A Multilevel Property Hedonic Approach to Valuing Parks and Open Space Treg Christopher Dissertation Seminar Oct. 15, 2009
Outline • Ecosystem Goods and Services and Valuation • Property Hedonic Model • Spatial Issues • Multilevel Modeling Methods • Research Results • Baltimore City Parks • Baltimore County Open Space
Benefits of Parks and Open Spaces • Protects water quality • Provides wildlife habitat • Improves physical & mental health • Educational opportunities • Flood regulation • Offsets urban heat sink
Valuing the Environment • If we can assign a quantitative monetary value on ecosystem goods and services, we can: • justify the use if public funds for restoration or protection projects; • make objective decision on the most efficient use of limited resources; • through cost-benefit analysis, set priorities for programs, policies or actions.
Valuation Methods • Stated Preference: • Uses surveys to ask people what they would be willing to pay. • How much would you be willing to pay to improve water quality in a nearby lake? • Revealed Preference: • Uses market prices to estimate how much people are willing to pay. • How much does proximity to a park contribute to the value of a property?
Types of Revealed Preferences • Market price method • Estimates economic value based on the price of marketable goods. • Productivity method • Estimates economic value based on the cost of producing marketable goods. • Hedonic price method • Estimates economic value based on effects on the price of other marketable goods. • Travel cost method • Estimates economic value of a site based on how much people are willing to pay to travel to visit the site.
Property Hedonic Approach • Assumes that a home buyer implicitly prices characteristics embodied in the property: • Structural (house size, age, # of baths, lot size) • Neighborhood (ethnicity, income, unemployment, crime) • Locational/Environmental (access/proximity to parks, schools,shopping) • To live in a location with higher levels of an amenity • Households pay higher house prices • Cost differences reflect households’ implicit valuation
Property Hedonic Approach • Hedonic prices are identified through a comparison of similar goods that differ for the quality of one characteristic Proximity to a park Proximity to a park Distance 100m 500m
Property Hedonics & Environmental Externalities • Negative externality • air pollution (Batalhone 2002) • proximity to hazardous waste sites (McCluskey 2003) • Positive externality • open space (Bastian 2002; Bolitzer 2000; Geoghegan 1997; Irwin 2002) • Improvements to water or air quality (Cho 2006; Kim 2003; Leggett 2000)
Previous Studies of Parks • Positive value to preserving most types of open space in urban-suburban areas • Close proximity to parks in urban areas has a significant positive impact on home value but depends on context: • Neighborhood Effects: • Parks in urban areas and more densely populated suburbs tend to show greater benefits than those in more sparsely-populated areas • Park Characteristics: • Natural, wooded areas have greater beneficial impacts • Larger parks have greater beneficial impacts • High crime in the areas surrounding parks will reduce the value of parks
Property Hedonic Limitations • Need large data sets and detailed information on all aspects that affect prices • We assume that buyers choose houses that maximize their utility • requires information that the buyer may not perceive • Assuming a single housing market for all consumers • Only measures “use” values of the environment • recreation and aesthetics • Numerous statistical assumptions
The Pitfalls of Spatial Analyses • Spatial dependencies (autocorrelation) • Data from location near to each other are more likely to be similar than data from location remote from each other • Causes bias in coefficients and standard errors • Heterogeneity of relationships (Non-stationarity) • Phenomena is not distributed evenly in space • Scale and the Modifiable areal unit problem (MAUP) • Results may depend on the areal unit used • Block Groups vs. Tracts (scale issue) • Block Groups vs. ‘Neighborhoods’ or Zipcodes (zoning)
Testing for SA:Moran’s Index • positive when attributes of nearby objects are more similar than expected • 0 when arrangements are random • negative when attributes of nearby objects are less similar than expected Close in space Repulsion of attributes Attributes independent of location Close in space Affinity of attributes
Spatial Non-Stationarity • Global models (e.g. OLS): Assume relationships are stationary and as such are location independent • Non-Stationarity: a different relationship in different parts of the study region • Local models: spatial decompositions of global models, the results of local models are location dependent
Spatial Scales • Conclusions about processes and relationships determined at one scale should not expected to be similar at other scales • Atomistic Fallacy • Inferences about broad scale/group level/aggregated data and relationships are based on small scale/individual level analyses • Ecological Fallacy • Inferences of fine-scale/individual level data and relationships are based on broad scale or aggregated data
“Tree scale”: Spatial relationship betw/ trees (the regular distribution) determined by competition for light, water, nutrients which prevents the trees from growing to closely to one another Negative association Small/ Fine “Stand or Community Scale”: Spatial relationship determined by same species having common needs (light, water nutrients) which are heterogenous across space SCALE “Forest Scale”: Spatial relationship determined by disturbances such forest fires, pest & diseases Large/Broad
Baltimore Data • Property data • MD PropertyView: Structural characteristics & Sale info • Sales between 1998-2002, $ converted to Yr2000 • Property records removed if: • Sale price <$50,000 • House size <500ft2 • Lot size <500ft2 • Number of bathrooms > 6 • Not townhouse or individual residence • Approx. 14,000 records • Census data • Block groups from 2000 Census • over 400 groups with at least 5 property sales
Non-Spatial Statistical Assumptions • Linearity - the relationships between the predictors and the outcome variable should be linear • Normality - the errors should be normally distributed • Homoscedasticity- the variance of errors should be stable across space • Model specification - the model should be properly specified (including all relevant variables, excluding irrelevant variables ) • Multicollinearity – independent variables should not be highly correlated with each other
Multilevel Models • Early history: Educational research • effects of context such as classroom and schools on individual scholastic achievement (Goldstein 1993; Raudenbush 1991). • Individuals that are members of a group cannot be modeled as independent observations • Statistical violation leads to erroneously small Standard Errors • spurious statistical significance of coefficients • Examine potential Non-stationarity • Avoiding the atomistic and ecological fallacies • Data is modeled at the appropriate scale • Allowing cross-level interactions between individual level factors and group level (contextual) factors.
