist0_2oo = 0 and dist200-500 = 1 is plugged in. The
corresponding elasticities and semi-elasticities are — /?3 and — The relevant sample mean
for WQm is then plugged in as needed in order to calculate the estimated semi-elasticities.
Horsch and Lewis (2009)
Although the authors' primary focus was on Eurasian milfoil (an invasive aquatic vegetation),
this study also examined water clarity (secchi depth) of lakes in Vilas County, Wisconsin. The
study estimated nine hedonic regression models, five of which included water clarity. Each
model only used waterfront homes in the estimations. Therefore, the study contributed a total of
five observations to the meta-dataset.
50
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The derivation of our standardized elasticity and semi-elasticity estimates is as follows.
Consider a simplified representation of the primary study's linear model.
p = yX + pWQft
The primary study WQ is expressed in terms of secchi depth in feet, which we re-express as
3 2 80 84 ft,
secchi depth in meters using the following conversion factor: WQft = WQm ¦ —.
Plugging this into the hedonic regression yields:
p=yX + (J(WQm ¦ 3.28084)	(1)
Taking the partial derivative with respect to WQm and then multiplying both sides by ^/p and
^®m/p yields the semi-elasticity and elasticity calculations, respectively.
dp -- = £¦ 3.28084	(2)
dWQm p p
dp WQm _ p _ 3_28084 ¦ ^	(3)
dWQm p
The relevant sample means for price and the converted mean secchi depth in meters are then
plugged in as needed.
Hsu (2000)
This study examined the effect of lake water clarity and aquatic plants on lakefront property
values across twenty lakes grouped into three distinct markets in Vermont. The metadata
includes seven observations from this study. Three of the observations are from model
specifications which exclude the aquatic plant variables and include only water clarity. The
other four observations on water clarity come from model specifications that include the aquatic
plant variables. All of the water clarity variables are specified as the interaction of the natural
log of the minimum water clarity in the year the property was sold multiplied by the total lake
surface area. The derivation of the standardized elasticity and semi-elasticity is as follows.
The lin-log specification can generally be expressed as:
p = yX + /? ¦ area ¦ In (WQ)	(1)
Taking the partial derivative of equation (1) with respect to WQ yields:
dp _ (p area\
dWQ ~ V WQ J
The formulas for the semi-elasticity equation (2) and elasticity equation (3) follow
dp 1 _ f r, . area\ _ 1
dWQ p ~ V WQ ) p	^
dP WQ _	1
		= B ¦ area ¦ -	(3)
dWQ p	p
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The relevant sample means for lake area, water clarity, and price are then plugged in as needed
in order to calculate the estimated elasticities and semi-elasticities.
Kashian et al. (2006)
This study examined water clarity in the lake community of Delavan, Wisconsin. The study
estimated three hedonic models, but only one included a water quality parameter, yielding a
waterfront and a non-waterfront observation. Therefore, the study contributed a total of two
observations to the meta-dataset.
The derivation of our standardized elasticity and semi-elasticity estimates is as follows.
Consider a simplified representation of model 3 from the primary study as an example.
p = yX + PWQ	(1)
In this case, WQ is expressed in terms of secchi depth in feet, which we re-express as secchi
3 28084 ft
depth in meters using the following conversion factor: WQft = WQm ¦ —.
Substituting this conversion into equation (1), we have
p=yX + (J(WQm ¦ 3.28084)
Taking the partial derivative with respect to WQ yields:
dp
—J— = P ¦ 3.28084
dWQm
The formulas for the semi-elasticity equation (2) and elasticity equation (3) follow
—- = — ¦ 3.28084	(2)
dWQmp p
dp wQm _ 3 28084 ¦ Egm	(3)
dWQm p r	p
The relevant sample means for WQm and price are then plugged in as needed in order to calculate
the estimated elasticities and semi-elasticities.
Krysel et al. (2003)
This study examined the effect of lake water clarity on lakefront property values across thirty-
seven lakes grouped into six distinct markets in Minnesota. There are two estimates based on
different model specifications for five of the groups and one estimate for the Bemidji group.
Thus, this study contributes 11 observations to the meta-dataset. The water quality variable used
in the study is the natural log of water clarity multiplied by lake size.
The lin-log specification can generally be expressed as:
p = yX + /? ¦ area ¦ In (WQ)	(1)
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Taking the partial derivative of equation (1) with respect to WQ yields:
dp _ (q area\
dWQ ~ V WQ )
Rearranging produces the formulas for the semi-elasticity equation (2) and elasticity equation
(3).
dP 1 _ n area 1
dWQ p ~ " WQ p	^ '
dP WQ „	1	. .
		= /? ¦ area ¦ -	(3)
dWQ p	p
The relevant sample means for WQ, p, and area are then plugged in as needed in order to
calculate the estimated elasticities and semi-elasticities.
Leggett and Bockstael (2000)
This study examined fecal coliform counts in the Chesapeake Bay. The study estimated 20
different hedonic regression models, all of which focused on waterfront homes in Anne Arundel
county, Maryland, and each yielded one observation. Therefore, the study contributed a total of
20 observations to the meta-dataset.
The derivation of our standardized elasticity and semi-elasticity estimates is as follows. The
primary study considered several different functional forms, but the fecal coliform count variable
of interest (WQ) always entered linearly. Consider a simplified representation Leggett and
Bockstael's linear model as an example.
p = yX + PWQ	(1)
Taking the derivative and dividing by p yields the semi-elasticity:
dp i _ P_	,2)
dWQ p p
The elasticity can then be expressed by taking equation (2) and multiplying by WQ, as follows:
dp WQ _ (iWQ
dWQ p	p
(3)
The relevant sample means for WQ and price from Table I of the primary study are then plugged
in as needed in order to calculate the estimated elasticities and semi-elasticities.
Liao et al. (2016)
This study examined water clarity in the Coeur d'Alene Lake, Idaho. The study estimated six
hedonic regression models, but only four included an objective water quality parameter of
interest for waterfront properties. Two of the hedonic models include two water quality
53
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parameters (one for northern division of the lake and one for southern division of the lake).
