Empirical Estimation

For my method, I use Portland’s American Community Survey (ACS)-defined block groups as my primary unit of analysis. The decision to use block groups was based largely on data availability—however, it also serves to account for the external benefits that a property value experiences from trees that are approximate to it but not on the property itself. I then use a Geographic Information System (GIS) analysis to determine the proportion of each block group covered by tree canopy, using 2012 orthoimagery sourced from the US Geologic Survey. and represent this as a fraction of the total area of the block group. I join this with 2011 ACS demographic data to construct my regressions.

The model I use occurs in two stages. The first is a hedonic analysis of housing price with tree canopy included as the variable of interest, and takes the form

$ln(HP) = \beta_{0} + \beta_{1}ln(TC) + \beta_{2}Structural + \beta_{3}Neighborhood + u$

Where $ln(HP)$ is the logarithm of median house price, $ln(TC)$ is the logarithm of Tree Canopy as a proportion of land area, $Structural$ represents characteristics of the property itself, $Neighborhood$ represents characteristics of the location in which the house stands, and $u$ is the error term. This regression gives the implicit price of tree canopy as a function of house price. Because both house price and tree canopy are logged so as to report a percent change, this gives the implicit price in the form of an elasticity—the percent change by which house price would respond to a percent change in tree canopy.

In this stage, I expect to see a positively-sloped relationship between the log of House Price and the log of Tree Canopy. This would indicate that a percent increase in tree canopy is associated with a percent increase in house price. For the Structural and Neighborhood characteristics, I expect a mixture of positive and negative relationships. For example, I would expect a percent increase in house price to associate with an increase in number of rooms or an increase in local school quality, but a percent decrease in house price to associate with an in increase in house age or an increase in local crime rates.

The second stage regression estimates residents’ willingness-to-pay for tree canopy based on the implicit price of tree canopy and the demographic characteristics of the residents. It takes the form

$ln(WTP) = \gamma_{0} + \gamma_{1}ln(TC) + \gamma_{2}ln(MHI) + \gamma_{3}Age + \gamma_{4}Edu + \gamma_{5}Race + v$

Where $WTP$ represents the implicit price, an additional variable calculated by the coefficient of the logarithm of tree canopy from the first-stage regression multiplied by House Price. $ln(MHI)$ is the logarithm of median household income, $Age$ is the median age of residents, $Edu$ is a set of binary variables indicating the level of education residents possess (e.g. high school diploma, bachelor’s degree, master’s degree), $Race$ is a set of binary variables indicating resident’s reported race and ethnicity, and $v$ is the error term. In theory, these demographic characteristics are important determinants of willingness-to-pay for tree canopy, and serve to differentiate the neighborhoods which would extract the greatest total benefits from an increase in tree canopy.

In this stage, I expect to see a positively-sloped relationship between the logarithm of willingness-to-pay and the logarithm of Tree Canopy, as this would indicate that a greater quantity of Tree Canopy demanded would associate with a greater willingness-to-pay for it. Indeed, the two variables should be highly correlated, as $ln(WTP)$ is constructed using the coefficient of $ln(TC)$ from the first equation in this section. I also expect to see a positively-sloped relationship between WTP and Income, as this would indicate that those with greater ability to pay for Tree Canopy are also more willing to do so. The relationship between WTP and Age, Education, and Race & Ethnicity is harder to predict, and I expect it will have a much smaller magnitude of effect than either of the previous variables. This notwithstanding, they are still a theoretically-important factor of willingness-to-pay for Tree Canopy and necessitate inclusion.