y1 r12 u2 0 γ0 u1 Do Groups Matter? House Price Null Multilevel Model OLS Model $1M+ y1 r1 02 $110,000 01 $50,000
Null/Baseline/Unconditional Model Price for any individual (i) within Block Group (j) is a function of the group mean and the individual-level error term • Combined model Each Block Group mean is a function of the grand mean and a group-level error term Individual level variance Group level variance
Intraclass Correlation Coefficient (ICC) • The ICC is the proportion of variance in property price between block groups to the total variance Individual level variance: σ2 Τ00/(Τ00 + σ2 ) 65.5% of the variance in property price is between block groups Group level variance: Τ00 0.17189 / (0.17189+0.0904)=0.655
Level 1 Model Fixed intercept, Fixed slope: OLS Model House Price House Size
Level 1 Model Random intercept, Fixed slope: Multilevel, L1 Model House Price House Size
Spatial Error Autocorrelation • Moran’s Index OLS (SPSS): Multilevel (HLM): Moran's Index: 0.227255 p-value: 0.000000 Moran's Index: 0.014214 p-value: 0.115993
Modeling Random Effects Random intercept, Random slope: Multilevel, L1 Model Random intercept, Fixed slope: Multilevel, L1 Model House Price House Size
Why Allow Slopes to Vary? 1. Helps reduce problem of heteroscedasticity from level 1 residual Fixed Slope Random Slope Test of homogeneity of level-1 variance ---------------------------------------- Chi-square statistic = 2291.81500 Number of degrees of freedom = 404 P-value = 0.000 Test of homogeneity of level-1 variance ---------------------------------------- Chi-square statistic = 2095.47234 Number of degrees of freedom = 387 P-value = 0.000
Why Allow Slopes to Vary? 2. Mapping non-stationarity
Level 2 Model: “Means as Outcomes”(MAO) The mean price for each group is an outcome to be predicted by group characteristics • Combined Equation
Compositional Effects of Structure • Price is determined by a property’s structural attributes & the structural attributes of neighboring houses Individual house attributes: Age, House Size, Lot Size Neighborhood averages of individual attributes • House Size and Age are significant at the neighborhood level Conclusions about processes and relationships determined at one scale should not expected to be similar at other scales
Cross-Level Interactions House Size Results MedHsInc w/ Cross-level interaction Cross-level interpretation: Not only does house size have a positive effect on price but the slope increases with increasing neighborhood income
Valuing Parks in the City of Baltimore • Include “official” city parks & other, undeveloped open spaces • n=81 • use parcels boundaries to verify and edit park boundaries • only parks > 2ha
Distance to Parks Euclidean Network Combined
Result of Park Coefficient Interpretation: a 0.003% (0.015% in OLS) decrease in price with every 1% increase in distance • Why Non-Significant in HLM Models vs OLS? • Spatial Autocorrelation? • Non-stationarity?
Explaining Non-Stationarity of Park Coef. • Interaction variables • Structural: House Size, Age, Lot Size • Park: Crime, Size of Park (ha), % Open • Neighborhood (cross-level): MedHsInc, %Unemployment, Crime, PopDensity • Results: Lack of significant interaction • What if Block Groups are divided?
Conclusions: Valuing Parks in the City of Baltimore • The effect of park proximity on property price varies across space • Previous studies using Global Models are unable to examine such variation • For neighborhoods that do positively value proximity to parks: • larger and more open parks tend to be more highly valued • neighborhoods with high population densities tend to place higher value on park proximity • Unknown interactions for neighborhoods that negatively value proximity to parks
Valuing Open Space in Baltimore County • Proportion of different land uses that surround a home: • commercial, residential, open space • Are their differences between open space types? • Difference in value between different spatial scales?
Valuing Open Space in Baltimore County • Open space types: • Private, Conserved • easements and riparian buffers • Private, Developable • “Public” • publicly accessible • golf courses, cemeteries, school fields, campuses • About 75% wooded and 25% open: grass or farms
Land Use at Multiple Scales • Do the effects of proportions of open space and other land uses vary with the scale at which they are examined? • Block group, 1km, • 500m,100m 1 km 500m 100m
Conclusions • Private, Conserved > Private, Developable > Public • Preference for visual amenities over direct use (recreation) • Preference for absence of negative externalities vs presence of positive amenities such as recreation • Results do change with scale
Future Research • Include a 3rd level • group block groups by tracts, PRIZM (consumer behavior) classes, school districts • Cross-classified design • use a non-nested grouping where properties “belong” to a socio-economic group (neighborhood) and the park to which they are closest Property Block Group Tract Park Block Groups Park
Multilevel Weaknesses • Need for bounded (discrete) L2 groups may result in artificial boundaries being formed whereas processes and associations may be more diffuse • Block Group (Census units) boundaries are created to minimize the heterogeneity within groups • Requires large datasets (min 30 groups & 5 observations/group) • Shrinkage of unreliable estimates of random effects is towards the grand mean rather than neighboring groups
Multilevel Valuation of ES • Valuation of Ecosystem Service is dependent on context • supply of services & demand of consumers • Context is scale dependent • variables should be measured at appropriate scale(s) • interactions can occur across scales
Thanks for Listening! Questions?
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