We propose a framework for doing sharp nonparametric welfare analysis in discrete choice models with unobserved variation in choice sets. We recover jointly the distribution of choice sets and the distribution of preferences . To achieve this we use panel data on choicesand assume nestedness of the latent choice sets . Nestedness means that choice sets of different decision makers are ordered by inclusion . It is satisfied, for instance, when the choice set variation is the result of either a search process or unobserved feasibility. Using variation of the uncovered choice sets we show how to do ordinal (nonparametric) welfare comparisons. When one is willing to make additional assumptions about preferences , we show how to nonparametrically identify the ranking over average utilities in the standard multinomial choice setting .
We propose a framework for nonparametric identification and estimation of discrete choice models with unobserved choice sets. We recover the joint distribution of choice sets and preferences from a panel dataset on choices. We assume that either the latent choice sets are sparse or that the panel is sufficiently long. Sparsity requires the number of possible choice sets to be relatively small . It is satisfied, for instance, when the choice sets are nested, or when they form a partition. Our estimation procedure is computationally fast and uses mixed-integer optimization to recover the sparse support of choice sets. Analyzing the ready-to-eat cereal industry using a household scanner dataset, we find that ignoring the unobservability of choice sets can lead to biased estimates of preferences due to significant latent heterogeneity in choice sets .
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doing sharp nonparametric welfare analysis in
nonparametric identification and estimation of
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variation in
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jointly the
the joint
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the distribution of preferences . To achieve this we use panel data on choicesand assume nestedness of
preferences from a panel dataset on choices. We assume that either
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. Nestedness means that choice sets of different decision makers are ordered by inclusion
are sparse or that the panel is sufficiently long. Sparsity requires the number of possible choice sets to be relatively small
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set variation is the result of either a search process or unobserved feasibility. Using variation of the uncovered choice sets we show how to do ordinal (nonparametric) welfare comparisons. When one is willing to make additional assumptions about preferences , we show how to nonparametrically identify the ranking over average utilities in the standard multinomial choice setting
sets are nested, or when they form a partition. Our estimation procedure is computationally fast and uses mixed-integer optimization to recover the sparse support of choice sets. Analyzing the ready-to-eat cereal industry using a household scanner dataset, we find that ignoring the unobservability of choice sets can lead to biased estimates of preferences due to significant latent heterogeneity in choice sets