Theoretical framework

The basic framework for the hedonic property price model was provided by Rosen (Reference Rosen1974), where consumers choose between differentiated products with multiple attributes to maximize their utility. In applying this model to housing markets, let Z = (z ₁, z ₂, …, z _n) be a vector of observable attributes where z _i measures the amount of the ith attribute of a house that includes property attributes (such as age, square footage, and number of bedrooms), neighborhood attributes (such as distance to schools and highways), and environmental attributes. Water supply unreliability (WSR) is included as a separate attribute that combines both neighborhood and environmental elements. Here, we assume that information about WSR is obtained by consumers of housing from BWNs that have been issued prior to the sale (BWN₀).

Assuming a single competitive housing market and full information, the housing consumer decision problem is described as

(1)$$\matrix{ {{\rm max}\,U\langle X, \;Z, \;{\rm WSR}\{ {E( {{\rm BW}{\rm N}_0} ) , \;\;{\rm DE}[ {E( {{\rm BW}{\rm N}_0} ) } ] } \} } \cr } \rangle $$

(2)$$\matrix{ {{\rm subject\;to}\;Y = X + P\{ {Z, \;{\rm WSR}[ {E( {{\rm BW}{\rm N}_0} ) } ] } \} + {\rm DE}[ {E( {{\rm BW}{\rm N}_0} ) } ] } \cr } $$

where X is the numeraire good, WSR is a measure of water supply unreliability which is positively related to consumer expectations as derived BWN₀, Y is income, P is the hedonic price schedule, and DE represents the associated defensive expenditures incurred (i.e., bottled water and water filter) when the water supply is unreliable so that (dDE)/(dBWN₀) > 0.

Furthermore, we assume an expectation function:

(3)$$\matrix{ {E( {{\rm BW}{\rm N}_0} ) = 0\;\quad \forall \quad {\rm BW}{\rm N}_0 \le {\rm \pi }\;} \cr } $$

(4)$$\matrix{ {E( {{\rm BW}{\rm N}_0} ) > 0\quad \forall \quad {\rm BW}{\rm N}_0 > {\rm \pi }\;} \cr } $$

where π represents a threshold on the number of BWN that housing consumers use when deciding whether water service provided to the house is deemed unreliable. When the number of BWNs issued prior to the sale is higher than π, then expectations of unreliable water supply are formed about the impacted property. Water supply unreliability will generate negative utility to the consumer, leading to a decrease in the price of the house.

Assuming that E(BWN₀) > 0, the first-order conditions lead to:

(5)$$\underbrace{{\displaystyle{{\displaystyle{{\partial U} \over {\partial {\rm WSR}}}\cdot \displaystyle{{{\rm \partial }{\rm WSR}} \over {\partial E( {{\rm BW}{\rm N}_0} ) }} + \displaystyle{{\partial U} \over {\partial {\rm WSR}}}\cdot \displaystyle{{\partial {\rm WSR}} \over {\partial {\rm DE}}}\cdot \displaystyle{{d{\rm DE}} \over {dE( {{\rm BW}{\rm N}_0} ) }}} \over {\displaystyle{{\partial U} \over {\partial X}}}}}}_{{{\rm Marginal\;rate\;of\;substitution}}}-\underbrace{{\displaystyle{{\partial {\rm DE}} \over {\partial E( {{\rm BW}{\rm N}_0} ) }}}}_{{{\rm Marginal\;cost\;of\;DE}}} = \underbrace{{\displaystyle{{\partial P} \over {\partial {\rm WSR}}}\cdot \displaystyle{{d{\rm WSR}} \over {dE( {{\rm BW}{\rm N}_0} ) }}}}_{{{\rm Marginal\;implicit\;price}}}$$

Equation 5 shows that, at the optimum, the marginal implicit price of BWN₀ from a hedonic property price model (RHS) reflects the marginal rate of substitution between water supply unreliability and the numeraire good X on the LHS along with a second term that measures the marginal change in defensive expenditures associated with BWN₀ in order to achieve water supply reliability.

