Examining Implicit Price Variation for Lake Water Quality

1. Introduction

Lakes are an important resource providing drinking water, aesthetics, and recreational opportunities. However, nutrient pollution in US lakes is widespread, with 40% of lakes sampled in 2012 exceeding recommended levels of phosphorous and 35% exceeding recommended levels of nitrogen (USEPA2016). Phosphorous and nitrogen are natural components of lake ecosystems, but in high levels, impact water quality through increased algae growth and reduced water clarity. An important consideration for policy analyses is the value people place on protecting lakes from the “effects” of nitrogen and phosphorous on water quality (Corona et al.2020; Griffiths et al.2012; Keiser2019; Newbold et al.2018). One way to assess the economic effects is to study how water quality is capitalized in housing markets using hedonic models (Bishop et al.2020), and a number of studies have estimated the implicit prices of water quality embedded in sale prices of lake homes (e.g., Gibbs et al.2002; Michael et al.1996; Moore et al.2020; Walsh and Milon2016).

Hedonic price models require variation in water-quality measures to estimate an implicit price. As lake water quality changes slowly over time, researchers often use cross-sectional data where there is spatial variation in water quality across lakes (Gibbs et al.2002; Kashian et al.2006; Michael et al.1996; Walsh et al.2011; Wolf and Klaiber2017).¹ These studies typically identify sale observations for each lake occurring over several years in one or more distinct regions within a state. However, some recent studies consider only temporal variation within a single lake (Liao et al.2016; Singh et al.2018; Weng et al.2020). While individual lake and regional studies demonstrate that people value lake water quality; questions remain as to whether the value estimates can be scaled to support policy analyses at state and national levels.

Moore et al. (2020) took a broad geographic perspective, pooling data from 113 lakes across 32 states in a single hedonic model to estimate the “national” benefits of water quality in lakes. The water-quality data for their study is from a nationally representative sample of lakes identified in US EPA’s National Lakes Assessments in 2007 and 2012 (USEPA2009, 2016). The challenge for the Moore study is the reverse of that for the local/regional studies. Is the nation a market that can be represented in a single hedonic or is it better to represent the nation as a portfolio of regional market hedonics?

Thus, there is a tension between expanding the geographic scope of hedonic estimation to support state and national policy analyses at the risk of going to such a large area that markets with differing water quality capitalization impacts are accidentally merged in the estimation. Estimation at broad geographic scales potentially obscures important differences in implicit prices across markets. In fact, prior research suggests this heterogeneity is realized with substate implicit prices varying across distinct regions in New Hampshire and Maine (Gibbs et al.2002; Poor et al.2001). Despite these examples and other empirical evidence, Moore et al. (2020) conclude preferences for water quality are consistent across all 32 states and therefore nationally representative.

The goal of this paper is to further explore the implications of scaling up a hedonic model for lake water quality over a broad region, a la Moore et al., compared to the more standard approach of considering lakes within small geographic regions that might be assumed to be part of a common real estate market. We estimate implicit prices across multiple states in the northeast and upper Midwest in the Unites States of America to examine how the use of cross-sectional data over varying geographic areas affect implicit-price estimates. This line of investigation is important as the Clean Water Act (CWA) is the basis of national policies that protect water quality in lakes and guides state-level actions.² Thus, estimated implicit prices should accurately represent the impacts of water quality on lake housing markets.

We find implicit-price estimates are heterogenous at both substate and state-levels, which is not accounted for when estimating state-level or multistate hedonic models. We further find that the estimation results at a broad geographic scale can be driven by a single region within the broader geographic study area. The key insight from our research is that using a single hedonic model over a large geographic area may obscure important heterogeneity in implicit prices and therefore estimates of marginal values for water quality improvements. Regional heterogeneity is important because US EPA provides guidance for state programming while land use, which directly affects nutrient loadings to lakes, is controlled at the community and county levels.

2. Investigating Implicit-Price Spatial Heterogeneity

Selecting the appropriate spatial extent of a hedonic model is challenging, as researchers use many different approaches to define housing markets and submarkets, and much of the existing research primarily focuses on large metropolitan areas. Housing market areas have been defined by a variety of arbitrary geographic boundaries or by economic conditions relating to labor markets, household migration patterns, and the market search process (Jones2002). Housing markets, especially in metro areas, can be divided into submarkets based on topography, quality of homes, or other structural attributes (Islam and Asami2009). As the performance of different market segmentation approaches is assessed by the ability to predict sale prices, this type of housing market analysis almost always considers sales from within a single municipality (Goodman and Thibodeau2007). In this respect, there may be valid theoretical concerns with pooling data across broad geographic areas.

Such analyses and market delineation are more challenging for hedonics applied in rural areas where many lakes are located. There may be a density of residences located around a lake and then they become sparse as one moves away from a lake. In addition, sale prices of lake properties are driven by second-home buyers who may search across broad geographic areas, which is quite different from searches of primary homes in cites. Thus, for many environmental applications, where the focus is not on sale-price prediction but the estimation of the coefficients on an environmental amenity or disamenity variables, market boundaries are often aligned with geopolitical boundaries.

