Estimating demand systems when outcomes are correlated counts

We describe and employ a Bayesian posterior simulator for fitting a high-dimensional system of ordinal or count outcome equations. The model is then applied to describe the multiple site recreation demands of individual agents, and we argue that our approach provides advantages relative to existing methods commonly applied in this area. In particular, our model flexibly adjusts to match observed frequencies in trip outcomes, permits a flexible correlation pattern among the sites visited by individuals, and the posterior simulator for fitting this model is relatively easy to implement in practice. We also describe how the posterior simulations produced from the model can be used to conduct a variety of counterfactual experiments, including predicting behavioral changes and describing welfare implications resulting from shifts in exogenous demographic and site characteristics. We illustrate our method using data from the Iowa Lakes Project by modeling the visitation patterns of individuals to a set of twenty-nine large Iowa lakes. Consistent with previous findings in the literature, we see strong evidence that own and cross-price effects on trip demand are negative and positive, respectively, that higher income increases the likelihood of visiting most sites, and that a commonly used indicator of water quality, Secchi transparency, is positively correlated with the number of trips taken. In addition, the correlation structure among the errors reveals a complex pattern in which unobserved factors affecting trip demand are generally (though not strictly) positively correlated across sites. The flexibility and richness with which we are able to characterize the demand system provides a solid platform for counterfactual analysis, where we find significant behavioral and welfare effects from changes in site availability, water quality, and travel costs.