Therefore, the study contributed a total of six observations to the meta-dataset.
The derivation of our standardized elasticity and semi-elasticity estimates is as follows.
Consider a simplified representation of model 1 in Table 2 of the primary study as an example.
The hedonic double-log specification can generally be specified as:
In(p) = yX + P \n(WQ)
Rearranging for p,
p = exp(yX + (J In(WQ))	(1)
Taking the partial derivative of equation (1) with respect to WQ yields:
5p = exp (yX + p In (WQ))
dWQ	r v	WQ
The formulas for the semi-elasticity equation (2) and elasticity equation (3) follow
dp l _ p
dWQ p WQ
dp WQ
dWQ p
(2)
= P	(3)
The relevant coefficient and sample means for WQ are then plugged in as needed in order to
calculate the estimated elasticities and semi-elasticities.
Liu et al. (2014)
This working paper examined sediment loads, dissolved oxygen, nitrogen and phosphorous
levels, and secchi depth in the Hoover Reservoir, as well as nitrogen and phosphorous in rivers,
focusing on the Upper Big Walnut Creek watershed in Ohio. The study estimated a single
hedonic regression model, that included interaction terms for each specific water quality measure
and waterbody combination listed above, yielding seven observations corresponding to
waterfront homes and seven corresponding to non-waterfront homes. Therefore, the study
contributed a total of 14 observations to the meta-dataset. Only eight of these observations,
however, can be included in any subsequent meta-analysis. Standard errors for all the relevant
coefficient estimates in the other six cases lacked the necessary number of significant digits and
were essentially listed as zero. This prevented us from simulating the corresponding standard
errors associated with our standardized elasticity and semi-elasticity estimates.15
The derivation of our standardized elasticity and semi-elasticity estimates is as follows.
Consider a simplified representation of the model that focuses on nitrogen levels in the Hoover
Reservoir as an example. Note that although numerous water quality measures are included in
15 Subsequent correspondence with the primary study authors to obtain the necessary estimates, as well as the
covariances, were unsuccessful as the available working paper was said to be undergoing revisions.
54
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the single hedonic regression from this study, they will cancel out when taking the partial
derivative with respect to each water quality measure of interest. The hedonic regression can be
represented as:
ln(p) = yX + fcWQ + (32{WQ ¦ distmiles)
where distmiies is distance to the Hoover Reservoir, measured in miles. Since the distances for
the standardized waterfront and non-waterfront estimates in the meta-dataset are noted in meters,
we must convert the distance measure by applying the following conversion factor: distmiies =
^ Plugging this into the hedonic equation yields:
ln(p) = yX + fcWQ + fo (wQ ¦ ^j)	(1)
Taking the partial derivative and rearranging yields the semi-elasticity and elasticity calculations
(equations (2) and (3) below, respectively).
dp -=B1 + B2 -ii££zL.	(2)
I * 1 Ana q a.	^ ^
dWQp rl	1609.34
dp WQ
dWQ p
= (ft+ft^>
The relevant sample means for WQ are then plugged in as needed in order to calculate the
estimated elasticity and semi-elasticities. The mean distance for waterfront homes was not
reported, and so in calculating the waterfront estimates a distance of 50 meters was assumed (as
done for other studies where such information was needed but unavailable), and an assumed 250
meters was used for the representative non-waterfront home.
Liu et al. (2017)
This study examined chlorophyll in Narragansett Bay, Rhode Island. The study estimated 13
hedonic regression models, each yielding a waterfront and non-waterfront estimate. Therefore,
the study contributed a total of 26 observations to the meta-dataset.
The derivation of our standardized elasticity and semi-elasticity estimates is as follows. As an
example, consider a simplified representation of the "well-informed" model for waterfront
properties, which used the 99th percentile for Chlorophyll concentration as the relevant water
quality measure.
In(p) = yX + fcWQ + (32WQ ¦ dist0_100m
Rearranging for p,
p = exp(yX + fcWQ + (32WQ ¦ dist0_100m)	(1)
In this case, WQ is expressed in terms of micrograms per liter, which we re-express as
milligrams per liter using the following conversion factor: WQng^ = WQmg^	.
55
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dist0_100m is a dummy variable representing waterfront properties within 100m of the Bay.
Substituting this conversion into equation (1), we have
p = exp(yX + /?xWQmgj • 1000 + p2WQmgj^ ¦ 1000 ¦ dist0_100m)
Taking the partial derivative with respect to WQ yields:
= exp (yX + fi^WQmg j ¦ 1000 + /?2WQmgj ¦ 1000 ¦ dist0_100m)(p1 ¦ 1000 + /?2 1 1000 ¦
dist o-ioom)
Plugging in pfrom equation (1) yields:
^ = V ¦ (Pi ¦ 1000 + P2 ¦ 1000 ¦ dist0_100m)
The formulas for the semi-elasticity equation (2) and elasticity equation (3) follow
~dWQ~p = 1000(0! + 02^i5tO-lOOm)	(2)
5^^ = WQmsk ¦ 1000(ft + p2dist0-lmm)	(3)
For waterfront properties, we set dist0_100m = 1. The relevant coefficients and sample means
for WQ are then plugged in as needed in order to calculate the estimated elasticities and semi-
elasticities.
Michael et al. (2000)
This study examined water clarity in 22 lakes of Maine that are divided into three groups. The
study estimated nine hedonic regression models per group, each yielding one waterfront
observation. Therefore, the study contributed a total of 27 observations to the meta-dataset.
The derivation of our standardized elasticity and semi-elasticity estimates is as follows.
Consider a simplified representation of Group l's CMIN model as an example. CMIN
represents the minimum water clarity for the year the property was sold.
The lin-log specification can generally be expressed as:
p = yX + jffln (WQ)	(1)
Taking the partial derivative of equation (1) with respect to WQ yields:
— = (/?—)
dW V WQJ
The formulas for the semi-elasticity equation (2) and elasticity equation (3) follow
-p--={p—)~	(2)
dWQ p V WQJ p	v '
56
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(3)
dWQ p \ pj
The relevant coefficient and sample means for WQ and price are then plugged in as needed in
order to calculate the estimated elasticities and semi-elasticities.
The functional form of WQ varied across specifications. Table 4 in Michael et al. presents
CMAX/CMIN or CMAX/CMIN% as additional water clarity specifications. However, in Table