Consider the equation of a general hedonic model for a pooled housing market (1a) and for $J$ subregions within the market (1b).

where $P$ is the sale price of properties, $\beta$’s are vectors of implicit prices for property characteristics $z$, and $\epsilon$’s are random error terms. Pooling subregions to estimate a single hedonic imposes the assumption that ${\beta }_{ij}={\beta }_i,\forall j$. This strict assumption might be relaxed to ask whether $b_{ij}=b_i$ solely for the policy variable of interest and lake water quality in this paper. If the data pooling assumption, for a common real estate market, is not satisfied, the estimated coefficients may be biased, and spatial heterogeneity needs to be considered when developing policy insights. On the other hand, if the data pooling assumption is satisfied, estimating regional hedonics creates an unnecessary scaling step to provide information to support policy analyses at larger geopolitical scales.

There have been several large spatial scale hedonic analyses in environmental economics literature. Chay and Greenstone (2005) present one of the earliest national scale hedonic studies evaluating the effects of air quality. Additionally, with the rise of nationally availably property sale data from providers such as Zillow and CoreLogic, researchers are using national hedonic models to study other environmental amenities, including sea level rise (Bernstein et al.2019; Murfin and Spiegel2020), land use regulations (Leonard et al.2021), and residential heat pumps (Shen et al.2021).

In the context of lake water quality, Moore et al. (2020) and Zhang et al. (2022) estimate national scale models. Moore et al. (2020) investigated spatial heterogeneity effects on their water-quality coefficient and concluded that there was none. Zhang et al. (2022) consider the nationwide effects of harmful algal blooms (HABs). However, rather than estimating a single national hedonic model, they divide the country into seven multistate climate regions and examine regional heterogeneity.

These large geographic scale hedonic analyses studies address potential spatial heterogeneity across markets by including spatial fixed effects to control for location-specific attributes. An argument could be made that buyers of lakefront properties are not constrained by job markets, schools, and other factors that limit the search radius for primary homes, but, still, it is relevant to ask how much the spatial scale can realistically be expanded without obscuring important market heterogeneity differences. Thus, it is important to investigate the outcome of moving from limited spatial-scales consistent with the early environmental literature and the housing literature to large spatial scales in support of policy analyses designed to address benefits and costs of national policy guidance and state implementation of the guidance.

In the extant lake literature, Gibbs et al. (2002) estimated hedonics for four regions in New Hampshire each of which was closely aligned with a real estate multiple listing area. Likewise, Michael et al. (2000) report hedonic estimates for four areas in Maine that are aligned with multiple listing areas. Both these latter studies show substantial market heterogeneity in implicit-price estimates. In contrast, Moore et al. (2020) estimated a version of the stylized model (1a) and investigated heterogeneity at the state level vis-à-vis the national model by estimating water quality coefficients for Florida, Indiana, and Washington using interaction terms. As the coefficients on the interaction terms were found not to be significantly different from zero, the authors concluded that there is no regional heterogeneity in capitalized property impacts for Secchi depth across the 32 states in their sample.³

The conclusion in the Moore study not only contradicts the findings of Poor et al. (2001) and Gibbs et al. (2002), but diverges from other trends present in the literature. In Table 1, we compare capitalized property impacts of lake water quality from studies conducted throughout the country with similar model specifications. The impact of a 1m increase in water clarity for a lakefront home ranged from $1,000–$19,000 across subregions in Maine and New Hampshire, while the largest impact of $51,000 was found in Orange County, Florida. Researchers also found differences for individual lakes, $21,000 on Coeur d’Alene Lake in Idaho and $29,000 on Lake Mendota in Wisconsin. The Moore et al. national implicit-price estimate of $43,000 would substantially overestimate the capitalized effect of improved water clarity in in all regional applications except the Florida study. Turning to Chlorophyll-a (Chl-a), there appears to be less variation present with $3,000 in Wisconsin and $6,000 in Florida when considering only lakefront properties.

There are other empirical examples that pooling hedonic estimation over large geopolitical regions may be problematic. Bastian et al. (2002) find that differences in the value of fish, elk, and land cover diversity capitalized in land prices vary across the state of Wyoming. Even when modeling a single urban county, Goodman and Thibodeau (2003) show that pooling submarkets at the zip code and census tract level reduces prediction accuracy, concluding “smaller is better” in regards to the spatial scale of the hedonic model. Yet, there is limited knowledge on how much implicit prices vary when estimated at different geopolitical scales. This topic is important for national policy makers that want to ensure benefits estimation is based on robust and repeatable research methods. At the state level, officials want to ensure that important heterogeneities are not missed that may guide the allocation of lake water quality management funds across different regions of their states.

