PARAMETRIC MODELS FOR CONTINGENT VALUATION

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• PARAMETRIC MODELS FOR CONTINGENT VALUATION

Presented by Yuliya Bolotova Manuel Filipe Tomo
Ishikawa Rafael Uaiene
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• Layout
• 1. Background on CV
• 2. Parametric dichotomous choice model
• 3. Random utility model
• 3.1 Random utility model w/ linear utility
• 3.2 Random utility model w/ linear income
• 3.3 Random utility model w/ Box Cox transf. of
  income
• 4. Random WTP or expenditure difference model
• 5. Conclusion

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Introduction

• Valuing WTP for Some goods/service is hard
• EX Natural resources use improvement
• CV is appropriate

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Contingent Valuation (CV)

• A method of recovering information about
  preferences or willingness to pay from direct
  questions.
• Estimate WTP for changes in the quantity or
  quality of goods or services.
• Also used for estimating the effect of covariates
  on WTP.

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• Questionnaire is important step in the analysis
• The way the question is asked
• Open ended CV
• Bidding games CV
• Payment cards CV
• Dichotomous choice or discrete choice CV
• Incentive compatibility problem
• The latter out-performs the other methods when
  using the 12 NOAA guidelines
• So we are going to talk about modeling
  dichotomous choice CV models

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Parametric Model for Dichotomous Choice Questions

• Goal Estimate WTP
• Incorporate demographics in WTP function
• Increasing information on validity of CV
• More convincing
• Extrapolation of results to larger population

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Random Utility Model

• The basic model
• where
• Uij is the jth individual utility under scenario
  i
• i0,1
• Yj is the jth individual income
• Zj is the jth individual demographics
• ?ij is the error term

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• Let F? be the probability of ? be below a
  critical number, t the jth individual payment
• And the deterministic and stochastic portions of
  utility are additive separable
• The probability of an individual answering yes to
  CV question is stated as
• which assumes that
• Next specification of utility form and error
  distribution

Prob (yes)1-F? (-( ))
Prob(Yes) Prob (U1gtU0)
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Estimation Procedure

• Define the yes (1)/no(0) response to the CV
  question
• Define a data matrix X containing the matrix Z
  and the offered fee vector t
• Run a probit/logit model with a yes/no response
  as the dependent variable, and the matrix X as
  the matrix of RHS (independent) variables
• Recover the parameter estimates.
• Estimate willingness to pay

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The Random Utility Model with a Linear Utility
Function

• The linear utility function results when the
  deterministic part of the preference function is
  linear in income and covariates.
• Assuming that the marginal utility of income is
  constant and that the error term ej is
  independently and identically distributed (IID)
  with mean zero,

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The Random Utility Model with a Linear Utility
Function

• Convert ej (N(0, s2) to a standard normal
  (N(0,1)).
• Then, probit is

• When e is distributed logistic, elogistic (0, p
  2 sL2/3), logit is

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The Random Utility Model with a Linear Utility
Function

• Practically, the estimation of parameters are
  obtained by maximizing the log likelihood
  function. With the 1/0 yes/no responses as the
  dependent variable, run a probit or logit model.
  
• Reported parameter estimates are a/s for matrix z
  and ß/s for matrix t. Define the matrix Xj
  zj,tj, and its corresponding parameter vector
  ß a/s, ß/s, and run a probit or logit for
  the linear random utility function.

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Estimating WTP with the Linear Random Utility
Model

• Using the coefficients a/s for matrix z and ß/s
  for matrix t obtained,

However, when the marginal utility of income is
not constant across scenarios posed by the CV
questions, modifications are necessary.
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The Random Utility Model Log Linear in Income

• After defining dichotomous CV questions,
• 1. Define a data matrix X, containing the
  covariate matrix z and the composite income term
  ln(yi - tj)/yi.
• 2. Run a probit or logit model with 1/0 yes/no
  responses as the dependent variable and the
  matrix X as the independent variables.
• 3. Assuming ej (N(0, s2) for probit and
  elogistic (0, p 2 sL2/3) for logit, median WTP
  is calculated for both probit and logit as
  follows

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The Box-Cox Transformation of Income
Where
is the income term in the utility function
The marginal utility of income become
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Box Cox as a Nested Generalized Functional Form
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Box-Cox with ? Constant
If e are normally distributed, then

F
(
If e are logistically distributed then
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Testing FF using Box-Cox Model

• Maximum Likelihood estimate of ? gives the
  highest Likelihood function
• Likelihood Ratio Test Statistics (LRS)
• -2(log likelihood value form the restricted
  model less the log likelihood value from the
  unrestricted model) LRS -2(llfr-llfu)
• The principles for calculating the WTP are the
  same as in the utility function.

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The Random Willingness to Pay (Expenditure
Difference) Model

• The Basic Idea
• Willingness to pay is well-defined concept by
  itself
• Advantages of WTP function
• the WTP function is modeled directly
• more transparent than the utility difference
• does not require the utility function for
  derivation
• may be derived from indirect utility
  function

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The Random WTP (Expenditure Difference) Model/
General Case

• WTP is the amount of income that makes the
  respondent indifferent between the initial and
  the final state
• A respondent answers Yes if
• WTP (yj, zj, ej) gt tj
  (1)
• v1(yj-tj, zj)e1j gt v0(yj, zj)e0j
  (2)
• yj - income of the j-th respondent
• Zj - a vector of the characteristics of the j-th
  respondent
• tj required payment if a program is introduced
• e independently and identically distributed
  (iid)

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The Random WTP Model/ Linear WTP Function Case

• WTP (zj,?j) ?zj ?j
  (3)
• ?j symmetric iid with mean zero ? is N(0, s2)
• ? and zj m-dimensional vectors of parameters to
  be estimated and covariates associated with
  respondent j
• Pr (yes)Pr WTP gt tj
• Pr ?zj ?j gt tj Pr(?zj - tj ) gt
  ?j (4)
• Pr (?zj - tj )/s gt ?j
  (5)
• (4)(5) after standardizing ? ? is N(0, 1)

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The Random WTP Model/ Linear WTP Function Case

• Estimation of WTP
• WTP (zj,?j) ?zj ?j
• E (WTP zj,?) ? zj zj
• ?/s and -1/ s are the logit (probit) estimates
  for z and t

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Conclusion

• Contingent Valuation is an appropriate method for
  WTP evaluation when efficient allocation of
  resources is considered
• CV has a relatively simple procedure
• Yes/no response (interview, survey)
• Characteristics of the respondents
• Payment fee
• Estimation of a model (random utility, random
  WTP model, others) using probit/logit procedure
  to recover the parameters