Abstract
The benefits of large patches of tree canopy are estimated by applying a hedonic price model to the sale of single-family residential properties in Portland, Oregon. The first-stage analysis provides evidence of diminishing returns from increasing tree canopy past a certain level. The second-stage analysis uses a survey of property owners’ preferences and socioeconomic characteristics to overcome the problem of endogeneity. Average benefit estimates for the mean canopy cover within ¼ mile of properties in the study area, using the second-stage model, are between 0.75% and 2.52% of the mean sale price. (JEL Q21, Q51)
I. Introduction
Large contiguous patches of tree canopy are considered to be an important part of an urban environment. In addition to the benefits received by private property owners, such as shade and privacy, these areas provide wildlife habitat, improve air quality, reduce runoff and flooding, lower noise levels, and moderate climate.
The Portland metropolitan area is highly urbanized and development is constrained by an urban growth boundary. Despite these pressures, the percentage of tree canopy in the city of Portland increased between 1972 and 2002 (Poracsky and Lackner 2004). This increase is attributed to a natural environment that is conducive to growing trees, Oregon’s land-use laws, Portland’s environmental zoning regulations, land purchases by the regional government, and planting efforts by nonprofit organizations (Poracsky and Lackner 2004).
Portland’s Urban Forestry Management Plan (Portland Parks and Recreation 2004, 12) lists “protect, preserve, restore, and expand Portland’s urban forest” as one of its goals. The effect of this objective on the sale price of single-family residential properties is unknown but is important to assess since the incentives for private property owners to preserve tree canopy may—or may not—be consistent with this goal.
This paper estimates the effect of tree canopy located on single-family residential properties, and in the area within ¼ mile of these properties, on their sale price. In addition to estimating marginal effects this paper estimates, for the first time, the per-property benefits of nonmarginal changes in tree canopy using a second-stage hedonic price model. The second-stage model involves estimating an inverse demand curve for the percentage of tree canopy, which is necessary for measuring the per-property benefits of nonmarginal changes in tree cover. These estimates are provided for existing levels of tree canopy and for several hypothetical increases in tree canopy coverage.
II. Literature
Several studies have examined the relationship between open spaces and the sale price of single-family residential properties in Portland, Oregon (Bolitzer and Netusil 2000; Lutzenhiser and Netusil 2001; Mahan, Polasky, and Adams 2000; Netusil 2004a, 2005b). Tree canopy on a property and in the surrounding neighborhood is represented by a series of dummy variables in one paper (Netusil 2005a) and captured indirectly as a characteristic of natural area parks and forested wetlands in the other papers (Bolitzer and Netusil 2000; Lutzenhiser and Netusil 2001; Mahan, Polasky, and Adams 2000).
Multiple hedonic studies have found that property values increase if trees are located on a property (Anderson and Cordell 1985; Dombrow, Rodriguez, and Sirmans 2000; Morales 1980). Other hedonic studies have focused on the relationship between property values and forested areas in the surrounding neighborhood (Tyrvainen and Miettinen 2000), with some studies finding negative effects (Garrod and Willis 1992; Geoghegan, Wainger, and Bockstael 1997; Kestens, Theriault, and Rosiers 2004; Tyrvainen 1997).
Tyrvainen (1997) used apartment sales in Joensuu, Finland, to estimate how their sale price is influenced by distance to the nearest wooded recreation area, nearest forested area, and the relative amount of forested areas in the housing district. Sale prices are estimated to increase with proximity to wooded recreation areas and with increases in the amount of forested areas in the housing district. However, the sale price of apartments is found to increase as the distance from a forested area increases. The author attributes this result to the shading effects from dense forests in the study area.
In a related study, Tyrvainen and Miettinen (2000) estimated that a 1-km increase in the distance to the nearest forested area leads to an average 5.9% decrease in the sale price of residential properties in the district of Salo in Finland. Dwellings with a view of forests were found, on average, to be 4.9% more expensive than dwellings with similar characteristics.
