Choice Modelling

1
Choice Modelling

• Theory and Application

2
Overview

• Background
• Examples
• Survey instrument design
• Survey analysis
• Future direction of research

3
Background

• The value of market goods is generally uncovered
  in economic markets through the interaction of
  supply and demand.

Price
Supply
CS for environmental good is total area under
demand curve
PM
Demand
Quantity
QM
4
Background

• Generally, there is market failure for
  environmental goods and services
• Externalities
• Public good characteristics
• Lack of fully defined property rights

5
Background

• Although there is market failure (and therefore
  no market price) for environmental goods
• people do attain utility (value) from
  environmental goods.
• It is important that we account for these values
  when we make decisions about environmental
  resources.
• Environmental valuation aims to measure the
  consumer surplus for environmental goods.

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Total Economic Value
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Environmental Valuation Techniques

• Revealed preference approaches.
• Observes actions within surrogate markets
  (travel, house prices) taken in response to
  environmental change.
• Largely restricted to use values
• Examples Travel Cost Method, Hedonic Price
  Method.
• Stated preference approaches.
• Attempts to elicit preferences by experiments or
  questionnaires
• May estimate both use and passive use values
• Examples Contingent Valuation Method, Choice
  experiments.
• Combined approaches
• Draws on the benefits of the above approaches
• Examples Contingent behaviour

8
Choice experiments overview

• Survey based approach
• Introductory material
• Environment good specific questions
• Descriptions of hypothetical for the
  environmental good and method of provision
• Choice tasks
• Socio-economic and attitudinal data

9
CE choice task

• Respondents are required to consider a series of
  choice tasks.
• Each choice task comprises
• three choice options (including a status quo)
• each choice option is described in terms of
  policy attributes and levels
• One attribute is a payment vehicle (increase in
  tax)
• Attributes and levels assigned according to an
  experimental design

10
Choice experiment example Forest recreation.
11
Choice task example Coastal defence amenity at
Borth.
Choice


12
Borth example attributes and levels

• Visual timber groynes,
• rock groynes,
• Multi-purpose reef
• Wall SQ,
• raise height
• Surf SQ,
• improved surf
• Amenity SQ,
• calm waters
• Tax 5 levels

13
Experimental design

• In the CE, we need to create a survey design that
  allows us to compare all levels of all
  attributes.
• A full factorial design would require 32225
  1080 comparisons practically challenging!
• Therefore use of orthogonal main effects
  fractional factorial design.

14
Fractional factorial designs

• involve the selection of a particular subset
  (e.g. fraction) of a complete factorial, so that
  particular effects can be estimated as
  efficiently as possible.
• Fractional designs, however, involve
• a loss of statistical information.
• requires assumptions about the non-significance
  of higher order effects, i.e. the interaction
  between two or more attributes.

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Fractional factorial design (23)
16
Fractional factorial designs

• Fraction 1 is the irregular fraction, i.e. ABC
  -1
• A -BC
• B -AC
• C -AB
• Fraction 2 is the regular fraction, i.e. ABC
  1
• A BC
• B AC
• C AB
• In the design of CE, we use the regular fraction.
• The fractional factorial design now only requires
  4 treatments (instead of 8 in the full
  factorial).
• In the Borth example, factorial designs allow us
  to reduce the number of treatments from 1080 to
  24!

17
Fractional factorial designs

• In the 23 CE example which has 4 treatments
• Our estimate of the main effect (A) could be the
  estimate of A or the two-way interaction BC or
  some other combination of A and BC.
• Thus, we will only estimate A if and only if the
  two-way interaction BC is not significant (equals
  zero).
• Thus, we need to avoid collinearity in our
  attributes within the CE design, i.e. we need to
  ensure that our attributes are not linked to each
  other.
• This assumption is known as the Independence of
  Irrelevant Alternatives (IIA)

18
Choice set design

• In designing a CE choice set, we have
• Status quo (described as existing levels of
  attributes)
• Choice A (described according to a fractional
  factorial design)
• Choice B (described according to a different
  fractional factorial design)

19
Choice set design (23)
Right is the 23 fractional factorial design.
Below is the design of 1 of the 4 choice sets.
20
Choice set design

• Generally, respondents can cope with 8 choice
  tasks within a single questionnaire.
• In the Borth example, the 3123 51 design gave
  rise to 24 choice sets. The choice tasks were
  therefore split between 3 sub samples (each
  receiving 8 choice tasks).

