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 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 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 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 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 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 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 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

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

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

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

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

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

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 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

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

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

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

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

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

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

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

As distance increases, sales price rises to the average level

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