Revealed preferences

1
Hedonic pricing method
Summer School 2013 Economics of Food Safety,
Competitiveness and Applied Microeconometrics

• Revealed preferences
• No questionnaire!
• We gather data that come from the market
• No need to build a hypothetical market
• Where do we decide to live?
• Why do we choose a specific location?
• Which factors push companies to choose one
  location rather than another?
• Which characteristics of an area affect housing
  prices?
• Which are the important elements of a house that
  determine its price?

2
The choice of localization
Summer School 2013 Economics of Food Safety,
Competitiveness and Applied Microeconometrics

• The choice of housing is a composite good
• Distance from work, availability of public
  services, distance from schools, availability of
  green areas, availability of sport facilities,
  characteristics of housing ( of bedrooms, of
  bathrooms, flat, detached, etc.) etc.
• We assume that buyers choose houses that maximize
  their utility
• The constraints in the maximization problem are
  given by income, the price of the houses and the
  level of taxes
• gt therefore, the housing market give us some
  information on buyers preferences for housing and
  for their localization

3
Composite goods
Summer School 2013 Economics of Food Safety,
Competitiveness and Applied Microeconometrics

• Goods (or sites) can be described by a set of
  attributes or characteristics.
• The hedonic pricing method uses the same idea
  that goods are composed by a set of
  characteristics.
• Consider the characteristics of a house
• Number of floors, presence of a garden, number of
  bedrooms, number of bathrooms, square footage of
  the house, type of house, age, materials, etc.
• And also
• Distance from public transport, distance from the
  city centre, distance from main roads, distance
  from shops, distance from sport facilities, crime
  rate, average income of inhabitants, presence of
  a university, etc.
• The composite good has a price, but there is no
  explicit price for each characteristic that
  compose the good.

4
The hedonic pricing method
Summer School 2013 Economics of Food Safety,
Competitiveness and Applied Microeconometrics

• Problem of estimating hedonic equations
• Hedonic prices are identified through a
  comparison of similar goods that differ for the
  quality of one characteristic
• The basic idea is to use the systematic variation
  in the price of a good that can be explained by
  an environmental characteristic of the good. This
  is the starting point to assess the WTP for the
  environmental characteristic
• We look at market data!
• Real transactions!

5
Example
Summer School 2013 Economics of Food Safety,
Competitiveness and Applied Microeconometrics

• Lets consider 2 residential properties identical
  in all characteristics and localization.
• The only difference is that house A has 2
  bedrooms, while house B has 3 bedrooms.
• In a competitive market, the price difference
  between the two houses reflects the value of the
  additional room of house B.
• If the price difference between the two houses is
  less than buyers WTP for the additional room,
  then buyers will try to buy house B, driving up
  its price until the equilibrium is reached.
• In the same way, if house A costs much less than
  house B, buyers will increase the demand for
  house A, driving up its price.

6
Summer School 2013 Economics of Food Safety,
Competitiveness and Applied Microeconometrics

• The hedonic pricing method applies this simple
  concept to the environmental characteristics of
  residential properties
• The price difference between houses that have
  different levels of environmental quality,
  keeping constant all other characteristics,
  reflects the WTP for the different level of
  environmental quality
• gt we can assess the value of an environmental
  quality, according to market prices of
  residential properties
• gt variation in environmental quality affects the
  price of housing

7
A bit of history
Summer School 2013 Economics of Food Safety,
Competitiveness and Applied Microeconometrics

• 1926 Waugh studies the variation of prices of
  vegetables
• 1938 Court looks at the car market in Detroit
• 1967 first application to the housing market
  Ridker and Henning gt effects of air pollution on
  prices of housing
• 1974 Rosen describe the first formal model of the
  hedonic pricing method
• Other applications
• Agricultural goods
• Cars
• Wine
• Job market

8
Rosens model
Summer School 2013 Economics of Food Safety,
Competitiveness and Applied Microeconometrics

• Consumers (buyers) have a utility function
• U(s,n,c)
• s house characteristics
• n characteristics of the area where the house
  is located
• c other consumption goods
• Budget constraint
• m c p(s,n)
• m income
• p(s,n) expenditure for a house
• p(s,n) is assumed to change in a non linear
  relationship with the characteristics of houses.
  That is, the cost of houses change in an unknown
  relationship with number of rooms, etc.
• c is the expenditure for all other goods

