Consumer Heterogeneity

Definition

Consumer heterogeneity refers to the systematic variation in preferences, tastes, and sensitivities across individuals. In structural models of demand, it is captured by individual-specific parameter vectors $\beta_i$ that govern utility or choice probabilities. The cross-sectional distribution $p(\beta_i | \tau)$ — the heterogeneity distribution with hyperparameters $\tau$ — is a core modelling decision that determines whether the model can recover individual behaviour, support targeted marketing, and generate realistic predictions for new products.

Key Ideas

• Rossi-Allenby (2003) framework: a coherent Bayesian marketing model has three components: (1) within-unit likelihood $p(y_i | \beta_i)$; (2) cross-unit heterogeneity distribution $p(\beta_i | \tau)$; (3) an action rule from a loss function applied to the posterior. See Bayesian Hierarchical Model.
• Normal heterogeneity: $\beta_i \sim \mathcal{N}(\bar\beta, V_\beta)$; conjugate Gibbs sampler; posterior estimates for each consumer. Limitation: unimodal and symmetric.
• Mixture-of-normals heterogeneity: $p(\beta_i | \tau) = \sum_k \pi_k \mathcal{N}(\mu_k, V_k)$; accommodates multimodal or heavy-tailed preference distributions without the constraint that predictions lie in the convex hull of component means.
• Observable heterogeneity: when individual covariates $z_i$ are available, $\beta_i = B z_i + u_i$ with $u_i \sim \mathcal{N}(0, V_\beta)$; allows partial explanation of between-individual differences.
• Managerial implications: individual posterior estimates $E[\beta_i | y_i]$ enable one-to-one marketing, optimal targeting, and personalised pricing.

Why It Matters

Ignoring heterogeneity (treating all consumers identically) produces aggregation bias: estimated price elasticities, willingness to pay, and cross-effects can differ dramatically from their disaggregate counterparts.

Related

• Conjoint Analysis
• Multinomial Probit
• Market Segmentation
• Bayesian Hierarchical Model
• Mixture of Normals
• Random Coefficient Model
• Nonhomothetic Preferences
• Rossi-Allenby (2003)