Convergent Validity of Satellite and Secchi Disk Measures of Water Clarity in Hedonic Models

1. Introduction

Freshwater lakes are an important natural resource in the United States because they provide aesthetic value and recreational opportunities to residents and visitors, help regulate the climate, and are diverted daily to generate power and grow crops. Near-lake and waterfront homeowners are perhaps the biggest beneficiaries of these ecosystem services given their direct, year-round access. These benefits are reflected in higher sale prices for homes located near or adjacent to lakes and can vary based on the water clarity for a given lake. Waterfront properties have been observed to decrease by as much as $23,000 from a 10% reduction in water clarity, for instance (Walsh et al. 2017).¹ It is not unreasonable to expect that programs designed to maintain or improve water quality are of particular importance to local residents.²

In general, water quality across the United States is expected to deteriorate because of elevated summer temperatures caused by climate change (Paerl and Huisman 2008), increased nutrient loads (Verhoeven et al. 2006), and waterfront development (Poor, Pessagno, and Paul 2007). Over one-third of U.S. lakes have excessive concentrations of nitrogen or phosphorous, and nearly 40% have detectable levels of microcystin, a freshwater toxin produced by harmful algal blooms (U.S. Environmental Protection Agency 2012). State and federal agencies are actively monitoring water quality in thousands of lakes (National Water Quality Monitoring Council 2019) to prevent and mitigate future damages.

Secchi depth has been the go-to method for water quality monitoring in many U.S. water-bodies.³ More than 41,000 Secchi measurements have been recorded across 7,000 lakes, rivers, and estuaries since 1994 by the National American Lake Management Society. The U.S. Geological Survey (USGS), U.S. Environmental Protection Agency (EPA), and U.S. Department of Agriculture also maintain a national water quality database that contains over 700,000 historic Secchi depth measurements taken from 35,000 sites (National Water Quality Monitoring Council 2019). Secchi depth measurements are often available when other water quality indicators are not because of the simplicity and accessibility of the testing procedure and equipment. It is unclear whether federal and state agencies will continue to fund Secchi depth monitoring at its current rate given the expansion of detailed water quality data from satellite images (Chipman et al. 2004; Olmanson, Bauer, and Brezonik 2008).

One potential reason public agencies may shift resources away from Secchi depth monitoring is because of how time- and labor-intensive it is. Practitioners must tow a boat to the lake, drive the boat to an open area, slowly lower the Secchi disk into the water, record the disk measurement, and repeat the process at other locations around the lake. Resource managers are limited in the number of lakes they can physically monitor due to budgetary constraints, likely leaving them with an incomplete picture of water quality in their jurisdiction. Satellite monitoring presents a lower-cost alternative to in situ sampling and allows for greater spatial and temporal monitoring coverage. Several states have already transitioned toward statewide water quality monitoring using satellite imagery (Wisconsin Department of Natural Resources 2015; Roush 2017; Minnesota Pollution Control Agency 2018), with reports usually released every one to five years. Despite this transition, it is unclear if satellite estimates of water clarity are a suitable or better substitute for traditional measures of water quality such as Secchi depth.

To answer this question, we combined housing transactions data (2013–2016) from two northern Wisconsin counties with in situ and satellite-derived water-clarity data. We focus on northern Wisconsin because of its extensive lake network, active monitoring community, and large lakefront property market. These characteristics allow us to estimate separate water quality capitalization estimates—one for each water transparency measure—with the same set of housing transactions. We make three contributions to the literature from this analysis: (1) we find that near-lake homeowners are more responsive to satellite estimates of water clarity, resulting in implicit prices up to 11% larger in magnitude; (2) we show the degree of agreement between implicit prices is heterogeneous across lake trophic status, with the greatest difference observed on very turbid or very clear lakes; and (3) we demonstrate that differences in aggregate valuation estimates can be policy-relevant—under a scenario in which regional water clarity is improved by 10%, property values are predicted to increase by an additional 12.5% when satellite estimates of water clarity are used in place of more traditional measures.