7, the specification is presented as CMIN/CMAX and CMIN/CMAX%. For models 6 and 7, we
estimate the elasticities as presented in Table 4, as suggested by the primary study authors.16
As an example, Model 6 from the primary study has the following form:
v , 0ln(CMAX)	, .
p=vX + B~r-—(1)
K 1 r In (WQ)	v '
where ln(CMAX) is an interaction term.
Taking the partial derivative of equation (1) with respect to WQ yields:
dp _ n ( In(CMAX) \
dWQ ~ " \WQ-\n(WQ)2 )
The formulas for the semi-elasticity equation (2) and elasticity equation (3) follow
dp 1 = _ o rjn(CMAX)_\ _ 1
dWQp	" \WQ-\n(WQ)2J p	^ '
dp WQ _ _ n qn(CMAX)\ _ 1
dWQ p	\ In (WQ)2 ) p
As another example, Model 7 from the primary study has the following form:
x + fjwcW()
K 1 r In (CMAX)	v '
Taking the partial derivative of equation (1) with respect to WQ yields:
dp / — (3 \
= (	^	)
\WQ ¦ ln(CMAX))
dWQ VVKQ ¦ ln(CMAX)
The formulas for the semi-elasticity equation (2) and elasticity equation (3) follow
——- = (	—	V-	(2)
dWQp \WQ-\n(CMAX)J p	v '
dp WQ _ - p 1
dWQ p In (CMAX) p	^ '
16 Personal communication with K. Boyle, December 8, 2017.
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Netusil et al. (2014)
This study examined a variety of water quality parameters including dissolved oxygen, E. coli,
fecal coliform, pH, temperature, and total suspended solids in Johnson Creek, Oregon, and Burnt
Bridge Creek, Washington. The study estimated five hedonic regression models for Johnson
Creek and one model for Burnt Bridge Creek, each yielding five water quality measures for
waterfront and non-waterfront properties. For this study, the dummy variable, disto-0.25,
representing properties within a 0.25 mile (402.34 meters) of the creeks includes both waterfront
and non-waterfront homes. Therefore, the study contributed a total of 60 observations to the
meta-dataset.
The derivation of our standardized elasticity and semi-elasticity estimates is as follows.
Consider a simplified representation of the Johnson Creek (Dry) OLS model from the primary
study as an example.
In(p) = yX + pWQ ¦ dist0_02S
p = exp(yX + (iWQ ¦ dist0_02S)	(1)
Taking the partial derivative of equation (1) with respect to WQ yields:
dp
— = exp(yX + /3WQ ¦ dist0_0 2S) p ¦ dist0_0 2S
Substituting in p from equation (1), the formulas for the semi-elasticity equation (2) and
elasticity equation (3) follow
= P ¦ dist0_0.25	(2)
dp WQ
dWQ p
— /3WQ-dist0_ 0.25	(3)
For both waterfront and non-waterfront properties, we set dist0_0 25=1. The relevant coefficient
and sample means for WQ are then plugged in as needed in order to calculate the estimated
elasticities and semi-elasticities.
Olden and Tamayo (2014)
This study examined water clarity in lakes located in King County, Washington. The study
estimated three hedonic regression models, each yielding a waterfront observation. Therefore,
the study contributed a total of three observations to the meta-dataset.
The derivation of our standardized elasticity and semi-elasticity estimates is as follows.
Consider a simplified representation of Model 1 from the primary study as an example.
p = yX + PWQ	(1)
Taking the partial derivative with respect to WQ yields:
58
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dp
—~ = P
dWQ H
The formulas for the semi-elasticity equation (2) and elasticity equation (3) follow
dp 1 _ p
dWQ p p
(2)
_dp_WQ= „WQ
dWQ p	p
The relevant sample means for WQ and p are then plugged in as needed in order to calculate the
estimated elasticities and semi-elasticities.
Poor et al. (2001)
This study estimated several hedonic regression models that included both objective and
subjective measures of water clarity (i.e., secchi depth) in lakes in Maine. The meta-dataset
focuses solely on objective measures of water quality, and so we examine the four hedonic
regression models that included objective secchi depth measurements as an explanatory variable.
Each model corresponded to one of four different housing markets in Maine and provided one
waterfront observation. Therefore, the study contributed a total of four observations to the meta-
dataset.
The derivation of our standardized elasticity and semi-elasticity estimates is similar to Boyle et
al. (1999) and is briefly re-summarized here. Consider a simplified representation of the linear-
log model presented in the primary study.
p = yX + /? ¦ area ¦ \n(WQ)	(1)
Taking the partial derivative of equation (1) with respect to WQ and some rearrangement yields
the semi-elasticity and elasticity calculations, equations (2) and (3) respectively:
dp „	1
-— = B ¦ area	
dWQ r	WQ
dV 1 _ p . area
i „ ~ P ' Mrn.-r,	v /
dWQ p r WQ-p
dp WQ _ p _ area	^
dWQ p
The relevant sample means for WQ\ area, and p are plugged in as needed for each of the four
study areas in order to calculate the estimated elasticities and semi-elasticities.
Poor et al. (2007)
This study examined concentrations of total suspended solids and dissolved inorganic nitrogen in
rivers throughout the St. Mary's watershed in Maryland. The study presented two hedonic
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regression models, one for each of the two water quality measures. The focus was on ambient
water quality, and so the sample encompassed both waterfront and non-waterfront homes
(although the distance gradient with respect to water quality was essentially assumed to be flat).
Therefore, each model contributed a waterfront and non-waterfront observation, implying that
the study provided a total of four observations to the meta-dataset.
The derivation of our standardized elasticity and semi-elasticity estimates is as follows.
Consider a simplified representation of the model as follows:
In (p) = yX + PWQ
p = eYx+PW(l	(1)
Taking the partial derivative of equation (1) with respect to WQ and some rearrangement yields
the semi-elasticity and elasticity calculations, equations (2) and (3), respectively:
dp - = $	(2)
dWQ p
dp WQ
dWQ p
= PWQ	(3)
The relevant sample means for WQ (either total suspended solids or dissolved inorganic nitrogen
depending on the model) are then plugged in as needed in order to calculate the estimated
elasticities and semi-elasticities.
Ramachandran (2015)
This study examined nitrogen concentrations in the Three Bays area of Cape Cod,
Massachusetts. The study estimated and presented four hedonic regression models, but only three
of these models included the relevant water quality measure as a control variable. Each model
yielded a waterfront and non-waterfront observation. Therefore, the study contributed a total of
six observations to the meta-dataset.
The derivation of our standardized elasticity and semi-elasticity estimates from the double-log
