1

Date August 1 9 , 2015

To Todd Doley, Julie Hewitt, and James Covington, U.S. Environmental Protection

Agency

From Matthew Ranson and Elena Besedin, Abt Associates

Subject Revised M emorandum: Accounting for Scope in the MRM2 Meta

- Regression Model

This memorandum addresses the issue of whether and how the meta

- model should account for the magnitude of the water quality changes presented to survey respondents in stated preference surveys

. In MRM1, water quality change is the key explanatory variable

— and it is highly statistically significant.

However , as described articulately in NCEE’s 4/23/2015 memorandum, the use of water qu ality change in a log specification results in a valuation function that does not satisfy the adding

- up property.

O verall, we understand and generally agree with NCEE’s desire to develop a meta

- model that satisfies that adding

- up property. Yet, economist s have long recognized that survey respondents often express preferences that appear inconsistent with this property (Diamond et al, 1993 ). Consistent with this general finding , our raw meta

- data also suggest that survey respondents express high marginal willingness

- to

- pay (WTP) for modest improvements in water quality, but then express much lower marginal WTP for additional improvements

— regardless of their current baseline level of water quality

. There are a number of potential explanations for this patt ern, including rational explanations such as income effects; survey design issues such as capturing warm glow effects or choosing water quality change scenarios that respondents have difficulty visualizing or interpret as being unrealistic ; and actual

inco nsistencies in respondents’ preferences.

Regardless of the cause of this pattern , developing a meta

- model that satisfies adding

- up requires a strategy for imposing the adding

- up property on the meta

- data. The approach currently used by MRM2 is

to exclud e water quality change from the MRM2 regression equation. In other words, MRM2 calculates marginal WTP values for a particular water quality level by averaging all relevant observations in the dataset, regardless of whether they are derived from surveys t hat asked respondents to value large, medium, or small water quality changes around that level. Effectively, this assumes that survey respondents’ preferences are best represented by their stated WTP for water quality improvements that are average in scop e in the underlying meta

- data.

The purpose of this memo is to propose an approach for augmenting MRM2 by conducting a sensitivity analysis to illustrat e how marginal WTP is influenced by the scope of the water quality change scenarios

valued in different stated preference studies . In particular, we propose estimating a modified version of MRM2 in which water quality change is treated as a study methodological characteristic . In other words,

we suggest including water quality change as a demand shifter v ariable that affects marginal WTP in the 

# Memorandum2

same way as other study methodological characteristics (e.g., the use of a choice experiment format, or a lump sum payment). Like those parameters, the water quality change parameter could be set to any desired val ue, based on the scope of water quality change s (small, medium, large) t hat a well

- designed stated preference survey would use if it were eliciting marginal WTP for the types of improvements expected under future Clean Water Act regulations. I mportantly, because water quality change would be treated as a methodological characteristic instead of as a scenario characteristic, the value assigned to the water quality change parameter need not correspond to the water quality change being valued. For the

same r eason, t he resulting model would completely satisfy the adding

- up condition , as long as the water quality change parameter were held constant across benefit transfer applications for different future regulatory analyses.

We believe that this approach has three strengths . First, it allows the meta

- model to account for water quality change, which as a purely empirical matter is a strong predictor of WTP

. 1 Second, this approach provides a transparent way of conducting an uncertainty analysis that explores how scope affects marginal

WTP

. Third, the resulting model satisfies the adding

- up condition for a given value of the water quality
parameter

.

In summary, the overall purpose of the meta

- analysis is to predict the WTP values that would be generated by co nducting a stated preference survey with a particular set of methodological, environmental, and participant characteristics. Including water quality change as a methodological

variable in MRM2 would allow EPA to understand how the framing of a stated pref erence survey

— in particular, the magnitude of the size of the water quality change considered

— affects the marginal WTP values implied by respondents’ stated preferences.