3. Study Areas and Data

The study areas consist of six states throughout the northeast and upper Midwest: Maine, Michigan, Minnesota, New York, Vermont, and Wisconsin (Figure 1). We focus on lakes in this area due to the availability of water-quality data at the state and substate levels. Once merged with property-sale data, the lakes and numbers of observations vary considerably across states. Thus, for multistate analyses, we consider differences at the state level with observations from Minnesota, New York, and Wisconsin with data from Maine, Michigan and Vermont grouped.⁴

The density of lakefront property sales in Minnesota and New York allows investigation at focused substate levels that might be presumed to represent different real estate markets. The two Minnesota substate regions include Otter Tail County and the Twin Cities metro area (excluding Hennepin County). Otter Tail is a rural county in western Minnesota dominated by agriculture and undeveloped land, whereas the Twin Cities region is made up of primarily urban and suburban neighborhoods. These two regions allow us to compare potential differences in water-quality implicit prices between rural and urban communities within a single state. In New York, we define the Adirondacks region using six counties where the dominant land use surrounding the lakes is a forest. Sale observations for the Finger Lakes region span seven counties in central New York where the surrounding area is predominantly agricultural with a few small cities. While not technically one of the Finger lakes, we include Oneida Lake in this region due to the proximity to this group of lakes.

3.1. Lake characteristic and water-quality data

Lake characteristic and water-quality data come from the Lake Multi-Scaled Geospatial and Temporal (LAGOS-NE) Database that provides spatially explicit data for lakes and surrounding areas with a broad range of water-quality measurements throughout the northeast and upper Midwest (Soranno et al.20152017).⁵ We use the LAGOS-NE R package developed by Stachelek et al. (2019) to access lake characteristics and other lake-identifying information from the LOCUS modules (Soranno and Cheruvelil2017a) and water-quality data from the LIMNO module (Soranno et al., 2017). Corresponding geospatial data is available in the GIS module (Soranno and Cheruvelil2017c).

The key water quality variables are Secchi depth (Secchi hereafter) and Chl-a concentration (Chl-a hereafter). These measures, respectively, reflect water quality as observed by homeowners and a common quality measure considered by limnologists. Secchi is a measure of water clarity frequently used as an indicator of water quality in hedonic models with homeowners willing to pay more for increased water clarity (Calderón-Arrieta et al.2019; Michael et al.2000; Wolf and Kemp2021). On the other hand, algal blooms are a disamenity to homeowners that are associated with high concentrations of Chl-a, and studies report negative implicit prices associated with higher Chl-a concentrations (Liu et al.2017; Walsh and Milon2016; Weng et al.2020).

We identified lakes in our study area larger than 4 ha with Secchi or Chl-a samples taken between June and September from 2000 to 2013. We consider only summer samples to prevent possible measurement bias toward lakes that do not freeze in the wintertime. Most lakes had more than one water quality measurement in a given summer, so we used the mean summer sample for those lakes.^6,7 It is assumed that home buyers observe water quality in the lake prior to purchase, but there is no conclusive information on what time frame is used in this decision making (Michael et al.2000). We, therefore, use the measurement in the year prior to the sale similar to Boyle and Taylor (2001) and Weng et al. (2020).

Summary statistics for the variables used in the estimation subset at the state and substate levels are reported in Table 2. Secchi data are more widely available in LAGOS-NE resulting in a larger share of total observations, 6,499 compared to 5,520 for Chl-a. The average water quality is 2.89m for Secchi and 17.90ug/L for Chl-a, but these values vary substantially across states. New York has the clearest water, 4.44m on average, and Wisconsin has the poorest water quality with an average of 35.99ug/L of Chl-a compared to 5.68ug/L found in New York. In Minnesota water quality also varies at the substate level, with the average Secchi in the Twin Cities half as deep as in Otter Tail and Chl-a — four times larger. In terms of lake area, Minnesota features many relatively small lakes less than 1,000 ha on an average, whereas the largest lakes are the Finger Lakes, averaging more than 14,000 ha.

As people choose sale price and water quality concurrently when they purchase a lakefront property, endogeneity of Secchi and Chl-a cannot be ruled out. We use two variables, forest buffer and total nitrogen, to serve as instruments for both Secchi and Chl-a. These variables are available in the LAGOS-NE database in the GEO model (Soranno and Cheruvelil2017d). LAGOS-NE identifies the percentage of area within a 500m buffer surrounding the lake covered by each National Land Cover database (NLCD) class. We sum the percentage of areas covered by the three NLCD forest classes for the 2001, 2006, and 2011 layers. These are matched, respectively, to sales during the periods 2001–2005, 2006–2010, and 2011–2014. LAGOS-NE further provides data for total nitrogen deposition for the hydrologic unit code 8 (HUC*) subbasin for 2000, 2005, and 2010. These were similarly matched to sales for 2001–2004, 2005–2009, and 2010–2014, respectively.

3.2. Property sale data

Often, state entities are the sources of parcel data with local municipalities providing tax records and sales data. As a result, the municipalities we include in this study are those that provide public access to tax and sales records or, in the case of Michigan, local tax assessors were willing to assist in accessing these data (see Table A.1). We accessed the data through government websites, parcel database downloads, and computer-assisted mass appraisal (CAMA) systems managed by private companies. Parcel data were used to identify properties with lake frontage. We then used parcel numbers for these lakefront properties to identify sales records and assessment data for property characteristics in each municipality’s online repository.⁸ In the Twin Cities, we accessed historical parcel data that contained the most recent tax records and sales for each year.⁹ Michigan property sales and tax records come directly from local assessors.¹⁰${}^{,}$¹¹ From the sales data we identify arm’s-length sales of single-family homes between 2001 and 2014 and record sale prices in 2018 dollars using the regional yearly consumer price index data from FRED.¹² The average sale price in our samples is approximately $260,000. The most expensive homes are found in the Adirondacks, with houses selling for more than $500,000 on average, while the least expensive are in the Finger Lakes at less than $200,000.