9
Summer School 2013 Economics of Food Safety,
Competitiveness and Applied Microeconometrics

• The maximization of the utility function subject
  to the budget constraint, gives the usual first
  order conditions.
• That is, the marginal rate of substitution
  between each characteristic n and the consumption
  of other goods is equal to the price
  (coefficient) of n and the price of c.
• The price of c is our numeraire and we put it
  equal to 1.
• The price of n describes the price of a marginal
  change in n.
• The first order conditions are
• (Un is the partial derivative of U with respect
  to n)
• First order conditions simply say that the
  consumer (buyer) is willing to pay pn for a
  marginal change of n

10
Utility maximization and budget constraint
Summer School 2013 Economics of Food Safety,
Competitiveness and Applied Microeconometrics
c
U(s,n,c)
mcp(s,n)
n
11
The hedonic price function
Summer School 2013 Economics of Food Safety,
Competitiveness and Applied Microeconometrics

• The function that describes how housing price
  changes when housing characteristics change
• p(s,n)
• is the hedonic price function
• The derivative of the function with respect to
  one of the characteristics n is the implicit
  price of n.
• If we knew the hedonic price function and the
  implicit price of n, we could estimate buyers
  WTP for n, given that this is equal to the
  marginal rate of substitution between n and the
  other goods (numeraire)

12
Indifference curves
Summer School 2013 Economics of Food Safety,
Competitiveness and Applied Microeconometrics

• The budget constraint says that what we dont
  spend for other goods is spent for housing
• p(s,n) c m p(s,n)
• The utility function can be written in this way
• U(s,n,c)U(s,n,m p(s,n))
• Therefore we can describe the utility function of
  consumers (buyers) with indifference curves (for
  given values of m and s)
• Each indifference curve gives for a constant
  level of utility the expenditure on housing and n
  for a given level of income and s.

p(s.n)
U
n
13
Heterogeneous consumers
Summer School 2013 Economics of Food Safety,
Competitiveness and Applied Microeconometrics

• People with different incomes have different
  indifference curves, even if they have the same
  preferences (U has the same functional form for
  all respondents)
• People with different preferences have different
  indifference curves
• In a world of heterogeneous consumers (buyers)
  that have different levels of income, we have a
  continuum of indifference curves

p(s.n)
n
14
Hedonic equilibrium
Summer School 2013 Economics of Food Safety,
Competitiveness and Applied Microeconometrics

• Suppose that consumers (buyers) consider
  exogenous the hedonic price function
• Consumers (buyers) maximize utility subject to
  the budget constraint and to the hedonic price
  function

p(s.n)
n
15
Hedonic equilibrium considering the supply
Summer School 2013 Economics of Food Safety,
Competitiveness and Applied Microeconometrics

• The hedonic price function comes from the
  equilibrium of demand and supply of housing. Both
  are considered exogenous.
• Sellers have isoprofit curves (p)

pb
p(s.n)
Sellers
pa
Uk
Buyers
Ui
n
16
Marginal Willingness To Pay
Summer School 2013 Economics of Food Safety,
Competitiveness and Applied Microeconometrics

• The main characteristic of the model is that
  buyers and sellers are efficiently matched along
  the hedonic price function
• At any point along the hedonic price function,
  buyers marginal willingness to pay (and sellers
  willingness to accept) for a change in n is given
  by the derivative of the hedonic price function
  with respect to n.
• This implicit price changes with n if the hedonic
  price function is non linear.
• The model can be generalized to the case where we
  consider several characteristics of residential
  properties and of the area where houses are
  located
• p(x1,x2,xk)

17
Model estimate
Summer School 2013 Economics of Food Safety,
Competitiveness and Applied Microeconometrics

• Now we need to specify a functional form for p.
• A common functional form is the double-log
• The implicit price can be estimated for specific
  value of the characteristics of houses (for
  example, the average value)
• For the double-log function, the implicit price
  of x1 is given by
• ß1 gives the percentage change in the price of
  housing given a percentage change in x1
• We usually estimate the implicit price at the
  average value of housing

18
Some limitations and assumptions
Summer School 2013 Economics of Food Safety,
Competitiveness and Applied Microeconometrics