The remainder of this memorandum is organized as follows. Section 1 describes MRM2 in detail, in order to ensure that we share a common understanding of this model with NCEE. Section 2 then

discusses the functional form of MRM2, and shows that it does not capture the strong relationship between WTP and water quality change that is apparent in the meta

- dataset . Finally, Section 3 presents our proposed approach for incorporating water quality change as a methodological parameter in MRM2

, and illustrates how it could be used to estimate benefits from the Steam Electri c Regulation

.

1 For example, including the log of wate r quality change as an additional variable in MRM2 increases the R 2 of the model from 0.61 to 0.72. This increase in explanatory power from the addition of a single variable is particularly striking, given that MRM2 already includes 23 other variables and a constan t.3



## 1. Estimating Willingness

- to

- Pay Using MRM2

This section provides a detailed discussion of the approach that MRM2 uses to estimate willingness

- to

pay for water quality changes. The purpose of this discussion is to ensure that our understa nding of MRM2 is correct, and to motivate the alternative modeling approach we present in Section 3 below.

In its most general form, MRM2 models marginal willingness

- to

- pay, MWT P i ≡ ∂WT P i ∂ Q , for observation i

, as follows:

ln ( MWT P i ) = α 0 + α 1 X i + f ( Q i ; β ) + ε i (1)

In this equation, α 0 is a constant, X i is a vector of study and resource characteristics that act as demand

shif t ers, Q i is the absolute water quality index level at which marginal willingness

- to

- pay is being

evaluated , and ε i is a zero

- mean normally

- distributed error term

. The function f (

⋅ ) expresses the core relationship between absolute water quality Q i and marginal WTP , and β is a vector of parameters that

define the functional form of f (

⋅ )

.

The key question of interest is what is an appropriate form for f (

⋅ ) . NCEE’s 4/23/2015 memorandum

assumes a reasonable and parsimonious functional form that is linear in Q i :

f ( Q i ; β ) ≡ β

⋅ Q i (2)

This leads to the following equation for marginal willingness

- to

- pay :

ln ( MWT P

i ) = α 0 + α 1 X i + β

⋅ Q i + ε i (3)

which corresponds to Equation (7) in NCEE’s 4/23/2015 memorandum.

However, one remaining empirical challenge is that MWT P i is not observed directly in the meta

- data, and

instead must be calculated from total willingness

- to

- pay as part of the estimation routine. This would require a nonlinear least squares or maximum likelihood estimation approach. A s a simpler alternative, NCEE’s 4/23/2015 memorandum assumes that marginal WTP can be approximated by average WTP per unit of water quality :

MWT P i ≈ WT P i
Δ Q i ( 4 )

with thi s approximation assumed to be valid at the midpoint of the water quality change valued for that

meta

- data observation:

Q i = Q i 0 + Q i 1
2 ( 5 )

Substituting Equations (4) and (5) into E quation ( 3 ) provides the version of MRM2 that is ultimately used as a regression model :4 ln ( WT P i
Δ Q i )

= α 0 + α 1 X i + β

⋅ ( Q i 0 + Q i 1
2 ) + ε i ( 6 )

The simplest version of this regression uses a n unweighted OLS approach to generate a vector of estimated parameter values ( α ̂ 0 , α ̂ 1 , β ̂

, σ ̂ 2 )

, where σ

̂ 2 is the sum of squared residuals from equation ( 6 ). MRM2 then substitutes these estimated values into Equation (3) above, to get an expression that can be

used to predict the log of marginal willingness

- to

- pay:

ln ( MWT P

i ) = α ̂ 0 + α ̂ 1 X i + β ̂

⋅ Q i + ε i ( 7 )

Taking t he exponent of both sides produces the following expression for marginal WTP evaluated for a particular set of study/resource characteristics X and a particular water quality index level Q :

MWTP = exp ( α

̂ 0 + α ̂ 1 X + σ ̂ 2 / 2 )

⋅ exp ( β

̂

⋅ Q ) ( 8 )

Small changes in water quality (e.g., less than one unit) could be valued using an approximation that

involves multiplying predicted MWTP from equation ( 8 ) by the amou nt of the water quality change. 2
Larger water quality changes must account for the curva ture of the marginal WTP function , and so must be calculated using the integral:

