Neural Demand Estimation with Habit Formation and Rationality Constraints

TL;DR

A flexible neural demand system for continuous budget allocation that estimates budget shares on the simplex by minimizing KL divergence and recovering elasticities and welfare accurately and show sizable gains when habit formation is present is present.

Abstract

We develop a flexible neural demand system for continuous budget allocation that estimates budget shares on the simplex by minimizing KL divergence. Shares are produced via a softmax of a state-dependent preference scorer and disciplined with regularity penalties (monotonicity, Slutsky symmetry) to support coherent comparative statics and welfare without imposing a parametric utility form. State dependence enters through a habit stock defined as an exponentially weighted moving average of past consumption. Simulations recover elasticities and welfare accurately and show sizable gains when habit formation is present. In our empirical application using Dominick's analgesics data, adding habit reduces out-of-sample error by c.33%, reshapes substitution patterns, and increases CV losses from a 10% ibuprofen price rise by about 15-16% relative to a static model. The code is available at https://github.com/martagrz/neural_demand_habit .

Figures (17)

• Figure 1: Observed vs. predicted budget share for Good 0 under the CES DGP. Left: Neural Demand (static). Right: LA-AIDS. The neural demand system achieves near-exact prediction across the full support; LA-AIDS exhibits a systematic fan pattern reflecting misspecification of the CES Marshallian demand curvature.
• Figure 2: Predicted budget-share demand curves under the CES DGP ($\pm$1 SE across runs). Budget shares plotted as a function of Good-1 (Fuel) price $p_1$; all other prices and income held at simulation means.
• Figure 3: Full $3 \times 3$ price elasticity matrices under the CES DGP for Ground Truth, LA-AIDS, QUAIDS, and Neural Demand (static). Diagonal: own-price quantity elasticities. Off-diagonal: cross-price quantity elasticities. Neural Demand recovers both diagonal and off-diagonal elements with near-exact accuracy; LA-AIDS and QUAIDS produce small biases on the Good-2 own-price elasticity and the Food-Other cross-price terms.
• Figure 4: Post-shock RMSE across five DGPs ($\pm$SE, 5 runs). LDS (Shared) and LDS (GoodSpec) dominate the Quasilinear column at RMSE $\approx 0.47$; Var. Mixture dominates Leontief at $0.17$. Neural demand variants are essentially invisible on static DGPs. BLP (IV) is included for reference only; it is not an appropriate structural comparator for the continuous-allocation DGPs (Section \ref{['sec:blp']}).
• Figure 5: RMSE heatmap: key model comparators across six DGPs (mean RMSE, SE in parentheses). Red = high error; green = low error.