A key component of this project was harmonizing housing data across a heterogeneous set of data sources. For a robust analysis, we focus on arm’s-length sales of lakefront properties classified as single family or seasonal residential recreational.¹³ Yet these definitions are not always well-defined across counties and states, with some municipalities providing limited zoning information. In rural counties with larger parcels, it was also necessary to consider rural residential properties, including small farms and rural land. Since not all data sources flagged arm’s-length or qualified sales, we removed the top percentile of sales per state. Then, we divided the sales between land sales and property sales and removed the top and bottom percentile of price per acre and price per square foot, respectively, for each state. A further challenge of multiple data sources across states was an incomplete set of property attributes. Some counties provided details on a wide range of property attributes that could be incorporated into the analysis, while others provided limited or no information. Given the importance of controlling for the size and quality of a property, we drop sales that do not include lot size, square footage of house and house age.

3.3. Other data sources

Data on other covariates that might affect sale prices were also accessed. Neighborhood attributes including census tract, block group, and median income for block group come from the 2000 and 2010 US Census data. We include the distance from the nearest Walmart as these stores are often popular shopping locations in rural areas and located near other retail establishments. We find the distance in miles from each property address to the nearest Walmart using Google Maps.¹⁴ Weather data are from the National Centers for Environmental Prediction (NCEP) Climate Forecast System Reanalysis (CFSR) (Saha et al.2010).¹⁵ This dataset includes daily temperature summaries for 2001–2014 from weather stations throughout our study area, which we averaged over the summer months in a given sale year for each weather station.

4. Model Specification and Data Groupings for Model Estimation

Our analysis consists of models estimated at three different spatial scales: multistate models, state-level models, and substate models (Figure 2). Here, we present the general specification of the models and in the following sections discuss each of the regional-level models in more detail.

While economic theory does not guide the specification of hedonic-price functions (Kuminoff et al.2010), there is evidence that nonlinear expressions for water quality may be appropriate. For example, Smeltzer and Heiskary (1990) find that as water clarity increases, people cannot see the increases beyond a certain point. Bishop et al. (2020) also recommend using a nonlinear price function as the best practice when estimating hedonic models for environmental amenities. These recommendations are based on conclusions by Ekeland et al. (2004) and Kuminoff et al. (2010) that equilibrium price functions are generally nonlinear and nonlinear models control for bias better than linear models. As such, it is common in the literature to express sales price as a natural log (Bin et al.2017; Liu et al.2017; Moore et al.2020; Wolf and Klaiber2017). We choose a double-log functional form for all continuous variables, whereby the estimated effects of these independent variables are elasticities. We specify the model :

where Price is the CPI adjusted sales price in 2018 $s, WQ is the water-quality measure of interest (Secchi or Chl-a), Area is the surface area of the lake, Temp is the mean summer ambient air temperature in the location of the lake, P is a vector of property characteristics, Y indicates sale year by census tract fixed effects, and Q indicates sale quarter fixed effects. Property characteristics include lot size, square footage of living area and age of home, and median income of the block group is a neighborhood characteristic. Secchi and Chl-a are investigated in separate equations to avoid collinearity issues, as in Weng et al. (2020).

Given the time span of our study (2001–2014) and wide geographic coverage, it is important to control for sale patterns over time, spatial dependence, and potential omitted variable bias. When a quasi-experimental framework is unavailable, repeat sale analyses are often considered the best way to control for these factors (Kuwayama et al.2022). However, outside of urban areas, data are often too limited to use this approach. Thus, temporal patterns are often addressed by sale-year (Walsh and Milon2016), sale-quarter (Moore et al.2020) or month (Weng et al.2020) fixed effects or a time trend (Mueller and Loomis 2008). Spatial dependence and omitted variables can be addressed by including a wide range of location attributes (Liu et al.2019), fine scale spatial fixed effects (Zhang et al.2022; Weng et al.2020), or spatial-lag and spatial-error models (Artell2014; Singh et al.2018). Kuminoff et al. (2010) show spatial-fixed effects minimize bias from omitted spatial variables when compared to spatial-lag and spatial-error models and Bishop et al. (2020) recommend incorporating spatial dummies as the best practice. We include sale-year by census-tract fixed effects to control for distinct temporal patterns in sales prices specific to individual locations and control for potential omitted variable bias relative to property location, as well as sale-quarter fixed effects to control for seasonal price variation.

There are growing concerns in the water quality literature about potential endogeneity of environmental quality and measurement error in hedonic estimation (Wolf et al.2022; Moore et al.2020; Keiser2019). The potential for endogeneity arises in lake applications because people choose homes across lakes, where both price and water quality vary. Thus, the water-quality choice is not exogenous to the hedonic estimation. Measurement error can arise when the water-quality measure, sampled in one part of the lake at a given time, is not reflective of the water quality observed by the home buyer. If either of these is the case, the water quality variable can be correlated with the error term, and the resulting hedonic coefficient estimate may be biased.

