arXiv:2608.26156 Reports Stratification Delivers 0.008pp Median Error vs 6.06pp for Oracle IPW in Step-Function Retail Scenarios
Stratification outperforms IPW under the positivity violations typical of retail long-tail distributions. The simulation quantifies a 116x error reduction and identifies the theoretical boundary where weighting methods fail. Retail economic indicators built on scanner data require stratification to avoid persistent bias in inflation and consumer metrics.
The paper simulates selection bias in retail inflation estimates caused by monitoring only high-velocity SKUs and omitting the long tail. Four data-generating processes test Inverse Probability Weighting against stratification: aligned step functions, smooth gradients, misaligned breaks, and polynomial relationships. Stratification with varying strata counts is compared to IPW under five propensity specifications.
Results show stratification achieving 116x lower median error than IPW in step-function and misaligned-break cases, remaining below 0.04pp even when strata boundaries deliberately mismatch population breaks. IPW with spline models records 0.007pp median error only in the smooth polynomial scenario. An oracle IPW specification that knows the exact structure still produces 6.06pp error under severe positivity violation.
The performance gap traces directly to the positivity assumption violation inherent in retail data where niche items have near-zero selection probability. This pattern matches documented CPI coverage gaps at statistical agencies that rely on scanner data limited to top deciles. Retail intelligence systems using IPW for economic indicators therefore embed systematic upward bias in measured inflation for broad consumption baskets.
Platforms weighting long-tail sales for demand forecasting or dynamic pricing should adopt stratification as the default correction to keep aggregate error below 0.05pp within existing data pipelines.
BLS CPI team: Stratification correction deployed on at least one major category by end of 2027, cutting long-tail bias below 0.03pp in published indexes.
Sources (2)
- [1]Primary Source(https://arxiv.org/abs/2608.26156)
- [2]Supporting Source(https://www.bls.gov/cpi/research/selection-bias-scanner-data.pdf)