2. Literature Review

Using environmental quality data derived from remote-sensing imagery has become common in the nonmarket valuation literature. Remote-sensing imagery has been linked with property transactions data to better understand how changes in tree coverage (Netusil, Chattopadhyay, and Kovacs 2010; Sander, Polasky, and Haight 2010; Franco and Macdonald 2018), land use (Nivens et al. 2002; Gibbons, Mourato, and Resende 2014), and viewsheds (Paterson and Boyle 2002; Cavailhès et al. 2009) are capitalized in nearby home and land values. Satellite imagery has been paired with survey response data to better understand how differences in harmful algal bloom concentrations (Wolf, Georgic, and Klaiber 2017; Wolf et al. 2019) and forest coverage (Brainard, Bateman, and Lovett 2001) affect recreation patterns.

This expansion of spatially and temporally detailed environmental quality data has also proven especially useful when valuing environmental amenities/disamenities where in situ sampling is either nonexistent, unreliable or sporadically taken. Soo (2018), for instance, combines satellite estimates of air quality with residential location information in Indonesia to recover some of the first-ever revealed preference air quality valuation estimates for Southeast Asia. Similarly, Freeman et al. (2019) use satellite imagery to estimate the economic value of a one-unit reduction in PM 2.5 (fine particulate matter) concentrations across Chinese households.

Despite this improvement in the quality and accessibility of data, usage of in situ water quality monitoring data remains common in the nonmarket valuation literature. In the last few years, in situ Secchi readings have been attached to recreational (Angradi, Ringhold, and Hall 2018) and residential property data (Liao, Wilhelm, and Solomon 2016; Bin, Czajkowski, and Villarini 2017; Kemp, Ng, and Mohammad 2017) to better understand the economic value of water quality. Relatively few valuation studies have derived estimates of water quality using satellite imagery (Moore, Provencher, and Bishop 2011; Wolf, Georgic, and Klaiber 2017; Wolf et al. 2019). This imbalance is likely to shift in the future as more state and federal agencies responsible for collecting water quality data transition toward satellite-based monitoring programs. There are two concerns with this transition that could have substantial effects on valuation estimates and lake management decisions. First, if satellite and in situ measures of water clarity are weakly correlated, policy makers may be apprehensive to form policy using satellite-based valuation estimates because the data may be considered inferior or unreliable. Second, satellite estimates of water clarity need to be at least as strongly correlated with “true” water quality as ground-based measures, otherwise this transition would introduce more attenuation bias into the model. The first concern has been discussed extensively in the literature (Cox et al. 1998; Nelson et al. 2003; Olmanson, Bauer, and Brezonik 2008; Hicks et al. 2013), whereas the second has not.

The level of agreement between in situ water quality measurements and their satellite counterparts can vary substantially across studies. Dörnhöfer et al. (2018) computed concentrations of chlorophyll a from satellite data and found (using in situ readings as a benchmark) that satellite measures were roughly 20% higher than their in situ counterparts. Adding to the dilemma, Nelson et al. (2003) demonstrated that the agreement between satellite and on-the-ground measurements of Secchi depth worsened as the variance of water clarity in the calibration dataset increased.

In comparison with studies that only predicted water clarity for one or a few lakes (Pattiaratchi et al. 1994; Cox et al. 1998), Nelson et al. (2003) found their model’s goodness-of-fit to be much lower (r² = 0.43) when predicting water clarity for 93 Michigan lakes.

Olmanson, Bauer, and Brezonik (2008), on the other hand, were able to closely match satellite data with field-collected Secchi depth measurements (r² = 0.78) using 20 years of Landsat imagery, spanning more than 10,000 lakes in Minnesota. Similarly, Hicks et al. (2013) found a strong relationship between surface reflectance signatures and three in situ water clarity measures, yielding goodness-of-fit measures (r²) that ranged between 0.67 and 0.94 for 10 monitored lakes in New Zealand. Despite a good deal of variability between sampling methods, satellite monitoring of water resources is expected to improve in the future because of advancements in remote-sensing technology and the recent launch of Landsat 8 (U.S. Geological Survey 2018). These advancements will probably strengthen the predictive capabilities of satellite monitoring and lessen the need for calibration with field data.

