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Estimating recreation benefits through joint estimation of revealed and stated preference discrete choice data

Empirical Economics volume 58, pages 2009–2029 (2020)Cite this article

Abstract

We develop econometric models to estimate jointly revealed preference (RP) and stated preference (SP) models of recreational fishing behavior and preferences using survey data from the 2007 Alaska Saltwater Sportfishing Economic Survey. The RP data are from site choice survey questions, and the SP data are from a discrete choice experiment. Random utility models using only the RP data may be more likely to estimate the effect of cost on site selection well, but catch per day estimates may not reflect the benefits of the trip as perceived by anglers. The SP models may be more likely to estimate the effects of trip characteristics well, but less attention may be paid to the cost variable due to the hypothetical nature of the SP questions. The combination and joint estimation of RP and SP data seeks to exploit the contrasting strengths of both. We find that there are significant gains in econometric efficiency and differences between RP and SP willingness-to-pay estimates are mitigated by joint estimation. We compare a number of models that have appeared in the environmental economics literature with the generalized multinomial logit model. Naïve (1) scaled, (2) mixed logit, and (3) generalized multinomial logit models produced similar results to a generalized multinomial logit model that accounts for scale differences in RP and SP data. Willingness-to-pay estimates do not differ across these models but are greater than those in the mixed logit error components model that accounts for scale differences.

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Fig. 1

Notes

  1. In the case where the willingness-to-pay estimates are economically different, analysts should use both estimates separately in sensitivity analysis.

  2. The RP cost will be unbiased under the assumption that the travel cost variable is not measured with error (Randall 1994).

  3. Attribute non-attendance is not limited to cost (e.g., Colombo et al. 2013).

  4. See Krucien et al. (2015), Lancsar and Swait (2014), and Fifer et al. (2014) for discussion in the health and transportation literatures.

  5. The ability of the GMXL to separately estimate individual-level scale and preference heterogeneity has been challenged recently by Hess and Rose (2012), who argue that the utility specifications in GMXL models simply allow for more flexible distributions of the preference parameters.

  6. Lew et al. (2010) describe the development, content, and structure of the three survey versions, their implementation, and a summary of the data.

  7. We find similar results when only one RP observation is used in the jointly estimated model.

  8. Alternatively, we could randomly choose each of the k = 4 sites for respondents who take more than one trip, but this would cause us to diverge from the simulation of an on-site survey to measure site choice which is typically used in creel surveys.

  9. These rates were calculated over trips targeting any species, not just those targeting halibut or salmon.

  10. These results and others mentioned in this section are available upon request.

  11. All of these models are estimated with NLOGIT software (Greene 2012; Chang and Lusk 2011).

  12. Throughout the results section we refer to “statistical significance” indicating a coefficient that is statistically different from zero at the p < 0.05 level in a two-tailed test.

  13. We also attempted to estimate the θ coefficient by including the SP dummy variable in the estimation of \( \tau \). However, this model did not converge successfully.

  14. The model fails to converge when \( \tau \) is unconstrained while including the SP dummy variable. Similar results, other than a larger \( \theta \) parameter, are found with \( \tau \) fixed at 0.25. When \( \tau \) is fixed at 0.75 the model fails to estimate satisfactorily.

  15. This is also true in the RP model that uses all 2245 trips instead of the typical trip.

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Acknowledgements

A previous version of this paper was presented at the Society for Benefit–Cost Analysis annual meeting in Washington, DC, March 2015 and seminars at Appalachian State University, Resources for the Future and Ohio State University. The authors thank Trudy Cameron, Steve Kasperski, Kristy Wallmo, seminar participants, and two anonymous journal referees for numerous comments and David Hensher for sharing his NLOGIT code for the generalized mixed logit. Funding for this research was provided by the Alaska Fisheries Science Center, National Marine Fisheries Service. Opinions expressed are those of the authors and do not reflect those of NMFS, NOAA, or the U.S. Department of Commerce.

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Authors and Affiliations

  1. Department of Economics, Appalachian State University, Boone, NC, 28607, USA

    John C. Whitehead

  2. Alaska Fisheries Science Center, NOAA National Marine Fisheries Service, Seattle, WA, 98115, USA

    Daniel K. Lew

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  1. John C. Whitehead
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Correspondence to John C. Whitehead.

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Whitehead, J.C., Lew, D.K. Estimating recreation benefits through joint estimation of revealed and stated preference discrete choice data. Empir Econ 58, 2009–2029 (2020). https://doi.org/10.1007/s00181-019-01646-z

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Keywords

  • Discrete choice experiment
  • Generalized multinomial logit model
  • Hypothetical bias
  • Revealed preference
  • Stated preference
  • Travel cost method

JEL Classification

  • Q51
  • Q22
  • Q26