We address these concerns by implementing an instrumental-variables approach. Thus, in addition to estimating with traditional ordinary least squares (OLS), two-stage least squares (2SLS) estimation is also employed. The first stage of the 2SLS approach (3a) purges the water quality variable of potential endogeneity with a projection matrix of the instruments ($P_Z$), and the second stage (3b) uses the resulting data matrix to compute the 2SLS elasticity estimates (Greene2003).¹⁶

While Wolf et al. (2022) and Moore et al. (2020) both use in-lake measurements of nitrogen and phosphorus as instruments for lake water quality, these measurements were not available for all lakes in our samples. Instead, we include the amount of forested land within a 500 m buffer around the lakes and the total nitrogen deposition in the HUC8 subbasin. Forest buffers around lakes absorb nutrients that reduce clarity and increase algal production; thereby, larger forest buffers protect water quality. Nitrogen concentration in upstream watersheds indicates the levels of this nutrient potentially flowing into the lake that can compromise water quality.¹⁷

4.1. Multistate models

The Multistate model combines all observations into a single model, a laMoore et al. (2020), with the implicit assumption of homogeneity of the lakefront property markets across geographic regions (Eq. (2)). We then estimate a model with state fixed effects (SFEs) interacting with the water quality variables, relaxing the homogeneity assumption in the policy variable of interest, which we refer to as the Multistate/SFE model:

where S denotes the SFEs. Minnesota, which includes the largest number of observations, is the omitted SFE. The estimated coefficients on the interaction terms indicate whether there are significant differences in the water-quality elasticity relative to Minnesota. While these models allow for heterogeneity in the effects of water quality, it continues to impose homogeneity in the effects of other independent variables. Since there are very few observations in Maine, Michigan, and Vermont, we estimate Multistate/SFE1 without these observations. In Multistate/SFE2 we reintroduce these observations, including an interaction term that collects the observations from these states into a single indicator. If the estimated elasticities for water quality are spatially robust, one would expect the coefficients on the state interaction variables to be insignificant.

To further investigate the sensitivity of the hedonic (Eq. (2)) to state-level aggregation, we estimate the Multistate model dropping observations from each state one at a time. These models are referred to as Remove States. If the estimated elasticities for water quality are spatially robust, one would expect the water-quality elasticity estimates to not be affected by removal of state observations.

4.2. State and substate models

Next, we estimate state-level models (again using Eq. (2)) for Minnesota, New York, and Wisconsin each singly. This estimation relaxes the assumption of homogeneity in the effects of all regressors, but we continue to focus on the elasticity estimates for water quality. These models will be referenced by the state names. If elasticity estimates differ across states, this would be the evidence of heterogeneity supporting estimation using data from smaller geographic regions.

Finally, we estimate regional models (again relying on Eq. (2)) for the Otter Tail and Twin Cities areas in Minnesota and for the Adirondacks and Finger Lakes areas in New York. The Minnesota and New York data are neatly partitioned between the substate regions with sufficient observations to estimate separate hedonics. These elasticity estimates for water quality are compared to the estimated elasticities for Minnesota and New York, respectively. Once again, robustness of the elasticity estimates will support hedonic estimation at the larger geographic scale and a lack of robustness is the evidence of important regional differences.

5. Model Results

In the Multistate model, we find positive and significant elasticity estimates for Secchi and negative and significant estimates for Chl-a (Table 3).¹⁸ We investigate endogeneity of both water quality variables and evaluate the strength and validity of the instruments, forest buffer around the lake and nitrogen deposition in the watershed. Bolded 2SLS elasticity estimates in Table 3 indicate that water quality is endogenous and instruments are strong and valid at the 5% level. The instrumental-variable analysis indicates strong instruments, and the models are not over identified for Secchi and Chl-a, but only endogeneity in the Chl-a model (see Table B.1). Thus, we report OLS and 2SLS models for all data groupings to consider whether endogeneity is present and the impact on elasticity estimates.

5.1. Investigating heterogeneity in the multistate model

We consider results from the Multistate/SFE models to investigate potential state-level heterogeneity in water-quality elasticities. The OLS and 2SLS elasticity estimates for Secchi match the corresponding estimates in the Multistate model in terms of sign and significance (Table 3). However, the Multistate/SFE1 model indicates that water quality is endogenous while the Multistate/SFE2 does not indicate endogeneity (see Table B.1).¹⁹ When considering the results for the interaction terms between water quality and the SFEs, there is only evidence of an interaction effect for New York in the 2SLS estimation of the Multistate/SFE2 model. These results mostly suggest that the effects of water quality are not heterogenous at the state level, i.e., the homogeneity assumption for the Multistate model may hold for Secchi.

Moving the Multistate/SFE estimation results for Chl-a, a slightly different pattern of results arises. The Multistate/SFE1 OLS and 2SLS elasticity estimates for Chl-a match the corresponding estimates in the Multistate model, but this is not the case for the Multistate/SFE2 estimation where the elasticity is not significant in the 2SLS results (Table 3). Water quality is not endogenous in the Multistate/SFE1 model for Chl-a. No-state interaction coefficient estimates are individually significant in the Multistate/SFE models. The results for Chl-a suggest the effects of water quality are not heterogenous at the state level, i.e., the homogeneity assumption holds for the Multistate model.