WTP = ∫ exp ( α

̂ 0 + α ̂ 1 X + σ ̂ 2 / 2 )

⋅ exp ( β

̂

⋅ Q ) Q 1 Q = Q 0 dQ ( 9 )

which is equal to:

WTP = exp ( α ̂ 0 + α ̂ 1 X + σ ̂ 2 / 2 )

⋅ exp ( β

̂

⋅ Q 1 )

− exp ( β

̂

⋅ Q 0 )

β ̂ ( 10 )

As noted in NCEE’s 4/23/2015 memorandum, calculating total WTP using this approach has the key strength of providing a valuation function that is consistent with the adding

- up property.

2 We note that 98% of reach miles affected by the S team E lectric Regulation would experience WQI changes that range between 0 and 1

.5



## 2. Marginal WTP Depends Strongly on Water Quality Change

The previous sec tion describes the functional form of the MRM2 model. In this section, we show that
this model’s functional form is not completely consistent with some underlying empirical patterns of the

meta

- dataset.

A key feature of MRM2 , as described in its general version in Equation (1) above, is that marginal WTP does not depend on the magnitude of the water quality change being valued. In other words, MRM2 assumes that marginal WTP for the one

- unit change from 49 to 50 on the water quality index is the same,

reg ardless of whether survey respondents live in an area where baseline water quality is 3 5 or 49

, and whether the expected total water quality change is 30 points or 2 points

.

As an empirical matter, the meta

- data do not support this assumption. Instead, t hey suggest that marginal

WTP is a nonlinear , decreasing function of water quality change. More specifically, the meta

- data show that survey respondents express high marginal WTP for modest improvements in water quality, but then

express much lower margin al willingness to pay for additional improvements.

To demonstrate this point , Figure 1 graphs total WTP as a function of water quality change, for meta

- data observations falling into four different baseline water quality levels: 0

- 19, 20

- 39, 40

- 59, and 6 0

- 80. (Note that there are no meta

- data observations with baseline water quality levels greater than 80.) This figure is reproduced from our hybrid model memorandum . Although there is considerable noise in the figure, these panels demonstrate that total WTP increases quickly for the first 10 to 20 units of additional water quality, and then plateaus. This implies that marginal WTP is large and positive for the first 10 to 20 units of additional water quality, and then declines toward zero

. This pattern is roughly consistent across all four panels, indicating that this stylized fact appears to hold true regardless of whether baseline water quality is low or high.6 Figure 1

. WTP by Water Quality Change and Baseline Water Quality

(a) Baseline WQ: 0

- 19 (b) Baseline WQ: 20

- 39

(c) Baseline WQ: 40

- 59 (d) Baseline WQ: 60

- 80

Notes: Each panel shows th e expected value and 95% confidence interval for mean WTP based on the

meta

- data , by 10

- unit water quality change bin. The dots in each panel show the raw meta

- data values.7



## 3. Accounting for Water Quality Change in the Meta

- Model

The previous section shows that the magnitude of water quality change has a strong influence on survey respondents’ valuations . Given this is an empirical feature of the meta

- dataset , what is the appropriate way to develop a meta

- model for predicting marginal willingness

- to

- pay?

3.1.1 Treating Water Quality Change as a Study Methodological Characteristic

W e propose addressing this issue by treating water quality change as a study methodological

characteristic . In other words, we propose modeling water quality change as a demand shifter that affects marginal WTP in the same way as other study methodological characteristics included in the me ta

- model (e.g., the use of a choi ce experiment format, or a lump sum payment). And, like those parameters, the water quality change parameter could be set to any appropriate value when the meta

- model is used for

benefit transfer . Importantly, because wat er quality change would be treated as a methodological characteristic instead of as a scenario characteristic, the value assigned to the water quality change
parameter need not correspond to the specific water quality change being valued. F or the same rea son, the resulting model will still satisfy the adding

- up property.

