Neural Demand Estimation with Habit Formation and Rationality Constraints

State dependence is empirically important in repeat-purchase demand and can materially change welfare conclusions from price variation. To this end, we introduce a flexible neural demand system for continuous budget allocation that allows current choices to depend on a low-dimensional summary of purchase history. In Dominick’s scanner data on analgesics, augmenting demand with a habit state reduces out-of-sample prediction error by about 33% relative to standard share systems, and a shuffled-history placebo eliminates the gain, indicating that the improvement reflects meaningful dynamics rather than additional covariates. State dependence also changes economic conclusions: conditioning on the habit state col-lapses the apparent aspirin–ibuprofen cross-price effect toward zero while preserving robust acetaminophen–ibuprofen substitution. These differences translate into welfare: for a 10% ibuprofen price increase, the habit specification implies compensating-variation losses about 15–16% larger than a static model. We also provide simulation evidence with known ground truth and report diagnostics of near-integrability to support welfare calculations. The code is available at https://github.com/martagrz/neural_demand_habit.