specification in the primary study is as follows.
In (p) = yX + filn (WQ)
v _ eyX+p\n(WQ)	Q)
Taking the partial derivative of equation (1) with respect to WQ and some rearrangement yields
the semi-elasticity and elasticity calculations, equations (2) and (3) respectively:
= JL	(2)
dWQp WQ	v '
—¦ = P	(3)
dWQ p r	v '
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The relevant sample mean for WQ is then plugged in as needed in order to calculate the
estimated elasticities and semi-elasticities.
Steinnes (1992)
This study examined the effect of water clarity across 53 lakes in Northern Minnesota. The
study used several measures of the appraised value of land as the dependent variable in the
hedonic price equation. However, the study did not report the average price nor the summary
statistics for the water clarity variable so neither the elasticity nor the semi-elasticity are
computed for this study.
Tuttle and Heintzelman (2015)
This study examined numerous ecological and water quality measures in lakes in the
Adirondacks Park in New York, including the presence of milfoil (an invasive species), loons (an
aquatic bird and indicator species of ecological health), and lake acidity (i.e., pH levels). The
only objective measure of water quality for inclusion in this meta-dataset is lake acidity, which is
measured as an indicator equal to one if pH levels are below 6.5. The study estimated and
presented four hedonic regression models that included the poor pH indicator as a control
variable. Two of these models included only lakefront homes, and thus contributed only a single
observation each to the meta-dataset. The other two models included waterfront and non-
waterfront homes in the estimating sample and thus provided two observations each. This study
contributed a total of six observations to the meta-dataset.
The relevant water quality measures are binary indicator variables in this case, and so the percent
change in price (%Ap) is calculated for the "semi-elasticity" variable in the meta-dataset. The
elasticity estimates are not applicable and are left as null. Consider a simplified representation of
Tuttle and Heintzelman's hedonic model.
In (p) = yX + DWQ
p = evx+DW(l	(1)
where D is the coefficient of interest corresponding to the poor pH dummy variable. Note that
the distance gradient with respect to water quality was assumed to be flat in this study, and so,
when appropriate, the calculations for waterfront and non-waterfront %Ap are the same. Let the
price for a representative home when the nearest lake does not and does have poor pH be
denoted as/>oandpi, respectively. These can be expressed as:
p0 = exp (yX)
px = exp (yX + D)
Plugging the above two equations into the percent change in price calculation yields:
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n/A„ Pi-Po exp(yX+D)-exp(yX)
%Ap = — =	S55ij	
And with some rearranging and simplification yields:
n/A„ exp(yZ)exp(D)-exp(yZ)
%ap =		
%Ap = exp(D) — 1
The relevant coefficient estimate for D is then plugged in as needed to calculate the percent
change in price.
Walsh and Milon (2016)
This study examined the effect of nutrients on properties on and/or near lakes in Orange County,
Florida. The study estimated several singular indicators of nutrients including Total Nitrogen
(TN), Total Phosphorus (TP), and Chlorophyll-a (CHLA). The study also examined several
composite indicators - the trophic status index (TSI) and what the authors label as the one-out,
all-out (OOAO) indicator that equals one if all the US EPA criteria for TN, TP, and CHLA are
achieved. Each model yields a waterfront and non-waterfront observation which contributes ten
observations, plus an additional model which includes TN, TP, and CHLA in a single model
yielding six more observations for a total of 16 observations from this study.
The derivation of the standardized elasticity and semi-elasticity estimates is as follows. Consider
simplified version of the basic specification used (see EQ1 on pg. 647 of the primary study):
In(p) = yX + P0distWF + /?x In(WQ) + /?2(1 n(WQ) ¦ distWF) + /33(\n(WQ) ¦ In(dist)) +
(34(\n(WQ) ¦ In (area)) + (35(\n(WQ) ¦ ClearLow)
where ClearLow is a dummy variable indicating that a lake is considered a clear lake with low
alkalinity. This equation can be simplified to:
ln(p) = yX + (30distWF + [/?x + (32 distWF + /?3 In (dist) + /?4 ln(area) +
(35ClearLow] In (WQ)
p = exp( yX + /?0 distWF + [/?x + (32 distWF + /?3 In (dist) + /?4 ln(area) +
(35ClearLow]\n(WQ))	(1)
Taking the partial derivative of equation (1) with respect to WQ yields:
exp( yX + p0distWF
+ [/?! + /?2 distWF + /?3 In (dist) + /?4 ln(area) + (3sClearLow] ln(I/K(2))
1
1 Wi + fodistwi? + /?3 In (dist) + /?4 ln(area) + (3sClearLow] ¦
Plugging in p from equation (1), and then rearranging yields the formulas for the semi-elasticity
and elasticity estimates, equations (2) and (3), respectively.
dp
dWQ
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= PWi + P2distWF + /?3 In (dist) + /?4 In (area) + (3sClearLow] ^
= [ft + fodistwp + p3 In (dist) + p4 In (area) + feClearLow] ^	(2)
dp wQm _ _j_ p2distWF + p3 in (dist) + /?4 ln(area) + (3sClearLow\	(3)
a	p
For waterfront observations, the relevant sample mean values for area are plugged in to
equations (2) and (3), the representative waterfront home distance of 50 meters is plugged in for
dist, and distwF is set equal to one. For non-waterfront observations, the corresponding sample
mean values are plugged in, but distwF is set equal to zero and the representative non-waterfront
home distance of 250 meters is plugged in for dist. The dummy variable ClearLow indicates
clear lakes with low alkalinity is set to one for model specifications that include that variable.
Walsh et al. (2011a)
This study examined water clarity (secchi depth) in lakes in Orange County, Florida. The study
estimated six hedonic regression models that varied in terms of the independent variables and
how they address spatial dependence. Each model yields a waterfront and a non-waterfront
observation. Therefore, the study contributed a total of 12 observations to the meta-dataset.
The derivation of our standardized elasticity and semi-elasticity estimates is as follows.
Consider a simplified representation model 3 or 3 S in the primary study as an example.
ln(p) =yX + p1 In (WQft) + p2(\n(WQft) ¦ distWF) + 03(ln (WQft) ¦ In (dist)) +
/?4(ln(area) ¦ In(VK
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equation (1), and then rearranging yields the formulas for the semi-elasticity and elasticity