• Perfect information
• Buyers observe the characteristics of houses and
  are able to perfectly describe the hedonic price
  function
• Buyers can purchase whatever combination of
  characteristics they desire.
• They can always find the combination of bedrooms,
  bathrooms, location of the house that they want
• Implicit prices allow us only to assess marginal
  variations in the characteristics of houses (but
  if we consider that all buyers are identical then
  we can consider non marginal changes as well
  too strong assumption!)
• Example if the average house has 3 bedrooms and
  costs X, I cannot say that buyers are willing to
  pay Y for a house that has 7 bedrooms. We cant
  say that an increase of 4 bedrooms is a marginal
  change
• The estimate of non-marginal variations requires
  the estimate of individual demand parameters,
  which is very difficult

19
Econometric problems
Summer School 2013 Economics of Food Safety,
Competitiveness and Applied Microeconometrics

• Multicollinearity
• if a house has several bedrooms, it will likely
  have several bathrooms, etc.
• distances dont use too many distances in your
  function
• Heteroskedasticity
• Spatial autocorrelation
• The value of one house will be influenced by the
  value of surrounding houses
• If I only use the data of sold properties and do
  not consider the characteristics of unsold
  properties, my coefficient can be biased (sample
  selection bias)
• Solution 2 steps estimate 1) Probit model for
  the probability of a sale with both sold and
  unsold properties 2) regression model with only
  sold properties Inverse Mills Ratio calculated
  in 1. Check if the coefficient of the inverse
  mills ratio is significantly different from zero.
  If it is not, then delete it from the regression

20
Example 1 Air quality
Summer School 2013 Economics of Food Safety,
Competitiveness and Applied Microeconometrics

• Air pollution is one of the first application of
  the hedonic pricing model
• Ridker, Henning (1967) The determinants of
  property values with special reference to air
  pollution Review of Economics and Statistics.
• No residential properties sale prices, but census
  tract data from St. Luis, 1960.
• Dependent variable median value of property
  prices
• Independent variables median characteristics of
  houses in a census tract, quality of schooling,
  access to highway, neighbourhood characteristics,
  tax levels, public services
• Air quality (SO2, SO3, H2S, H2SO4) measured as
  direct effects on houses and on human health.

21
Results (some variables)
Summer School 2013 Economics of Food Safety,
Competitiveness and Applied Microeconometrics
Coefficient Standard Error
Air pollution -245.0 88.1
Rooms 488.5 41.1
Distance from city centre (minutes) 320.2 138.7
New buildings () 48.36 7.20
Access to highway (dummy) 922.5 278.9
Number of persons in a house -3210.0 548.7
Median income per family 0.937 0.1057
Linear model House price falls by 245US if
pollution is present Ridker and Henning estimate
the environmental damage of air pollution in St.
Louis to be 82 million dollars gt need to compare
this estimate with the cost of a public program
to clean pollution
22
Problems of Ridker e Henning example
Summer School 2013 Economics of Food Safety,
Competitiveness and Applied Microeconometrics

• Multicollinearity
• Omitted variables
• Positive sign for the coefficient of the distance
  from the city centre
• They do not consider the price of single houses,
  but the median value of the houses sold in a
  census tract

23
Example 2 Water quality
Summer School 2013 Economics of Food Safety,
Competitiveness and Applied Microeconometrics

• Leggett and Bockstael (2000) Journal of
  Environmental Economics and Management
• 741 observations
• Effects of Chesapeake Bay water quality on prices
  of houses located along the bay
• Rather than using the characteristics of houses
  (rooms, bathrooms, etc.), Leggett and Bockstael
  use the appraised value of houses.
• Water quality is measured using information on
  the level of pollution of the bay publicly given
  by the Department of Health of Maryland