As noted above, t he approach adopted by MRM2 is to model marginal WTP using the average water quality change magnitude in the meta

- dataset. 3 In other words, MRM2 assumes that the averag e water quality change scenario in the meta

- dataset is what a well

- designed stated preference survey would use for eliciting respondents’ marginal WTP

. While this approach is reasonable, other strategies are also possible.

A hypothetical example may help to illustrate this point. Suppose that a particular contingent valuation study elicits WTP from respondents in two counties: County 1 and County 2. Respondents in County 1 have an average WTP of $30 for a +2 unit improvement from their current baseline of 64 to a future value of 66 (on the 100

- point Water Quality Index). Respondents in County 2 have an average WTP of $50 for a +10 unit improvement from their current baseline of 60 to a future value of 70. These results imply that marginal WTP for the 65 th unit of water quality is approximately $15 in County 1, and $5 in County 2. 4
These valuations clearly do not satisfy adding

- up, since the marginal value of water quality changes depends on the scope of the change being valued.

Nonetheless , the autho rs would like to use the results of their contingent valuation study to value the benefits of a small water quality improvement in a third county (County 3). County 3 is very similar to County 1 and 2, except that baseline water quality is 64.5. The ques tion the authors face is: what marginal willingness

- to

- pay value should they use to value a one

- unit water quality increase in County 3?

Unfortunately, there is no clear theoretical guidance for this decision. Values of $5 or $15 are certainly possibi lities, as is the average value of $10. And in some sense, all of these values are arbitrary, since the study might have gotten different marginal WTP estimates had it asked respondents to value water quality changes of different magnitudes. Thus, the mo st appropriate course of action might be to conduct a

3 Note that this statement is an approximation, since MRM2 uses a regression model (not an average) to calcula te marginal WTP. However, the basic intuition is correct.

4 These hypothetical marginal willingness

- to

- pay calculations use the same midpoint approximation approach as
MRM2.8

sensitivity analysis using marginal values of both $5 and $15 . I n effect, this would treat water quality change as a study methodological characteristic , and estimate marginal WTP using the range of wa ter quality change values found this particular survey

. We believe that an identical intuition applies to EPA’s

meta

- analysis.

3.1.2 Modeling Details

T o formalize th e alternative approach we are proposing , the following equation presents an expanded
version of MRM2 that allows the water quality change Δ Q i to enter as a methodological characteristic

. We refer to this model as MRM2

- S (where the “S” ind icates that the model takes into account the scope of the water quality change):

ln ( MWT P i ) = α 0 + α 1 X i + g ( Δ Q i ; φ ) + f ( Q i ; β ) + ε i (1 1 )

In this equation, Δ Q i is the magnitude of the water quality change for meta

- data observation i , and φ is a vector of parameters that specify the functional form for the function g (

⋅ ) . For simplicity, we model the
function g (

⋅ ) as a linear function of the water quality change : 5

g ( Δ Q i ; φ ) ≡ φ

⋅ Δ Q i (12)

Substituting Equations (4), (5), and (12) into Equation (11) gives the following regression model:

ln ( WT P i
Δ Q i )

= α 0 + α 1 X i + φ

⋅ Δ Q i + β

⋅ ( Q i 0 + Q i 1
2 ) + ε i (13)

Following the same logic described at the end of Section 1 , the estimated parameters from this equation can be used to generate an expression for both marginal WTP and total WTP :

MWTP = exp ( α

̂ 0 + α ̂ 1 X + φ

⋅ Δ Q + σ

̂ 2 / 2 )

⋅ exp ( β

̂

⋅ Q ) (14)

WTP = exp ( α

̂ 0 + α ̂ 1 X + φ

⋅ Δ Q + σ

̂ 2 / 2 )

⋅ exp ( β

̂

⋅ Q 1 )

− exp ( β

̂

⋅ Q 0 )

β ̂ (15)

Again, we emphasize that Δ Q is treated as a study methodological characteristic, not as a characteristic of

the benefit transfer water quality improvement scenario. Thus, in equations (14) and (15), the para meter
Δ Q need not be set equal to Q 1 − Q 0 .

