5IE475
Program Evaluation and Cost-Benefit Analysis
LECTURE 4
Demand estimations and contingent valuation Klára Kalíšková
Outline
• Valuing impacts of a project:
1. Shape and position of demand and supply curves is known (previous lecture)
• We know how to derive changes in CS and PS
2. Shape and position of demand and supply curves is unknown (today):
• Estimate demand curves from observed behavior of people
• Use survey to reveal individuals’ willingness to pay
•
Readings:
– Boardman book, Chapters 12 and 14
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Valuing benefits (impacts) of a project
• Impacts of the project on individuals are measured by changes in social surplus
– Sum of consumer and producer surplus
– Triangles bounded by supply and demand curves
• If we know shape and position of demand and supply curves, measuring impacts of the projects is straightforward
– However, this is often not the case!
– Then, we need to either estimate demand curves or find another way to assess the project impacts (e.g.
through surveys)
DEMAND CURVE ESTIMATION
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Estimating demand curves
• We focus on demand curves here, because
consumers usually experience most of the project benefits (impacts)
• We usually have information about:
– The market-clearing price
– Total quantity sold on the market
We know the point of intersection of the supply and demand curves
– We might also have information about price and quantity from different regions, time periods, …
How to estimate demand curves
• Consider three scenarios:
1. We know one point on the demand curve and previous research provides us with estimates of the elasticity or slope of the demand curve
2. We know a few points on the demand curve and this allows us to predict another point of
relevance
3. We have information about sufficient number of points on the curve that allows to estimate the whole curve
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SCENARIO 1. Knowing one point on the
demand curve and its slope or elasticity
Scenario 1a. Knowing one point and slope of the demand
• Assume demand curve is linear:
q = a
0+ a
1p
– How much less would people demand if the price increased by one dollar?
– If demand is linear, this is the same (a1) no matter where on the demand curve you are
• Knowing a slope estimate (a
1):
– Use slope estimates from previous research – Try to get as precise measure as possible
• Demand curve may change over time, be different in different places, using different populations,…
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Scenario 1b. Knowing one point and elasticity of the demand
• Apply the same assumption about linearity of the demand curve
• Knowing an elasticity estimate:
– Elasticity measures responsiveness of the quantity demanded to changes in price:
ed = a1 p/q
What is the definition of elasticity? What it means if elasticity of demand for tea is -0.2?
– Elasticity is always negative, because a1 is negative – Elasticity varies with price and quantity demanded
– If we know price and quantity at which elasticity was estimated, it is easy to derive slope of the demand curve (a1) from the
elasticity (ed)
Example: estimating impact of park entry fees
• Policy: increase an entry fee to a town park
–
Before the policy: a fee of $0.6 per entry
–
After the policy: fee increased to $1 per entry
• To estimate the impact of such a policy on
social surplus, we need to know the shape and position of the demand curve for park entry
–
Assume demand for park entry is linear
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Example: Knowing slope estimate
• We know one point on the demand curve:
– Before the fee is increased, each person in a town enters the park 2.6 times per month
– The one point on the demand curve we know: At price P0=$0.6, quantity demanded is Q0=2.6 entries per person and month.
1a. If we know the slope estimate:
– Previous research surveys park entry fees and park usage in several cities in the US.
