# Improving Drinking Water Quality in South Korea: A Choice Experiment with Hypothetical Bias Treatments

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## Abstract

**:**

## 1. Introduction

## 2. Survey Design and Data Collection

#### 2.1. Choice Experiment Design

#### 2.2. Hypothetical Bias

## 3. Methodology

#### 3.1. Random Utility Framework

_{n}is the choice set for individual n and ${\mathrm{x}}_{\mathrm{nti}}$ is a vector of observable independent variables that includes attributes of the alternatives, and socio-economic characteristics of the respondent. In order to estimate the coefficients of the RPL, it is necessary to maximize the likelihood ${\mathrm{P}}_{\mathrm{n},\mathrm{t},{\xdf}_{\mathrm{n}}}$ from Equation (1). To estimate the coefficient for representing a sample, a log-likelihood function is estimated through simulated methods, because (1) does not have a closed form.

#### 3.2. Latent Class Model (LCM)

#### 3.3. Attribute Non-Attendance (ANA)

#### 3.4. Cost-Benefit Analysis (CBA)

## 4. Empirical Results

#### 4.1. Benefits

#### 4.1.1. RPL

#### 4.1.2. LCM-ANA

#### 4.1.3. Willingness to Pay

#### 4.1.4. Estimation of Benefits

#### Willingness to Pay per Household

#### Total Benefits

#### 4.1.5. Cost Estimation

#### 4.1.6. Cost-Benefit Analysis (CBA)

#### Present Values of the Cash Flows

#### Benefit Flow

#### Sensitivity Analysis

#### Risk Premium Approach

#### Reduction of Business Life

#### Decrease in Benefits

#### Increase in Costs

#### Summary of Sensitivity Analysis

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

#### A Sample of the Questionnaire

## Appendix B

#### Latent Class Models

Classes | FAA of Using ASCs of HB | FAA of Using Interaction Terms of HB | |
---|---|---|---|

Sample Size | 406 | 406 | |

2 | BIC | 5506.8 | 5537.3 |

AIC | 5406.6 | 5461.2 | |

Log−likelihood | −2678.3 | −2711.6 | |

Pseudo−R^{2} | 0.2465 | 0.2379 | |

3 | BIC | 5384.0 | 5356.2 |

AIC | 5231.7 | 5240.0 | |

Log−likelihood | −2577.9 | −2591.0 | |

Pseudo−R^{2} | 0.2733 | 0.2706 | |

4 | BIC | 5363.7 | 5287.4 |

AIC | 5159.4 | 5131.1 | |

Log−likelihood | −2528.7 | −2526.6 | |

Pseudo−R^{2} | 0.2857 | 0.2877 | |

5 | BIC | 5348.8 | 5331.0 |

AIC | 5092.4 | 5134.7 | |

Log−likelihood | −2482.2 | −2518.4 | |

Pseudo−R^{2} | 0.2974 | 0.2889 | |

6 | BIC | 5354.5 | 5349.9 |

AIC | 5046.0 | 5113.6 | |

Log−likelihood | −2446.0 | −2497.8 | |

Pseudo−R^{2} | 0.3063 | 0.2936 | |

7 | BIC | 5375.8 | 5328.5 |

AIC | 5015.2 | 5052.1 | |

Log−likelihood | −2417.6 | −2457.0 | |

Pseudo−R^{2} | 0.3130 | 0.3040 | |

8 | BIC | 5437.7 | 5348.5 |

AIC | 5025.0 | 5032.0 | |

Log−likelihood | −2409.5 | −2436.9 | |

Pseudo−R^{2} | 0.3139 | 0.3086 | |

9 | BIC | 5499.5 | 5398.4 |

AIC | 5034.7 | 5041.8 | |

Log−likelihood | −2401.4 | −2431.9 | |

Pseudo−R^{2} | 0.3148 | 0.3090 |

## Appendix C

#### Socio-Economic Variables

Variable | Description |
---|---|

gender | dummy, 1 indicating a male, 0 female |

age | respondent’s age |

edu | years of education |

pinc | personal income |

hinc | the income per household of each respondent |

bill | the average monthly water bill for each respondent’s household |

family | the number of people in the family |

earner | the number of earners in their household |

infant | the number of infants in a respondent’s house; less than 4 years old |

elderly | the number of elders in a respondent’s house; more than 59 years old |

environ | the scale value of the preference for water-environment friendly policy |

head | dummy, 1 indicating if a respondent is a head of household |

spouse | dummy, 1 indicating if a respondent is a spouse of the household head |

others | dummy, 1 indicating if one is neither a head of household nor a spouse |