Garrod and Willis (1992) used observations on properties located adjacent to Forestry Commission land across Britain to estimate a first-stage model that includes three tree categories and a second-stage model of the demand for broadleaved woodland. An increase in the proportion of Forestry Commission land with broadleaved trees is estimated to increase a property’s sale price, while an increase in mature conifers is found to reduce sale prices. The double-log functional form used in the second-stage model, which uses a multiple market approach, results in an income elasticity estimate for the proportion of broadleaved woodland of 0.82 and an own price elasticity of −1.76.
The only second-stage hedonic model attempted for Portland, Oregon, is described by Mahan, Polasky, and Adams (2000). While the authors find evidence of market segmentation, they were unable to get reliable estimates of the demand curve for size of the nearest wetland.
III. Study Area, Property Characteristics, and Survey Data
The study area includes 91,250 acres of Portland, Oregon, located within Multnomah County (Figure 1). The study area is highly urbanized with an average lot size of 7,043 square feet. Between January 1, 1999, and December 31, 2001, there were 30,015 arms-length single-family residential property sales in the study area; these transactions are the core part of the data set used for the first-stage hedonic price model. Sale price and structural information were obtained from the Multnomah County assessor (2002).1 Sale prices were adjusted to 2000 dollars using the Consumer Price Index: All Urban Consumers (Bureau of Labor Statistics 2002). Table 1 contains a complete list of explanatory variables used in this analysis; more detailed information about the data set is provided by Netusil (2005a). Properties on the west side (NW and SW) have a higher mean sale price, are located in census tracts with higher median incomes, and have a higher percentage of tree canopy on the property and in the area within ¼ mile of the property than properties located east of the Willamette River (Table 2).
Study Area
Explanatory Variables
Summary Statistics (Standard Deviations in Parentheses)
The tree canopy variables were generated using a canopy cover layer derived from satellite images (Metro Data Resources Center 2006). The canopy cover layer used a minimum mapping unit of 1 acre and categorized canopy cover based on the amount of coverage provided by the crowns of trees. For this study we focus on canopy that provides between 76% and 100% coverage, that is, patches of tree canopy of 1 acre or largerwhere canopy crowns overlap and cover 76% to 100% of the patch.
The percentage of tree canopy on a property was estimated by combining the tree canopy layer with a property tax boundary layer. On average, properties in the study area have 3.48% of their land covered with tree canopy that provides 76% to 100% coverage and is part of a patch that is 1 acre or larger. This is because much of the study area has no tree canopy at the high-level of coverage of 76% to 100%. In each area (NW, SW, SE, NE, N) there were properties completely covered with tree canopy and properties with no tree canopy.
Tree canopy within ¼ mile of a property can be located on privately or publicly owned land. The majority of tree canopy for property sales in the data set is on privately owned land. North Portland is an exception with 1.25% and 1.41% of land covered by privately and publicly owned tree canopy, respectively (Table 3).
Tree Canopy within ¼ Mile of Properties
The second-stage hedonic price model uses socioeconomic and perception variables from a survey to estimate the inverse demand function; this function is then used to calculate the benefits of nonmarginal changes in tree canopy coverage. In the fall of 2005, a packet containing an eight-page survey, a cover letter, a map of the Portland-area highlighting seven regional parks, and a postage-paid return envelope was mailed to a random sample of 1,200 properties selected from the 2001 property sales.2 Of the 1,141 deliverable surveys, 42% (479) were returned, and out of the 479 surveys returned 92% (440) were useable in the second-stage hedonic price model. The survey sample and the Portland population have similar mean income and age, but the sample is, on average, more educated (Table 4).
Definitions and Summary Statistics of Homeowner Characteristics
The survey asked respondents for (1) their perception of attributes of Portland parks, (2) their use of prominent Portland parks,3 (3) their willingness to pay for a program to purchase and maintain a large regional park, (4) the features of their choice of residence, and (5) their socioeconomic characteristics. The perception variables of the attributes of Portland parks are from nine-scale Likert-type questions that ask about the influence of park attributes, such as tree canopy, on housing choice. The socioeconomic variables include age, education, income, and the number of family members in the household.
Table 4 includes summary statistics for the variables used as demand shifters and/or as instruments in the second-stage hedonic model. The section of our paper describing the estimation of the inverse demand function explains the hypothesized relationship between these variables and the demand for tree canopy.
