Nonlinear Meta-Regression for Benefit Transfer · 2018. 12. 13. · Intro Adding-up NL-MRM Model Comparison Empirical Example Conclusion Nonlinear Meta-Regression for Bene t Transfer

Intro Adding-up NL-MRM Model Comparison Empirical Example Conclusion

Nonlinear Meta-Regression for Benefit Transfer

Klaus Moeltner

Presented at the 2018 ACES Meetings,Washington, DC Area, Dec. 3-6, 2018

This research was partially funded under U.S. EPA contract number EP-C-13-039. The findings, conclusions,

and views expressed in this paper are those of the author and do not necessarily represent those of the U.S.

EPA. No agency endorsement should be inferred.

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Intro

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Intro

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Intro

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Intro

log (wtp) = A + βlog(y) + γ0q0 + γ∆ (q1 − q0) , or

wtp = yβexp (A + γ0q0 + γ∆ (q1 − q0))

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Intro

Sensitivity to scope?

∂wtp

∂q1|q0 = γ∆ ∗ wtp,

γ∆ > 0?

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Intro

Sensitivity to scope?

∂wtp

∂q1|q0 = γ∆ ∗ wtp,

γ∆ > 0?

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Intro

Adding-up property?

wtp (q2 − q0)?= wtp (q1 − q0) + wtp (q2 − q1)

yβexp (A) exp (γ0q0 + γ∆ (q2 − q0)) 6=yβexp (A) ∗(exp (γ0q0 + γ∆ (q1 − q0)) + exp (γ0q1 + γ∆ (q2 − q1))) ,

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Intro

Adding-up property?



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Intro

Adding-up property?



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Adding-up

• Adding-Up violation is a real “practical headache”

• Many EPA policies proceed in incrementsover time and/or space

• Example: Chesapeake Bay watershed implementation plan toreduce TMDLs

• Multiple phases across sectors and jurisdictions

• Example: Steam Electric Power Plants rule

• EPA needs to know partial benefits from partial cleanup ANDbenefits “still on the table”

• First raised in the peer-reviewed literature byNewbold et al. (2018)

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Adding-up








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Adding-up








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Adding-up








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Adding-up








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Adding-up








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Adding-up








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Adding-up

Example: from “boatable” (q=2.5) to “fishable” (q=5.1) to“swimmable” (q=7.0)

γ̂0 = −0.124

γ̂∆ = 0.2095

q0 = 2.5, q1 = 5.1, q2 = 7.0

wtp (q1 − q0) + wtp (q2 − q1)

wtp (q2 − q0)= 1.09

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Adding-up


γ̂0 = −0.124

γ̂∆ = 0.2095

q0 = 2.5, q1 = 5.1, q2 = 7.0

wtp (q1 − q0) + wtp (q2 − q1)

wtp (q2 − q0)= 1.09

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Adding-up


γ̂0 = −0.124

γ̂∆ = 0.2095

q0 = 2.5, q1 = 5.1, q2 = 7.0

wtp (q1 − q0) + wtp (q2 − q1)

wtp (q2 − q0)= 1.09

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Adding-up

Example: smaller steps around “fishable”

γ̂0 = −0.124

γ̂∆ = 0.2095

q0 = 5.0, q1 = 5.1, q2 = 5.2

wtp (q1 − q0) + wtp (q2 − q1)

wtp (q2 − q0)= 1.95

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Adding-up


γ̂0 = −0.124

γ̂∆ = 0.2095

q0 = 5.0, q1 = 5.1, q2 = 5.2

wtp (q1 − q0) + wtp (q2 − q1)

wtp (q2 − q0)= 1.95

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Adding-up


γ̂0 = −0.124

γ̂∆ = 0.2095

q0 = 5.0, q1 = 5.1, q2 = 5.2

wtp (q1 − q0) + wtp (q2 − q1)

wtp (q2 − q0)= 1.95

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NL-MRM

wtp =

∫ q1

q0

yβexp (A) exp (γq)dq =

yβexp (A)

(1

γ(exp (γq1)− exp (γq0))

)log (wtp) = A + βlog (y) + log

(1

γ(exp (γq1)− exp (γq0))

)

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NL-MRM

yis = x′isβ + log(γ−1 (exp (γq1,is)− exp (γq0,is))

