Valuation 10: Hedonic Pricing

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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

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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

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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?

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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

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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 well derive a function that can be estimated

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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

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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)

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Productive and unproductive pollution
Two cities with different pollution levels p2gt p1

• Cases A and B when pollution is productive wages
  rise
• Cases C and D when pollution is unproductive
  land prices decrease

r
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
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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

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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

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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

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The consumer

• The consumer buys one house as well as other
  goods x
• The consumers 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 consumers
  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

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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
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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

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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
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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
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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
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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

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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

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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 (1995-2004)
• 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

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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 229000 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

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Regression results
Significant at the 1 level significant at
the 5 level significant at the 10 level.
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As distance increases, sales price rises to the
average level
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The effect decays over time, but a significant
price effect remains