Models for Non-Exclusive Multinomial Choice, with Application to Indonesian Rural Households

Textbook discussions of discrete choice modelling focus on binomial and multinomial choice models in which agents select a single response. We consider the situation of non-exclusive multinomial choice. The widely used Marginal Logit Model imposes independence and has other disadvantages. We propose two models which account for non-exclusive and dependent multiple responses and require at least one response. In the first and simpler specification, the Poisson-multinomial, households first choose the number of responses to a specific shock, and then the specific choices are identified to maximize household utility conditional on the former choice. The second specification, the threshold-multinomial, generalizes the standard multinomial logit model by supposing that agents will choose more than one response if the utility they derive from other choices is “close” to that of the utility-maximizing choice. We apply these two approaches to reported responses of rural Indonesian rural households to demographic and economic shocks.