estimates, equations (2) and (3), respectively.
= viPi+ P2distWF + p3\n(dist) + p4\n(area)]
= Wi + P2distWF + p3\n(dist) + /?4ln(area)]	(2)
dwQm ^ = ^ + P2distwF + Psln(dist) + Aln(area)]	(3)
For waterfront observations, the relevant sample mean value for area is plugged into equations
(2) and (3), the representative waterfront home distance of 50 meters is plugged in for dist, and
distWF is set equal to one. The mean water quality value (from table 2 of the primary study) is
converted to meters and plugged in for WQm. For non-waterfront observations, the
corresponding sample mean values are plugged in, but distWF is set equal to zero and the
representative non-waterfront home distance of 250 meters is plugged in for dist.
Walsh et al. (2011b)
This study examined four water quality measures (chlorophyll-a, nitrogen, phosphorous, and a
trophic state index) for lakes in Orange County, Florida. The study estimated 12 hedonic
regression models, three for each of the four water quality measures, which varied in terms of
how the functional form accounted for spatial dependence. Each model yielded two
observations, one for waterfront homes and another for non-waterfront homes.
The derivation of our standardized elasticity and semi-elasticity estimates is as follows.
Consider a simplified representation of the Walsh et al.'s double-log hedonic model.
ln(p) = yX + /?x In (WQ) + (32(}n(WQ) ¦ distWF) + /?3(ln (WQ) ¦ In (dist)) +
/?4(ln(area) ¦ ln(I/K(2))
Which can be simplified to:
ln(p) = yX + [/?! + p2distWF + /?3ln (dist) + /?4ln (area)] In (WQ)	(1)
where WQ denotes the corresponding measure of interest.
Taking the partial derivative of equation (1) with respect to WQ yields:
dp _ QYX+[f>i+[>2distwF+[>3\n(.dist)+[!4,ln(area)]ln(WQ)
dWQ
1 Wi + fodistwi? + /?3ln (dist) + /?4ln (area)] —
Plugging in p from equation (1), and then rearranging yields the formulas for the semi-elasticity
and elasticity estimates, equations (2) and (3), respectively.
64
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= PiPi + P2distWF + p3\n(dist) + p4\n(area)] ^
= Wi + P2distWF + /?3ln(dist) + /?4ln(area)] ^	(2)
= iPi + P2 distWF + p3\n (dist) + p4\n (area)]	(3)
For waterfront observations, the relevant sample mean value for area is plugged in to equations
(2) and (3), the representative waterfront home distance of 50 meters is plugged in for dist, and
distWF is set equal to one. The corresponding mean water quality values are plugged in for WQ.
For non-waterfront observations, the corresponding sample mean values are plugged in, but
distWF is set equal to zero and the representative non-waterfront home distance of 250 meters is
plugged in for dist.
Walsh et al. (2017)
This study examined water clarity (light attenuation coefficient) in the Chesapeake Bay tidal
waters for 14 adjacent counties in Maryland. The study estimated 56 separate hedonic regression
models; four for each county, where the functional form (double-log versus semi-log) and period
for which the water quality measure is averaged over (one versus three years) varied. Each
model in turn yields a waterfront and non-waterfront estimate, implying 112 observations.
Furthermore, an additional 112 observations are derived from the same regression results by
converting the estimates to correspond to secchi depth (instead of the light attenuation
coefficient). Therefore, the study contributed a total of 224 observations to the meta-dataset.
The derivation of our standardized elasticity and semi-elasticity estimates is as follows.
Consider a simplified representation of Walsh et al.'s double-log models as an example.
In(p) = yX + ^(^(WQkd) ¦ distWF) + p2(\n(WQKD) ¦ dist0_S00)
+^3(1 ^(WQkd) ' dist500_1000)
where distWF is a dummy variable equal to one for waterfront homes, dist0_500 is a dummy
variable equal to one for non-waterfront homes within 0-500 meters of the water, and
dist500_1000 is a dummy variable equal to one for non-waterfront homes within 500-1000
meters of the water. The above equation can be simplified to:
p _ eYX+d31distWF+P2dist0-500+l33dist500-1000)ln(WQKD)
Calculating the elasticities and semi-elasticities with respect to the light attenuation coefficient
( WQkd) is straight forward and follows similar derivation as that below. Here we focus on
converting those estimates to secchi depth in meters ( WQw), using the following inverse
relationship estimated for this particular study area and noted in the primary study: WQKD =
lAS/WQm. Plugging this into the above hedonic regression yields:
(1 45 \
WQm)	m
65
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To calculate the semi-elasticity and elasticity estimates (equations 2 and 3, respectively), we take
the derivative with respect to WQm and then do some slight rearranging:
(145 \
WQ^J
dWQm ~ "
¦ —(Pidistwp + (32dist0_500 + P3dist500_1000) {lAS)WQm
dj)	j)
QWQm = —	+ fadisto-soo + ^3^^^500-1000)
dwQm~p ~ wo^^ldistwF + P2dist0_500 + (33dist500_1000)	(2)
dwQm p~ = ~^P^distWF + (32dist0_500 + Psdist500_1000)	(3)
After plugging in the appropriate value of zero or one for the corresponding dummy variables,
the elasticities and semi-elasticities for waterfront homes are simply — /?xand —
respectively. For non-waterfront observations, representative non-waterfront home distance of
250 meters is plugged in for dist, and so the corresponding elasticities and semi-elasticities are
—/?2 and ——. The relevant county specific sample means for WQm and p are then plugged in
WQm
as needed in order to calculate the estimated semi-elasticities.
Williamson et al. (2008)
This study examined acid mine drainage impairment in the Cheat River Watershed in West
Virginia. The study estimated one hedonic regression model, yielding a waterfront and non-
waterfront observation. For this study, the dummy variable, WQimpairo.25 representing properties
within a 0.25 mile (i.e., 402.34 meters) of the acid mine drainage impaired stream includes both
waterfront and non-waterfront. Therefore, the study contributed a total of two observations to
the meta-dataset.
Consider a simplified representation of Table 3 as an example.
ln(p) — yX + D-±WQimpairQ25 D2WQimpair0.50	(1)
Rearranging for p,
V ~ ®Xp(yX + D]WQim.pair0.25 ^2WQimpair0.50)
Because the functional form is log-linear, we use the following equation for calculating the
percent change in price, as first outlined by Halvorsen and Palmquist (1980): %Ap = Pl v°.
66
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Estimating the percent change for impaired river, let po denote the price when the dummy
