MetaFunctional Benefit Transfer for Wetland Valuation: Making the Most of Small Samples

1
Meta-Functional Benefit Transfer for Wetland
ValuationMaking the Most of Small Samples

• with Richard Woodward,Texas AM University

2
Motivation

• (1)Few (No?) full case studies of Meta-Functional
  BT(MFBT) driven by actual policy need in
  published literature
• Published lit. using MFBT has focused on
• BT as added component in studies on
  methodological considerations of meta-regression
  models (MRMs)
• Validity tests of BT (simulated or real data, but
  no actual policy context)
• Econometric considerations of MFBT, again without
  an actual policy context
• (2) Show how Bayesian methods can be used to deal
  with very small samples, which can arise in MFBT

3
Recap MRM and BT
Meta-Regression Model (MRM)
Attributes for Policy Site(Site
Characteristics,User Population)
Estimated Parameters
Benefit Estimatefor Policy Context
4
Policy Context

• Southern Nevada Water Authority (SNWA) proposes
  250 mile pipeline to draw 90,000 acre feet of
  groundwater per year from Spring Valley, Eastern
  NV, to the Las Vegas area. Construction to start
  in 2009.
• NV Office of the State Engineer must decide
• Commissioned several scientific and one
  regional-economic study on expected impacts of
  groundwater losses in Eastern NV (Lincoln White
  Pine Counties)
• Last minute decision Add a Non-market Valuation
  type study to assess economic impact of likely
  loss of local wetland areas
• Time Frame for Study 3 weeks
• BT only choice

5
Maps
6
Swamp Cedar Natural Area

• 3200 acres
• Marshy ecosystem
• Globally unique stand of Swamp Cedars
  (Juniperus scopulorum)
• Access via dirt road
• Some recreational opportunities, but no
  infrastructure

7
Shoshone Ponds Natural Area

• 1240 acres
• More Swamp Cedars
• Three man-made, spring-fed ponds that harbor two
  endangered fish species (Relict Dace, Pahrump
  Poolfish)
• Designated access road
• Some recreational opportunities, but no
  infrastructure
• Some educational opportunities (visiting school
  classes etc)

8
Source Studies for MRM

• Initial Criteria
• Geographic area U.S. or Canada
• No coastal / marine types of wetlands
• Economic values must include habitat,
  biodiversity, or species preservation
• No studies with sole purpose of flood control,
  water filtration, extractive use
• First cut 24 studies
• Further refinements
• Eliminate studies with identical survey
  instruments and target population
• Eliminate if response rates lt30 (only 1)
• Left with 9 studies, 12 observations

9
Choice of Regressors for MRM

• Based on
• Whats know for policy site
• Whats available from source studies / census
• Sample size 3 or 4 regressors at most
• Adj. R2 from prelim. OLS runs
• Final set
• Income (census info for policy site)
• Percentage of users (educated guess for policy
  site)
• Acreage (known for policy site)
• Adj. R2 in 0.6 0.9 range (dep. on functional
  form)

10
Meta-sample Stats
Simple mean transfer implausible
11
Desirable Sample Properties

• Nice geographic coverage
• Nice mix of publication sources
• All but one use same elicitation method (DC)
• Similar definition of target population
  (regional State-wide)
• All w/in last 15 years modern methods
• Policy site figures are within sample for all
  three regressors

12
Classical Estimation Issues

• Cant invoke asymptotics
• Cant test for HSK
• Robust s.e.s meaningless
• Conversion from log(WTP) to WTP problematic!
• Model uses log(WTP) to assure gt0
• BT Predictions require WTP in s
• Converted s.e.s and confidence interval requires
  use of Delta Method, an asymptotic concept
  meaningless for n12
• Confidence intervals for BT predictions will be
  imprecise and huge!
• Cant exploit extraneous info beyond data set

13
Bayesian Approach

• Does not rely on asymptotics
• Can model HSK with a hierarchical error structure
  and a single added parameter
• Can introduce added info through refinement of
  priors
• Each model receives a probability weight as
  by-product of posterior simulator
• This allows for model-averaged BT predictions

14
Kernel Model
Gewekes (1993) t-error model
15
Priors and Refinements
Reasonable starting point
Using info on slope estimates from source studies
and other meta-analyses
Based on preliminary OLS results
16
Model Space
Plus same 12 models with normal errors, for a
total of 24 models considered
17
Feed into Posterior Simulator
Models
18
Shake vigorously.....
19
Assess Model Fit and Probability
20
BT Predictions
21
Conclusions

• Reasonable BT is still possible with a small
  Meta-sample
• Careful study selection, good judgment still key
• Bayesian framework provides several advantages
  under small sample constraints
• Dont need to worry about asymptotics
• Useful diagnostic tools available
• Options for prior refinements
• Produces model weights as part of estimation
  routine
• Address model uncertainty through model
  averaging
• Future of MFBT probably lies with
  individual-level data

22
Go Pahrump Poolfish!!!