Overall, we place more confidence in the results of the Multistate/SFE1 model results relative to the Multistate/SFE2 model estimates. This is because of the small number of observations from Maine, Michigan, and Vermont, individually and collectively, and the statistical challenges when there are four potentially endogenous variables. Considering the Multistate/SFE1 estimation results, Secchi is endogenous, and Chl-a is not. One might not find this result surprising since Secchi represents what buyers and sellers see when they view a lake and Chl-a is a limnological measure via instrumentation.²⁰

To further investigate heterogeneity in the context of the Multistatemodel, we remove observations one state at a time for Minnesota, New York, and Wisconsin while considering the impact on the coefficients for Secchi and Chl-a (Table 4). The instrumental variable analysis implies that Secchi is not endogenous, and Chl-a is endogenous. Again, bolded 2SLS elasticity estimates indicate that water quality is endogenous and instruments are strong and valid at the 5% level. (The Multistate coefficient estimates for Secchi and Chl-a are replicated in the bottom row of Table 4 for comparison purposes.)

Notable differences in elasticity estimates for Secchi and Chl-a arise when Minnesota observations are removed from the data. For Secchi, the OLS elasticity estimate (no endogeneity) is nearly 30% smaller than the Multistate estimate when Minnesota data are removed from the estimation and is not significant (Table 4). While the 2SLS elasticity estimate for Chl-a (endogeneity present) remains significant when Minnesota data are removed, it is about 76% larger than in the Multistate model. The elasticity estimates are robust to removing observations for New York, Wisconsin, and Maine/Michigan/Vermont. This is an important result as it suggests the Multistate results are sensitive to, and perhaps driven by, the observations from Minnesota.

A couple preliminary insights arise here. First, from the results in Table 3, the 2SLS estimates are much larger than the OLS estimates for both Secchi and Chl-a. While endogeneity was only found in one of three models for Secchi and for Chl-a, these results show that the estimated magnitude of lake water quality capitalized into property values can be influenced by investigator modeling decisions and the effect might be greater than spatial heterogeneity perhaps. Second, considering the results of Table 4, spatial heterogeneity may be driven in part by the availability of property and environmental data. That is, hedonic models are not random representations of affected populations, but rather, driven by properties that are sold, the availability of these sale data and the ability to match with the environmental variable of interest. While more data are becoming available in both realms, both remain limited.

5.2. Investigating state and substate heterogeneity

As hedonic models are most often estimated on local/regional scales that may align with a real estate market such as a city, county, or multiple-listing area, we turn to estimation at smaller spatial scales three states (Minnesota, New York, and Wisconsin) and two substate regions within Minnesota and New York. Thus, rather than asking how state data affect estimation of water-quality elasticities at a larger geographic scale, we here ask how estimation outcomes vary by region.

For both Secchi and Chl-a, the Minnesota estimates match the Multistate model results in terms of sign, magnitude, significance, and endogeneity outcomes (Table 5).²¹ (The Multistate coefficient estimates for Secchi and Chl-a are replicated in the bottom row of Table 5 for comparison purposes.) This is not the case for the New York where both Secchi and Chl-a are endogenous, and the estimated elasticities are much larger than for Minnesota (and the Multistate model). The Secchi elasticity is not significant for Wisconsin, while Chl-a is significant, endogenous, and very much larger than those for New York, Minnesota, and the Multistate models. These results demonstrate considerable heterogeneity in the effects of water quality on sale prices at the state level and the similarity of the Minnesota estimates to those from the Multistate model are again notable.

Moving to the substate results, we find even more heterogeneity, which is consistent with the heterogeneity present in the prior literature. Within Minnesota, the Otter Tail elasticities for Secchi and Chl-a have the expected signs, are significant, endogenous, and are much larger than the state estimates (Table 5). Only the OLS Secchi elasticity is significant for the Twin Cities and is not endogenous, but it is much smaller than the state estimate.

For New York, neither Secchi nor Chl-a are significant for the Adirondacks area (Table 5). While both Secchi and Chl-a are significant with the expected signs in the Finger Lakes area, neither of them demonstrates endogeneity, which contrasts with the state level where both were endogenous. Like for the Otter Tail region in Minnesota, the Finger lakes elasticity estimates are much larger than the corresponding New York estimates.

Thus, both substate sets of estimation demonstrate substantial heterogeneity in elasticity estimates relative to state and Multistate estimation.

5.3. Robustness checks

To assess the robustness of the model estimates, we consider temporal and spatial dependencies in housing markets. First, we investigate the effects of the Great Recession (2008–2010) similar to Wolf et al. (2022), by introducing interactions between water quality and dummy variables for sales prior to 2008 (Pre2008) and after 2010 (Post2010):

Considering the OLS elasticities for Multistate, state and substate models, the Great Recession did not affect the Secchi elasticity estimates, except for perhaps the Finger Lakes coming out of the recession (Table 6). Whereas the Chl-a elasticity estimates are only significant before and after the recession for the Multistate model and note that the elasticities before ($-$0.15) and after ($-$0.17) the recession are nearly the same. As before, the Minnesota elasticities estimates match the estimates from the Multistate model with one important exception, the Chl-a estimate is only significant post-recession.