variable is turned off, and pi denote when it is turned on. These can be written out, respectively,
as:
Po = exp (yX)
px = exp (yX + D±)
Plugging in the above equations yields:
0/ a _ Pi-Po _ expjyX+D^-expjyX)
Po	exp (yX)
Some rearranging and simplification yields:
n/A„ exp(yZ)exp(D1)-exp(yZ)
%ap =		
%Ap = exp(D1) — 1
The relevant coefficient for Di is then plugged in as needed to calculate the percent change in
price.
Wolf and Klaiber (2017)
This study examined the effect of the density of harmful algae (as proxied by microsystin
concentrations) on properties across six counties surrounding four inland lakes in Ohio. The
study estimated nine hedonic models, each yielding a waterfront and non-waterfront estimate.
Therefore, the study contributed a total of 18 observations to the meta-dataset. The algae
concentrations are converted to a binary water quality dummy variable {Algae) that is set equal
to one when the algae density is above the World Health Organization's standard of lug/L for
drinking water for a period of time matching individual housing transactions data.
The derivation of the standardized elasticity and semi-elasticity estimates is as follows. Consider
simplified version of the basic specification used.
In(p) = yX + D-^Algae + D2(Algae • (dist0_20m + dist20-6oom)) + D3(Algae ¦ dist)
This can then be rewritten as:
p = exp (yX + D-^Algae + D2{Algae ¦ (dist0_20m + dist20_ 6oom)) + D3(Algae ¦ dist)) (1)
Let po denote the price when the algae dummy is turned off, and pi denote when it is turned on.
These can be written out, respectively, as:
Po = eyX
p^ — gy^+£,1+D2+D3(dtst)
67
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The percent change in price can then be expressed as %Ap
equations yields:
Vi—Vn eYX+D1+D2+D3(.dist) _gyX
%Ap =	^	—
p0	eV
Some rearranging and simplification yields:
eyXeD1+D2+D3(dist)_eyX
%AP = 	~tx	
%Ap = eDi+D2+D3(d^st) — \
The relevant coefficients and the appropriate representative home distance for dist (50 meters for
waterfront homes, 250 meters for non-waterfront homes) are then plugged in as needed in order
to calculate the estimated percent change in price.
= ——-. Plugging in the above
P 0
Yoo et al. (2014)
This study examined the effect of sediment loads on five lakes in Arizona. The sediment loading
observations are derived from a watershed level sediment delivery model. The sediment load is
interacted with the travel time from each property to the nearest lake in all models. Three semi-
log model specifications are estimated - OLS, spatial lag model, and spatial error model - for
both waterfront and non-waterfront homes. There are six observations from this study.
Derivation of the elasticity and semi-elasticity is as follows - recall that WQ in this study is
measured as sediment load. The primary study WQ is expressed in terms of tons/acre, which we
re-express as kg/sq.meters using the following conversion factor: WQtons = WQ kg ¦ 4.461.
acre	sqm
Plugging this into the hedonic regression yields:
In(p) =yX + fixWQkg_ ¦ 4.461 + p2WQkg_ ¦ 4.461 ¦ Time + (J3WQkg_ ¦ 4.461 ¦ Time2
sqm	sqm	sqm
which is rewritten as:
p = exp(yX + foWQk^ ¦ 4.461 + (J2WQkg_ ¦ 4.461 ¦ Time + (J3WQkg_ ¦ 4.461 ¦ Time2)
sqm	sqm	sqm
(i)
Now, the derivative with respect to WQ is:
= p . . 4.461 + p2 ¦ 4.461 ¦ Time + p3 ¦ 4.461 ¦ Time2)
and the semi-elasticity (equation 2) and elasticity (equation 3) are given by:
= 4.4610?! + h ¦ Time + ft • Time2)	(2)
-^^2 = WQm_ . 4.461(ft + ft • Time + ft • Time2)	(3)
^ "	sqm
68
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The relevant sample means for WQ and Time are then plugged in as needed in order to calculate
the estimated elasticities and semi-elasticities.
Zhang and Boyle (2010)
This study examined the interaction of water clarity and surface area of waterbody in the four
lakes and one pond in Rutland County, Vermont. The study estimated ten hedonic regression
models, but only six included a water quality parameter. These six models focused only on
waterfront homes, and therefore the study contributed a total of six observations to the meta-
dataset. Waterbody surface area was measured in acres in the original study (one acre equals
4046.86 square meters).
The derivation of our standardized elasticity and semi-elasticity estimates is as follows.
Consider a simplified representation of model Total Macrophytes-Quadratic as an example.
The hedonic double-log specification can generally be specified as:
In (p) =yX + fi- areaacres ¦ In (WQ)
Rearranging for p,
p = exp(yX + p ¦ areaacres ¦ ln(WQ))	(1)
Taking the partial derivative of equation (1) with respect to WQ yields:
3p	1
= exp(yX + P ¦ areaacres ¦ ln(W<2)) ¦ (jff ¦ areaacres) —
Substituting inp from equation (1) and rearranging, the formulas for the semi-elasticity equation
(2) and elasticity equation (3) follow
dp 1 _ (/?-areagcres)
dWQp~ WQ	^
dp WQ - _	.
dWQ p ~ ^ ' areaacres)	(3)
The relevant sample means for WQ and area are then plugged in as needed in order to calculate
the estimated elasticities and semi-elasticities.
Zhang et al. (2015)
This study examined the effect of water clarity on lakefront homes across 15 markets in Maine,
Vermont, and New Hampshire. The water quality variable used in the study is the natural log of
water clarity multiplied by lake size. There is one observation per market, thus this study
contributed 15 observations to the meta-dataset.
The specification used in all the models is:
69
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p = yX + (3 ¦ area ¦ \n(WQ)	(1)
Taking the partial derivative of the price equation with respect to WQ yields:
dp _ (p area\
dWQ ~ V WQ J
The formulas for the semi-elasticity equation (2) and elasticity equation (3) follow
dp 1 _ „ area 1
dWQ p ~ " WQ p	^
dp WQ _ _ _ area	. .
dWQ p	p
The relevant sample means for WQ\ price, and area are then plugged in as needed in order to
calculate the estimated elasticities and semi-elasticities.
70
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Appendix B: Supplemental meta-analysis results.
Table Bl. Meta-regression Results Examining Heterogeneity by Study Area Demographics.
VARIABLES
RE Panel 1 Mundlak 1 RE Panel 2 Mundlak 2 RE Panel 3 Mundlak 3
waterfront
waterfront cluster mean
median income (2017$ USD)
college degree (% population)
population density (households /sq. km.)
Constant
0.0807***
(0.020)
0.0000
(0.000)
0.0166
(0.056)
0.0644***
(0.019)
0.0632
(0.052)
0.0000
(0.000)
-0.0382
(0.074)
0.0812***
(0.018)
0.1538
(0.290)
0.0020
(0.045)
0.0643***
(0.018)
0.0541
(0.052)
0.1908
(0.298)
-0.0305
(0.059)
0.0863***
(0.019)
0.0002
(0.000)
0.0112
(0.020)
0.0643***
(0.018)
0.0762
(0.055)
0.0003
(0.000)