Rosen (Reference Rosen1974) also described the consumer's maximum ‘bid’ function for a house θ(Z;U, Y), where utility and income are fixed. This function represents the amount a consumer is willing to pay for different attribute vectors for a given utility–income index. Substituting the budget constraint into the utility function, we obtain:

(6)$$ \eqalign{ \matrix{ {U\langle Y-\theta \{ {Z, \;{\rm WSR}[ {E( {{\rm BW}{\rm N}_0} ) } ] } \} -{\rm DE}[ {E( {{\rm BW}{\rm N}_0} ) } ] , \;Z, }\cr \;{\rm WSR}\{ {E( {{\rm BW}{\rm N}_0} ) , \;\;{\rm DE}[ {E( {{\rm BW}{\rm N}_0} ) } ] } \} \rangle = \bar{u}\;} \cr } $$

If we implicitly differentiate θ( ⋅ ) with respect to BWN₀, we obtain:

(7)$$\matrix{ {\displaystyle{{\displaystyle{{\partial U} \over {\partial {\rm WSR}}}\cdot \displaystyle{{\partial {\rm WSR}} \over {\partial E( {{\rm BW}{\rm N}_0} ) }} + \displaystyle{{\partial U} \over {\partial {\rm WSR}}}\cdot \displaystyle{{\partial {\rm WSR}} \over {\partial {\rm DE}}}\cdot \displaystyle{{d{\rm DE}} \over {dE( {{\rm BW}{\rm N}_0} ) }}} \over {\displaystyle{{\partial U} \over {\partial X}}}}-\displaystyle{{\partial {\rm DE}} \over {\partial E( {{\rm BW}{\rm N}_0} ) }} = \displaystyle{{\partial \theta } \over {\partial {\rm WSR}}}\cdot \displaystyle{{d{\rm WSR}} \over {dE( {{\rm BW}{\rm N}_0} ) }}\;} \cr } $$

Combining conditions (5) and (7), we find that the marginal bid or the marginal WTP (MWTP) for a housing characteristic is equal to its equilibrium marginal price. The first-stage hedonic property price function P( ⋅ ) represents an envelope of a consumer's bid functions in equilibrium. Therefore, it can be used to obtain the marginal value that consumers place on housing attributes. This means that the marginal price of an attribute is equal to the MWTP for that attribute (Taylor Reference Taylor, Champ, Boyle and Brown2003). Econometrically, we obtain the marginal price of any attribute by regressing the price of the house on the attribute of interest, i.e.,BWN₀ as a measure of WSR.

Empirical framework

Models stemming from the above theoretical framework could be estimated using OLS. However, recent studies adopt alternative estimation techniques to account for spatial dependence, i.e., the existence of a functional relationship between what happens at one location and what happens elsewhere (Anselin Reference Anselin2013). This issue may occur in hedonic property price models when houses in one location are impacted by the prices or characteristics of nearby houses compared with houses that are farther apart (Anselin and Lozano-Gracia Reference Anselin, Lozano-Gracia, Mills and Patterson2009). Also, spatial dependence may occur in hedonic property price models because of the presence of common practical issues such as measurement errors in explanatory variables, omitted variables, and other forms of model misspecification (Baumont Reference Baumont2004). Traditional OLS hedonic property price models do not consider the spatial dimension of housing price data, and ignoring spatial dependence may result in biased and inconsistent or inefficient estimates depending on the type of spatial process involved with the model (LeSage and Pace Reference LeSage and Pace2009).

Therefore, spatial econometric techniques are used to address this problem and to obtain reliable coefficient and standard error estimates.Footnote ² To address this, we account for potential spatial price spillovers using the spatial lag model as suggested by the Lagrange multiplier test results in Table 1. Thus, we can write the model as

(8)$$\matrix{ {\ln ( P ) = {\rm \rho }W\,{\rm ln}( P ) + ZB + {\rm \varepsilon }} \cr } $$

where ln(P) is the natural log of the sale price, Z is a N × K matrix of property characteristics, B is a K × 1 vector of coefficients, W is a N × N spatial weight matrix associated with the autoregressive process in house prices and in the error term, and ɛ is a N × 1 spatial autoregressive error.

Table 1.

