  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.