-0.0316
(0.042)
Dependent variable: home price elasticity with respect to water clarity (secchi depth). ***p<0.01, **p<0.05, *p<0.1. Standard errors
in parentheses. Regressions estimated using n=260 observations, from K=63 unique housing market clusters. Random Effects Panel
(RE Panel) regressions estimated using the "mixed" routine in Stata 14, where the n=260 observations are weighted by the cluster-
adjusted Random Effect Size (RES) weights and the cluster specific effects are defined according to the K=63 unique housing market
clusters. Mundlak (1978) regressions estimated by first calculating cluster means for independent variables that vary within each
cluster, and then by running the subsequent model via the "mixed" routine in Stata 14, where the residual cluster-specific effect is
maintained.
71
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Table B2. Unit value mean elasticity estimates.
Water quality measure
Cluster Adjusted
RES Mean
Cluster Adjusted
FES Mean
Chlorophyll a
waterfront
non-waterfront w/in 500 m
Dissolved oxygen
waterfront
non-waterfront w/in 500 m
E-coli
waterfront
non-waterfront w/in 500 m
Fecal coliform
waterfront
non-waterfront w/in 500 m
Lake trophic state index
waterfront
non-waterfront w/in 500 m
Light attenuation
waterfront
-0.026***
(-0.031, -0.021)
0.009***
(0.006, 0.012)
-0.010
(-0.257, 0.237)
0.642***
(0.374, 0.910)
-0.081***
(-0.129, -0.032)
-0.081***
(-0.129, -0.033)
-1 3E-4***
(-1.8E-4, -0.7E-4)
-0.052***
(-0.096, -0.008)
-0 797***
(-1.330, -0.264)
-0.682**
(-1.296, -0.068)
-0.082***
(-0.093, -0.070)
-0.027***
(-0.032, -0.021)
-0.001
(-0.003, 0.001)
0.064
(-0.217,0.345)
0.209
(-0.095,0.513)
-0.094***
(-0.140, -0.048)
-0.094***
(-0.140, -0.048)
-2.2E-5***
(-2.8E-5, -1.6E-5)
-0.036***
(-0.046, -0.027)
-0 797***
(-1.330, -0.264)
-0.682**
(-1.296, -0.068)
-0.071***
(-0.078, -0.064)
Standard Cluster Unweighted
RES Mean	Weighted Mean	Mean
-0.022***
(-0.031, -0.013)
0.001
(-0.006, 0.009)
0.324*
(-0.036, 0.685)
0.010
(-0.085,0.105)
0.737*
(-0.044, 1.517)
0.005
(-0.201,0.211)
0.098
(-0.669, 0.865)
0.992***
(0.343, 1.641)
-0.014
(-0.262, 0.235)
0.666***
(0.395, 0.937)
0.089
(-0.207, 0.384)
1.063***
(0.708, 1.419)
-0.089***
(-0.147, -0.031)
-0.089***
(-0.147, -0.031)
-0.073***
(-0.124, -0.021)
-0.073***
(-0.125, -0.022)
-0.073***
(-0.124, -0.021)
-0.073***
(-0.125, -0.022)
-0.2E-4
(-0.6E-4, 0.1E-4)
-0.024***
(-0.036, -0.011)
-0.037
(-0.088, 0.014)
-0.059*
(-0.090, -0.005)
-0.018***
(-0.026, -0.011)
-0.020***
(-0.034, -0.006)
-0 797***
(-1.330, -0.264)
-0.682**
(-1.296, -0.068)
-0.920***
(-1.545, -0.295)
-0.682**
(-1.296, -0.068)
-0.920***
(-1.545, -0.295)
-0.682**
(-1.296, -0.068)
-0.070***
(-0.076, -0.063)
-0.086***
(-0.099, -0.074)
-0.086***
(-0.099, -0.073)
-------
non-waterfront w/in 500
Nitrogen
waterfront
non-waterfront w/in 500
Percent Water Visibility
waterfront
non-waterfront w/in 500
Phosphorous
waterfront
non-waterfront w/in 500
Salinity
waterfront
non-waterfront w/in 500
Sediment
waterfront
non-waterfront w/in 500
Sedimentation Rate
waterfront
non-waterfront w/in 500
m	-0.013***
(-0.020, -0.006)
-0.220***
(-0.244, -0.196)
m	-0.136***
(-0.156, -0.116)
-1.659***
(-1.900, -1.418)
m
-0.107***
(-0.122, -0.092)
m	-0.005
(-0.012,0.003)
0.552***
(0.279, 0.824)
m
-0.003
(-0.008, 0.001)
m	-0.006
(-0.014,0.003)
-0.113***
(-0.134, -0.091)
m	-0.113***
(-0.134, -0.091)
-0.011***
(-0.014, -0.007)
-0.131***
(-0.149, -0.113)
-0.030***
(-0.036, -0.023)
-1.659***
(-1.900, -1.418)
-0.093***
(-0.106, -0.081)
0.003
(-0.002, 0.008)
0.552***
(0.279, 0.824)
4.9E-6**
(0.2E-6, 9.7E-6)
4.9E-6**
(0.2E-6, 9.7E-6)
-0.113***
(-0.134, -0.091)
-0.113***
(-0.134, -0.091)
-0.011
(-0.014, -0.007)
-0.014***
(-0.022, -0.006)
-0.014***
(-0.022, -0.006)
-0.245***
(-0.321, -0.170)
-0.130***
(-0.184, -0.077)
-0.242***
(-0.271, -0.215)
-0.184***
(-0.210, -0.157)
-0.292***
(-0.326, -0.257)
-0.221***
(-0.254, -0.187)
-1.659***
(-1.900, -1.418)
-1.655***
(-1.896, -1.414)
-1.655***
(-1.896, -1.414)
-0 114***
(-0.154, -0.074)
-0.002
(-0.015,0.010)
-0.107***
(-0.123, -0.092)
-0.019***
(-0.032, -0.005)
-0.115***
(-0.130, -0.100)
-0.016**
(-0.029, -0.003)
0.552***
(0.279, 0.824)
0.553***
(0.281, 0.826)
0.553***
(0.281, 0.826)
4.9E-6**
(0.2E-6, 9.7E-6)
4.9E-6**
(0.2E-6, 9.7E-6)
-0.012
(-0.059, 0.035)
-0.012
(-0.059, 0.035)
-0.018
(-0.088, 0.052)
-0.018
(-0.088, 0.052)
-0.113***
(-0.134, -0.091)
-0.113***
(-0.134, -0.091)
-0.132***
(-0.183, -0.082)
-0.132***
(-0.183, -0.082)
-0.132***
(-0.183, -0.082)
-0.132***
(-0.183, -0.082)
-------
Temperature
waterfront
non-waterfront w/in 500 m
Total Suspended Solids
waterfront
non-waterfront w/in 500 m
Turbidity
waterfront
non-waterfront w/in 500 m
-0.164
(-0.688,0.361)
-0.164
(-0.687, 0.360)
-0.032**
(-0.064, -0.000)
-0.032**
(-0.064, -0.000)
-0.036***
(-0.057, -0.016)
-0.118
(-0.603, 0.366)
-0.119
(-0.602, 0.365)
-0.039**
(-0.073, -0.005)
-0.039**
(-0.073, -0.005)
-0.036***
(-0.057, -0.016)
-0.164
(-0.226, 0.533)
-0.164
(-0.226, 0.532)
-0.013
(-0.055, 0.029)
-0.013
(-0.055, 0.029)
-0.036***
(-0.057, -0.016)
-0.177
(-0.720, 0.366)
-0.177
(-0.719, 0.365)
-0.026
(-0.057, 0.005)
-0.026
(-0.057, 0.005)
-0.036***
(-0.057, -0.016)
0.138
(-0.240, 0.516)
0.137
(-0.240, 0.515)
0.002
(-0.31,0.036)
0.002
(-0.31,0.036)
-0.036***
(-0.057, -0.016)
Water clarity
waterfront
non-waterfront w/in 500 m
pH
waterfront
non-waterfront w/in 500 m
Trophic state index
waterfront
non-waterfront w/in 500 m
0.105***
(0.095,0.114)
0.026***
(0.017, 0.034)
0.779**
(0.019, 1.540)
-0.188
(-1.086,0.711)
-0.158***
(-0.181, -0.136)
0.015**
(0.001, 0.029)
0.031***
(0.028, 0.034)
0.012***
(0.010, 0.015)
0 4^9***
(0.183,0.654)
-0.188
(-1.086,0.711)
-0.135***
(-0.160, -0.110)
-0.001
(-0.011,0.010)
0.090***
(0.078, 0.102)
0.018***
(0.008, 0.028)
0.424
(-0.285, 1.133)
-0.379
(-1.084,0.326)
-0 177***
(-0.229, -0.124)
0.022
(-0.007,0.051)
0.182
(-17.398, 17.762)
0.042***
(0.025, 0.059)
1.986***
(-.840, 3.133)
0.008
(-1.405, 1.422)
-1.60***
(-0.184, -0.137)
0.018**
(0.003, 0.034)
0.155
(-6.102, 6.413)
0.028***
(0.020, 0.036)
2173***
(1.015, 3.331)
-0.334
(-1.126, 0.457)
-0.181***
(-0.209, -0.154)
0.029***
(0.007, 0.050)
177
83
13
6
18
*** p<0.01, ** p<0.05, * p<0.1.
where each cluster defined at the
Confidence intervals at the 95% level are displayed in parentheses,
housing market level as defined in the primary studies.
Observations weighted by cluster-adjusted RES weights,
74
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Table B 3. Unweighted OLS Meta-regression Results.
VARIABLES	(1A)	(2A)	(3A)	(4A)	(5A)	(6A)
waterfront
0.1279***
0.0972***
0.0908**
0.0911**
0.0547
0.0602*