Concerning the second problem, it is not clear whether remote sensing data are as accurate for predicting true water clarity as in situ monitoring data are. Remote sensing is distant by its very nature, while on-the-ground water quality monitoring is immediate. Further compounding on this issue is the disagreement observed between immediate objective and subjective measures of water clarity. In the authors’ experience, it is not uncommon to read citizen monitoring reports with Secchi disk readings of just 1 ft. but with subjective comments that read: “Beautiful, could not be nicer.” This lack of correspondence raises several questions that have mostly not been addressed in the literature.⁴

The study by Poor et al. (2001) is one exception. They considered the convergent validity of subjective and objective measures of water clarity in a hedonic pricing context by combining housing transactions from four real estate markets in Maine with Secchi disk measures and individual perceptions of water clarity collected from mail surveys. The objective measure of water clarity (Secchi depth) was found to be a better predictor of sale price in two of the four housing markets. This was somewhat surprising given that one might expect subjective evaluations to drive consumer behavior. The authors speculated that it was perhaps due to homeowners consistently underreporting the tails of the water-clarity distribution in their mail survey responses, which reduced the efficiency of the subjective parameter estimates. These findings suggest the convergent validity of different sampling methods is not as clear as initially expected and is an ongoing research question.

3. Econometric Model

We use the familiar first-stage hedonic model by Rosen (1974) to examine homeowners’ responsiveness to traditional and satellite measures of water clarity. Interactions between home buyers and sellers define an equilibrium hedonic price schedule that relates the price of a home with the bundle of underlying attributes that define it. Included in this bundle are structural characteristics of the home (i.e., bathrooms, square footage, age), nearby public amenities (i.e., parks, shopping centers), and other locational attributes, including water quality. To isolate water clarity’s effect on nearby property values, we specify the hedonic price equilibrium as follows: [1] where P_ijt is the price of home i sold in location j at time t, WC_it is a measure nearby water clarity, LA_i is the surface area of the nearest lake, LakeProximity_i is a vector of lake proximity measures, and X_i is a vector of structural characteristics. For brevity, we abbreviate the interaction between the natural log of water clarity (ln WC_it) and the natural log of lake area (ln LA_i as WCLA_it. The decision to interact water clarity with lake area is due to the expectation of there being a positive relationship between water-clarity premiums and lake size, which parallels specifications used by Michael, Boyle, and Bouchard (2000), Boyle and Taylor (2001), Gibbs et al. (2002), Krysel et al. (2003), Zhang and Boyle (2010), and Zhang, Boyle, and Kuminoff (2015). We further log-transform water clarity because it was found to provide a better statistical fit than other linear and semi-log specifications and is consistent with the expectation that improvements in water transparency are more noticeable as water-clarity levels decrease (Smeltzer and Heiskary 1990; Gibbs et al. 2002; Walsh, Milon, and Scrogin 2011; Walsh et al. 2017). Also, Cropper, Deck, and McConnell (1988) find the semi-log and double-log models performed better than more complicated models when either misspecification or proxy variables are present.

Year fixed effects Y_t, month fixed effects M_t, and spatial fixed effects L_j are also included in the hedonic price function, while β is a vector of parameters to be estimated, and ε_ijt is an error term. The inclusion of spatial fixed effects controls for time-invariant factors that influence a home’s value (i.e., average property tax rates, school quality, proximity to urban amenities) and mitigates unobserved sources of bias by limiting identification of the key parameters—β₁ and β₂—to come from only spatial and temporal variation in the area defined by the spatial fixed effect. The addition of year and month fixed effects is also important because they control for aggregate and seasonal shifts in the housing market.

The marginal value from an improvement in water clarity is expected to diminish, and eventually equal 0, as a property becomes more distant from an affected waterbody (Walsh, Milon, and Scrogin 2011; Wolf and Klaiber 2017). This has led researchers to make one of two decisions: (1) limit the sample to only include lake adjacent or near-lake homes (Tuttle and Heintzelman 2015; Zhang, Boyle, and Kuminoff 2015), or (2) include all housing transactions in a given housing market but spatially limit water clarity’s effect by interacting it with a distance band dummy (Walsh et al. 2017; Wolf and Klaiber 2017) or a continuous measure of lake proximity (Liu, Oplauch, and Uchida 2017). We implement both approaches with the former, our preferred specification, taking the following form: [2]

Notice that LakeProximity_i is decomposed into two terms in equation [2]: LakeAdjacent_i and . The first term—LakeAdjacent_i—is an indicator variable (0/1) for whether a property is adjacent to a lake and controls for any premium that is attributed to owning a lakefront home. Homes that are near but nonadjacent to a lake are also expected to receive a premium; we control for these additional benefits through a second lake proximity term, , which assumes the benefits of lake proximity increase at an increasing rate as one moves closer to a lake.⁵

