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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. Last two weeks we looked at.

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Valuation 10: Hedonic Pricing

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Valuation 10 hedonic pricing l.jpg

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

Last two weeks we looked at l.jpg

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

The price of land l.jpg

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?

Starters l.jpg


  • 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

Wages land prices and pollution l.jpg

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

The consumer l.jpg

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

The producer l.jpg

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)

Productive and unproductive pollution l.jpg

Productive and unproductive pollution

Two cities with different pollution levels: p2> p1

  • Cases A and B: when pollution is productive wages rise

  • Cases C and D: when pollution is unproductive land prices decrease











Sum up l.jpg

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 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

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Consumer choice

  • Hedonic price function and two bid functions for two different levels of utility





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

Producer choice l.jpg

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)


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









Air quality z

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Willingness to pay


Marginal implicit price function and marginal WTP for one more unit of z for consumers 1 and 2




Air quality z

Sum up18 l.jpg

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

The effect decays over time but a significant price effect remains l.jpg

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

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