(0.033)
(0.035)
(0.037)
(0.037)
(0.036)
(0.036)
estuary

-0.0841**

-0.0653

-0.0486


(0.033)

(0.048)

(0.075)
mean clarity


0.0195**
0.0068

-0.0504***



(0.009)
(0.013)

(0.019)
midwest




-0.1485***
-0.2673***





(0.046)
(0.064)
south




-0.1705***
-0.3242***





(0.040)
(0.095)
west




-0.1212
-0.0856





(0.085)
(0.085)
constant
0.0276
0.0854**
0.0071
0.0653
0.1928***
0.4247***

(0.027)
(0.035)
(0.029)
(0.051)
(0.046)
(0.098)
R-squared
0.055
0.079
0.073
0.080
0.122
0.146
Dependent variable: home price elasticity with respect to water clarity (Secchi disk depth).
***p<0.01, ** p<0.05, *p<0.1. Standard errors in parentheses. Regressions estimated using n=260 unweighted
observations and the OLS regression routine "regress" in Stata 14.
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Table B 4. Random Effect (RE) Panel Meta-regression Results: Clustered at Study Level.
VARIABLES (1A)	(2A)	(3A)	(4A)	(5A)	(6A)
waterfront
0.0954***
0.0539**
0.0461*
0.0440*
0.0334
0.0350

(0.023)
(0.026)
(0.024)
(0.026)
(0.031)
(0.029)
estuary

-0.0767**

-0.0509

0.0073


(0.032)

(0.056)

(0.024)
mean clarity


0.0210***
0.0102

-0.0053



(0.006)
(0.014)

(0.024)
midwest




-0.0415
-0.0520





(0.056)
(0.087)
south




-0.1183***
-0.1452*





(0.030)
(0.082)
west




-0.0915
-0.0906





(0.097)
(0.103)
constant
0.0308*
0.0938***
0.0131
0.0639
0.1397***
0.1631

(0.018)
(0.036)
(0.015)
(0.065)
(0.036)
(0.121)
Dependent variable: home price elasticity with respect to water clarity (Secchi disk depth).
***p<0.01, ** p<0.05, *p<0.1. Standard errors in parentheses. Random Effects Panel (RE Panel)
regressions estimated using the "mixed" routine in Stata 14, where the n=260 observations are weighted by
the cluster-adjusted Random Effect Size (RES) weights and the cluster specific effects are defined according
to the K=18 primary studies.
76
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Table B 5. Mundlak Model Meta-regression Results: Clustered at Study Level.
VARIABLES	(1A)	(2A)	(3A)	(4A)	(5A)	(6A)
waterfront
0.0681***
0.0631***
0.0632***
0.0619***
0.0601***
0.0599***

(0.006)
(0.010)
(0.009)
(0.010)
(0.010)
(0.010)
waterfront cluster mean
0.0828
-0.0471
-0.2119
-0.1985
-0.2553*
-0.2817

(0.066)
(0.113)
(0.162)
(0.170)
(0.147)
(0.186)
estuary

-0.0884*

-0.0457

0.0224


(0.052)

(0.067)

(0.028)
mean clarity


0.0166
0.0156

0.0133



(0.024)
(0.024)

(0.025)
clarity cluster mean


0.0270
0.0160

-0.0035



(0.030)
(0.034)

(0.031)
midwest




-0.1044***
-0.0914*





(0.027)
(0.048)
south




-0.2260***
-0.2210***





(0.073)
(0.078)
west




-0.0915
-0.0931





(0.097)
(0.087)
constant
-0.0102
0.1267
0.0989
0.1399
0.3683**
0.3487**

(0.044)
(0.105)
(0.070)
(0.109)
(0.145)
(0.144)
Dependent variable: home price elasticity with respect to water clarity (Secchi disk depth).
***p<0.01, ** p<0.05, *p<0.1. Standard errors in parentheses. Regressions estimated using n=260 observations.
Observations are weighted by the cluster-adjusted Random Effect Size (RES) weights, where each cluster is defined as one of
the K= 18 unique primary studies. Mundlak (1978) regressions estimated by first calculating cluster (primary study) means
for independent variables that vary within each cluster, and then by running the subsequent model via the "mixed" routine in
Stata 14, where the residual cluster-specific effect is maintained.
77
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Appendix C: Variance-Covariance Matrix for Random Effects Panel Model 3A.
Table CI. Variance-Covariance Matrix for Random Effects Panel Model 3A (from Table 3).
waterfront mean clarity constant
waterfront
mean clarity
constant
0.00040212


-0.00006911
0.00004695

-0.00008892
-0.00005674
0.00029653
78
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