Lagrange multiplier (LM) diagnostics for spatial dependence

A spatial weight matrix defines the relationship between neighbors in the model (i.e., how the value in one location in the system is affected by the values in other locations). This relationship can be based on either the distance or the contiguity between observations. For the spatial weight matrix, we use K-nearest neighbor (KNN) weights, in which all observations have the same numbers of neighbors (K) irrespective of the distance. This method is recommended to avoid the possibility of islands (i.e., observations without neighbors), which may result in loss of degrees of freedom, since all unconnected observations will be eliminated in the spatial model (Anselin and Bera Reference Anselin, Bera, Ullah and Giles1998). Also, this type of spatial weight matrix has been used frequently in other hedonic studies (e.g., Mueller and Loomis Reference Mueller and Loomis2008; Pandit et al. Reference Pandit, Polyakov, Tapsuwan and Moran2013; Netusil, Kincaid, and Chang Reference Netusil, Kincaid and Chang2014; Liu, Opaluch, and Uchida Reference Liu, Opaluch and Uchida2017). We also use a row-standardized weight matrix. For the number of neighbors K, we follow LeSage and Pace (Reference LeSage and Pace2009), and we choose the number that maximizes the value of a log-likelihood function. Using the log-likelihood function criterion, we find that using five nearest neighbors results in the maximum log-likelihood value.Footnote ³

In our data, BWNs are not equally distributed across housing price transactions (Table 2). On average, properties transacted at the lower-price quantiles experience more water supply reliability problems than the properties sold at the higher-price quantiles. Therefore, we focus our analysis and look at the impact of water supply unreliability across the price distribution instead of assessing its impact with a focus on the mean. To do this, we employ the quantile regression approach (see Koenker and Bassett Reference Koenker and Bassett1978; Koenker and Hallock Reference Koenker and Hallock2001; Hao and Naiman Reference Hao and Naiman2007) to examine the impact of housing characteristics at different points (quantiles) across the distribution of housing prices.

Table 2.

Boil Water Notices (BWNs) means by price quantile

Unlike OLS, quantile regression specifies changes in the conditional quantile, which allows us to observe how housing characteristics are valued differently by consumers of housing at different price ranges. Similar to equation 8, the spatial quantile lag model is expressed as

(9)$${\rm ln}( P ) = {\rm \rho }( {\rm \tau } ) W\,{\rm ln}( P ) + ZB( {\rm \tau } ) + {\rm \varepsilon }( {\rm \tau } ) $$

which will result in estimates based on the conditional quantile, taking account of the spatial effect at the same time.

To estimate the spatial quantile model, the two-stage quantile regression approach proposed by Kim and Muller (Reference Kim and Muller2004) is used to account for the endogeneity in the spatially lagged variable. In the first stage, the spatially lagged exogenous variables WZ and Z are used to predict the spatially lagged endogenous variable W ln(P) at an individual quantile. The predicted $\widehat{{W\,{\rm ln}( P ) }}$ is substituted for W ln(P) in the spatial lag model to eliminate the correlation between the spatially lagged endogenous variable and the error term. Then, the second-stage regression for that quantile is performed to obtain ρ(τ) and β(τ). This two-stage procedure is then repeated for each quantile.

Boil water notices

To measure water supplier unreliability, we use BWNs issued by either public water systems or the Marion County Health Department. The OEHS provides information on all BWNs in West Virginia starting from 2012. Between January 2012 and December 2017, there were a total of 440 BWNs in Marion County, varying annually between 64 and 80 with no discernible trend over time. For each notice, the provided information includes the following: when the notice is issued and lifted, the name of the public water system plus its PWSID, the public health sanitation district where the notice is issued, the reason for the notice, and details about the affected areas or street names.Footnote ⁴ Using information from the SDWIS/Fed database and details from each notice, we obtained city and county affected by each notice.Footnote ⁵

Housing data

The Marion County Assessor provides data for all residential property sales between January 2012 and December 2017. This data set contains 7,972 residential property transactions. By dropping all property sales without structures, the number of transactions declined to 5,525. To ensure only arm's length sales in our analysis, a process following Herriges, Secchi, and Babcock (Reference Herriges, Secchi and Babcock2005) is used to drop all properties that were less than 50 percent of their assessed values and/or sold for less than $5,000. Therefore, after eliminating these sales, the total number of transactions included in our analysis is 1,985 single-family residential properties.Footnote ⁶