To investigate whether the inclusion of nonproximate homes influences our parameters of interest, we expand our dataset to include homes outside of lake communities. This modification also requires equation [2] be updated to include interaction terms between our two measures of water clarity and a distance band dummy: [3]

The interaction terms—WCLA_it*NearLake_i and In WC_it*NearLake_i—limit the influence of water clarity to only adjacent and near-lake homes, where NearLake_i is an indicator variable (0/1) for whether a property is located near a lake. NearLake_i is also included by itself in equation [3] to control for any additional lake proximity effects that are not already taken into account by LakeAdjacent_i or . Because lakefront homes are both near and adjacent to a lake, the value of their proximity will be captured by the sum of β₃ and β₄, while the value from living near but not adjacent to a lake will be captured by the sum of β₄ and . To determine which measure of water clarity is a better predictor of house price, we follow Poor et al. (2001) by conducting a non-nested J-test (Davidson and MacKinnon 1981). We begin by simplifying and restating equation [2] in terms of the two water-clarity measures: [4] [5] where the new subscript on WCLA and WC denotes whether the satellite or Secchi disk measure of water clarity is employed, A_k is a vector of control variables (i.e., structural characteristics, temporal and spatial fixed effects, lake proximity variables) mentioned earlier, Ψ and Λ are vectors of coefficients, and ε and ξ are normally distributed error terms with a mean of 0 and variance of σ².⁶ Given this updated notation, the four-step process to conduct a J-test can be explained as follows. First, equation [5] is estimated and used to predict the natural log of house price . A second equation is estimated by regressing the natural log of house price on and all of the covariates from the right-hand side of the alternative model (equation [4]): [6]

This constrained model can then be used to test the hypothesis of whether the model with WCLA_SAT and ln WCLA_SAT should be rejected in favor of the model with WCLA_DISK and ln WC_DISK. If the null hypothesis from equation [6] is rejected (i.e., H₀ : α = 0), this provides evidence that homeowners are more responsive to changes in on-the-ground measurements of water clarity compared with satellite estimates. The third and fourth steps follow along the same line of logic. Specifically, the third step requires equation [4] be estimated and then used to predict the natural log of housing prices . In the fourth step, the natural log of housing price is regressed on along with the right-hand side of the alternative model (equation [5]): [7]

If the null hypothesis from equation [7] is rejected (i.e., H₀: δ = 0), then the equation with WCLA_DISK and ln WC_DISK should be rejected in favor of the equation with ln WC_SAT and WCLA_SAT. This finding would provide evidence that homeowners are more responsive to changes in satellite estimates of water clarity compared with on-the-ground measurements.

The hypothesis tests from equations [6] and [7] need to be considered jointly to determine which measure of water clarity is best at predicting housing prices. There are four potential outcomes of a J-test, which are as follows: (1) if the null hypothesis for α is rejected and the null hypothesis for δ is not rejected, then it can be concluded that the equation with Secchi depth measurements of water clarity is preferred; (2) if the null hypothesis for α is not rejected and the null hypothesis for δ is rejected, then it can be concluded that the equation with satellite estimates of water clarity is preferred; (3) if the null hypothesis for α and δ are both rejected, then both specifications are rejected in favor of the other and the J-test provides little guidance in determining which model is best; (4) finally, if the null hypothesis for α and δ are not rejected, then neither specification is preferred over the other, leading to a similar conclusion as (3).

As a final point of comparison, we calculate the implicit price for both clarity measures by taking the derivative of equation [2] with respect to either WC_SAT or WC_DISK: [8] [9] Both implicit prices are assumed to increase with lake size and home value but decrease with ambient clarity conditions. A 1 ft. improvement in Secchi depth, in other words, is expected to be of greater value to homeowners living near a turbid lake as compared to homeowners living near a clear lake, ceteris paribus. This inverse relationship between p_SAT and WC_SAT and p_DISK and WC_DISK aligns with the aforementioned expectation that homeowners are more responsive and cognizant of water-clarity changes as ambient clarity conditions worsen.