boil | dummy, 1 indicating a respondent drinks after boiling drinking water |

purify | dummy, 1 indicating a respondent drinks water by using purifier |

bottle | dummy, 1 indicating a respondent purchases bottled water |

well | dummy, 1 indicating a respondent drinks water from well |

apart | dummy, 1 indicating a respondent lives in an apartment |

detach | dummy, 1 indicating a respondent lives in a detached house |

terrace | dummy, 1 indicating a respondent lives in a terraced house |

multiple | dummy, 1 indicating a respondent lives in a multiplex house |

full | dummy, 1 indicating a respondent has a full-time job |

part | dummy, 1 indicating a respondent has a part-time job |

retired | dummy, 1 indicating a respondent is retired |

lookjob | dummy, 1 indicating a respondent is unemployed and looking for a job |

notlook | dummy, 1 indicating a respondent is unemployed, not looking for a job |

otherjob | dummy, 1 indicating a respondent has other jobs; student, homemaker |

## Appendix D

#### Confidence Intervals for the Median WTP

- (1)
- Use the coefficient vector and the variance-covariance matrix of an LCM to generate one coefficient vector from the multivariate distribution and to calculate a WTP measure of each class.
- (2)
- Simulate an LCM and calculate the individual class probabilities according to the generated coefficient vector.
- (3)
- Multiply the simulated individual class probabilities with the simulated WTPs of all classes, and generate one WTP for each respondent.
- (4)
- Make one WTP distribution of calculating the WTPs of all respondents, and measure one median WTP from the distribution.
- (5)
- After repeating the steps 1 to 4 many times, the median WTP space (reference [49] reports that MWTP space is defined as in reference [50], who calculated the space by using the ratio of the attribute’s coefficient to the price coefficient in a random parameter logit model) can be obtained, and the standard error of the median WTP can be calculated.
- (6)
- Repeat the simulation 1000 times, and calculate a median WTP space (NLOGIT 5 was used for the simulation). The ANA 1 model is chosen for the simulation. Table A3 shows the result of simulation for calculating the median WTP space of the ANA1.

Attribute | Average | Standard Deviation | 95% Confidence Interval | Simulation |
---|---|---|---|---|

Safety | 0.04531 | 0.00505 | 0.03649–0.05450 | 1000 |

Taste and odor | 0.00629 | 0.00235 | 0.00614–0.00643 | 1000 |

Attribute | Mean | Standard Error | 95% Confidence Interval | Simulation |
---|---|---|---|---|

Safety | 0.04671 | 0.000057 | 0.0465–0.0470 | 1000 |

Taste and odor | 0.00623 | 0.000079 | 0.0060–0.0066 | 1000 |

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Net Present Value (NPV) | $\mathrm{NPV}={\displaystyle {\displaystyle \sum}_{\mathrm{t}=1}^{\mathrm{T}}}\frac{\mathrm{E}\left({\mathrm{NB}}_{\mathrm{t}}\right)}{{\left(1+\mathrm{r}\right)}^{\mathrm{t}}}-{\mathrm{I}}_{0}$ NB _{t} = B_{t} − C_{t} (the flow of net benefits in time t period) |

B/C ratio (B/C) | $\frac{\mathrm{B}}{\mathrm{C}}\mathrm{ratio}={{\displaystyle \sum}}_{\mathrm{t}-0}^{\mathrm{T}}\raisebox{1ex}{${\mathrm{B}}_{\mathrm{t}}$}\!\left/ \!\raisebox{-1ex}{${\left(1+\mathrm{r}\right)}^{\mathrm{t}}$}\right./{{\displaystyle \sum}}_{\mathrm{t}=0}^{\mathrm{T}}\raisebox{1ex}{${\mathrm{C}}_{\mathrm{t}}$}\!\left/ \!\raisebox{-1ex}{${\left(1+\mathrm{r}\right)}^{\mathrm{t}}$}\right.$ |

Internal Rate of Return (IRR) | $\displaystyle \sum}_{\mathrm{t}=0}^{\mathrm{T}}}\frac{{\mathrm{B}}_{\mathrm{t}}}{{\left(1+\mathrm{IRR}\right)}^{\mathrm{t}}}={\displaystyle {\displaystyle \sum}_{\mathrm{t}=0}^{\mathrm{T}}}\frac{{\mathrm{C}}_{\mathrm{t}}}{{\left(1+\mathrm{IRR}\right)}^{\mathrm{t}$ |

_{0}—initial investment cost.

