Estimating individual valuation distributions with multiple bounded discrete choice data

Abstract

This article presents a new modelling strategy that estimates individual valuation distributions with Multiple Bounded Discrete Choice (MBDC) data. An individual's valuation of a commodity or service is assumed to have a distribution rather than being a single number. Likelihood responses to the MBDC questions are numerically coded and treated with a new panel technique. The proposed estimation strategy is empirically compared with previous data analysis methods.

Notes

¹However, the modelling strategy that Evans et al. (2003) adopted is not fully consistent with the random valuation theory which specifies that each individual has a valuation distribution and the population distribution should be determined by the individuals. Individual characteristics can neither be properly integrated into the modelling approach of Evans et al. (2003), because the distribution parameters in their models are for population but not for individual respondents.

² In contrast to the estimation model presented in Wang and Whittington (2005), Equation 7 adds an error term to the probability model, which reflects the consideration that probability values given by respondents may have deviations from their valuation distributions.

³ The major intention in doing so is to minimize the potential interviewer bias. The interviewers read another copy of identical questionnaire to the respondents, but cannot directly work on the questionnaire that a respondent is working on, and the respondents do not need to speak out their answers to the interviewers. But just like with a mail survey, the final quality of the questionnaire completion cannot be controlled by the enumerators.

⁴ A similar question on cancer prevention is also asked. Persons interested may contact the authors for more details.

⁵ Those responses are similar to the zero bids in open-ended CV surveys.

⁶ The missing values and unreasonable answers could raise some issues in using the data for policy analyses, even though this does not affect the robustness of our test on the modelling approaches presented in this article.

⁷ This is close to the household income. If a respondent is a worker, his/her salary would almost be the whole part of the household income. For a farmer, the income reported is the total benefit from his/her land.

⁸ To get the total, or mean, WTP estimation for the whole sample, one will need to account for those zero values for 588 respondents and for those values higher than 1000 yuan for 104 respondents. WTP values for the remaining 560 observations cannot be estimated because of missing values and other reasons.

⁹ We believe that keeping this redundant response will bias the estimation results.

¹⁰ The values of 1 and 0 cannot be used to recode the answer ‘definitely yes’ and ‘definitely no’ because a normal distribution function is assumed in the analysis.

¹¹ We also tested to use the linear model (11) to estimate individual WTP distributions, and found that the linear model (11) produced a higher estimate of the population mean value of the individual mean WTP. This can be understood given the transformation of the dependent variable from Equation 7 to Equation 11.

¹² Several MBDC studies have been successfully conducted, including one using the SPC approach, an approach similar to but more complicate than the MBDC approach. For details, see Wang and Whittington (2005).

¹³ Interested readers can contact the authors for aggregated demand curves.

¹⁴ Our dataset does give an upward bias of the linear model as compared to the nonlinear model of Equation 7. The transformed linear model gives an estimation of about 120 yuan for the mean WTP at the first stage, which is significantly higher than that of the nonlinear Equation 7.

¹⁵ One constraint is that the population mean value should be equal to the summation of the individual mean values.

¹⁶ The individual observations with the one-stage modelling process have been in fact weighted by their effective answers within their individual valuation distributions. The more the responses received for a respondent's valuation distribution, the higher the precision a researcher can get for the estimation of the distribution. The weights range from two to 11 with this sample.