Kavli Affiliate: David Muller
| First 5 Authors: David Müller, Emerson Melo, Ruben Schlotter, ,
| Summary:
This paper introduces the distributionally robust random utility model
(DRO-RUM), which allows the preference shock (unobserved heterogeneity)
distribution to be misspecified or unknown. We make three contributions using
tools from the literature on robust optimization. First, by exploiting the
notion of distributionally robust social surplus function, we show that the
DRO-RUM endogenously generates a shock distributionthat incorporates a
correlation between the utilities of the different alternatives. Second, we
show that the gradient of the distributionally robust social surplus yields the
choice probability vector. This result generalizes the celebrated
William-Daly-Zachary theorem to environments where the shock distribution is
unknown. Third, we show how the DRO-RUM allows us to nonparametrically identify
the mean utility vector associated with choice market data. This result extends
the demand inversion approach to environments where the shock distribution is
unknown or misspecified. We carry out several numerical experiments comparing
the performance of the DRO-RUM with the traditional multinomial logit and
probit models.
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