IV. Hedonic Price Method: Firstand Second-Stage Models
The first-stage hedonic price model relates the sale price of properties to their structural characteristics, neighborhood amenities, and location. While estimates for marginal changes in attributes can be derived from the first stage, the second stage is needed to estimate per-property benefits from nonmarginal changes.
Rosen (1974) proposed that marginal prices from the first stage be used in a second-stage model to estimate the demand curve for the attribute of interest. However, for reliable estimation of the second stage, the inverse demand function must address two important econometric issues: identification of the second-stage demand parameters from the first-stage parameters, and endogeneity of the price and level of the attribute.
Problems with parameter identification arise because the attributes of the composite good cannot be unbundled, resulting in a nonlinear hedonic price function. Consequently, the same set of information is used for the first and second stages—leading to an identification problem unless additional information or structure is included in the second-stage model. Ekeland, Heckman, and Nesheim (2004) provide an interesting theoretical discussion of the identification issue, suggesting that the nonlinearities of the hedonic model be used to nonparametrically identify the structural parameters. Endogeneity arises because the marginal price of an attribute, and its level, are simultaneously determined. Under these conditions ordinary least squares (OLS) leads to inconsistent estimation of the second-stage parameters, but two-stage least squares (2SLS) will produce efficient estimates if the instruments used are correlated with the observed levels of the attribute but uncorrelated with the unobserved homeowner’s tastes.
As in previous studies (Chattopadhyay 1999), we identify the second-stage parameters using functional-form restrictions, specifically, a quadratic model for the first-stage hedonic price function, and linear and double-log models for the second-stage inverse demand functions. To overcome endogeneity bias we use individual-level survey responses and socioeconomic characteristics of a randomly selected group of property owners who purchased their homes in 2001. While the first-stage hedonic price function uses all 30,015 transactions, the estimation of the inverse demand function involves combining the information derived from the first-stage results with survey responses from a relatively small subset of property owners: 440 observations for the linear model and 377 for the double-log model. We expect that this aspect of the estimation will provide additional structure to the second-stage estimation and a strong set of instruments for efficient 2SLS estimation of the inverse demand parameters.
V. Results
First-Stage Hedonic Price Model Our a priori expectation is that tree canopy will have either a positive but diminishing effect on a property’s sale price, or will increase a property’s sale price to a maximum point past which increases in tree canopy will cause a property’s sale price to decline. Two models were developed to explore these expectations; the natural log of a property’s real sale price was used as the dependent variable in both models.
In the first model, the percentage of tree canopy on a property, and within ¼ mile of a property, is represented by a quadratic function, while the natural logs of these variables are used in Model 2. To preserve observations, the minimum amount of tree canopy on each property, and within 1/4 mile of each property, was set at 0.1% for Model 2, that is, observations with zero tree canopy for either (or both) categories were recoded to 0.1%—an approach justified by Smith and Cicchetti (1974) and Johnson and Rausser (1971). Of the 30,015 observations in the data set, there are 9,353 observations with no tree canopy within ¼ mile of the property and 27,583 properties with no tree canopy on the property.
The results from both models are presented in Table 5. The estimated coefficients for the structural, amenity, and location variables are consistent with those of other studies (Netusil 2005a, 2005b). The estimated coefficients on home characteristics (lot square footage, building square footage, etc.), house style (one story, one story with finished basement, etc.), base zoning (low residential, medium residential, etc.), distance to the central business district, and nearest commercial and industrial districts are not included in Table 5. Full results are available from the authors. In Model 1, 40 of the 52 explanatory variables are significant at the 5% level, while in Model 2, 36 of the 46 explanatory variables are significant at the 5% level. In Model 1, the percentage of tree canopy that is estimated to have the largest impact on a property’s sale price is approximately 18%.4 The estimated coefficient on Model 2 is significant and negative, implying that the optimal tree canopy coverage on a property is zero, on average.
