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Summer School 2013 Economics of Food Safety, Competitiveness and Applied Microeconometrics
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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?
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Summer School 2013 Economics of Food Safety, Competitiveness and Applied Microeconometrics
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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.
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We assume that buyers choose houses that maximize their
utility
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The constraints in the maximization problem are given by
income, the price of the houses and the level of taxes
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=> therefore, the housing market give us some information
on buyers preferences for housing and for their localization
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Summer School 2013 Economics of Food Safety, Competitiveness and Applied Microeconometrics
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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.
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Summer School 2013 Economics of Food Safety, Competitiveness and Applied Microeconometrics
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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!
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Summer School 2013 Economics of Food Safety, Competitiveness and Applied Microeconometrics
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Let’s 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.
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Summer School 2013 Economics of Food Safety, Competitiveness and Applied Microeconometrics
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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
=> we can assess the value of an environmental
quality, according to market prices of residential
properties
=> variation in environmental quality affects the
price of housing
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Summer School 2013 Economics of Food Safety, Competitiveness and Applied Microeconometrics
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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 => effects of air pollution on
prices of housing
1974 Rosen describe the first formal model of the
hedonic pricing method
Other applications:
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Agricultural goods
Cars
Wine
Job market
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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
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Summer School 2013 Economics of Food Safety, Competitiveness and Applied Microeconometrics
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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:
U n ( s, n, c)
 p n ( s , n)
U c ( s, n, c)
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(Un is the partial derivative of U with respect to n)
pn 
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p ( s, n)
n
First order conditions simply say that the consumer (buyer) is
willing to pay pn for a marginal change of n
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Summer School 2013 Economics of Food Safety, Competitiveness and Applied Microeconometrics
c
Un
 p n ( s*, n)
Uc
U(s*,n,c)
m=c+p(s*,n)
n
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Summer School 2013 Economics of Food Safety, Competitiveness and Applied Microeconometrics
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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)
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Summer School 2013 Economics of Food Safety, Competitiveness and Applied Microeconometrics
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The budget constraint says that what we don’t 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
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Summer School 2013 Economics of Food Safety, Competitiveness and Applied Microeconometrics
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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
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Summer School 2013 Economics of Food Safety, Competitiveness and Applied Microeconometrics
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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
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Summer School 2013 Economics of Food Safety, Competitiveness and Applied Microeconometrics
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The hedonic price function comes from the equilibrium of
demand and supply of housing. Both are considered
exogenous.
Sellers have isoprofit curves (π)
πb
p(s*.n)
Sellers
πa
Uk
Buyers
Ui
n
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Summer School 2013 Economics of Food Safety, Competitiveness and Applied Microeconometrics
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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)
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Summer School 2013 Economics of Food Safety, Competitiveness and Applied Microeconometrics
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Now we need to specify a functional form for p.
A common functional form is the double-log:
ln pi    1 ln x1i  2 ln x2i  ... k ln xki   i
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:
p
p
 1 *
x1
x1
β1 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
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Summer School 2013 Economics of Food Safety, Competitiveness and Applied Microeconometrics
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Perfect information:
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Buyers can purchase whatever combination of characteristics
they desire.
◦ Buyers observe the characteristics of houses and are able to
perfectly describe the hedonic price function
◦ They can always find the combination of bedrooms, bathrooms,
location of the house that they want
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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 can’t say that an increase of 4 bedrooms is a
marginal change
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The estimate of non-marginal variations requires the
estimate of individual demand parameters, which is very
difficult
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Summer School 2013 Economics of Food Safety, Competitiveness and Applied Microeconometrics
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Multicollinearity
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Heteroskedasticity
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Spatial autocorrelation
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◦ if a house has several bedrooms, it will likely have several
bathrooms, etc.
◦ distances: don’t use too many distances in your function
◦ 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
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Summer School 2013 Economics of Food Safety, Competitiveness and Applied Microeconometrics
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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.
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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
-3210.0
548.7
0.937
0.1057
Number of persons in a house
Median income per family
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 => need to compare this estimate
with the cost of a public program to clean pollution
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Summer School 2013 Economics of Food Safety, Competitiveness and Applied Microeconometrics
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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
…
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Summer School 2013 Economics of Food Safety, Competitiveness and Applied Microeconometrics
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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
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Summer School 2013 Economics of Food Safety, Competitiveness and Applied Microeconometrics
Variable
Description
Media N=741
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
DISBA*DISAN
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
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Summer School 2011 Economics of Food Safety, Competitiveness and Applied Microeconometrics
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
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Summer School 2013 Economics of Food Safety, Competitiveness and Applied Microeconometrics
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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.
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Summer School 2013 Economics of Food Safety, Competitiveness and Applied Microeconometrics
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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.
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Summer School 2013 Economics of Food Safety, Competitiveness and Applied Microeconometrics
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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
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Summer School 2013 Economics of Food Safety, Competitiveness and Applied Microeconometrics
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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
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Summer School 2013 Economics of Food Safety, Competitiveness and Applied Microeconometrics
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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.
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Summer School 2013 Economics of Food Safety, Competitiveness and Applied Microeconometrics
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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
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Summer School 2013 Economics of Food Safety, Competitiveness and Applied Microeconometrics
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Summer School 2013 Economics of Food Safety, Competitiveness and Applied Microeconometrics
OBSERV
PRICEX NUMROOINDEPE DISTAN MURDER BROADL REDHOU COMPON
1
50,847
1
0
6
1.8
2
21
2
2
53,593
2
0
44
3.1
4
25
3
3
54,019
2
0
45
4.5
6
23
4
4
59,940
3
0
41
2.5
5
28
5
5
60,849
2
0
7
3.5
8
32
4
6
61,947
3
0
39
2.2
1
34
4
7
75,908
2
0
10
1
6
30
3
8
81,304
4
0
50
4.5
5
36
2
9
85,028
3
0
48
2.1
30
43
2
10
88,484
4
0
35
3
10
38
2
11
98,648
2
1
13
1.5
15
49
3
12
98,920
3
0
9
0.9
13
55
3
13
111,049
3
0
24
1.2
18
72
2
14
121,345
4
0
50
0.5
22
68
3
15
132,049
4
1
6
0.1
11
62
4
16
136,018
4
0
15
0.5
7
78
5
17
142,546
6
0
43
0.1
28
74
4
18
145,584
4
0
3
1.5
5
80
3
19
173,394
4
1
5
1.4
42
92
4
20
173,904
3
0
3
0.9
23
87
5
21
180,394
4
1
4
0.3
11
85
3
22
198,765
3
0
5
0.7
40
93
4
23
212,038
5
1
0.5
0.1
45
96
6
24
234,194
5
1
0.5
0.6
90
80
4
25
241,879
5
1
7
0.4
70
93
5
26
267,944
4
0
0.1
0.1
85
78
4
27
267,975
7
1
24
0.6
80
83
6
28
271,039
6
1
10
0.1
75
98
3
29
294,048
5
1
12
0.4
39
105
4
30
295,536
4
1
1
0.1
80
110
4
Sample average
148,973
3.70
0.37
18.67
1.34
29.20
64.93
3.67
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Summer School 2013 Economics of Food Safety, Competitiveness and Applied Microeconometrics
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OBSERV - Number of the observation
PRICEX - Price of house (US$, 1995)
NUMROO - Number of rooms in the house
INDEPE - Dummy variable: INDEPE=1 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
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Summer School 2013 Economics of Food Safety, Competitiveness and Applied Microeconometrics
Trasformazione Box-Cox
Summer School 2013 Economics of Food Safety, Competitiveness and Applied Microeconometrics

