Combining revealed preference and stated preference data without invoking the weak complementarity condition: Kevin J. Egan
Introduction The valuation of public goods is routinely conducted using revealed preference data on complementary private goods. The analysis requires an untestable assumption about the relationship between the observed private good (e.g. recreation trips to a lake) and the public good of interest (e.g. water quality at the lake). The most common assumption is weak complementarity (WC; see e.g. Mäler 1974), which implies that an individual receives no utility from the public good if the resource is not visited. However, as LaFrance (1994) and Herriges et al. (2004) discuss, invoking WC, or any similar assumption, imposes a cardinal restriction on consumer preferences, as a utility function and a monotonic transformation of this utility function potentially generate different welfare measures, even though both will yield identical underlying ordinary demands. Since revealed preference (RP) data alone cannot distinguish between a utility function that satisfies WC and a monotonic transformation that does not, the WC restriction is also untestable (von Haefen 2007). LaFrance (1994: 77) argues strongly throughout his paper against using WC, stating,
the difficulty with the [weak complementarity assumption] (and its relatives) is that for the very reason that this hypothesis permits welfare measurement with observations on market choices, it also introduces a cardinal transformation of preferences. The cardinal nature of this transformation influences the size, and at times even the sign, of the welfare measures obtained.