Individual welfare analysis: Random quasilinear utility, independence, and confidence bounds

We introduce a novel framework for individual-level welfare analysis. It builds on a parametric model for continuous demand with a quasilinear utility function, allowing for heterogeneous coefficients and unobserved individual-good-level preference shocks. We obtain bounds on the individual-level consumer welfare loss at any confidence level due to a hypothetical price increase, solving a scalable optimization problem constrained by a novel confidence set under an independence restriction. This confidence set is computationally simple and robust to weak instruments, nonlinearity, and partial identification. The validity of the confidence set is guaranteed by our new results on the joint limiting distribution of the independence test by Chatterjee (2021). These results together with the confidence set may have applications beyond welfare analysis. Monte Carlo simulations and two empirical applications on gasoline and food demand demonstrate the effectiveness of our method.