24
Descriptive Statistics
Summer School 2013 Economics of Food Safety,
Competitiveness and Applied Microeconometrics
Variable Description Media N741
Price (1000) Sale price 335.91
VSTRU Apprised value of the house 125.84
ACRES House acreage 0.90
ACSQ acreage2 2.42
DISBA Distance from Baltimore 26.40
DISAN Distance from Annapolis 13.30
ANBA DISBADISAN 352.50
BDUM DISBA( commuters) 8.04
PLOD of land not intensively developed 0.18
PWAT of land with water or humid areas 0.32
DBAL Minimum distance from a polluting source 3.18
F.COL Median concentration of fecal coliform 109.70
25
Results
Summer School 2011 Economics of Food Safety,
Competitiveness and Applied Microeconometrics
Dependent variable sale price Linear model Dependent variable sale price Linear model Dependent variable sale price Linear model
Coefficient Standard Error
Intercept 238.69 47.44
VSTRU 1.37 0.040
ACRES 116.9 7.62
ACSQ -7.33 0.79
DISBA -3.96 1.74
DISAN -11.80 2.50
ANBA 0.36 0.09
BDUM -10.2 -0.03
PLOD 71.69 0.27
PWAT 119.97 0.35
DBAL 2.78 2.50
F.COL -0.052 0.025
26
Welfare change
Summer School 2013 Economics of Food Safety,
Competitiveness and Applied Microeconometrics

• The presence of fecal coliform is equal to -0.052
  dollars per 1,000 dollars of the value of the
  house
• Suppose fecal coliform increase from 109 (average
  value) to 159
• The welfare change is equal to
• (159-109)(-0.052) -2.6
• This means that a person that is buying a house
  is willing to pay 2,600 more to avoid the
  increase in the concentration of fecal coliform.

27
Measuring Welfare Via Hedonic Methods
Summer School 2013 Economics of Food Safety,
Competitiveness and Applied Microeconometrics

• The above calculations give the change in the
  house price due to fecal coliform changes but do
  not really give the changes in welfare, in the
  sense of the addtional consumer surplus you get
  from the change.
• The following example shows how that consumer
  surplus can be calculated. It entails a two
  stage estimate procedure, the first stage is the
  hedonic price estimates as above and the second
  stage is a follow on regression based on
  households willingness to pay the implict price.

28
Case Study - Overview
Summer School 2013 Economics of Food Safety,
Competitiveness and Applied Microeconometrics

• This exercise presents an application of the
  Hedonic Price Method for the valuation of
  benefits brought about by the improvement of the
  broadleaf coverage rate in an urban area.
• The local government decided to improve the
  quality of urban parks and green spaces near
  residential areas.

F. Caracciolo Case Study N.1, Portici 2011
29
Case Study - Overview
Summer School 2013 Economics of Food Safety,
Competitiveness and Applied Microeconometrics

• This study focuses on the valuation of only one
  of them, namely the increase of broadleaf
  coverage.
• To elicit the value assigned to a change in
  broadleaf coverage, the prices of houses in areas
  with different coverage rates are observed.

F. Caracciolo Case Study N.1, Portici 2011
30
Methodology
Summer School 2013 Economics of Food Safety,
Competitiveness and Applied Microeconometrics

• Collection of data
• Resident households were randomly selected from
  the council directory of resident households.
• The broadleaf coverage rate within the ray of 300
  meters for every house was calculated.
• The price of the house was determined looking at
  estate agency bulletins and recent transactions.
  Expert advice on prices for some properties was
  also required. (Nb sample selection bias not
  addressed).
• The collection of information on the
  socio-economic features of the household was done
  looking at recent census data.

31
Methodology
Summer School 2013 Economics of Food Safety,
Competitiveness and Applied Microeconometrics

• Calculation of the value of environmental
  quality
• Estimation of the House Price Function.
• Calculation of the Implicit Marginal Price of the
  environmental good (the responsiveness of the
  house price function with respect to the
  environmental quality, ie the first derivative c
  x P/Zm) for each observation.
• Estimation of the Implicit Inverse Demand
  Function for the environmental good. (implicit
  price as a function of the environmental good and
  socio-economic features of individuals).
• Calculation of the Consumer Surplus

32
Database for Case Study
Summer School 2013 Economics of Food Safety,
Competitiveness and Applied Microeconometrics

33

Summer School 2013 Economics of Food Safety,
Competitiveness and Applied Microeconometrics
34
Key
Summer School 2013 Economics of Food Safety,
Competitiveness and Applied Microeconometrics

• OBSERV - Number of the observation
• PRICEX - Price of house (US, 1995)
• NUMROO - Number of rooms in the house
• INDEPE - Dummy variable INDEPE1 Detached house.
  0 otherwise.
• DISTAN - Distance from downtown (Km)
• MURDER - Murder rate of the area (murders/year
  per 1000 residents)
• BROADL - Broadleaves tree coverage rate (covered
  area/total area)
• REDHOU - Annual income of the household (Usd,
  1995)
• COMPON - Number of components in the household