First-Stage Model Estimated Coefficients and Robust Standard Errors
To test for the presence of spatial error autocorrelation in the first-stage hedonic regression model, we carry out Moran’s I-test, separately, for the data from 1999, 2000, and 2001. The results of the tests are as follows:
1999 data: Moran’s I-statistic = 0.3956, p-value = 0.01 (n = 9,913)
2000 data: Moran’s I-statistic = 0.4131, p-value = 0.01 (n = 9,537)
2001 data: Moran’s I-statistic = 0.3716, p-value = 0.01 (n = 10,474)
The tests indicate the presence of statistically significant spatial error autocorrelation for each year of the data. However, it remains unclear whether the spatial error process is due to spatial dependence or spatial heterogeneity. An appropriate spatial lag model can correct for spatial dependence, but spatial heterogeneity can be the result of error heteroskedasticity (Anselin and Bera 1998).
Correcting for spatial dependence involves specification of an appropriate spatial lag model (Anselin et al. 1996; Anselin and Bera 1998). Addressing spatial dependence requires at least two years of cross-sectional data that are temporally separated. This enables testing of the stability and asymptotic validity of the spatial lag parameters to determine the appropriate spatial lag specification to correct for spatial dependence (Anselin 2000). Unfortunately, our home sale data are for three consecutive years and, as such, do not enable us to specify a statistically accurate spatial lag model. A recent study that compares implicit prices of a hedonic price model with and without spatial dependence finds that spatially corrected estimates of implicit prices are found to be nearly the same as those obtained by OLS (Mueller and Loomis 2008). We address error heteroskedasticity, which could be the result of spatial heterogeneity, by estimating the regressions with robust standard errors (White 1980). In large samples, like the present case, heteroskedasticity-robust estimation can take care of the spatial clustering effect that is often encountered when using housing data (Anselin and Bera 1998).
Marginal implicit prices were derived using the results presented in Table 5. The estimated coefficients are consistent with the a priori expected relationship between the percentage of tree canopy within 1/4 mile of a property and its sale price in Model 1 for properties in SE, NE, and N Portland. However, increases in tree canopy up to 16.80% in SW Portland, and 97.36%in NW Portland, are estimated to decrease the sale price of properties located in those areas (Table 6).
Implicit Prices for Tree Canopy within 1/4 Mile of Properties
The estimated coefficients in Model 2 are consistent with a priori expectations for properties in SE, NE, and N Portland, but properties in NW and SW Portland are estimated to experience a decline in sale price from increases in tree canopy. Negative marginal implicit prices in NW and in SW Portland make intuitive sense since further increases from already large amounts of dense tree canopy within 1/4 mile of properties may block highly desirable views of mountains, city lights, and the Willamette River.
Inverse Demand Function (Second-Stage Hedonic Price Model)
The marginal implicit prices estimated in the first stage are used as the dependent variable in the estimation of the inverse demand function. Since the marginal implicit price of tree canopy and the percentage of tree canopy are simultaneously determined, instruments need to be used that are correlated with the observed levels of the attribute, but uncorrelated with the unobserved homeowner’s tastes to avoid endogeneity bias.
Perception variables of park attributes such as view, tree canopy, and hiking, and on-site time variables for visits to natural parks, such as SITETIME, reflect respondents’ preferences for parks. The demand for tree canopy near a property is likely related to these preferences because parks are a logical substitute for tree canopy near a home, that is, homeowners who have little or no tree canopy on or near their property may make greater use of these parks.
Socioeconomic variables such as age, education, income, and the number of young children in a household are also related to the demand for tree canopy. Individuals who are older may have a preference for more tree canopy near their homes because they have more time available for passive recreation activities such as bird-watching; those with more education may desire neighborhoods with more tree canopy because there is a greater understanding and appreciation of the ecosystem services of tree canopy. Income may increase the demand for tree canopy near a home because of a greater ability to spend on amenities, while the number of family members in a household of different age groups influences household activities.
There was no a priori expectation about the functional form for the second-stage model, so two models were estimated: linear and double-log. We retained the negative marginal implicit prices estimated in the first-stage models in the linear model since these appear to be valid estimates for the study area. Other authors have taken a similar approach, although some authors have set these prices equal to zero or dropped these observations entirely (Zabel and Kiel 2000).
