Abstract
A substantial literature exists combining data from revealed preference (RP) and stated preference (SP) sources, aimed either at testing for the convergent validity of the two approaches used in nonmarket valuation or as a means of drawing on their relative strengths to improve the ultimate estimates of value. In doing so, it is assumed that convergence of the two elicitation approaches is an “all or nothing” proposition; i.e., the RP and SP data are either consistent with each other or they are not. The purpose of this paper is to propose an alternative framework that allows for possible divergence among individuals in terms the consistency between their RP and SP responses. In particular, we suggest the use of a latent class approach to segment the population into two groups. The first group has RP and SP responses that are internally consistent, while the remaining group exhibits some form of inconsistent preferences. An EM algorithm is employed in an empirical application that draws on the Alberta and Saskatchewan moose hunting data sets used in earlier combined RP and SP exercises. The empirical results suggest that somewhere between one-third and one-half the sample exhibits consistent preferences. We also examine differences in welfare estimates drawn from the two classes.
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Notes
The model specified here is a site selection model, rather than a model that also characterizes the participation decision, as in the repeated logit framework of Morey, Rowe and Watson Morey et al. (1993). We focus on the site selection aspect of the individual’s decision to be consistent with the earlier analyses of these same databases by Adamowicz et al. (1997), Haener et al. (2001), and von Haefen and Phaneuf (2008).
Individual specific characteristics such as age, gender and education can also impact the site utilities, typically through interactions between individual and site characteristics. For now, we ignore these interaction effects for the sake of notational simplicity, but incorporate them later in both the Monte Carlo analysis and subsequent application.
The emphasis in our paper is on relaxing the assumption that consistency between the RP and SP responses is an all or nothing proposition. However, as suggested by a reviewer, a natural generalization of our framework would be to allow heterogeneity within each of the consistent and inconsistent classes. This could be done using a continuous mixture (random parameters) model for each class or by introducing latent subclasses for both the consistent and inconsistent classes. In the latter case, information criteria (e.g., AIC and BIC) could be used in selecting the number of subclasses.
Estimates for the alternative specific constants \(\alpha _j^{RP}\) and \(\xi ^C_j\) are not reported in Table 1 for the sake of space, but are available from the authors upon request. Also, estimates for the parameters \(\beta ^{RP}\) are obtained through a second stage regression based on the fitted alternative specific constants from the first stage and using the relationship in (3).
As noted in footnote 4 above, a generalization of our modeling framework would be to allow for heterogeneous preferences within each of the consistent and inconsistent classes. As an initial exploration into this possibility, we also conducted a generated data experiment using two latent subclasses for each of the main classes. Our model was then estimated using (a) a single subclass for each of the main classes and (b) two subclasses for each of the main classes. The results from this exercise are reported in Appendix Table 10. In all of the Monte Carlo runs, the two subclass model was consistently preferred to the single subclass model on the basis of both AIC and BIC measures and the two subclass model parameter estimates were generally consistent with the underlying data generating process. This is an area for future research, but beyond the scope of the current manuscript.
See McLeod et al. (1993) for additional details regarding the sampling and data collecting procedures.
In the empirical setting, we include a dummy variable for ‘not hunting’ (SP dummy) to capture impact of the opt-out option.
The log-likelihood values for the estimated models are as follows. For the Alberta data set: SC-C: −5377.94; SC-RP: −1868.11; SC-SP: −3468.56; LC: −4813.10. For the Saskatchewan data set: SC-C: −7482.15; SC-RP: −1162.66; SC-SP: −6301.20; LC: −6896.32.
The parameter estimates reported here for the single class models have the same signs and are similar in magnitude to those reported in von Haefen and Phaneuf (2008), though the specifications differ in that von Haefen and Phaneuf incorporate a mixed logit structure.
One exception is the main effect for the “unpaved” site access, since this characteristic varies across sites and individuals because individuals choose different roads to access the sites.
In general, one could estimate \(\beta ^{RP}\) using a second stage regression, as suggested by Murdock Murdock (2006). Doing so would allow for a total of five welfare measures, paralleling those available for the site loss scenario. However, in the current case we have too few of sites to do so. Even with more sites, endogeneity concerns would require the use of suitable instruments, which may not always be available.
Since the parameters used in constructing Measures #3 through #5 are jointly estimated, we can test for pairwise differences among the measures. In all pairwise comparisons, the differences are not statistically significant.
This generalization was estimated using the Alberta Moose Hunting data, but none of the available demographic factors were found to significantly impact class membership.
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Jeon, H., Herriges, J.A. Combining Revealed Preference Data with Stated Preference Data: A Latent Class Approach. Environ Resource Econ 68, 1053–1086 (2017). https://doi.org/10.1007/s10640-016-0060-0
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DOI: https://doi.org/10.1007/s10640-016-0060-0