1. Valuation 10: Hedonic Pricing
A partial equilibrium model of prices, wages and pollution
The hedonic price equation
From hedonic prices to welfare
Application: Environmental hazards

2. Last two weeks we looked at
The household production function approach, which assumes that certain observable behaviour is a complement (e.g., travel to recreate) or substitute (e.g., airbag for road safety) to unobservable consumption of an environmental good or service
A simple travel cost model of a single site
Multiple sites
Implementation
The zonal travel cost method
The individual travel cost model
Travel cost with a random utility model

3. The price of land
The asset price equals the value of the stream of services that the parcel can be expected to provide in the future, netted back to the present
uncertainty about the future
The rental price of land is the value of renting for a short period
e.g., for agricultural land, the difference between expected yield times prices minus the costs of labour, seeds, pesticides etc
expectations about the future play little or no role
Pollution degrades value and thus price
What is the WTP to clean up the pollution?

4. Starters What is the WTP to clean up pollution?
Consider agricultural land in a valley, half of which is upwind a polluting plant, the other half downwind
If this is a small valley with a local market for agricultural goods the land value change will not fully capture the value for cleaner air
If this is a small valley in a large market the difference between land value is a proxy of the value of pollution
Consider an open city, with free mobility
Utility must be the same everywhere
So land prices exactly compensate for pollution
In a closed city, reducing non-uniform pollution would affect property values as well as utility

5. Wages, land prices and pollution
Arguably, pollution should suppress land prices – but we see that urban land is worth more than rural land
Urban wages are also higher than rural wages – do wages rise to compensate for deteriorating environmental quality?
We will construct a model of urban land prices, wages and pollution -- first, analytically and then we‘ll derive a function that can be estimated

6. The consumer
Consider a number of cities that have different levels of pollution p; firms produce a composite good X (at price 1) and move about freely; the wage rate w and the land rent r vary between cities
Consumers are identical, purchase X and land for housing L
Each consumer has the utility maximization problem:
The utility level for a particular set of w, r and p is
Assuming free movement, utility is the same everywhere

7. The producer
In a constant cost industry, the average cost of producing X equals the product price which is the same for all cities
The price for the product is the same, but the composition of inputs can differ
If rents are higher in one city, wages must be lower to compensate, otherwise the firm would relocate
Pollution may affect costs in different ways
Unproductive (pollution hinders production)
Productive (pollution regulation hinders production)
Neutral (no affect on the firm, but wages and rents affect production)

8. Productive and unproductive pollution
Two cities with different pollution levels: p2> p1 r
Cases A and B: when pollution is productive wages rise
Cases C and D: when pollution is unproductive land prices decrease
c(w,r,p2)=1
c(w,r,p1)=1
V(w,r,p1)=k
V(w,r,p2)=k C A B D w

9. Sum up
Because the utility levels of the citizens must be the same, higher pollution must be compensated by either higher wages, lower land rents or both
If pollution is productive, the firm spends less on pollution control
To keep costs constant for higher levels of pollution, wages or land prices must rise
Putting consumers and producers together
If pollution is productive, pollution raises wages but has an ambiguous effect on land rents
If pollution is unproductive, pollution depresses land prices but has an ambiguous effect on wages
If pollution is neutral, pollution decreases land prices and increases wages

10. Hedonic price theory
In the “real world” we are often confronted with bundles of goods with a single price for the whole bundle
We are interested in the price of an element of the bundle
This is the focus of the hedonic price theory
By observing the prices of many houses with different characteristics, we can infer the implicit value that is being placed on one characteristic, e.g. air quality
By observing wages associated with many different occupations we can infer the value of small changes in e.g. risk
Applied to prices of farmland as early as 1922
Rosen (1974) developed the formal theory of hedonic prices

