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Intra-respondent Heterogeneity in a Stated Choice Survey on Wetland Conservation in Belarus: First Steps Towards Creating a Link with Uncertainty in Contingent Valuation

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Abstract

Applications of discrete choice models in environmental valuation increasingly use a random coefficient specification, such as mixed logit, to represent taste heterogeneity. The majority of applications rely on data containing multiple observations for each respondent, where a common assumption is that tastes stay constant across choices for the same respondent. We question this assumption and make use of a model developed in the transport field which allows tastes to vary over choices for each consumer in addition to variation across consumers. An empirical analysis making use of a stated choice dataset for wetland conservation in Belarus shows that superior performance is obtained by allowing jointly for the two types of heterogeneity and that recovery of these intra-respondent variations is not possible using standard approaches, such as allowing for scale heterogeneity across tasks. We show also that intra-respondent heterogeneity can be especially high for attributes which respondents are unfamiliar with, and that a failure to account for it can substantially affect welfare estimates. We interpret this as an indication that this heterogeneity relates primarily to uncertainty. Finally, we offer initial insights into the relationship between intra-respondent heterogeneity and findings on uncertainty in a contingent valuation context.

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Notes

  1. See for example: McFadden and Train (2000), Hensher and Greene (2003), Train (2003). Also see Hoyos (2010) for an overview of MMNL applications into environmental valuation. While the random coefficients specification focusses on random variations in marginal utility parameters, the error components specification primarily aims to capture correlation across alternatives or heteroscedasticity. The two specifications are mathematically equivalent.

  2. Our empirical work shows that the retrieved intra-respondent heterogeneity is not systematic across tasks and does not seem to relate to either learning or fatigue. This makes the case for the specific random treatment we use, and the interpretation of the variation as linking to uncertainty.

  3. Going much further than for example the Baerenklau and Bill (2005) work which allows for serial correlation in the random coefficients through an AR1 process.

  4. For more detailed description of the programmes and the policy site see Valasiuk et al. (2013).

  5. We used MNL models here as the cross-sectional focus on structural intra respondent heterogeneity would conflict with the panel nature of the MMNL model.

  6. Remembering the effects coding for chemical removal.

  7. Noting that we also show a WTP for chem now given the effects coding.

  8. The non-cost coefficients are assumed to follow a Normal distribution, with correlation between the inter-respondent components but independently distributed intra-respondent components. The mean sensitivities are given by the \(\mu \) parameters. For the inter-respondent heterogeneity, \(\sigma _{\alpha ,kl}, \,with\, 1\le l\le k\le 5\) represent Cholesky terms, with the variance for coefficient \(m\) being \(\left( {\mathop \sum \nolimits _{l=1}^m \sigma _{\alpha ,ml} ^{2}} \right) \) and the covariance between coefficients \(m \) and \(p\) (with \(m<p\)) being \(\left( {\mathop \sum \nolimits _{l=1}^m \sigma _{\alpha ,ml} \sigma _{\alpha ,pl} } \right) \). For the intra-respondent heterogeneity, \(\sigma _{\gamma ,k},\, with\, 1\le k\le 5\), represent the standard deviation estimates.

  9. We allowed for a non-zero bound through estimating an offset parameter \(\kappa _{cost} \), in addition to the mean for the underlying Normal distribution of \(\mu _{co} \) and standard deviation terms for the inter-respondent and intra-respondent components of \(\sigma _{\alpha ,co} \) and \(\sigma _{\gamma ,co}\), respectively. The cost coefficient was uncorrelated with other coefficients after initial modelling results showed a lack of correlation.

  10. In the simple MNL model, we estimate the \(\mu \) parameters as marginal sensitivities for the non-cost attributes, \(\upkappa \)_cost as the cost coefficient, and finally the four interactions with socio-demographic characteristics. In the MMNL model with inter-respondent heterogeneity only, we additionally estimate \(\upmu \)_co and the sixteen \(\upsigma \_(\upalpha ,\cdot )\) parameters, while, in the MMNL model with additional intra-respondent heterogeneity, we also estimate the six \(\upsigma \_(\upgamma ,\cdot )\) parameters.

  11. This is made possible by clustering together observations from the same respondent when calculating the BHHH matrix that enters the computation of the sandwich matrix. The latter is often referred to as giving robust standard errors – this is independent of whether observations for the same respondent are clustered together or not, doing so simply means that the computation also accounts for the repeated choice nature of the data, generally resulting in an upwards correction of standard errors (cf. Daly and Hess 2011).

  12. We use here a simple \(\upchi ^{2}\) critical value, where, with the null hypothesis being comfortably rejected, the issue of critical values being too high in the naïve approach are of little concern, noting only that with mixture \(\upchi ^{2 }\) critical values, the null would be rejected even more strongly (see Chen and Cosslett 1998; Moeltner and Layton 2002).

  13. The calculations relate only to the random part, excluding socio-demographic effects. We use the estimates from the Cholesky matrix to compute standard deviations for inter-respondent heterogeneity for the five non-monetary parameters For the intra-respondent heterogeneity, the standard deviations are obtained directly from the estimates of \(\sigma _{\gamma ,\cdot } \), while the taste heterogeneity estimates for cost relate to the underlying Normal distribution, i.e. the distribution of \(ln\left( {-\beta _{co} } \right) \), ignoring the insignificant offset parameter. The levels of heterogeneity for the combined intra-respondent and inter-respondent components are obtained through simulation.

  14. We acknowledge a degree of simplification in this comparison, not least as we’re combining evidence from multiple parameters estimated on the SC data, each with their own estimation error, and compare this to a single measure from CV.

  15. SC can be considered as a variant of DC–CV whereas CIOE question is a variant of open-ended question, so these findings are relevant to our study.

  16. We work here with the coefficient of variation given the differences in mean levels between CV and SC but also the small changes in mean levels we see in SC when incorporating intra-respondent heterogeneity.

  17. Unlike with mechanical mowing or chemical process, people were familiar with burning, and during the focus groups, respondents had mixed feelings about the possibility of burning being used. In our opinion, there are two possible explanations for the large intra-respondent variation for burning. The first is that the tradition of using burning in the past, combined with anti-burning actions carried out in Belarus in recent years, could result in respondents’ uncertainty regarding the use of this method for an active protection. The other possible explanation is that most people were familiar with burning but only on a small scale. The use of this method on such a large scale (1,000–4,000 ha) was novel to the respondents during the focus group.

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Acknowledgments

The authors are grateful for the comments of Thijs Dekker and one anonymous referee which helped to significantly improve the paper. The authors would like to thank Sviataslau Valasiuk for providing the SC and CV data. The work on this paper was supported by the Polish National Science Centre Grant DEC-2012/07/E/HS4/04037.

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Hess, S., Giergiczny, M. Intra-respondent Heterogeneity in a Stated Choice Survey on Wetland Conservation in Belarus: First Steps Towards Creating a Link with Uncertainty in Contingent Valuation. Environ Resource Econ 60, 327–347 (2015). https://doi.org/10.1007/s10640-014-9769-9

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