Results from the second-stage linear model are presented in Table 7. The estimated coefficient on the percentage of tree canopy is negative and significant. Income and age are positive, as expected, but not significant. Education, which is modeled as a quadratic, reaches a minimum at 16.46 years, which is close to the average education level in the survey data set, but much higher than the average education level in Portland. The availability of a substitute for tree canopy within 1/4 mile of a property is measured by SITETIME, the sum of the average on-site time spent per trip at five natural parks in the Portland-area. The estimated coefficient on this variable is negative, as expected, but is not significant.
Estimated Coefficients: Quadratic First Stage, Linear Second Stage (Standard Errors in Parentheses)
Table 8 contains the results from the double-log model. For this model it is assumed that the minimum tree canopy within 1/4 mile of each observation is 0.1%; observations with a first-stage negative marginal implicit price are dropped, which decreases the number of observations to 377. The estimated coefficient on tree canopy is negative and significant: a 1% increase in tree canopy within 1/4 mile of a property is estimated to decrease the implicit marginal willingness-to-pay for tree canopy by 0.1682%. The coefficient on income is positive and significant, providing evidence that tree canopy is a normal good.
Estimated Coefficients: Quadratic First Stage, Double-Log Second Stage (Robust Standard Errors in Parentheses)
The coefficient on SITETIME, a variable that measures a substitute for tree canopy within 1/4 mile of a property, is negative and significant. Increasing the amount of tree canopy within 1/4 mile of a property by 1% is estimated to decrease the amount of time spent at the five natural parks in the Portland area by 0.0937%. Age is again positive but not significant. The negative sign on education is counterintuitive and is possibly the result of the double-log model’s inability to represent the nonlinear relationship between the demand for tree canopy and education observed in the linear model.
Endogeneity
To examine the effectiveness of the 2SLS results we conducted tests for underidentification, weak identification, and overidentification of the instruments. As shown in Table 9, Anderson’s likelihood ratio test (Kleibergen-Paap rk-LR-statistic) indicates the model is identified for both specifications; however, the Craig-Donald statistic (Kleibergen-Paap rk Wald F-statistic) suggests that both specifications of the model are only weakly identified. Sargan’s statistic (Hansen’s J-statistic) indicates that the instruments are valid, that is, not correlated with the error term and also correctly excluded from the estimated equation.
Instrument Tests
Per-Property Benefit Estimates
Per-property benefit estimates for a range of tree canopy levels are calculated using the second-stage results (Table 10). The estimated demand curve is integrated from zero canopy coverage to different tree canopy levels for each observation; the observation level benefits are then averaged over the entire sample. Figure 2 is a graphical representation of the estimated demand curves.
Per Property Benefit Estimates for Alternative Canopy Cover and 95% Confidence Intervals
Second-Stage Demand Curves
The tree canopy levels evaluated include (1) the lowest average tree canopy coverage (2.53%), (2) the mean coverage (7.21%) for the study area, (3) a coverage level (15%) reflecting roughly a doubling of the average tree canopy within the study area, and (4) the level of tree canopy where we see a decline in benefit estimates in the quadratic model (40%). The average benefit estimates for the mean canopy cover (7.21%) within 1/4 mile of properties in the study area represent between 0.75% and 2.52% of the mean sale price of $175,160 under the two different specifications. A test of significance of the population mean benefits is performed for each estimated benefit reported in Table 10. The t-ratios for these tests against the alternative that the population mean benefit is different from zero are all greater than 100, signifying that the benefits are significantly different from zero. A 95% confidence interval for the population mean benefit is reported for each benefit estimate in Table 10.
The results also allow us to compute the change in the per-property benefits from a change in the level of tree canopy coverage. For example, for each observation in our data set we compute the difference between the per-property benefits obtained by integrating the second-stage benefit function from 0% to 7.21% and the per-property benefits obtained by integrating the second-stage benefit function from 0% to 2.53%. This difference, when averaged over the sample, produces a Marshallian surplus of $2,745 for a change in tree canopy coverage from 2.53% to 7.21% (Table 11). In Table 11 we report the results of increasing tree canopy from (1) 2.53% to the study average of 7.21%, (2) 7.21% to 8.21%, that is, a 1 percentage point increase in tree canopy cover, and (3) a doubling of tree canopy coverage from 7.21% to 15%.
