Abstract

Nested logit is increasingly advocated as a tool of recreational demand and benefit estimation. The intent of this short monograph is to lay out, in a simple fashion, the theory behind the nested-logit model of site choice and the nested-logit model of participation and site choice. Rigorous but straightforward derivations of the properties of nested-logit models are provided, including the probability of choosing a particular alternative, likelihood functions, expected maximum utility, and compensating and equivalent variations. Also discussed are the properties of the underlying distribution, estimation, regularity conditions, the interpretation of the scaling parameters, and the relation between those scaling parameters and the Independence of Irrelevant Alternatives ( IIA) assumption(s) embedded in both the nested logit model and its special cases. Examples are used to link the theory to recreational demand and benefit estimation. Those familiar with the 1994 version of this paper will find a few corrections, many more references, and much more elaboration, particularly with respect to the extreme value distribution, regularity conditions, parameter estimation, and consumer’s surplus estimation. Joint decisions of this type can also be modeled in other frameworks, but these other frameworks are not the topic of this paper. See Bockstael et al. (1986, 1987 and 1991), Carson et al. (1987),, Morey et al. (1993, 1995 and 1997), Kling and Thomson (1996), and Hoehn et al. (1996). Additional examples of discrete-choice models of recreational demand between 1988 and 1997 are Bockstael et al. (1989), Creel and Loomis (1992), Jones and Sung (1992), Hausman et al. (1995), Milon (1988), Morey et al. (1991), Parsons and Kealy (1992 and 1995), and Parsons and Needleman (1992). Earlier examples are Caulkins et al. (1986), Feenburg and Mills (1980), Hanemann (1978), and Morey (1981). Policy analysts often require the consumer’s surplus associated with a change in the costs or characteristics of a group of consumption activities. The consumer’s choice of consumption activity generally involves two simultaneous decisions: whether to participate in a given class of activities and, if so, which alternative to choose from that class. For example, one simultaneously decides both whether to participate in a given class of site-specific recreational activities, and if so, which site to visit. Joint decisions of this type can be modeled in either a multinomial logit (ML) framework or a nested-logit (NL) framework. Use of the NL model, in contrast to the ML model, is increasingly advocated, particularly when the intent is to model simultaneously both the decision to participate and the choice of site. The argument is that the Independence of Irrelevant Alternatives (IIA) assumption, implicit in the ML model, although often reasonable when all the alternatives are recreational sites of a particular type, can be unreasonable when the sites differ by type or one of the alternatives is nonparticipation. Participation and site choice should therefore be modeled as a two or more stage nested decision that does not impose IIA a priori across all pairs of alternatives. For example, stage one models the participation decision, and stage two models the choice of site given participation. The individual makes the participation and site choice decisions simultaneously. It is common, but unnecessary, to assume that NL models require a sequential decision process.