revealed preferences no questionnaire! we gather data that come from the market no need to build...

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

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

=> therefore, the housing market give us some information on buyers preferences for housing and for their localization

2


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.

3


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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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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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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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:◦ Agricultural goods◦ Cars◦ Wine◦ Job market

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Consumers (buyers) have a utility function:

U(s,n,c)s = house characteristicsn = characteristics of the area where the house is locatedc = other consumption goods

Budget constraint:

m = c + p(s,n)

m = income p(s,n) expenditure for a housep(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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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

9

),(),,(

),,(nsp

cnsU

cnsUn

c

n

n

nsppn

),(


10

n

c )*,( nspU

Un

c

n

U(s*,n,c)

m=c+p(s*,n)


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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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.

12

U

n

p(s*.n)


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:

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p(s*.n)

n


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:

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p(s*.n)

n


The hedonic price function comes from the equilibrium of demand and supply of housing. Both are considered exogenous.

Sellers have isoprofit curves (π)

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p(s*.n)

n

Ui

Uk

Buyers

πa

πb

Sellers


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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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:

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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1

*x

p

x

p

17

ikikiii xxxp ln...lnlnln 2211


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 can’t 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

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Multicollinearity◦ if a house has several bedrooms, it will likely have several

bathrooms, etc. ◦ distances: don’t 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

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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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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

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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


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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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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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 24


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 0.02525


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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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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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.

28F. Caracciolo Case Study N.1, Portici 2011


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.

29F. Caracciolo Case Study N.1, Portici 2011


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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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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32


OBSERV PRICEX NUMROOINDEPE DISTAN MURDER BROADL REDHOU COMPON1 50,847 1 0 6 1.8 2 21 22 53,593 2 0 44 3.1 4 25 33 54,019 2 0 45 4.5 6 23 44 59,940 3 0 41 2.5 5 28 55 60,849 2 0 7 3.5 8 32 46 61,947 3 0 39 2.2 1 34 47 75,908 2 0 10 1 6 30 38 81,304 4 0 50 4.5 5 36 29 85,028 3 0 48 2.1 30 43 2

10 88,484 4 0 35 3 10 38 211 98,648 2 1 13 1.5 15 49 312 98,920 3 0 9 0.9 13 55 313 111,049 3 0 24 1.2 18 72 214 121,345 4 0 50 0.5 22 68 315 132,049 4 1 6 0.1 11 62 416 136,018 4 0 15 0.5 7 78 517 142,546 6 0 43 0.1 28 74 418 145,584 4 0 3 1.5 5 80 319 173,394 4 1 5 1.4 42 92 420 173,904 3 0 3 0.9 23 87 521 180,394 4 1 4 0.3 11 85 322 198,765 3 0 5 0.7 40 93 423 212,038 5 1 0.5 0.1 45 96 624 234,194 5 1 0.5 0.6 90 80 425 241,879 5 1 7 0.4 70 93 526 267,944 4 0 0.1 0.1 85 78 427 267,975 7 1 24 0.6 80 83 628 271,039 6 1 10 0.1 75 98 329 294,048 5 1 12 0.4 39 105 430 295,536 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 33


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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Trasformazione Box-CoxSummer 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

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_cons 10.78918 .1581469 68.22 0.000 10.46278 11.11558 lnnumeroc .5085497 .1332022 3.82 0.001 .2336338 .7834657 indepe .1369724 .0960569 1.43 0.167 -.0612793 .335224 lndistan -.0895227 .0313272 -2.86 0.009 -.154179 -.0248664 lnmurder -.0578538 .0457 -1.27 0.218 -.152174 .0364664 lnbroadl .1687055 .0489774 3.44 0.002 .067621 .26979 lnpricex Coef. Std. Err. t P>|t| [95% Conf. Interval]

exp((lnbroadl*.17)+(-.058*-.30)+(-.090*2.18)+(.137*.367)+(.509*1.23)+(1*10.79)) *exp(0.5*rmse^2)


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)

800

00

100

00

01

200

00

140

00

01

600

00

180

00

0E

stim

ate

d H

edon

ic P

rice

func

tion

0 20 40 60 80 100Broadleaves tree coverage rate (covered area/total area)

Estimated Hedonic Price function is not linear:

38


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:

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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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Results of regression analysis:

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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_cons 6.341192 .294986 21.50 0.000 5.73484 6.947544 lnbroadl -.8530434 .0387789 -22.00 0.000 -.9327546 -.7733323 lnredhou .7618994 .0929804 8.19 0.000 .5707755 .9530233 lncompon .1073393 .0991395 1.08 0.289 -.0964449 .3111234 lnimplicit Coef. Std. Err. t P>|t| [95% Conf. Interval]


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

43


44

050

0010

000

1500

0Im

plic

it m

argi

nal p

rice

of c

over

age

0 20 40 60 80 100Broadleaves trees coverage rate


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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46

surplus1 broadl observ32912.53 2 124453.89 4 219908.35 6 321903.04 5 416952.95 8 541687.59 1 619908.35 6 721903.04 5 87024.416 30 914842.29 10 1011453.08 15 1112581.64 13 1210123.16 18 138797.876 22 1413992.77 11 1518293.61 7 167391.047 28 1721903.04 5 185449.304 42 198523.569 23 2013992.77 11 215656.788 40 225167.326 45 232982.945 90 243651.009 70 253124.007 85 263280.427 80 273454.947 75 285767.148 39 293280.427 80 30


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.

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revealed preferences no questionnaire! we gather data that come from the market no need to build...

Documents

characteristics of housing

type of house

price difference

economics of food safety

summer school

environmental characteristics

explicit price

additional room of house