Pricing And Promotion Optimization

What's being tested

Interviewers probe your ability to translate sales and pricing data into actionable causal estimates and evaluations that drive merchandising and promotional decisions. They want to see competency in causal inference (separating price/promotional effects from confounders), appropriate metric design (revenue, margin, units, lift), and pragmatic model choices (panel regressions, hierarchical pooling, experiments vs. observational IVs). Walmart cares because small errors in elasticity or promotion-lift estimates scale to large revenue/margin impacts across millions of SKUs and stores.

Core knowledge

Price elasticity definition and estimation: elasticity ε = %ΔQuantity / %ΔPrice; in log-log models ln(Q)=α+β ln(P)+Xγ, β is point elasticity. Understand interpretation, sign, and nonlinearity across ranges.
Endogeneity of price: prices are often set in response to demand shocks (simultaneity). Naive OLS will be biased; plan for instrumentation or experiments to obtain causal effects.
Instrumental variables (IV): valid instruments affect price but not demand directly (e.g., cost shocks, supplier promotions, competitor price changes). Check relevance (F-stat > 10) and exclusion restriction plausibility.
Panel fixed-effects: use store-SKU-time fixed effects to absorb unobserved heterogeneity; difference-in-differences (DiD) for policy/promo rollouts. Beware serial correlation—use clustered standard errors at the store or SKU level.
Promotions & cannibalization: model promotional flags, depth, and cross-price effects; cross-price elasticity matrix captures substitution between SKUs. Track cannibalization to avoid overestimating incremental units.
Censoring & zero sales: use Tobit, zero-inflated, or Poisson pseudo-maximum-likelihood (PPML) estimators when many zeroes or censoring from stockouts exist; log models require handling zeros (e.g., ln(Q+1) or PPML).
Hierarchical / Bayesian pooling: partial pooling across SKUs or stores stabilizes noisy elasticity estimates; hierarchical models borrow strength while allowing heterogeneity. Use for portfolios of thousands of SKUs.
Experiment design for pricing: prefer randomized price or promo experiments when feasible; cluster-randomize by store/region to avoid interference, pre-stratify on baseline demand, and power for ratio metrics (revenue per store-day).
Time-series causal methods: for single-unit interventions, use synthetic controls or Bayesian structural time-series (e.g., CausalImpact) to estimate counterfactual demand after a price change.
Uplift modeling and targeting: build models predicting incremental response to a promotion (heterogeneous treatment effects) using causal trees/forests (e.g., uplift random forests); evaluate on holdout promotion groups, not standard predictive metrics.
Evaluation metrics & business tradeoffs: report incremental revenue, incremental margin, units, and LTV; tie elasticity to profit optimization by solving max_{price} E[profit] = (P-C) * E[Q(P)].
Multiple testing & sequential testing: correct for multiple SKUs/tests using Benjamini-Hochberg FDR or family-wise corrections; for sequential decisions use pre-specified stopping rules or sequential methods (alpha spending).

Worked example — "Estimate price elasticity for a product using observational sales & price history"

First 30s: ask clarifying questions—target elasticity granularity (SKU-store vs SKU-chain), horizon (short-term campaign vs long-term baseline), presence of promotions/stockouts, and available covariates (competitor prices, marketing, cost). Skeleton answer pillars: (1) Data prep: build a panel with daily store-SKU sales, price, promo flags, competitor price, holidays, and stockout indicators. (2) Identification strategy: start with a log-log fixed-effects panel ln(Q_{it}) = α_i + δ_t + β ln(P_{it}) + X_{it}γ, then test for endogeneity using Durbin-Wu-Hausman; if endogenous, propose instruments (supplier cost shock, regional wholesale price changes). (3) Estimation & validation: estimate IV-first-stage strength (F>10), IV second stage for β, cluster s.e. at store or region, and run placebo periods and pre-trend checks. Tradeoff to flag: IV reduces bias but increases variance — wide CIs matter for pricing decisions. Close with next steps: if more time, run a small randomized price experiment for high-variance SKUs or fit a hierarchical Bayesian model to pool across similar SKUs and produce shrinkage estimates with uncertainty.

A second angle — "Design an experiment to test a promotion across stores"

Here the framing shifts to randomized design and interference. You’d propose cluster randomization by store (or zip code) with stratification on baseline sales and store format. Define treatment unit (store-day) and guard band to limit spillover between nearby stores. Choose primary metric as incremental gross margin per store-week, compute power for store-level variance, and pre-register analysis window. Address interference/cannibalization by including geographic spill variables and measuring cross-store uplift. If stores are limited, consider a stepped-wedge rollout to gain power while eventually exposing all stores.

Common pitfalls

Pitfall: Ignoring price endogeneity and treating observed price drops as exogenous promotions.
This yields biased elasticity estimates; always test for endogeneity and prefer IVs or randomized experiments when possible.

Pitfall: Reporting point estimates without uncertainty or business interpretation.
Present elasticities with CIs, translate to expected revenue/margin impact for plausible price changes, and provide decision thresholds (e.g., change only if expected profit gain > operational cost).

Pitfall: Overfitting short promotional windows and extrapolating to long-run elasticities.
Short-term promotional lift often differs from long-run sensitivity; explicitly model time-varying elasticity or obtain long-horizon experiments before permanent price decisions.

Connections

Interviewers may pivot to assortment optimization (how price interacts with product assortment), demand forecasting (feeding elasticity into forecasts), or inventory optimization (price as a lever for stock-clearing). Be prepared to connect causal estimates to downstream optimization problems.