)+ us + εis

us ∼ n(0, σ2

u

),

εis ∼ n(0, σ2

εωis

), where ωis ∼ ig

(ν2 ,

ν2

)

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Model Comparison

Meta-Data:

• 140 obs., 51 studies

• wtp for water quality change, 100-point scale

• 22 explanatory variables

• used by EPA to inform steam electric rule revision (ongoing)

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Model Comparison

Meta-Data:





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Model Comparison

Meta-Data:





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Model Comparison

Meta-Data:





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Model Comparison

Meta-Data:





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Model Comparison

Model comparison via Bayes Factors

NL-MRM vs: log-Bayes Factor

MRM1linlin -24.285MRM1linlog -20.958MRM1loglog -23.742

MRM2 -6.560MRM2Slin -9.053MRM2Slog -23.870

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Empirical Example

BT context:

• riperian ecosystem

• can be borrow from remaining (lake) data?

• Bayesian Stochastic Search Variable Selection

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Empirical Example

BT context:




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Empirical Example

BT context:




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Empirical Example

BT context:




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Empirical Example

River data (n=96)

Lake data (n=44)

WTP

WTP

Interactionterms

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Empirical Example

ys = X1sβx + Msβm + Zsδ+

log(

(γ + δγds)−1 (exp ((γ + δγds)q1,s)− exp ((γ + δγds)q0,s)))

+ isus + εs

p (δj ) = p0 ∗ n(0, c2t2

)+ (1− p0) n

(0, t2

),

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Empirical Example

ys = X1sβx + Msβm + Zsδ+

log(

(γ + δγds)−1 (exp ((γ + δγds)q1,s)− exp ((γ + δγds)q0,s)))

+ isus + εs

p (δj ) = p0 ∗ n(0, c2t2

)+ (1− p0) n

(0, t2

),

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Empirical Example

Scenario 1: WQI 25-51, 51-70 (boatable, fishable, swimmable)

BT results, SSVS, total WTP ($)

NL-MRM MRM1linlinscenario (WQI) low mean high low mean high

25 to 51 0.00 50.99 156.53 0.72 32.33 85.5951 to 70 0.00 26.33 80.10 0.94 24.08 63.6525 to 70 0.00 77.19 235.89 0.91 41.12 108.12

adding-up error 0.17% 37.18%

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Empirical Example

Scenario 1: WQI 25-51, 51-70 (boatable, fishable, swimmable)



25 to 51 0.00 50.99 156.53 0.72 32.33 85.5951 to 70 0.00 26.33 80.10 0.94 24.08 63.6525 to 70 0.00 77.19 235.89 0.91 41.12 108.12


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Empirical Example

Scenario 2: WQI 73-73.5, 73.5-74(option D of Steam Electric rule)



73 to 73.5 0.00 0.57 1.74 0.46 16.26 43.8973.5 to 74 0.00 0.57 1.73 0.47 16.21 43.7973 to 74 0.00 1.14 3.47 0.28 16.36 43.98


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Empirical Example

Scenario 2: WQI 73-73.5, 73.5-74(option D of Steam Electric rule)



73 to 73.5 0.00 0.57 1.74 0.46 16.26 43.8973.5 to 74 0.00 0.57 1.73 0.47 16.21 43.7973 to 74 0.00 1.14 3.47 0.28 16.36 43.98


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Empirical Example

• Option D of SER: $ 1.14/HH

• 84.5 million HHs affected

• Benefits: $96 million (2007 dollars)

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Empirical Example




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Empirical Example




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Conclusion

• Existing MRMs for quality change theoretically flawed

• Adding-Up: serious problem of high practical relevance

• NL-MRM provides compromise of theoretical consistency andreasonable empirical fit

• Bayesian methods allow for rigorous model comparison,full exploitation of meta-data for BT application

THANK YOU!

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Conclusion





THANK YOU!

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Conclusion





THANK YOU!

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Conclusion





THANK YOU!

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Conclusion





THANK YOU!

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Conclusion





THANK YOU!

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Documents

Nonlinear Meta-Regression for Benefit Transfer · 2018. 12. 13. · Intro Adding-up NL-MRM Model Comparison Empirical Example Conclusion Nonlinear Meta-Regression for Bene t Transfer