To capture housing attributes previously found in the literature to influence housing prices, we include variables for housing characteristics in the hedonic model such as size, story height, age, number of bedrooms, total number of bathrooms, and existence of house amenities (e.g., air-conditioning and fireplace). In addition, we control for two variables that have been consistently neglected in hedonic property price models: (1) house physical condition and (2) material and workmanship quality. Based upon assessor data for physical condition, we rank houses from Unsound = 1 to Excellent = 6. For quality, we use the quality grade factor provided by the county's assessor ranging from E = Poor (0.5) to X = Excellent (2.5). According to the assessor, these two variables are unrelated, as the first one measures only the physical condition, but the second measures the quality of the building regardless of the physical condition. We compute a simple correlation coefficient, and we find that it is equal to 0.60, indicating a moderate correlation between the physical condition and the quality of the building.

All property sales are geocoded using house's street address with ArcGIS to measure neighborhood and proximity characteristics such as crime, school quality, distance to Fairmont State University, and to the nearest highway interchange.Footnote ⁷ For crime, we use the total crime index that compares the average local crime level to that of the entire U.S. (an index of 100 is average). This index includes both property and violent crimes for 2010 at the block group level, and it is obtained from the ArcGIS database. For school quality, we follow the literature and use proficiency tests as a proxy (Brasington Reference Brasington1999). Specifically, we use the percentage of students in elementary school who scored at or above proficiency levels in math tests. We obtain these shapefiles for attendance zones in the county from the National Center for Education Statistics (NCES) and the data for math tests from the GreatSchools website. For distance variables, we obtain the shapefiles for Fairmont State University and highway interchange locations from the Census Bureau TIGER/Line database. Finally, we include year-fixed effects to control for housing market changes over time.

Linking BWNs to housing transactions

There were 440 BWNs in Marion County between 2012 and 2017, but 90 BWNs could not be used due to insufficient information about the affected locations (54 BWNs) or because the date when the BWNs were lifted are unavailable (36 BWNs). Thus, the total number of BWNs used in the analysis is 350. Then, based upon the details provided for each BWN along the street address for each property transaction, West Virginia Property Viewer was used to allocate properties and BWNs among the 22 tax districts in Marion County.Footnote ⁸ Following this, the details of each BWN are linked to all affected houses based on street addresses or affected areas. For example, if a BWN affects Street A and is issued on January 1, 2014 and lifted on January 5, 2014, houses located at Street A and sold between January 1, 2014 and January 1, 2015 are assigned the appropriate values for each BWN variable utilized in the analysis.

Table 3 shows the distribution of property transactions, BWNs, and properties affected by BWNs in each tax district in Marion County between 2012 and 2017. Over the entire county from 2013 to 2017, about 35 percent of residential property transactions are affected by a BWN, and as expected, Fairmont has the largest number of transactions and BWNs. Specifically, about 41.6 percent of the transactions happen in Fairmont with 29 percent of these transactions being affected by BWNs.

Table 3.

Property transactions and BWNs by tax districts in Marion County, West Virginia, between 2012 and 2017

^a Part of Fairmont City.

^b BWNs that affect districts 14 and 15 usually affect other districts as well.

Two variables are used to measure water supply unreliability: (1) the number of days a sold house is under BWNs within one year prior to its sale date and (2) a binary variable indicating that if a sold house is affected by the BWN or not within one year prior to its sale date.Footnote ⁹ For these variables, property sales from January 1, 2013 to December 31, 2017 are used in the analysis and BWNs from January 1, 2012 to December 31, 2016.

Table 4 provides summary statistics and descriptions for all variables included in the analysis. Explanatory variables are grouped into four categories. The first category consists of focus variables related to BWNs as proxy measures of water supply unreliability. We expect these variables to have negative impacts on housing prices. The second category is structural variables that include building characteristics and house amenities. Except for story height, construction material, and house age, all the other variables are expected to have positive impacts on housing prices. Property variables are the third category, and these include parcel characteristics of lot size and fencing with positive impacts and sidewalks with a negative impact, since they are associated with cleaning responsibilities. Finally, there are neighborhood and proximity variables. For the variables crime level and distance to highway plus a major employer (Fairmont State University), negative impacts are expected, whereas school quality should have a positive impact on housing prices.

Table 4.

Summary statistics and variable descriptions

Note: Observations = 1,985.