Per-Property and Per-Acre Benefit Estimates from Percentage Changes in Canopy Coverage and 95% Confidence Intervals
An increase in tree canopy cover from 7.21% to 8.21% is estimated to increase per-property benefits from $149 to $528. This 1 percentage point change represents an additional 1.35 acres of tree canopy within 1/4 mile of a property, which corresponds to a per-acre benefit ranging from $111 to $391. The null hypothesis that the mean per-property benefit associated with the change from one level to another is zero is rejected with t-ratios all greater than 100. This suggests that the per-property benefit associated with each of the estimates in Table 11 is statistically different from zero.
The linear second-stage specification produces substantially higher benefit estimates than the logarithmic second-stage specification. One plausible explanation is that the perceived benefits of tree canopy decrease with increases in the quantity of tree canopy, but at an increasing rate. A linear demand function would not capture this nonlinearity and would produce benefit estimates that are too large. Thus, one should be careful in deciding which set of estimates to use for policy analysis.
VI. Conclusions
Portland, Oregon, is described as a “particularly green and well-treed city” (Poracsky and Lackner 2004, 1). The mean percentage of tree canopy within 1/4 mile of properties in the data set is 7.21% with 5.55% on privately owned land and 1.66% on publicly owned land. This average, however, masks large differences in the distribution of tree canopy across the study area.
The estimated coefficients from the first-stage hedonic price model indicate that an increase in tree canopy in parts of the study area with small amounts of tree canopy (N, NE, SE Portland) is expected to increase the sale price of properties. However, in the heavily treed areas of SW and NW Portland, increases in tree canopy are estimated to decrease sale prices. This effect is attributed to the already large percentage of tree canopy in these areas and the potential that highly desirable views will be blocked.
The coefficients on the percentage of tree canopy within 1/4 mile of a property are consistently negative and statistically significant across specifications for the second-stage model; the signs on other explanatory variables are consistent with a priori expectations. Per-property benefit estimates for the mean canopy cover within 1/4 mile of properties in the study area range from 0.75% to 2.52% of the mean sale price of $175,160.
The hedonic price method is only able to capture benefits that are capitalized into the sale price of properties. The attribute that was the focus of this study—tree canopy that provides between 76% and 100% coverage and encompasses at least one continuous acre—generates many public benefits such as wildlife habitat, improved air quality, reduced runoff and flooding, lower noise levels, and climate moderation. Future research can use the results of this study to analyze the benefits and costs of Portland’s urban forest (McPherson et al. 2002).
The small average lot size for residential properties in the study area points to the need for a coordinated effort to maintain and enhance tree canopy. Current regulations in the study area prohibit cutting healthy trees on large lots if doing so would create a “significant negative impact” on the “erosion, soil stability, soil structure, flow of surface waters, water quality, health of adjacent trees and understory plants, or existing windbreaks” and “the character, aesthetics, property values, or property uses of a neighborhood” (City of Portland, Oregon 2005). Our empirical results suggest that these regulations, tree planting programs sponsored by nonprofit associations, and efforts by the regional government to educate property owners about the benefits of wildlife habitat in their neighborhood will maintain, or perhaps enhance, the sale price of single-family residential properties in Portland, Oregon.
Footnotes
The authors are, respectively, Stanley H. Cohn Professor of Economics, Reed College; professor of economics, San Francisco State University; and research assistant professor, Department of Resource Economics, University of Nevada–Reno. This research was supported by a Paid Leave Award from Reed College and a Goldhammer Summer Research Grant. The authors gratefully acknowledge research assistance provided by Sarah Klain and David Kling; Gary Odenthal provided help with the data used in our analysis. Helpful comments were provided by Joe Poracsky, participants at the 2005 W1133 meeting, and an anonymous referee.
↵1 Assessment and taxation property records, January 1997 to June 2002, Multnomah County Assesor’s Office.
↵2 For additional information on the survey see Kovacs and Larson (2008).
↵3 These include Forest Park, Mount Tabor, Tryon Creek State Park, Willamette Park, and Powell Butte.
↵4 This estimate is derived by solving the quadratic equation for a maximum.
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