Additionally, we consider spatial-lag and spatial-error models (Walsh et al.2011; Walsh and Milon2016; Artell2014). Given differences in distances between sales across geographic areas, we use the four nearest neighbors to construct weight matrices and run spatial diagnostics against the OLS models.²² We find limited and mixed evidence of spatial dependence (see Table D.1). We say limited evidence because not all data groups experience spatial dependence and mixed evidence because, in cases where there is evidence of spatial dependence, not all tests indicate spatial dependence. Spatial error was identified for Secchi in the New York model, for Chl-a in the Minnesota and Wisconsin models, and spatial lag was identified in the Finger Lakes model. Most importantly, we do not find substantial differences between our OLS and corresponding spatial-dependence estimates. The New York elasticity estimate for Secchi remains insignificant as does the Wisconsin elasticity estimate for Chl-a. The Minnesota elasticity estimates for Chl-a are $-$0.10 for both the OLS and spatial-error models. For the Finger lakes, the elasticity estimates are $-$0.22 and $-$0.24. These results are consistent with prior findings by Walsh et al. (2011) and Singh et al. (2018) which report little difference between Secchi elasticity estimates after introducing spatial lag and error terms.

5.4. Capitalized impacts on property values

Moving beyond elasticity estimates, from a policy analysis perspective, the change in capitalized values of residential properties is the key measure. We consider a 1-m increase in Secchi and a one-ug/l decrease in Chl-a. Note the decrease in Chl-a is a smaller increment than the increase in Secchi so one would expect the Secchi capitalized values to be larger.

The Secchi increases in capitalized values of lake properties range from $17,000 for the Finger Lakes region to $197,000 for New York (Table 7). The New York elasticity estimate was unusually large, and this capitalized value is not believable. We do not have a clear explanation for this anomaly but can offer a couple thoughts. It may be that nitrogen deposition aggregated at the HUC8 level is not a suitable instrument for Secchi in New York due to collinearity in the Finger Lakes region. When we estimate this model without nitrogen as an instrument, Secchi is no longer significant. Thus, the upper bound from our estimates might be $42,000 for the Otter Tail region, which is comparable to the national estimate from Moore et al. (2020) of $43,000 and is within the range of the other estimates reported in the literature (see Table 1).²³

Because many location-specific factors can influence house prices, we also consider the percentage change in house prices relative to the average CPI adjusted sale price for each sample in Table 2. The relative magnitudes change considerably between the implicit prices and percentages. For example, with the 1m Secchi increase. The Twin Cities has a larger implicit price than the for the Multistate but a smaller percentage. In contrast, the Finger Lakes has a smaller implicit price then the Multistate but a larger percentage.

The Chl-a capitalized value ranges from $6,000 for the Multistate model to $40,000 for New York. Again, the New York elasticity estimate is unusually large and perhaps the upper bound is more realistically $18,000 for Otter Tail. The range from the existing literature is $3,000 to $6,000 (Table 1), which makes even the Otter tail estimate appear large. However, relative to the average house prices, the percentage change in Otter Tail is not much larger than in the Finger Lakes.

The bottom line is that the elasticity estimates demonstrate considerable heterogeneity that could affect policy decisions and suggest caution in how hedonic models are estimated and the estimates are used to support policy analyses. Further, while the implicit prices provide dollar amounts for conduct of benefit-cost analyses, they miss the relative market-specific importance shown by the percentage changes. More on this in the discussion and conclusion to follow.

6. Discussion and Conclusion

This study presents a detailed analysis of hedonic estimation at broad spatial scales to capture the capitalized value of water quality in lakefront properties. Most critically, we detect spatial heterogeneity in water quality elasticities at the state level relative to the multistate model, and at the substate levels relative to the state and multistate models. Further, our results indicate that only considering SFE as done by Moore et al. (2020) may not be sufficient to detect spatial heterogeneity.

Implicit in our results is that the effects of spatial heterogeneity on coefficient estimates and thereby capitalized effects on property values are influenced by available data and modeling decisions. A caveat of our study results is that the Minnesota data appear to be the key driver of the Multistate model estimate. Yet, within Minnesota, there is substantial heterogeneity between the two substate regions. Data can be a limiting factor due to availability, cost of acquisition, and investigator choices. Modeling is purely driven by investigator choices. Thus, outcomes that might over or underestimate the capitalized impact by substantial amounts are driven by data availability and investigator choices. The former is important, because hedonic data are not representations of affected populations but are driven by data availability. It is well known that investigator choices affect empirical outcomes. Both concerns heighten the need for robustness investigations and careful selection of estimates to move forward to support decision making.

Decisions to protect or improve lake water quality are made at three spatial scales of government. The US EPA sets guidance and provides support for actions by state environmental agencies. State environmental agencies must also follow guidance from state laws, which affect actions by local communities. Local communities are responsible for land-use regulations that can be detrimental to lake water quality or the last line of defense to protect lake water quality. The US EPA likely needs national value estimates to support economic analyses of laws and regulations, while state agencies are likely more focused on state-level data, and local communities want to know economic effects in their communities. These differences in jurisdiction speak, collectively, to all the models we estimated in this paper, but which model is correct or best? Substate models may closely align with nebulous boundaries of real estate markets, while larger spatial scale models likely include data from multiple markets. Regional models to support regional decision making are likely supported by their alignment with real estate markets defined by multiple-listing areas. However, when moving to state and national scales, it is an open question of whether scaling up many regional models or just estimating an aggregate model is best.