11. Hedonic price theory (2)
Consider an homogenous area that can be considered a single market from the point of view of, say, houses
For simplification, each house is characterised by a single characteristic, z, say, air pollution
We are interested in the relation between price and air quality, p = p(z)
The price function is an equilibrium concept (partial equilibrium) resulting from interaction of supply and demand
We assume that the market is perfect
Both producers and consumers take p(z) as given

12. The consumer The consumer buys one house as well as other goods x
The consumer’s problem is:
What is the amount of x for particular values of z to achieve a certain level of utility:
The budget for buying the house, guaranteeing a certain level of utility is
Alternatively, we can define the consumer’s problem as
This is known as the bid function – it tells you the maximum amount a consumer is willing to pay as a function of income and air pollution

13. Consumer choice
Hedonic price function and two bid functions for two different levels of utility $
p(z)
Q(y,z,U0)
Q(y,z,U1)
Utility increases
Air quality z

14. The producer
The costs c of producing one house depend on input prices r and the characteristics z: c(r,z)
The producer maximises profits
Alternatively the price to obtain a certain level of profit given a level of z is
This is known as the offer function – it tells you the minimum amount a producer is willing to accept as a function of costs and air pollution

15. Producer choice
Hedonic price function and two offer functions for two different levels of profit $
F(r,z, p2)
Profits increase
F(r,z, p1)
p(z)
Air quality z

16. Market equilibrium
In the equilibrium, the marginal bid, the marginal offer, and the house price are identical – all parties in the market value the house the same, at the margin
p(z) $ F3 Q3 F2 Q2 F1 Q1
Air quality z

17. Willingness to pay $/unit
Marginal implicit price function and marginal WTP for one more unit of z for consumers 1 and 2
MWTP2(z)
MWTP1(z)
p‘(z)
Air quality z

18. Sum up
The hedonic price function tells you how price varies with environmental quality and other factors (income)
Take the derivative of the rental price to environmental quality – this gives the price of environmental quality
This is the first-stage estimation procedure
Do this for various income levels
This gives the price of environmental quality as a function of income – that is, an inverse demand function
This is the second-stage estimation procedure
This assumes, that different individuals making choices along the hedonic price function are variants of the same person
As the second-stage estimation procedure uses no additional data beyond the already contained in the hedonic price function, it can only reproduce the coefficients estimated from the hedonic price function
Recent applications of the method estimate only the first-stage

19. Theory and practice Theory and practice differ substantially
Niceties such as the difference between compensated and uncompensated demand functions are typically ignored
Critical assumptions:
Households have full information on all housing prices and attributes, transaction and moving costs are zero
Prices adjust instantaneously to changes
Market distortions are ignored
Only one market (housing) is analysed
The reason: data; although wages and house prices are known, it is hard to get data because of privacy

20. Application: Environmental hazards
Do environmental hazards such as the proximity to a major fuel pipeline affect house prices?
Study by Hansen, Benson and Hagen (Land Economics, 2006)
They use data for Bellingham, Washington,
the site of a 1999 rupture and explosion and compare housing prices before and after the accident ( )
The results suggest that the event led to a significant increase in perceived risk and perhaps to an increase beyond the actual risk
Before the accident public awareness was low and risks were irrelevant indicating a deviation between perceived and actual risk

21. Data and modelling strategy
In Bellingham, two major transmission pipelines run through residential area
The Olympic pipeline (refined petroleum) and the Trans Mountain pipeline (crude oil)
On June 10, 1999, the Olympic pipeline ruptured, spilling gallons of gasoline into the Whatcom Creek
Sales of all houses located within one mile of either pipeline was sampled for the period 1995 to 2004
A number of housing characteristics were included as well as the distance to a pipeline
To test the hypothesis (sales price are not affected in the absence of an effect) they split the sample to estimate the model for each sub-sample, the pre-event and the post-event sample

22. Regression results
* Significant at the 1% level; ** significant at the 5% level; *** significant at the 10% level.

23. As distance increases, sales price rises to the average level

24. The effect decays over time, but a significant price effect remains