35
Trasformazione Box-Cox
Summer School 2013 Economics of Food Safety,
Competitiveness and Applied Microeconometrics
36
Estimation of Hedonic House Price Function
Summer School 2013 Economics of Food Safety,
Competitiveness and Applied Microeconometrics

• Regression of LnPriceX on other variables
• The coverage rate of broadleaves exhibits a
  positive relevant relationship with the price,
  other things equal.
• Hedonic function

exp((lnbroadl.17)(-.058-.30)(-.0902.18)(.137
.367)(.5091.23)(110.79)) exp(0.5rmse2)
37
Retro transformation problem (predlog in stata)
ln y xßu y exp(xß)exp(u) E(yx)
exp(x ß) Eexp(u) Eexp(u)
exp(0.5s2) E(yx) exp(x ß) exp(0.5s2)

38
Estimation of Hedonic House Price Function
Summer School 2013 Economics of Food Safety,
Competitiveness and Applied Microeconometrics

• Estimated Hedonic Price function is not linear

39
Calculation of Implicit Price
Summer School 2013 Economics of Food Safety,
Competitiveness and Applied Microeconometrics

• This function, as described in the methodology,
  is the first derivative of the house price
  function with respect to the broadleaf tree rate.
  The implicit price function is
• IMPLIP (0.16871 / BROADL) PRICEX 
• This function is used for estimating, observation
  by observation, the implicit price of an
  additional unit of broadleaf coverage

40

41
Estimation of inverse demand curve
Summer School 2013 Economics of Food Safety,
Competitiveness and Applied Microeconometrics

• The estimation of the inverse demand function is
  a second stage estimation based on the result of
  the first estimation (i.e. the house price
  function and related first derivative).
• The estimated implicit price of the broadleaf
  coverage unit (in this case, the percent point)
  is regressed on the observed coverage rate and
  the socio-economic features of the owners.

42
Estimation of inverse demand curve
Summer School 2013 Economics of Food Safety,
Competitiveness and Applied Microeconometrics

• Results of regression analysis
• The inverse demand function is therefore
  estimated as
• Demandexp(6.34(1.25.107)(4.06.762)(-.853lnb
  roadl)) exp(0.5rmse2)

43
Inverse Demand Function
Summer School 2013 Economics of Food Safety,
Competitiveness and Applied Microeconometrics

• The inverse demand function can be shown. The
  variables COMPON REDHOU and are fixed at the
  sample mean level.

44
Inverse Demand Function
Summer School 2013 Economics of Food Safety,
Competitiveness and Applied Microeconometrics
45
Calculation of Consumer Surplus
Summer School 2013 Economics of Food Safety,
Competitiveness and Applied Microeconometrics

• The consumer surplus is calculated by estimating
  the area under the demand curve.
• This is done by integrating the inverse demand
  curve with respect to the implicit price and
  calculating the definite integral observation by
  observation (between the present coverage rate
  (E1BROADL) and the coverage rate (new_broadl)
  planned by the policy maker (increase of 10 of
  the coverage)

46
Summer School 2013 Economics of Food Safety,
Competitiveness and Applied Microeconometrics
surplus1 broadl observ 32912.53 2 1 24453.89 4 2 1
9908.35 6 3 21903.04 5 4 16952.95 8 5 41687.59 1 6
19908.35 6 7 21903.04 5 8 7024.416 30 9 14842.29
10 10 11453.08 15 11 12581.64 13 12 10123.16 18 13
8797.876 22 14 13992.77 11 15 18293.61 7 16 7391.
047 28 17 21903.04 5 18 5449.304 42 19 8523.569 23
20 13992.77 11 21 5656.788 40 22 5167.326 45 23 2
982.945 90 24 3651.009 70 25 3124.007 85 26 3280.4
27 80 27 3454.947 75 28 5767.148 39 29 3280.427 80
30
47
Discussion
Summer School 2013 Economics of Food Safety,
Competitiveness and Applied Microeconometrics

• This information can be used first to calculate
  the average consumer surplus per household and
  can be multiplied by the number of households to
  get a measure of the total benefits which can be
  compared with the cost of the intervention.
• On distributional grounds, notice that a 10
  increase for people living in areas with high
  coverage rate does not change the consumer
  surplus much, compared to those living in low
  coverage rate areas.