Regression of LnPriceX on other variables:
lnpricex
Coef.
lnbroadl
lnmurder
lndistan
indepe
lnnumeroc
_cons
.1687055
-.0578538
-.0895227
.1369724
.5085497
10.78918
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Std. Err.
.0489774
.0457
.0313272
.0960569
.1332022
.1581469
t
3.44
-1.27
-2.86
1.43
3.82
68.22
P>|t|
0.002
0.218
0.009
0.167
0.001
0.000
[95% Conf. Interval]
.067621
-.152174
-.154179
-.0612793
.2336338
10.46278
.26979
.0364664
-.0248664
.335224
.7834657
11.11558
The coverage rate of broadleaves exhibits a positive relevant
relationship with the price, other things equal.
Hedonic function
exp((lnbroadl*.17)+(-.058*-.30)+(-.090*2.18)+(.137*.367)+(.509*1.23)+(1*10.79)) *exp(0.5*rmse^2)
36
Retro transformation problem (predlog in stata)
ln y = x’β+u
y = exp(x’β)exp(u)
E(y|x) = exp(x’ β) E{exp(u)}
E{exp(u)} = exp(0.5σ2)
E(y|x) = exp(x’ β) exp(0.5σ2)
Summer School 2013 Economics of Food Safety, Competitiveness and Applied Microeconometrics
100000
120000
140000
160000
180000
Estimated Hedonic Price function is not
linear:
80000

0
20
40
60
80
Broadleaves tree coverage rate (covered area/total area)
100
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Summer School 2013 Economics of Food Safety, Competitiveness and Applied Microeconometrics
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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:
39
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Summer School 2013 Economics of Food Safety, Competitiveness and Applied Microeconometrics
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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.
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Summer School 2013 Economics of Food Safety, Competitiveness and Applied Microeconometrics
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Results of regression analysis:
lnimplicit
Coef.
lncompon
lnredhou
lnbroadl
_cons
.1073393
.7618994
-.8530434
6.341192

Std. Err.
.0991395
.0929804
.0387789
.294986
t
1.08
8.19
-22.00
21.50
P>|t|
0.289
0.000
0.000
0.000
[95% Conf. Interval]
-.0964449
.5707755
-.9327546
5.73484
.3111234
.9530233
-.7733323
6.947544
The inverse demand function is therefore estimated
as:
Demand=exp(6.34+(1.25*.107)+(4.06*.762)+(.853*lnbroadl)) *exp(0.5*rmse^2)
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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.
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0
5000
10000
15000
Summer School 2013 Economics of Food Safety, Competitiveness and Applied Microeconometrics
0
20
40
60
Broadleaves trees coverage rate
80
100
44
Summer School 2013 Economics of Food Safety, Competitiveness and Applied Microeconometrics
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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 (E1=BROADL) and the
coverage rate (new_broadl) planned by the policy
maker (increase of 10% of the coverage)
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Summer School 2013 Economics of Food Safety, Competitiveness and Applied Microeconometrics
surplus1
32912.53
24453.89
19908.35
21903.04
16952.95
41687.59
19908.35
21903.04
7024.416
14842.29
11453.08
12581.64
10123.16
8797.876
13992.77
18293.61
7391.047
21903.04
5449.304
8523.569
13992.77
5656.788
5167.326
2982.945
3651.009
3124.007
3280.427
3454.947
5767.148
3280.427
broadl
2
4
6
5
8
1
6
5
30
10
15
13
18
22
11
7
28
5
42
23
11
40
45
90
70
85
80
75
39
80
observ
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
46
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.
47