Demand estimation is at the core of many economic problems. With the availability of large amounts of unstructured/high-dim data, there has been increased focus on (1) to allow for unstructured data in demand estimation settings and (2) to address endogeneity issues while using observational data. Extant workhorse models (e.g., Berry et al. 1995) are highly parameterized and rely on availability of exogeneous variations to ascertain identification. In this paper, we borrow from the literature on partial identification and propose the Deep Causal Inequalities (DeepCI) estimator that overcomes both these issues. Instead of relying on observed labels, the DeepCI estimator uses inferred moment inequalities from the observed behavior of agents in the data. This by construction can allow us to circumvent the issue of endogenous explanatory variables in many cases. We provide theoretical guarantees for our estimator and prove its consistency under very mild conditions. We demonstrate through extensive simulations that our estimator outperforms standard supervised machine learning algorithms and existing partial identification methods. Finally, we demonstrate how to use deep inequalities in the differentiated products demand estimation framework. The flexibility of the method allows for highly unstructured data like images, which we exploit in the empirical application based on the consumer-level purchase data. Job Description • Run simulations using deep learning models with image data Qualifications • Proficient in deep learning with PyTorch, and experience with computer vision • Willing to devote at least 20 hours/week to the project and participate in weekly Zoom meetings • Students who wish to pursue PhD degrees (especially in the intersection of Business and Data Science) are particularly welcome Benefit • Recommendation letters from PIs • Opportunities for coauthorship on conference papers • Opportunities to be enrolled in UW PhD programs PIs • Amandeep Singh, Assistant Professor of Information Systems, Foster School of Business, University of Washington • Jiding Zhang, Assistant Professor in Operations Management, NYU Shanghai

• Proficient in deep learning with PyTorch, and experience with computer vision • Willing to devote at least 20 hours/week to the project and participate in weekly Zoom meetings • Students who wish to pursue PhD degrees (especially in the intersection of Business and Data Science) are particularly welcome