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Choice experiments theory

• Lancastrian theory of consumer choice
• The attributes of a good is important in consumer
  purchase decisions.
• Random utility theory
• Where
• U is respondents utility
• V is observable component of U
• ? is unobservable component of U
• ? is the coefficient of X
• X is a vector of attributes of alternatives
  socio-economic and attitudinal characteristics of
  respondents

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Choice experiments theory

• If Independence of Irrelevant Alternatives
  (IIA) assumption holds, we can solve with
  Conditional logit model

23
Choice experiments theory

• IIA violations (Hausman test), use random
  parameters logit (RPL) model
• RPL utility function
• Where ?in ? f (?n?) is a random term with zero
  mean and a general distribution, with a general
  density function f and ? are fixed parameters of
  the distribution (e.g. mean and variance).

24
Choice experiments theory

• RPL model
• The RPL choice probabilities do not have a
  mathematical closed form. Requires simulation to
  solve.

25
Choice experiments theory

• Welfare estimates

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Data preparation
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NLOGIT coding

• nlogit
• Lhschoice
• Model
• U(c1) bvis1vis1 bvis2vis2
  bwallwall bsurfsurf bamenityamenity
  btaxtax bnsurfnosurfas
• U(c2) bvis1vis1 bvis2vis2
  bwallwall bsurfsurf bamenityamenity
  btaxtax bnsurfnosurfas
• U(SQ) B0 bvis1vis1 bvis2vis2 bwallwall
  bsurfsurf bamenityamenity btaxtax
  bnsurfnosurfas
• Wald
• labels b1, b2, b3, b4, b5, b6, b7, b8, b9
  ?b7cost
• start b
• var varb
• fn1 (b2b3) / b7 ? timber
• fn1 -(b2)/b7 ? rock
• fn1 -(b3)/b7 ? reef
• fn1 -(b4b8)/b7 ? wall
• fn1 -(b5 b9)/b7 ? surf
• fn1 -(b6)/b7 ? amenity

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NLOGIT output

• Normal exit from iterations. Exit status0.
• ---------------------------------------------
• Discrete choice (multinomial logit) model
  
• Maximum Likelihood Estimates
  
• Model estimated Jun 08, 2005 at 035211PM.
• Dependent variable Choice
  
• Weighting variable None
• Number of observations 960
• Iterations completed 5
• Log likelihood function -887.5745
• Log-L for Choice model -887.57452
• R21-LogL/LogL Log-L fncn R-sqrd RsqAdj
• Constants only -950.2473 .06595 .06254
• Response data are given as ind. choice.
• Number of obs. 960, skipped 0 bad obs.
• ---------------------------------------------
• ----------------------------------------------
  ----------
• Variable Coefficient Standard Error
  b/St.Er.PZgtz
• ----------------------------------------------
  ----------

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NLOGIT output RPL

• Random Parameters Logit Model
• ----------------------------------------------
  ----------
• Variable Coefficient Standard Error
  b/St.Er.PZgtz
• ----------------------------------------------
  ----------
• Random parameters in utility functions
• BWALL -.6746982765 .31024699
  -2.175 .0297
• BSURF .1912226937 .22963670
  .833 .4050
• Nonrandom parameters in utility
  functions
• B0 -1.243803846 .17339223
  -7.173 .0000
• BVIS1 -.4642925510 .82626493E-01
  -5.619 .0000
• BVIS2 .7506976836 .11040487
  6.799 .0000
• BAMENITY .4226909308 .11772520
  3.590 .0003
• BTAX -.1470164418E-01 .34102835E-02
  -4.311 .0000
• Heterogeneity in mean,
  ParameterVariable
• BWALLOW 1.111014897 .36629910
  3.033 .0024
• BWALSUR -.1622615622 .35474299
  -.457 .6474
• BSURLOW -.2020528914 .26123642
  -.773 .4393
• BSURSUR 1.030179784 .32694115
  3.151 .0016

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Results Conditional logit model
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Results Implicit prices
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Key observations

• Visual timber groyne negative
• Visual rock groyne negative
• Visual reef positive
• Family amenity positive

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Key observations

• Model 1 seawall and improved surf were
  insignificant
• Model 2 (lower) and 3 (upper)
• Seawall now significant.
• Lower Borth want generally want sea wall
• Upper Borth dont.
• Model 4 (non-surfer) and 5 (surfer)
• Surf conditions now significant for surfers, who
  want improved surf
• Non-surfers still insignificant

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Amenity value associated with coastal protection
proposals at Borth
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Future directions of CE research

• Heterogeneity of preferences
• RPL
• Latent class analysis
• Benefits transfer
• Combining methods