Deep Causal Inequalities: Demand Estimation in Differentiated Products Markets

Supervised machine learning algorithms fail to perform well in the presence of endogeneity in the explanatory variables. In this paper, we borrow from the literature on partial identification to propose deep causal inequalities that overcome this issue. Instead of relying on observed labels, the DeepCI estimator uses inferred inequalities from the observed behavior of agents in the data. This by construction can allow us to circumvent the issue of endogeneous explanatory variables in many cases. We provide theoretical guarantees for our estimator and demonstrate it is consistent under very mild conditions. We demonstrate through extensive simulations that our estimator outperforms standard supervised machine learning algorithms and existing partial identification methods.