Willingness to pay to avoid arsenic-related risks: a special regressor approach

Abstract

Subjective probabilities often better explain behaviours than science-based risks. Incorporating them into a behavioural model has important ramifications for environmental and health policy, but if these risks are measured with error or endogenous, then doing so leads to possible troubles in interpretation of results. Our application is to mortality risks associated with arsenic found in drinking water in various spots in the United States. The behaviour of interest is a yes/no response to a willingness to pay (WTP) question to reduce these risks. We apply the special regressor approach to handle the endogeneity and measurement error in the WTP model and find that doing so leads to different implications for policy that could be pursued to reduce the risks.

Keywords:

• subjective probabilities
• arsenic in drinking water
• willingness to pay
• special regressor
• risk

Acknowledgements

The authors thank the editor and three reviewers for their comments, which have helped substantially in improving the paper. They also thank Yvette Zhang, Marco Palma, Ximing Wu, and other seminar participants at Texas A&M for helpful comments. Data collection was supported by an EPA Star grant.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. The econometric issues related to errors in variables in stated preference studies are the main focus of this paper. However, similar problems may be at issue when the revealed preference data are used.

2. Bias from errors in variables would also arise if science-based estimates are not accurately assigned to subjects.

3. There are few economic theories that could be relied upon to determine high-quality instruments for use in a model to explain the variation in stated probabilities, although logic and psychology literature are helpful here.

4. A 20-year baseline risk of getting cancer from a regular consumption of tap water containing high level of arsenic has been shown to respondents in order to give them some clues about long-term arsenic exposure. Actually, we will see that for the valuation question, they are asked to pay a certain amount per month during five years.

5. Strictly speaking, a stated probability cannot be less than zero, nor greater than one, so it is not normally distributed. As such, using ordinary least squares (OLS) (as done in a host of early cigarette smoking studies by Viscusi [1990, 1991]); as well as more recently by Shaw, Jakus and Riddel [2012]) is problematic. The potential consequences of using OLS are the usual ones associated with the use of the linear probability model, including possible out-of-bound predictions, implied negative probabilities, and/or heteroskedastic errors. The beta distribution has been used to model variation in stated probabilities in a number of studies including Heckman and Willis (1977), Viscusi and Magat (1992), and more recently by Riddel and Shaw (2006).

6. We conducted a likelihood ratio test using the middle of the intervals for uncertain people for the risk variable, a dummy variable for certainty, and its interaction with other variables. Based on this, we concluded that the parameters are indeed different between certain and uncertain people.

7. Note that the parameters of the logit and probit models are only identified up to the location and scale; therefore, marginal effects and estimated WTP are not influenced by the normalisation that is chosen.

8. We used only the point estimate data and ran a two-step least squares regression. We used the Stock and Yogo test for our instruments: nvsmoke and curresid. The statistic is 5.510, which is lower than the lowest critical value of Stock Yogo: 7.25. Therefore, we accept the null hypothesis: the instrument set is weak.

9. Note that bootstrapped standard errors are calculated only for model (3). Standard techniques were used for models (1) and (2).

10. For those on private system, their stated risks for others, when given as a point estimate, are not significantly different from their own stated risks. Therefore, we assume that this estimate of a household's own risk is a good measure of others’ risks.