4. Data

Vilas and Oneida Counties in northern Wisconsin (pictured in Appendix Figure A1) were selected as our study area due to the availability of detailed housing transaction data and extensive water-clarity data derived from Secchi disk readings and satellite imagery.⁷ The sale price and structural characteristics of single-family homes sold between 2013 and 2016 were collected from the Wisconsin Department of Revenue. Housing features recorded in this dataset include square footage, number of bathrooms, and age of a home as well as indicators for the presence of a fireplace, garage, and deck. Homes that were labeled delinquent or vacant or had extreme physical characteristics were excluded from the sample to mitigate bias introduced by these types of properties.⁸ Properties that were sold more than once over a 12-month span were also removed to eliminate potential biases associated with house flippers.

Each housing transaction was then geo-referenced using parcel shapefiles collected from the Wisconsin Statewide Parcel Map Initiative. Knowing the exact spatial location of each property allowed us to create a distance to the nearest lake measure using GIS and hydrology shapefiles maintained by the USGS. Lakes smaller than 10 acres in size were excluded from this calculation as many of these water bodies were not consistently monitored for water clarity, did not have an active housing market nearby,⁹ or lacked a public access point (Wisconsin Department of Natural Resources 2016). Indicators for lake adjacency (< 40 m) and whether the property was near a lake (< 500 m) were then defined using this distance measure.¹⁰ Proximity measures to other nearby amenities/disamenities—including highways, parks, and boat ramps—were attached to housing transactions using GIS.¹¹ Finally, census boundary shapefiles were overlaid onto parcel shapefiles to identify each home’s census block group. Five-year (2013-2017) estimates of census block group-level socioeconomic characteristics were then merged to each housing transaction using data collected from the American Community Survey (U.S. Census Bureau 2017). A total of 54 census block groups were identified in our study region, with the average block group comprising 390 to 2,140 people. Summary statistics for structural and locational attributes of homes in the study region are shown in Table 1, and a description of the variables is provided in Appendix Table A1.

The average property in Vilas and Oneida sold for approximately $224,000, had 1.75 bathrooms and 1,370 ft.², was 40 years old, and was located approximately 400 m away from a 5 km² lake. Sixty-six percent of these homes were located within 500 m of a lake, and 6% were lake adjacent. The average near-lake home (< 500 m), in comparison, was more likely to have a deck and a fireplace, was located closer to a boat ramp, and was valued approximately $50,000 higher. In addition, 9% of these homes were lake adjacent, which is similar to other rural housing markets (Wolf and Klaiber 2017).

Satellite-derived water-clarity data and Secchi disk readings, denoted by WC_SAT and WC_DISK, respectively, for 104 lakes in Vilas and Oneida Counties were collected from the Wisconsin Department of Natural Resources (WDNR). Satellite-derived water-clarity data are only available between the months of June and October, while year-round Secchi disk measurements are available for some, but not all lakes. We drop Secchi disk readings that are taken between November and May to keep both datasets as similar as possible and eliminate concerns stemming from differences in the timing of when measurements are taken. A total of 3,141 Secchi disk reading and 1,337 satellite measurements were available after this cleaning process. The minimum water-clarity measurement from the closest lake, taken during the 12 months before the month of the sale, was attached to each housing trans-action.¹² We exclude water-clarity readings taken during the month of the sale to remove the possibility that future water clarity is used as a predictor of housing price. Finally, lake characteristics (i.e., trophic status,¹³ surface area, presence of a public boat ramp) were obtained from the WDNR and merged with the housing transactions. Summary statistics of lake characteristics and the two measures of water clarity are displayed in Appendix Table A2 and Table 2, respectively, and Figure 1 shows the location of all 104 lakes in the study area.

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Figure 1

Housing Transactions and Lakes in Study Area

Substantial variation in water clarity needed to identify our key parameters of interest is observed in both the Secchi disk readings and satellite measurements. The average housing transaction in Vilas and Oneida Counties had a minimum ground-based measurement of water clarity of 7.07 ft. and 7.14 ft., respectively, which is considered to be a characteristic of lakes with good water quality in Wisconsin (Lillie and Mason 1983). Minimum satellite clarity measures were similar across both counties but tended to be less disperse than their ground-based counterparts. The clarity measures ranged in value from about 1 ft. to more than 20 ft. and were highly correlated ( r ≥ 0.70 for both counties).¹⁴

There are a few factors that could help explain why there is water-clarity variation in Vilas and Oneida Counties. Several local media outlets reported the emergence and spread of harmful algal blooms in Vilas and Oneida Counties during the sample timeframe (Jablonski 2013; Krall 2014), which can be caused by leaky septic systems, runoff from farms and wastewater treatment plants (Moberg 2018), and climate-induced eutrophication (Paerl and Huisman 2008). Oneida County officials have also echoed concerns about agricultural and residential runoff by listing reductions of nonpoint source water pollution as their fourth highest goal in their most recent land and water resource management plan (North Central Wisconsin Regional Planning Commission 2019).