Variable | RPL 1 | RPL 2 |
---|---|---|

x1 (safety; cancer risk) | −0.0563 (0.0000) | −0.0437 (0.0000) |

S.D of coefficient of x1 | 0.0419 (0.0000) | 0.0613 (0.0000) |

x2 (taste and odor) | 0.0089 (0.0000) | 0.0087 (0.0000) |

S.D of coefficient of x2 | 0.0219 (0.0000) | 0.0220 (0.0000) |

x3 (color) | 0.0174 (0.2118) | 0.0058 (0.6541) |

S.D of coefficient of x3 | 0.1675 (0.0000) | 0.1667 (0.0000) |

x4 (cost/price) | −1.0791 (0.0000) | −0.6511 (0.0000) |

D_{both} x4 | - | −0.2343 (0.0145) |

D_{cheap} x4 | - | −0.2730 (0.0027) |

D_{honest} x4 | - | −0.6582 (0.0000) |

ASC Of Ozone | −1.1352 (0.1927) | −2.2388 (0.0092) |

Elderly | −0.6303 (0.0224) | −0.6712 (0.0111) |

Bill | 0.0385 (0.0185) | 0.0397 (0.0096) |

Environ | 0.6553 (0.0000) | 0.6113 (0.0000) |

Fulltime | −0.4936 (0.0488) | |

D_{both} | −2.1771 (0.0000) | − |

D_{cheap} | −1.8695 (0.0000) | − |

D_{honest} | −2.5258 (0.0000) | − |

ASC Of GAC | 1.7204 (0.0053) | 0.5395 (0.3684) |

Elderly | −0.5236 (0.0075) | −0.4764 (0.0112) |

Bill | 0.0137 (0.2999) | 0.0138 (0.2414) |

Environ | 0.2205 (0.0292) | 0.2241 (0.0277) |

Fulltime | − | −0.4086 (0.0273) |

D_{both} | −1.1580 (0.0000) | − |

D_{cheap} | −2.2261 (0.0000) | − |

D_{honest} | −1.6462 (0.0000) | − |

Sample size | 406 | 406 |

Log Likelihood | −2655.96 | −2692.9 |

AIC | 5353.9 | 5425.8 |

BIC | 5438.1 | 5487.9 |

Pseudo ${\mathrm{R}}_{\mathrm{adj}}^{2}$ | 0.2533 | 0.2430 |

Variable | Class 1 | Class 2 | Class 3 | Class 4 | Class 5 |
---|---|---|---|---|---|

x1 (safety) | −0.0115 (0.1685) | −0.0787 (0.0000) | −0.0315 (0.0000) | −0.0992 (0.0000) | −0.0659 (0.0000) |

x2 (t&o) | 0.022 (0.0016) | 0.0 (fixed) | 0.0 (fixed) | 0.0091 (0.0763) | 0.0249 (0.0000) |

x3 (color) | 0.1635 (0.0001) | 0.0000 (fixed) | 0.0000 (fixed) | 0.0000 (fixed) | 0.0000 (fixed) |

X4 (cost) | −0.4385 (0.0162) | −1.6890 (0.0000) | −1.85815 (0.0000) | −0.4291 (0.0084) | −1.2237 (0.0000) |

of Ozone, one | 3.9368 (0.4143) | −10.3007 (0.0001) | −18.6362 (0.2240) | 1.6704 (0.5182) | −2.4698 (0.0445) |

Elderly | −1.5635 (0.1843) | −0.8538 (0.1485) | −5.6905 (0.9938) | 8.1582 (0.9840) | −0.1390 (0.7508) |

Bill | −0.0546 (0.3322) | −0.1164 (0.0432) | 0.3009 (0.0442) | 0.1269 (0.0093) | 0.0249 (0.2348) |

Environ | 0.0982 (0.8803) | 2.6911 (0.0000) | 2.4889 (0.2331) | 0.0109 (0.9686) | 0.7965 (0.0003) |

Dboth | −3.6684 (0.0472) | −4.2468 (0.0000) | −8.6509 (0.9438) | −1.9746 (0.2125) | −1.6949 (0.0136) |

Dcheap | 4.3111 (0.9981) | −2.1275 (0.0303) | −8.3258 (0.9792) | −5.2732 (0.0014) | −1.0262 (0.1561) |

Dhonest | 5.2144 (0.9988) | −4.4826 (0.0000) | 0.0695 (0.9661) | −4.9345 (0.0023) | −2.6401 (0.0000) |

of GAC, one | 4.5498 (0.3429) | −0.9715 (0.5377) | 2.6276 (0.0002) | 2.5140 (0.3604) | −0.6299 (0.6164) |