3.1.3 Regression Results

Table 1 presents regression results for two versions of MRM2

- S. Column (b) shows the linear version, exactly as described in Equation (13). Column (c) presents an alternative version, which instead includes the natural log of the change water quality. As a reference, C olumn (a) presents regression results for the

main MRM2 model.

5 We also consider a specification in which we model g (

⋅ ) as a linear function o f the natural log of water quality change.9

In general, the coefficients on the methodological, socioeconomic, and resource characteristic control variables are quite similar across the three models . There are some differences in magnitude and significance , but the signs of all variables remain consistent

.

Focusing on the absolute water quality variable ( Qavg2 ) shows that water quality h as a larger effect on marginal WTP under MRM2, compared to the MRM2

- S models. The coefficient is

- 0.017 (p<.01) under
MRM2,

- 0.012 (p<.05) under the linear water quality change MRM 2

- S model, and

- 0.008 (ns) under the log water quality change MRM2

- S model

. This pattern suggests that after accounting for the change in water quality, absolute water quality may have less of an effect on marginal willingness to pay. However,

we do note that a t

- test would fail to reject the equality of these coefficients.

The MRM2

- S models also include water quality change variables: either quality_ch or lnquality_ch

. Columns (b) and (c) show that in both models, these variables are negative and highly significant. This pattern indicates that marginal WTP is decreasing in the size of the water quality change being valued. This is consistent with the patterns from the raw meta

- data, as discussed in Section 2 above.

Overall, a comparison of the R 2 values from these three models indicates MRM2

- S has greater explanatory po wer than MRM2. MRM2 has a R 2 value of 0.612. In contrast, the R 2 value for the linear

MRM2

- S model is 0.677, and the R 2 value for the log MRM2

- S model is 0.722. Given that MRM2 already has 23 variables and a constant, this substantial increase in R 2 fro m one additional variable suggests that water quality change (or log water quality change) is an important variable to include in the

model.10 Table 1

. Regression Results for MRM2 with Water Quality Change Included
(a ) (b) (c)

Parameter MRM2 MRM2

- S: Water Quality Change MRM2

- S: Log Water Quality Change

ce 0.53 0 ( 0.308 ) 0.503* ( 0.241 ) 0.512* (0.199)
thesis 0.631* ( 0.246 ) 0.723** ( 0.196 ) 0.702** (0.184) lnyear

- 0.356** ( 0.101 )

- 0.404** ( 0.089 )

- 0.452** (0.080)
volunt

- 1.468** ( 0.225 )

- 1.337** ( 0.219 )

- 1.272** (0.206) outlier_bids

- 0.494** ( 0.175 )

- 0.380* ( 0.150 )

- 0.391** (0.122)

nonparam

- 0.577** ( 0.119 )

- 0.478** ( 0.111 )

- 0.503** (0.110) non_reviewed

- 0.578** ( 0.200 )

- 0.638** ( 0.177 )

- 0.686** (0.165) lump_sum 0.879** ( 0.190 ) 0.809** ( 0.154 ) 0.786** (0.141) WTP_median

- 0.348 ( 0.342 )

- 0.305 ( 0.242 )

- 0.265 (0.223)
northeast 1.058** ( 0.321 ) 0.846** ( 0.271 ) 0.593* (0.254)
central 0.545** ( 0.161 ) 0.621** ( 0.130 ) 0.611** (0.113)
south 1.351** ( 0.171 ) 1.427** ( 0.152 ) 1.429** (0.138)

nonusers

- 0.454** ( 0.151 )

- 0.428** ( 0.124 )

- 0.448** (0.122)
lnincome1 0.212 ( 0.420 ) 0.461 ( 0.370 ) 0.638 (0.325) mult_bod

- 0.680** ( 0.205 )

- 0.599** ( 0.151 )

- 0.527** (0.142)
river1

- 0.092 ( 0.151 )

- 0.136 ( 0.113 )

- 0.230* (0.111) swim_use

- 0.384* ( 0.184 )

- 0.307 ( 0.172 )