Increasing or decreasing water levels is also a source of water-clarity change (Canfield and Bachmann 1981), although this could introduce bias into the model as water levels are also directly correlated with housing price. We collected rainfall and flooding data from the National Oceanic and Atmosphere Administration to investigate this concern and found only one flood and four heavy rainfall events were reported in Vilas and Oneida Counties between 2012 and 2016, with total property damages from these events estimated to be $2,000. In comparison, the average county in Wisconsin experienced 2.65 floods, 2.12 flash floods, 2.51 heavy rainfall events, and over $950,000 in property damages over the same time period (National Centers for Environmental Information 2019). Data collected from the National Flood Insurance Program (NFIP) further suggest very few floods have occurred in Vilas and Oneida Counties in general. Only 5 NFIP claims have been made cumulatively (through July 2019) by homeowners in Vilas or Oneida Counties, which is significantly lower than the cumulative claim count of 115 for the average county in Wisconsin (National Flood Insurance Program 2019).¹⁵

Turning our attention back to Table 2, it is interesting to note that when water-clarity measures are aggregated to an annual mean (as opposed to an annual minimum), the satellite and ground-based measures begin to diverge. The average WC_DISK measure is between one-half and 1 ft. larger than the corresponding WC_SAT measure across both counties due in part to the number of housing transactions with high water-clarity values. Only 4 housing transactions have a WC_SAT reading greater than 20 ft., while 42 housing transactions have a WC_DISK reading greater than 20 ft. Despite these differences, the correlation coefficients and percentage of households where |WC_DISK − WC_SAT|>1 ft. is similar regardless of the aggregation method. Approximately 30% of properties had a satellite estimate of water clarity that was within 1ft. of the Secchi depth measurement, while 71% were within 1 m (3.28 ft.). Poor et al. (2001) report a similar finding when comparing subjective and objective measures of water clarity. Specifically, they find 18% of near lake homeowners in Augusta, Maine, had a subjective water clarity measure that was within 1 ft. of the objective measure (Secchi depth), despite a high degree of correlation between the two (r = 0.65).

5. Results

Results for three versions of the base specification (equation [2]) are provided in Table 3. Property attributes, lake features, block group characteristics, and month, year, and county fixed effects are all included in model 1. Models 2 and 3 build on this initial specification by swapping the block group characteristics and spatially coarse county fixed effect with block group fixed effects. Inclusion of fine-scale fixed effects has become a common econometric strategy to mitigate or remove omitted variable bias in a hedonic price function (Kuminoff, Parmeter, and Pope 2010; Abbott and Klaiber 2011) as they control for observed and unobserved neighborhood-level characteristics of a home that are time-invariant (i.e., proximity to urban areas, average property tax rates, school quality). They also limit identification of the hedonic price coefficients to come from variation within a given area; in this case, only within-block group variation is used to identify the hedonic price function coefficients.

We also include in model 1 measures of water clarity and lake surface area, and an interaction between the two using satellite estimates (column 1) or ground-based measures (column 2). For models 2 and 3, we remove either ln WC (model 2) or ln LA (model 3) as block group fixed effects are added in.¹⁸ This is done to prevent issues arising from multicollinearity as including ln WC, ln LA, WCLA, and block group fixed effects in the same specification leads to imprecisely estimated water-clarity coefficients. This problem has been frequently encountered in the water quality valuation literature (Boyle, Poor, and Taylor 1999; Poor et al. 2001; Krysel et al. 2003; Walsh, Milon, and Scrogin 2011) and has been addressed in a similar manner. Specifically, modelers remove the level water clarity and lake surface area terms and focus exclusively on the interaction term (Michael, Boyle, and Bouchard 2000; Boyle and Taylor 2001; Gibbs et al. 2002; Zhang and Boyle 2010; Zhang, Boyle, and Kuminoff 2015).

