Using wages and property values to value environmental amenities1 Using wages and property values to value environmental amenities November 4, 2014 (Note to Edward: maybe add some of the hedonic notes from Popps Ferry) This method of valuation is driven by the basic insight that the use values associated with site-specific environmental amenities get capitalized into wage rates, land prices, or both That is, ceteris paribus (c.p.), in nice places, wages are lower and land prices are higher. Also, nice houses sell for more money than do crappy ones. Capitalized as in built into2 Such model predictions are based on the following sort of assumptions: • Either everyone has similar preferences, or, to the extent preferences vary, there are a substantial number of individuals in each preference group. • Either everyone has the same skill level, or to the extent that skill levels vary, there are a substantial number of individuals in each skill group. • People are mobile (they are willing and able to change jobs and locations/move) • People get utility from market goods and nonmarket commodities including environmental commodities.3 Expressing utility for an individual who live in city i in terms of exogenous variables that describe city i: ),,,(iiiiiArwpuu = where iindexes the city of residence ipis the price index for goods and services in city i iwis the wage rate iris the rental price of housing (reflects the cost of land) iA is a vector of the characteristics (weather, crime rate, schools, environmental amenities, etc).1 Note that above we restrictively assumed everyone in city i has the same utility, because they have the same preferences (utility function) and experience the same constraints. (This assumption can be relaxed, but this simplifying assumption makes the presentation of the hedonic technique simpler.) Since all that is important is relative prices, we can rewrite the utility function as2 ),~,~(),/,/(iiiiiiiiiArwuAprpwuu == where ir~is the relative price of housing and iw~is the real wage. 1 For now we will assume no individual-specific non-market commodities, stuff like where your friends and family live. 2 Actually is what is called an indirect utility function because it is utility as a function of the constraints one faces, not a direct function of the chosen bundle.4 Imagine there are only four places to live, Boulder, Aspen, Pueblo and Denver. i = 1 is Boulder, 2 is Aspen, 3 is Pueblo and 4 is Denver. For example, utility from living in Pueblo is ),~,~(3333Arwuu = Given that we have assumed that everyone has the “same” preferences and that people are mobile, an individual will move from city m to city n if mnuu >.3 Therefore, everyone will be happy staying put (in equilibrium) only when 4321uuuu === What will cause equilibrium to occur? As individuals move from city m to city n the supply of labor will decrease in city m and increase in city n. This will cause mw~to increase and nw~to decrease. Everything else constant the individuals leaving m and going to n makes m more attractive in terms of wages and n less attractive in terms of wages. In addition, as individuals move from city m to city n the demand for housing will decrease in city m and increase in city n. This will cause mr~to decrease and nr~to increase. That is, everything else constant, the individual’s leaving m and going to n makes m more attractive in terms of housing prices and n less attractive in terms of housing prices.5 In addition, as individuals move from city m to city n,mAand nAwill change. City n will possibly become more congested, more polluted, etc, while city m will become cleaner and less congested. In summary as individuals move from city m to city n, ),~,~(nnnArwu likely decreases and ),~,~(mmmArwulikely increases, making it less attractive to move and bringing the system into equilibrium. Obviously, the real world is complicated by the fact that everyone does not have identical preferences, moving is costly, some city characteristics (e.g. family and friends) are individual specific, and some amenities increase when a city’s population increases,4 but you get the idea. 3 Actually, the utility difference has to be enough to cover the cost of moving. 4 Small towns won’t provide a ballet, or opera, or a bunch of fancy restaurants.6 When the system is in equilibrium, the values of the amenities in city i will be capitalized intoir~and iw~. That is, nice places will have lower wages and higher housing prices. Therefore, we can estimate use values for environmental amenities by seeing how r~and w~ vary across cities as a function of the environmental and other components of A.7 Studies that value amenities in this manner are called hedonic studies. There are three types of hedonic studies: hedonic property-value studies, hedonic wage studies, and joint property-value and wage studies. A hedonic property-value study estimates changes in housing prices as a function of the characteristics of the house and its surrounding amenities. In contrast, a hedonic wage study estimates how wage rates vary across localities as a function of the amenities in the locality. For example, assume that within Boulder amenity values (crime rates, school quality, access to open space, traffic, etc) vary from neighborhood to neighborhood. Housing prices will differ across neighborhoods and one can use these variations to value neighborhood amenities such as distance to open space. Imagine two neighborhoods that are identical (types of houses, crime, etc.) in every respect, including the characteristics of the houses, except for distance to open space, which varies across neighborhoods. The difference in the average price of a house in the two neighborhoods values the difference in distance to open space. That is, it determines what a representative individual is willing to pay for being closer to open space.8 To do a hedonic property-value study of the value of open space in Boulder, one would want to estimate something like the beta in the following function (obviously one would have to include all the determinants of the price of a house and maybe your function will need to have a bunch of nonlinear terms and interaction terms jijijijijidistsofbathroomsquareftrebbba++++= )()(#)(~3210 where jir~is the price of house j in neighborhood i, relative to the price index for goods. One collects a bunch of data on house prices, the characteristics