Stress Testing Structural Models of Unobserved Heterogeneity: Robust Inference on Optimal Nonlinear Pricing

We propose a suite of tools for empirical market design in adverse-selection settings where point identification based on exogenous price variation is hampered by multi-dimensional unobserved heterogeneity. Despite significant data limitations, we are able to derive informative bounds on counterfactual consumer demand under out-of-sample price changes. These bounds arise because empirically plausible DGPs must respect the Law of Demand and the observed shift(s) in aggregate demand resulting from a known exogenous price change(s). The bounds facilitate robust policy prescriptions using rich, internal data sources similar to those available in many real- world settings, including our empirical application to rideshare demand. Our partial identification approach enables viable, welfare-improving, nonlinear pricing design while achieving robustness against worst-case deviations from baseline model assumptions. As a side benefit, our framework also provides novel insights into optimal experimental design for pricing RCTs.