Elderly | −0.4004 (0.7747) | −1.4895 (0.0001) | −0.5352 (0.0751) | 8.0302 (0.9842) | −0.5649 (0.0825) |

Bill | −0.0086 (0.8787) | −0.1341 (0.0018) | 0.1134 (0.0000) | 0.1071 (0.0359) | −0.0386 (0.1066) |

Environ | −0.2475 (0.7083) | 1.1416 (0.0000) | −0.2641 (0.0455) | −0.0863 (0.7796) | 0.8243 (0.0003) |

Dboth | −1.8130 (0.3076) | −3.5534 (0.0000) | −0.6633 (0.0817) | −1.7025 (0.2631) | −1.3913 (0.0233) |

Dcheap | 4.7046 (0.9979) | −2.2884 (0.0000) | −1.4024 (0.0000) | −5.6954 (0.0005) | −1.8048 (0.0091) |

Dhonest | 6.8215 (0.9984) | −3.1666 (0.0000) | 0.2009 (0.6191) | −4.5187 (0.0051) | −3.1014 (0.0000) |

Class probability | 0.185 (0.0000) | 0.167 (0.0000) | 0.220 (0.0000) | 0.181 (0.0000) | 0.247 (0.0000) |

Sample size: 406, Log−likelihood: −2439.1, AIC: 5054.2, BIC: 5406.7, Pseudo−R2: 0.3071 |

Mean WTP | Median WTP | |||||||
---|---|---|---|---|---|---|---|---|

Model | RPL 1 | RPL 2 | ANA 1 | ANA 2 | RPL 1 | RPL 2 | ANA 1 | ANA 2 |

Safety | 0.0523 | 0.0491 | 0.0666 | 0.0974 | 0.0510 | 0.0434 | 0.0468 | 0.0396 |

Taste and odor | 0.0082 | 0.0146 | 0.0146 | 0.0217 | 0.0090 | 0.0100 | 0.0063 | 0.0177 |

Color | 0.0171 | 0.0048 | 0.0690 | 0.0284 | 0.0017 | 0.0000 | 0.0000 | 0.0020 |

KRW 1000 | Safety | Taste and Odor | Color | Sum | |
---|---|---|---|---|---|

Median of WTP (m) | 0.04676 | 0.00630 | 0 | ||

GAC | change of attribute ($\Delta {\mathrm{x}}_{\mathrm{i}})$ | 34 (40 to 6) | 80 (10 to 90) | 9 (90 to 99) | |

Benefit (m × $\Delta {\mathrm{x}}_{\mathrm{i}}$) | 1.590 | 0.504 | 0 | 2.094 | |

Ozone + GAC | change of attribute ($\Delta {\mathrm{x}}_{\mathrm{i}}$) | 39 (40 to 1) | 89.9 (10 to 99.9) | 9.9 (90 to 99.9) | |

Benefit (m × $\Delta {\mathrm{x}}_{\mathrm{i}}$) | 1.824 | 0.567 | 0 | 2.391 |

KRW | RPL 1 | RPL 2 | ANA 1 | ANA 2 | |
---|---|---|---|---|---|

GAC | Mean | 3.206 | 3.270 | 4.056 | 5.370 |

Median | 2.467 | 2.274 | 2.094 | 2.781 | |

Ozone + GAC | Mean | 3.633 | 3.703 | 4.596 | 6.035 |

Median | 2.813 | 2.589 | 2.391 | 3.156 |

Monthly | Annual | |||||||
---|---|---|---|---|---|---|---|---|

KRW Million (USD Thousand) | RPL 1 | RPL 2 | ANA 1 | ANA 2 | RPL 1 | RPL 2 | ANA 1 | ANA 2 |

GAC | 485 (412) | 447 (380) | 412 (350) | 547 (465) | 5823 (5026) | 5368 (4558) | 4944 (4199) | 6565 (5575) |

Ozone + GAC | 553 (470) | 509 (433) | 470 (399) | 621 (527) | 6744 (5724) | 6111 (5190) | 5643 (4793) | 7451 (6327) |

System | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | Year 6 | … | Year 24 |
---|---|---|---|---|---|---|---|---|

