When examining consumer behavior using household level data, it is typical in many applications to find that consumers consume only a subset of the available goods, setting their demand to zero for the remaining goods. Examples of this include labor supply and food demand, as well as the demand for Leisure Studies; In multiple site recreation demand data sets, one usually observes that individuals visit only a subset of the available recreation sites, yet visit these sites multiple times during a season. Theoretically, these corner solutions are effectively modeled using non-negativity constraints in the utility maximization problem. Empirically estimating such a model is more challenging however, since most econometric techniques rely on the assumption of an interior solution;This dissertation examines estimation of generalized corner solution models of consumer choice as they apply to recreation demand. The emphasis is on providing utility consistent characterizations of the demand for recreation, which can then be used to perform welfare analysis. Specifically, the Kuhn-Tucker model of Wales and Woodland (1983) and the dual approach of Lee and Pitt (1986) are estimated for a four site recreation model. Welfare measurement techniques are developed for each, relying on Monte Carlo integration to arrive at consistent estimates of the compensating variation associated with changes in site attributes or the elimination of a site;The application focuses on the demand for fishing in the Wisconsin Great Lakes region. Data is available describing angler behavior during the 1989 fishing season, including both users and non-users of the Great Lakes fishery. Variables describing catch rates for the major sport fishing species, as well as pollution levels in the lakes, are included in the estimation. Welfare experiments are conducted by analyzing the effects of hypothetical changes in the quality variables;This research will be of interest not only to those working in recreation demand and resource valuation, but also those working in other areas of consumer choice, where the use of household level data is becoming more prevalent and operational methods for dealing with corner solutions are necessary.