Primary Submission Category: Design of Experiments
Semiparametric Manski-Style Inference and Optimal Experimental Design in Demand Modeling
Authors: Jia Wan, Antoine Scheid, Guy Aridor, Nathan Kallus, Aurélien Bibaut,
Presenting Author: Jia Wan*
A key challenge for online platforms is measuring demand in environments with limited price variation. In this paper we study what platforms can learn about demand via experiments that vary the set of recommendations presented and apply it to counterfactuals of interest. We consider a canonical model of choice – the mixed multinomial logit model – and develop a semiparametric framework for sharp Manski-style bounds on linear functionals of counterfactual choice probabilities with no restrictions on preference heterogeneity. This provides identification bounds of counterfactual shares of particular goods (or overall engagement) under a range of counterfactuals, including procurement of new goods and alternative recommendation algorithms. Our main characterization shows that the first-order sensitivity of these bounds admits a Riesz representer on the constraint range – equivalently, the dual multipliers of an infinite-dimensional linear program – which yields an efficient influence function. For inference, we compute identification bound endpoints by scanning a KL distance-to-feasibility functional, evaluated via an EM-type alternating KL projections for the mixture nuisance, and then apply a cross-fitted one-step correction to obtain asymptotically normal inference. Finally, we study optimal experimental design – selecting a set of recommendation slates – to minimize the worst-case bound width for a target counterfactual and support our findings with simulation results.