GAC | 1605 | 3776 | 11,479 | 11,479 | 11,930 | 451 | 451 | 451 |

(USD) | (1369) | (3220) | (9790) | (9790) | (10,175) | (385) | (385) | (385) |

Ozone | 466 | 1096 | 3332 | 3332 | 3332 | 41 | 41 | 41 |

(USD) | (397) | (935) | (2842) | (2842) | (2842) | (35) | (35) | (35) |

Factor | Range | |
---|---|---|

Business life (years) | 10–20 | |

Social discount rate (%/year) | 1–10 | |

Benefit | WTP of safety (KRW 1000) | 0.0365, 0.0465–0.0468 |

WTP of taste and odor (KRW 1000) | 0.0063, 0.0060–0.0066 | |

Advantaged household | 165,828–196,712 | |

Construction period (years) | 4–6 | |

Construction cost (KRW per m^{3}/day) | 127,645–153,425 |

KRW Million (USD Thousand) | GAC | Ozone Plus GAC |
---|---|---|

Monthly Social Benefit | 412 (350) | 470 (399) |

Annual Social Benefit | 4943 (4198) | 5644 (4793) |

**Table 11.**Cash flows of the GAC and GAC plus ozone alternatives (summarizing cost and benefit flows).

GAC | GAC Plus Ozone | |||
---|---|---|---|---|

Net Value | Present Value | Net Value | Present Value | |

2015 | −1605 | −1605 | −2071 | −2071 |

2016 | −3776 | −3579 | −4872 | −4662 |

2017 | −11,479 | −10,313 | −14,811 | −13,563 |

2018 | −11,479 | −9776 | −14,811 | −12,979 |

2019 | −6987 | −5859 | −9618 | −8065 |

2020 | 4492 | 3605 | 5152 | 4134 |

… | … | … | … | … |

2038 | 4492 | 1632 | 5152 | 1872 |

50,022 | 15,788 | 51,706 | 13,067 |

KRW Million | Present Cost | Present Benefit | NPV | B/C Ratio | IRR |
---|---|---|---|---|---|

GAC | 40,556 | 56,344 | 15,788 | 1.389 | 8.97% |

(USD thousand) | (34,589) | (48,055) | (13,465) | ||

Ozone + GAC | 51,269 | 64,336 | 13,067 | 1.255 | 7.46% |

(USD thousand) | (43,726) | (54,871) | (11,145) |

Scenario | B/C | NPV (KRW) (Unit: Million) | IRR (%) | |||
---|---|---|---|---|---|---|

GAC | Ozone + GAC | GAC | Ozone + GAC | GAC | Ozone + GAC | |

Basic | 1.389 | 1.255 | 15,788 (USD 13.5) | 13,067 (USD 11.1) | 8.97 | 7.46 |

Discount rate increases (4.5–>10%) | 1.286 | 1.159 | 11,176 (USD 9.5) | 7901 (USD 6.7) | 8.97 | 7.46 |

Business life reduces (20–>10 years) | 0.889 | 0.798 | −4268 (USD −3.6) | −9937 (USD −8.5) | 2.12 | 0.06 |

Benefits decline to zero | 0.800 | 0.723 | −8099 (USD −6.9) | −14,208 (USD −12.1) | 0.23 | −1.11 |

Benefits during 10 years | 1.012 | 0.909 | 479 (USD 0.4) | −4493 (USD −3.87) | 4.72 | 2.83 |

Benefit with lower bound WTPs | 1.149 | 1.037 | 6053 (USD 5.2) | 1886 (USD 1.6) | 6.32 | 4.95 |

Exclusion of households without Benefits | 1.126 | 1.014 | 5100 (USD 4.4) | 730 (USD 0.6) | 6.04 | 4.68 |

Cost increase (20%) | 1.181 | 1.064 | 8630 (USD 7.4) | 3852 (USD 3.3) | 6.64 | 5.26 |

One year delay of construction | 1.362 | 1.234 | 14,324 (USD 11.7) | 11,666 (USD 10.0) | 8.31 | 7.04 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Gschwandtner, A.; Jang, C.; McManus, R.
Improving Drinking Water Quality in South Korea: A Choice Experiment with Hypothetical Bias Treatments. *Water* **2020**, *12*, 2569.
https://doi.org/10.3390/w12092569

**AMA Style**

Gschwandtner A, Jang C, McManus R.
Improving Drinking Water Quality in South Korea: A Choice Experiment with Hypothetical Bias Treatments. *Water*. 2020; 12(9):2569.
https://doi.org/10.3390/w12092569

**Chicago/Turabian Style**

Gschwandtner, Adelina, Cheul Jang, and Richard McManus.
2020. "Improving Drinking Water Quality in South Korea: A Choice Experiment with Hypothetical Bias Treatments" *Water* 12, no. 9: 2569.
https://doi.org/10.3390/w12092569