- 0.347* (0.172) gamefish 0.526 ( 0.308 ) 0.483 ( 0.241 ) 0.290 (0.179) boat_use

- 0.715** ( 0.226 )

- 0.500** ( 0.181 )

- 0.382* (0.156) ln_ar_agr

- 0.344** ( 0.100 )

- 0.361** ( 0.102 )

- 0.387** (0.088) ln_ar_ratio1

- 0.075** ( 0.026 )

- 0.070* ( 0.028 )

- 0.071** (0.025) sub_frac 1.135** ( 0.237 ) 0.908** ( 0.211 ) 0.714** (0.182) Qavg2

- 0.017** ( 0.005 )

- 0.012* ( 0.005 )

- 0.008 (0.005) quality_ch

- 0.027** ( 0.008 ) lnquality_ch

- 0.664** (0.119)

_cons 0.15 0 ( 4.611 )

- 2.172 ( 4.051 )

- 2.725 (3.484)
Observations: 140 140 140
R 2 0.6 12 0. 677 0.722 Weights No No No
Random Effects: No No No
Notes: The table shows coefficients for each model, with standard errors in parentheses. * denotes p<.05; ** denotes p<.01 . Due to time constraints, the standard errors in the table are taken directly from the OLS regressions, and do not use the bootstrapping approach described in NCEE’s 4/23/2015 memorandum

.

3.1.4 Determining an Appropriate Value for the Water Quality Change P arameter in MRM2

- S

If the MRM2

- S model were used to estimate the benefits of the Steam Electric Rule (or other future EPA regulations), EPA would need to determine an appropriate value for the water quality change parameter.

This section discusses some co nsiderations related to that choice.

The key underlying question is: why does marginal WTP depend on the scope of the water quality change being valued? There are several potential hypotheses that could explain why survey respondents’ implied marginal WT P appears to depend on baseline water quality conditions in the area in which they

live.

 One hypothesis is that this pattern simply reflects an income effect.11

 A second hypothesis is that survey respondents may have difficulty visualizing very large or very small water quality changes. This could lead them to understate their willingness

- to

- pay for large changes, and to overstate their willingness

- to

- pay for small changes.

 A third hypothesis is that survey respondents may find large water quality changes implausible. As a result, they might discount their stated valuations for these large changes to account for what they perceive as the low probability of the changes actually occurring.

 A fourth hypothesis is that stated preference surveys captur e “warm glow” effects (Diamond et al, 1993). In other words, survey respondents may provide WTP values that reflect their desire for action, or their utility from doing good deeds. Under this hypothesis, much or all of their monetary WTP would reflect th is general warm glow, instead of their actual valuation for the specific resource change under consideration. Note, however, that researchers have had some success using cheap talk scripts , certainty adjustments, and other methods reduce and minimize hypo thetical biases (e.g., Champ et al. 1997, 2004; Cummings and Taylor 1999; Johnston 2006; Ready et al. 2010). Recently published findings of Ready et al. (2010, p. 363), for example, show that contemporary certainty adjustments “successfully mitigated hypot hetical bias.” While the

broader evidence regarding the ability of researchers to ameliorate hypothetical biases is mixed,

there is no evidence that such biases are unavoidable , and Murphy et al. (2010) state that there is a “small but growing literature i s suggesting the absence of hypothetical bias in aggregate in induced value settings”.

 A fifth hypothesis is that the water quality levels and changes described in some stated preference studies may translate imperfectly to the 100

- point water quality inde x, resulting in measurement

error in the meta

- regression. A related hypothesis is that the water quality changes in the meta

data could be correlated with some other omitted variable that also influences marginal WTP.

 A final hypothesis is that respondent s’ utility from water quality improvements may endogenously depend on water quality in the area in which they live. This could occur in at least two ways. First, in a spatial hedonic equilibrium, people are likely to move to areas that where the marginal cost (broadly interpreted) of accessing natural amenities is approximately equal to the marginal utility benefits provided by those amenities. Alternatively, even if water quality has little effect on residential sorting, people and communities may make recreational investments (e.g., in skills, equipment, or facilities) that are appropriate for their local environmental

conditions . For example, towns located in areas with very poor water quality might not build public swimming beaches

— thus reducing the marginal benefit of large improvements in water quality.

