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Extensive summary of the course Urban Economic Challenges and Policies at the VU
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Extensive summary of the course Urban Economic Challenges and Policies at the VU Amsterdam.
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Urban Economic Challenges and Policies - notes & summaryWeek 1 - Hedonic Pricing
Cost-benefit analysis determine whether a policy is good for society given utility gains and losses.
- Utility gain = willingness-to-pay
- Utility loss = willingness-to-accept
When is a project beneficial to society?
- Kaldor-Hicks criterion: if the benefits are large enough to compensate the losses.
o You can use some of the gains (e.g. by taxing those who gain from the project) to
make the net effect of the project non-negative for all and positive for some (i.e. if
the project could result in a Pareto-improvement)
o Procedure: list all the costs and benefits associated with a project translate them
into the corresponding willingness-to-pay and willingness-to-accept add them to
check if a Pareto improvement results.
Anticipation effect = If an improvement in public transport is expected properties in the vicinity of
the stations will increase in value as soon as it is announced. This complicates measurement of the
effect. Also, there is often uncertainly about realization, time of opening. Construction works may
temporarily make the property less attractive.
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Example: the effect of proximity to water on the house price
Proximity to water is positively correlated with the WTP. How do we measure these benefits?
Ideal comparison: two houses that differ in proximity to water, but are otherwise identical
- Proximity to water is the only remaining difference and therefore the only reason for a
difference in price
- The ceteris paribus condition should be valid
- The difference in price reveals the willingness to pay for proximity to water
Potential pitfalls: omitted variable bias. Characteristics that are correlated with x (proximity to
water), what happens if we don’t observe them?
Possible solution: dummies for small groups of observations. Coefficients for these dummies capture
the impact of all variables that are common for the observation within the group
- A very powerful way to deal with omitted variable bias You don’t need to observe all the
variables for which you control by the fixed effects
- It’s only the variation within the selected groups of observations that determines the
estimated coefficient
- Fixed effects control for unobserved characteristics. Result in lower (but still significant)
effects of proximity to water
Measuring the value of proximity to water:
- Closer approximation of the ceteris paribus conditions leads to a lower impact of proximity to
water on house prices
- This suggests that unobserved quality aspects correlated with proximity to water are indeed
important
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,Hedonic pricing theory = a description of the equilibrium prices of varieties of a heterogeneous good,
which is influenced by demand and supply. Hedonic price theories are often used to measure the
price of public goods.
- Looks like a contract curve for supply and demand
- Not the same for everyone, people are heterogeneous value functions
- Economic theory does not tell much about the shape of the hedonic price function
- Cannot expected to be stable over time
- The hedonic price function is sensitive to changes in preferences, and quality or quantity of
the goods on offer. It looks like p(k) and is equal to the first parameter in a single regression.
The hedonic price function reveals the marginal wtp for quality characteristics of heterogeneous
goods. This marginal wtp is important for the purpose of economic welfare analysis.
The powerful characteristic of hedonic price techniques is that house prices provide information on
the WTP of people for public goods and location characteristics, for which it is otherwise hard to
measure the benefits.
When estimating the hedonic price function, one relies on OLS by regressing the total price of a
property on its characteristics. However, there are at least two issues when estimating the hedonic
price function:
- Omitted variable bias: price may depend on a variable that is not included in the model.
- Only the average WTP is calculated because preferences are heterogeneous.
How is the hedonic price function related to economic theory?
Let’s assume a utility maximizing household u = u (q, k) budget constraint: y = q + p (k)
- q denotes the composite good
- k denotes an attribute (e.g. house size) (has heterogenous quality)
This equation shows that the marginal rate of substitution (MRS) is equal to the implicit price for k.
The MRS indicates the amount of money a consumer is willing to pay to get an additional unit of the
attribute (e.g. additional square meter) while holding utility constant. Problem: households don’t
have the same utility functions.
When people are heterogeneous, how do we find an equilibrium? use the value function (it’s
some sort of indifference curve for price versus quality).
To define the value function, we insert P (the total price a consumer is willing to pay for the
heterogeneous commodity rewrite the utility function: u = u (y - P, k) = u*
We now ask; what is the price the consumer is willing to pay for quality k if her utility must be equal
to the fixed level of u*?
,Value function: P = y −u−1(u*, k) gives the wtp for different consumers.
, Note that the hedonic price function (p(k)) gives the market price and the value functions (P1 and P2)
represent the willingness to pay for the heterogeneous good of a single consumer as a function of
her income and a given utility level.
Each value function gives the combination of price and quality that allow the consumer to reach a
particular level of utility. The hedonic price function shows the combination of price and quality that
is available to the consumer. A utility maximizing consumer tries to reach the highest possible
indifference curve and the lowest possible value function. In the figure above, the optimal
combination of price and quality is found at the point where the value function is tangent to the
hedonic price function. Hence, the utility maximizing consumer pays price p* for quality k*. However,
since consumers are heterogeneous, the curvature of the value functions and the p*/k* will be
different for other consumers.
A final important aspect of Figure 2.1 is that the value function and the hedonic price function are
tangent to each other. They have only one point in common. At that point, the marginal willingness
to pay for quality of the consumer equals the slope of the hedonic price function. Other points of the
hedonic price function coincide with the marginal willingness to pay of other consumers. The
implication is that it is in general not appropriate to compare different points of hedonic price
function and to interpret the difference in price as the willingness to pay for the difference in quality.
Remember the example of the two otherwise identical houses that are located on sites that differ in
air quality. The consumers in both houses have chosen different levels of air quality (which is the
variable k in this example) on the basis of their differing preferences. By comparing their choices, we
compare points that are located on different value functions, while the willingness to pay is
measured by comparing points on the same value function.
How can we determine the demand for an attribute k (e.g. open space) for an individual?
- Demand function: k =f (α )
- Inverse demand function: α =f (k )
Rosen (1974) suggested a three-step procedure:
1. Estimate the hedonic price function
2. Calculate the implicit price
3. Estimate the inverse demand functions by a regression of marginal prices ( α ) on the amount
consumed of attribute k.
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How would the demand functions look like for a linear and log-linear hedonic price function?
Example of a linear hedonic price function
Regression equation: price = α 0 + α 1 size + ui
d price
which represents the hedonic price α 1 = $2139 for every house size
d ¿ ¿ α1 ¿
Example of a log-linear hedonic price function
Regression equation: log price = α 0 + α 1 log size + ui
d price
α 1 = 0.9276 and we want to know the slope of the line at a given point α ∗price
d¿¿ 1¿¿¿ ¿
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