We suggest the appropriate modeling approach may depend on the nature of the proposed policy. Our results demonstrate how aggregate models can provide average effects over large areas that may be appropriate for policy analyses over broad geographic regions (e.g., national or state levels where policy decision are made and implemented). However, in such applications it is crucial that data be well-distributed across the aggregated areas to avoid any one subregion to drive the model results and that spatial fixed effects are included to control for remaining spatial heterogeneity. This approach seems more tractable that attempting to estimate small, spatial-scale hedonic models and scaling them to the larger geographic region of interest. For policies targeting smaller geographic regions (e.g., communities or counties where land-use regulations are implemented and enforced), we suggest regional studies are likely more appropriate. Thus, there is a tension between the limited spatial scale of hedonic estimation and the broader spatial scale of policy analyses that is unlikely to be resolved analytically; analysts and decisions makers using the empirical outcomes should be aware of the potential errors and limitations.

Acknowledgment

We acknowledge recommendations of the reviewers that helped strengthen this paper.

Notes

¹ Nicholls and Crompton (2018) provide an extensive literature review of hedonic studies prior to 2018 for different water-quality measures and aquatic features.

² See the following for more information about CWA and state specific water quality standards: https://www.epa.gov/laws-regulations/summary-clean-water-act, and https://www.epa.gov/wqs-tech/state-specific-water-quality-standards-effective-under-clean-water-act-cwa

³ Moore et al. (2020) did not estimate interaction terms for all states due to limited numbers of state-level observations.

⁴ While Poor et al. (2001) report results for four regions in Maine, we are using more recent data that does not have the same water-quality data coverage as the Poor study.

⁵ More information is available at: https://lagoslakes.org/.

⁶ Among lakes greater than 4 ha, 3.2% and 2.5%, respectively, had a single Secchi or Chl-a measurement for the given sample year.

⁷ We also ran each model using minimum and maximum observations within calendar years with similar results to the means analyses.

⁸ Code used to collect online data is available at https://github.com/swedkm/Housing-Data2020. This code makes use of multiple open-source python packages, including Selenium, Beautiful Soup, and Requests (Reitz2020; Richardson2020; Software Freedom Conservancy2021).

⁹ We merged the shapefiles for each county and year for lakefront parcels using Geopandas (Jordahl et al.2020).

¹⁰ We would like to thank Robert Englebrecht, Andrew Giguere, and Clayton McGovern for their assistance in this project.

¹¹ Lakefront parcels were clearly identified in Leelanau and Cheboygan datasets. For Evangeline, we geocoded parcel addresses using ArcGIS Pro to identify lakefront properties.

¹² FRED data located at https://fred.stlouisfed.org/.

¹³ This classification is common for lakefront properties that are not the primary residence of the homeowners but are occupied temporarily for recreational purposes. See https://www.revenue.state.mn.us/sites/default/files/2011-11/acp_07_resuse.pdf

¹⁴ Sample code available at: https://github.com/swedkm/Housing-Data2020.

¹⁵ NCEP data obtained from https://globalweather.tamu.edu/.

¹⁶ See Greene (2003) for further reference.

¹⁷ More information concerning hydrologic units is available at: https://water.usgs.gov/GIS/huc.html.

¹⁸ The open source package linear models (Sheppard et al.2021) and statsmodels (Seabold and Perktold2010) were used for OLS and 2SLS estimation, respectively, for all models except the Multistate/SFE models.

¹⁹ Estimating the Multistate/SFE models using 2SLS was challenging. In addition to instrumenting water quality, these models require instrumenting each of the interaction terms with water quality resulting in three (Multistate/SFE1) and four (Multistate/SFE2) potentially endogenous. Assessing the strength of the instruments requires evaluating minimum eigenvalue statistics and 2SLS relative bias critical values, which only exists in the literature for at most three endogenous variables. The 2SLS estimation for both Multistate/SFE models was performed in Stata 13.1, which provides minimum eigenvalue statistics when there is more than one potentially endogenous variable. A 2SLS relative bias critical value is not available in the literature when more than three endogenous regressors are present. However, the critical value at 5% bias threshold for three endogenous regressors and six instruments is much larger than the minimum eigenvalue statistic (12.20 compared to 0.47, respectively) leading us to conclude they are weak instruments (Stock and Yogo2005).

²⁰ For Secchi, the Multistate model does not exhibit endogeneity but the Multistate/SFE1 model does. It is relevant to note that we investigated endogeneity significance at the 5% and 1% levels due to the large sample sizes, but the Multistate model would contain endogeneity if it was tested at the 10% level. For Chl-a, endogeneity is not identified for the Multistate/SFE1 model due to weak instruments. For further insight, please see Table B.1.

²¹ Full model results for each state and substate region are reported in Tables C.1 and C.2, respectively.

²² We use PySAL spreg (Rey and Anselin 2007) to run the models and apply diagnostic tests as outlined by Anselin (2017).

²³ CPI adjusted, see: https://fred.stlouisfed.org/.