Modelling Strategies for Discontinuous Distance Decay in Willingness to Pay for Ecosystem Services

Distance decay is a well-known phenomenon affecting welfare measures of localized improvements in environmental quality. We focus on an often overlooked issue in the distance decay literature, namely the modeling of jump discontinuities, i.e. when the willingness to pay distance decay function makes a vertical jump up or down. In an empirical stated choice experiment concerning localized water quality improvements where a toll bridge presents a barrier in the landscape that causes a sudden jump in travel costs, we first estimate individual-specific willingness to pay. We then investigate distance decay in these obtained estimates. We find that the degree of distance decay depends on which type of ecosystem services respondents are primarily motivated by. Besides modelling distance decay with a range of commonly used parametric functional forms, we also test a nonparametric generalized additive model specification. We find only minor differences between the different distance decay specifications, with no generally superior model specification. The nonparametric approach tends to capture distance decay in WTP just as well as any of the parametric specifications, but without requiring the analyst to make assumptions concerning the functional form of the distance decay relationship.