They estimate that a $1 increase in price for entry leads to decrease of park usage by 0.5 entries per person and
month:
→ a1 = -0.5
Example: Knowing elasticity estimate
1b. If we know elasticity estimate:
–
Previous research reports that the elasticity of
demand for park entry is -0.1545 at average price
$0.81 per entry and at average quantity demanded 2.62 entries/person/month
–
To calculate the slope from the elasticity, recall that elasticity is defined as follows:
ed = a1 p/q
→ a1 = ed q/p = -0.1545*2.62/0.81
→ a1 = -0.5
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Example: Constructing demand curve
• Constructing demand curve from one point and a slope estimate:
• point: P=0.6, Q=2.6, slope a1= -0.5
1. Determine the intercept (quantity at zero price) 2. Write down the equation for the demand curve
(quantity as a function of price)
3. Express price as a function of quantity and draw it in a graph
4. Estimate the impact of increased entry fee on the quantity of entries
5. Estimate changes in social surplus
Example: Demand curve and CS
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Quantity
(entries/person/month) Price per entry
D Q0 = 2.6
Q1 = 2.4 P0 = 0.6
P1 = 1
CS0 CS1
2.9 5.8
SCENARIO 2. Knowing few points
on the demand curve
Extrapolating from a few points
• Suppose previous policy changes gave you more than one observation of price-quantity
combinations
– For example, policy reforms have changed the price of highway tolls and after each change we observed the change in demand for highways
• Can we extrapolate from these previous changes?
– If previous increase of toll by $100 decreased demand by 150 cars per day, will another $100 toll increase
have the same effect?
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Extrapolating from a few points: Issues
1. Do we assume demand curve is linear or do we assume another functional form?
– If demand curve is linear, another price increase will have the same impact on quantity as the previous one
– If it is not linear, the impact might be very different – Often, we assume that the demand curve has
constant elasticity
→ In general, the further we extrapolate from past experience, the more sensitive our predictions are to functional form assumptions (linear vs. non-linear).
Linear vs. constant elasticity demand curves
Source: Boardman book, Figure 12.3 18
Past observations:
a: P=$0.01, Q=2.52 b: P=$0.025, Q=2.4
What will happen if price is raised to $0.05?
Extrapolating from a few points: Issues
2. Are we certain that the observed change in quantity demanded was caused by the policy change?
– Were there any other factors influencing demand which might have changed over time?
– The drop in demand for highways might have been caused by other factors than highway tolls –>
examples?
→ Collect data on other potential factors and use
econometric techniques to determine their effect and the policy effect.
SCENARIO 3. Knowing sufficient
number of points on the demand curve
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Econometric estimation with many observations
• If we have many observations on quantities demanded at different prices, it might be possible to construct the whole demand curve
1. Collect data
2. List important determinants of demand (explanatory variables):
• E.g. price of the good, price of substitutes, income, …
3. Specify functional form of the model:
• Linear form: q = a0 + a1 p + a2ps + a3i
• Constant elasticity form: q = b0 pb1 psb2 ib3
4. Use econometric techniques for estimation
• Both linear and constant elasticity form can be estimated by OLS (take logarithm of the constant elasticity form)
VALUING IMPACTS THROUGH SURVEYS
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Eliciting WTP
• Ideally, we observe individuals’ valuations of goods (WTP) in the markets
– Because these reveal true preferences
– Example: WTP for childcare facilities is observed through the amount of childcare parents use (at a given market price)
• However, often we do not / cannot observe valuations on the markets
– Some things are simply not marketed (water quality, green areas, species protection, …) and thus we
cannot observe from people‘s behavior how much do they value them
Contingent valuation surveys
• If WTP cannot be observed on the market (from real life behavior), we have to elicit valuations through questionnaires
• Questionnaires designed to elicit preferences are called contingent valuation (CV) surveys
–
Asking hypothetical questions about valuations of certain goods
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Contingent valuation: method
1. Identify a sample of respondents from a population
2. Ask respondents about their valuations of some good
3. Estimate willingness to pay (WTP) of respondents from the survey answers
4. Extrapolate respondents’ WTP to the entire population
– If respondents are a random sample of population, multiply the average WTP of respondents by the size of population to get the aggregate WTP
Methods used to elicit WTP
1. Open-ended willingness-to-pay method:
–
Ask respondents directly what is their maximum WTP for the good or policy
• “What is the most you would be prepared to pay to have a new park build outside the city?”
–
Drawbacks:
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Methods used to elicit WTP
1. Open-ended willingness-to-pay method:
–
Ask respondents directly what is their maximum WTP for the good or policy
• “What is the most you would be prepared to pay to have a new park build outside the city?”