Turning our attention to the variables of interest—ln WC and WCLA—we find that improvements in water clarity are positively capitalized in a home’s value through the interaction term, while the level water-clarity term is statistically indifferent from 0. The range of water-clarity coefficients in Table 3 suggest a 10% improvement in water clarity will appreciate home values by 0.52% ($1,405) to 1.35% ($3,648) for properties located on an average-sized lake (5.97 km²).19 Overall, the WCLA coefficients and appreciation estimates are larger when satellite measures of water clarity are used in place of ground-based measures, although the difference is not statistically significant in any model.

Coefficients on structural and locational characteristics across all three models (Appendix Table A3) exhibit the expected sign. Property values increase at a decreasing rate as either parcel lot acreage or structural square footage increase. Near-lake homes with a deck or a fireplace are valued on average more than homes without these features. Proximity to nearby (dis)amenities is also an important consideration for home buyers. Lake adjacency, for instance, can add substantially more value to a home than being near but non-adjacent, while proximity to areas with heavy automobile traffic, such as highways and boat ramps, are predicted to devalue a property.

Finally, the results from the Davidson and MacKinnon J-test reveal which measure of water clarity is preferred for models 1-3:

• model 1: reject H₀ : α = 0, and reject H₀: δ = 0 (p_α = 0.03; p_δ= 0.01),

• model 2: fail to reject H₀: α = 0, and reject H₀: δ = 0 (p_α= 0.40; p_δ= 0.08),

• model 3: fail to reject H₀: α = 0, and reject H₀: δ = 0 (p_α= 0.96; p_δ= 0.06).

As mentioned in Section 3, rejection of H₀: δ = 0 in conjunction with a failure to reject H₀: α = 0 indicates that the preferred model includes ln WC_SAT and WCLA_SAT. It can therefore be concluded that ln WC_SAT and WCLA_SAT is a better predictor of house price than ln WC_DISK and WCLA_DISK in models where fine-scale fixed effects are employed. This conclusion cannot be made in model 1, where both null hypotheses are rejected at the 5% significance level, indicating that one measure of water clarity cannot be considered superior over the other.

6. Conclusion

The importance of water quality monitoring at the local, state, and federal levels has been highlighted by the increased threat to freshwater lakes across the United States. In situ water quality monitoring strategies are limited because of how time- and labor-intensive traditional monitoring practices are. Monitoring agencies have begun to shift their resources toward a lower-cost alternative in response to this situation, which involves estimating water clarity using satellite imagery. The network of monitored lakes has expanded as a result of this shift, leading to an increase in the availability of spatially and temporally detailed water-clarity data.

Future water-clarity valuation studies are likely to use these data, as similar trends have been observed in the land use and tree coverage valuation literature, where satellite estimates of environmental quality data are readily available. It is unclear if satellite imagery is a better or even suitable substitute for traditional measures of water quality, such as Secchi depth. To answer this question, we create a novel dataset with housing transaction information merged with a satellite and ground-based measure of water clarity. Separate hedonic price equilibria are estimated—one for each water-clarity measure—to determine which measure homeowners are more responsive to.

We find the average near lake homeowner in Vilas and Oneida Counties in Wisconsin to be more responsive to changes in water clarity derived from satellite images, with satellite-derived implicit prices approximately 11% higher than their ground-based counterparts. Satellite estimates of water clarity are also found to be statistically equivalent and, in some cases, superior to traditional water-clarity measures in predicting housing price. Finally, we find that the disagreement between satellite and ground-based valuation estimates can lead to meaningful differences in aggregate outcomes. Aggregate property value gains associated with a 10% improvement in regional water clarity, for instance, are 12.5% larger when satellite estimates of water clarity are used in place of more traditional measures. This difference could lead to substantially different policy outcomes depending on which clarity measure is used.

Overall, we believe these are encouraging results as the availability of satellite data on environmental quality continues to expand. Indeed, increased access to remote sensing data will likely make it possible to determine environmental damages or benefits of mitigation in communities where in situ sampling is not an economically viable option. Much of the developing world suffers from impaired bodies of water. Remote sensing may provide a lower-cost method to determine the costs associated with these impairments. Our findings further suggest that additional funding for satellite-based water quality monitoring is a worthwhile venture for budget-constrained monitoring agencies. Similarly, these results will hopefully lessen the concerns of policy makers and homeowners that satellite-based water quality measures are somehow inferior.