Does quantity matter for distance decay? Evidence from two choice experiments on urban green

The value of environmental goods to individuals often depends on spatial features such as distance. The most common approach of accounting for distance decay is to model utility as some function of distance. It has been suggested to instead model the value as a function of the quantity of an environmental good within a certain distance. We develop three novel quantity-within-distance models that may be more suited for evaluating quantity changes in an environmental good. We argue that these models could capture spatial patterns better than distance-based models when i) secondary benefits are a relevant source of welfare, ii) the environmental change is spatially scattered, iii) the distribution of the endowment, i.e. the present availability of the environmental good, matters. Using data from choice experiments on the extension of green space and trees in two urban areas, we compare required assumptions, model fit, and size and precision of aggregated welfare estimates. Our results indicate limited differences in model fit. However, the quantity-within-distance models consistently produce aggregate welfare estimates roughly half of common distance decay models and have narrower confidence intervals. While it is not possible to infer which is more accurate, the large differences can have considerable policy implications.