–
Drawbacks: Unrealistic answers if respondents are given no guidance for evaluation (these
hypothetical questions are difficult to answer).
Methods used to elicit WTP
2. Closed-ended iterative biding method:
– Ask respondents if they would be willing to pay a certain amount.
• If yes, increase the amount until they would no longer be willing to pay it.
• If no, decrease the amount until they would be willing to pay it.
• “Suppose there is a proposal to build a park outside the city and the costs are to be divided between all citizens by an extra tax. If this extra tax was 500 CZK per year, would you be willing to support the proposal?”
– Drawbacks: Very sensitive to the initial (starting) value
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Methods used to elicit WTP
2. Closed-ended iterative biding method:
– Ask respondents if they would be willing to pay a certain amount.
• If yes, increase the amount until they would no longer be willing to pay it.
• If no, decrease the amount until they would be willing to pay it.
• “Suppose there is a proposal to build a park outside the city and the costs are to be divided between all citizens by an extra tax. If this extra tax was 500 CZK per year, would you be willing to support the proposal?”
– Drawbacks: Very sensitive to the initial (starting) value
Methods used to elicit WTP
3. Contingent ranking method
– Respondents are asked to rank combinations of quantities of the good and monetary payments
– Example: combinations of low water quality and low price vs. high water quality and high price
– These combinations are ranked from the most preferred to the least preferred
• In general, it is easier for respondents to answer ranking questions than state valuations directly
– Drawbacks: sensitive to the order in which
alternatives are presented and the way combinations are created
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Methods used to elicit WTP
3. Contingent ranking method
– Respondents are asked to rank combinations of quantities of the good and monetary payments
– Example: combinations of low water quality and low price vs. high water quality and high price
– These combinations are ranked from the most preferred to the least preferred
• In general, it is easier for respondents to answer ranking questions than state valuations directly
– Drawbacks: sensitive to the order in which
alternatives are presented and the way combinations are created
Methods used to elicit WTP
4. Dichotomous-choice method
– Ask each respondent whether s/he would be willing to pay a particular price for the good or policy.
– Prices are selected from a certain range and each
respondent is asked to respond to only one particular price offer (take-it-or-leave-it offer)
– For each price, researcher can then calculate the
probabilities that people are willing to pay this price.
• Histogram of these probabilities approximates the demand curve of an average individual.
• Or instead of histogram, use econometrics model to explains probability of acceptance with price (and other factors)
• WTP of average individual is the area below the demand curve
– Drawbacks: needs large sample size
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Methods used to elicit WTP
4. Dichotomous-choice method
– Ask each respondent whether s/he would be willing to pay a particular price for the good or policy.
– Prices are selected from a certain range and each
respondent is asked to respond to only one particular price offer (take-it-or-leave-it offer)
– For each price, researcher can then calculate the
probabilities that people are willing to pay this price.
• Histogram of these probabilities approximates the demand curve of an average individual.
• Or instead of histogram, use econometrics model to explains probability of acceptance with price (and other factors)
• WTP of average individual is the area below the demand curve
– Drawbacks: needs large sample size
Histogram of dichotomous-choice responses
Source: Boardman book, Figure 14.1 34
Contingent valuations: choices
1. Making valuation questions as real as possible
– Specify a payment vehicle, i.e. a way in which the costs of the project would be paid to make the payment more
realistic (taxes, higher product prices, fees, …)
2. Choosing the type of survey: in-person, telephone, mail
– Each type has different costs, pros and cons
3. Sample design
– What is the target population?
– How to choose individuals from this population for a survey?
• Random sample, stratified random sample
• Sample size
Summary
• To estimate social benefits of policies, we need to know what is the change in social surplus
– If we know the shape and position of demand and supply curves, we can calculated social surplus
changes (previous lecture)
– The shape and position of demand and supply curves is in general unknown, se that we can either:
• Estimate demand curves from observed behavior of people and then apply knowledge from the previous lecture
• Use surveys to reveal individuals’ willingness to pay and then estimate the aggregate WTP (consumer surplus)
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