Overall, the data from the meta

- analysis do not provide any simple way of testing or ruling out these different possibilities. This makes choosing a single value for the water quality change paramet er in

MRM2

- S difficult. Our recommendation is instead to c onduct a sensitivity analysis, using the range of water quality change scenarios found in the meta

- dataset. The purpose of this sensitivity analysis would be to explore the range of values that wo uld be generated if EPA were to conduct a well

- designed stated preference survey designed to elicit marginal WTP for the types of water quality improvements expected

under future CWA regulations.

To aid in choosing appropriate water quality change values, Figure 3, on the following page, presents a histogram of the water quality changes valued in studies in the meta

- dataset. The figure shows that the water quality changes in the dataset range from +2.5 units to +57 units. The average change in the dataset

is +20.7 units. To put these values in context, note that the water quality index ranges from a minimum of12

0 (for water that is so polluted that it has no uses) to 100 (for water that is drinkable without treatment). For example, an index value of 45 me ans that rough fishing is possible, and an index value of 50 means that game fishing is possible. Thus, on this scale, even relatively small changes can provide noticeable improvements.

Based on the range of water quality changes in the meta

- data , we be lieve that a reasonable sensitivity analysis might use MRM2

- S to predict marginal WTP under the following three alternative values of the water quality change parameter: +5 units, +20 units, and +50 units.

Figure 2

. Distribution of Water Quality Change in the Meta

- Dataset

3.1.5 Estimated Marginal Willingness

- To

- Pay

To illustrate the implications of different choices of the change in water quality parameter, th is section presents estimates of marginal WTP based on MRM2 and MRM2

- S.

Figure 3 shows predicted marginal WTP from MRM2

- S, based on the specification that is linear in water quality change. The figure presents sensitivity analysis results for three different values of the water quality change methodology variable: +5 units, +20 units, and +50 units . For comparison, the figure also present results from MRM2 (which does not depend on water quality change). Overall, the figure shows

that when MRM2

- S is evaluated at a water quality change of +20 units, it produces results that are very

similar to MRM 2. This is not surprising, given that MRM2 is essentially evaluating marginal WTP at the average water quality change in the dataset (which is +20.7 units). The main difference is that under

MRM2

- S, marginal WTP has a flatter slope with respect to water quality.

Figure 3 also shows that w hen MRM2

- S is evaluated using a water quality change parameter of +5 0 units, it produces marginal WTP values that are roughly 50% lower than when MRM2

- S is evaluated at +2013

units. Conversely, when MRM2

- S is evalu ated at +5 units, it produces marginal WTP values that are roughly 40% to 50% higher than when MRM2

- S is evaluated at +20 units.

Figure 4 presents a similar comparison of MRM2 and MRM2

- S, but using the version of MRM2

- S based on the specification that inc ludes the log of water quality change. Overall, one main difference is that this

version of MRM2

- S produces marginal WTP curves that are even flatter with respect to water quality. At the same time, marginal WTP values from this model are more sensitive to the choice of the water quality change parameter. In particular, marginal WTP values are substantially higher when the water quality change parameter is set equal to +5 units

.

Figure 3

. Predicted Marginal WTP, for MRM2

- S with Water Quality Change14

Figure 4

. Predicted Marginal WTP, for MRM2

- S with Log Water Quality Change

The marginal WTP values predicted here for MRM2 are in the range of $3 to $11 per unit. This range is fairly comparable to the average WTP per water quality unit from the meta

- dataset, which is $6.30. However, this range is quite a bit higher than the predicted MRM2 values from the peer review report, which ranged from approximately $1 to $3 (see Fig 11 from that report). These differences are due to changes in the values assigned to the control variable parameters in MRM2, and to the fact that the model is relatively sensitive to the choices of certain variables.

