Inferring Willingness-to-Pay for Health Attributes of Air Quality Using Information on ranking of Alternatives and Cognitive Ability of Respondents

We investigate the use of variable scale parameters to account for heterogeneity in responses to a stated preference survey of willingness to pay for air quality. The survey instrument collected full rankings of four alternatives in each of nine choice sets. Nine of 54 pairwise comparisons involved dominated alternatives; selection of a dominated alternative is interpreted as indicating cognitive difficulties. We allow the scale parameter in a conditional logit model to vary by the ranking considered (first, second or third choice) and by the degree of cognitive difficulty encountered. We investigate the effect of this on the magnitude and precision of estimated willingness-to-pay using empirically-based confidence intervals. The size of the scale parameter is significantly and positively related to the frequency with which respondents chose dominated choices, even after corrections designed to eliminate endogeneity bias. Ignoring heterogeneity in the cognitive ability of respondents biases willingness-to-pay estimates upwards. Consideration of second and third choices narrows the confidence intervals on WTP estimates. Introducing a variable scale parameter related to ranking by itself does not improve the precision of the estimate. Sample STATA code is provided.