Uniformly Consistent Semi-nonparametric Demand Estimation with Micro-Data

This paper develops a profiled sieve minimum-distance estimator for a semi-nonparametric differentiated-products demand model with micro-level choice data. Building on Berry and Haile (2024), the estimator uses within-market variation in consumer covariates to recover a flexible consumer-heterogeneity function and market-specific composite intercepts. Excluded price instruments then separate these intercepts into a flexible price-side function and structural demand shocks. The main statistical challenge is that the number of profiled market intercepts grows with the number of markets. I show that, when both the number of markets and the minimum within-market sample size grow, this profiling step is asymptotically negligible and the common structural functions are uniformly consistently estimated. Monte Carlo evidence supports the consistency result and illustrates the value of flexible price-side estimation for counterfactual demand analysis.