As a reference, Table 2 shows the parameter values at which the meta

- regression model was evaluated,

for the purposes of generating the marginal WTP values shown in Figures 3 and 4. Other choices for these parameters are possible, and we welcome EPA’s guidance on selecting appropriate values.15 Table 2

. Assigned Values for Meta

- Regression Parameters

Parameter As signed Value
C e 0.518
T hesis 0
L nyear 2.525
V olunt 0 outlier_bids 1
N onparam 0 non_reviewed 0 lump_sum 0 WTP_median 0
N ortheast 0.101
C entral 0.389
S outh 0.327
N onusers 0
lnincome1 10.894 mult_bod 0
river1 1 swim_use 0.264
G amefish 0.057 boat_use 0.114 ln_ar_agr

- 1.267 ln_ar_ratio1 1.238 sub_frac 0.0239 Qavg2 varies quality_ch varies lnquality_ch varies

_cons 1

3.1.6 Application to the Steam Electric Rule

This section uses the MRM2

- S marginal WTP values from the previous section to generate back

- of

- the

envelope estimates of the yearly benefits of the Steam Electric Rule

, once it fully takes effect

. Table 3 presents the results of these calculations , as well as estimates based on MRM2 . Note that this table makes

a number of simplifications. In particular, it assumes that all 85 million households affected by the rule reside in areas in which baseline water quality is 50 on the water quality index. It also assumes that the water quality improvement is a homogenous 0.1 units everywhere. These values are approximations, and should be interpreted only as order

- of

- magnitude estimates of the benefits of the Steam Electric Regulation. They do not account for the time required for roll

- out of the regulation, or for discounting.

T able 3 shows that under MRM2, annual benefits are predicted to be $42.5 million per year. When

MRM2

- S is evaluated at a water quality change parameter of +20 units, it generates similar predictions: $46.4 million per year for the linear water quality ver sion, and $41.1 for the log water quality version. Under the linear water quality version of MRM2

- S, benefits range from $20.3 million per year to $69.9 million per year, when evaluated using water quality change parameter values of +50 units and +5 units

, respectively. Under the log water quality version of MRM2

- S, benefits are higher, and range from $22.4

mill ion per year to $103.3 million per year.16 Table 3

. Approximate Benefits Estimates for the Steam Electric Rule

(a ) (b) (c) (d) ( e )

Affected
Households Baseline

Water Quality
Index Average

Change in Water Quality
Index Marginal WTP

per Year, at
Baseline Water Quality Yearly

Benefits (millions)

MRM2 85 million 50 0.1 $5.00 $42.5

MRM2

- S with ΔWQ
ΔWQ=+5 85 million 50 0.1 $8.22 $69.9
ΔWQ=+20 85 million 50 0.1 $5.46 $46.4
ΔWQ=+50 85 million 50 0.1 $2.39 $20.3

MRM2

- S with ln(ΔWQ)
ΔWQ=+5 85 million 50 0.1 $12.15 $103.3
ΔWQ=+20 85 million 50 0.1 $4.84 $41.1
ΔWQ=+50 85 million 50 0.1 $2.63 $22.4

Notes: Note that this table presents estimates of yearly benefits once the Steam Electric Regulations reaches full effect. Due to discounting and the time required for the roll

- out, actual annualized benefits will be considerably smaller (i.e., by perhaps 30%).17



## 4. Next Steps

Thi s memo presents our recommendations for incorporating a water quality change variable into the

MRM2 meta

- regression model, and treating it as a methodological characteristic . We believe that there are good theoretical and empirical reasons for doing so

. T he resulting MRM2

- S model satisfies the adding

- up property , while at the same time controlling for how survey respondents’ implied marginal WTP values are affected by the scope of the resource change presented to them in the survey. At the same time, the MRM2

- S model provides a substantial increase in R 2 relative to MRM2. It also provides EPA with a way to conduct a sensitivity analysis that accounts for the full range of marginal WTP values that might be generated using reasonable stated preference tech niques.

We would be happy to discuss the material in this memo further, or to run alternative versions of the analysis based on other sets of input parameters. We look forward to EPA’s guidance on whether and how to implement and apply this version of the meta

- regression model.18



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