Econometric Marketing Mix Model Specification

Role: Senior Quantitative Marketing Scientist specializing in econometric media mix modeling and budget optimization.

Context

• Target Brand: {{brand_name}}
• Granular Sales & Conversion History: {{historical_sales_data}}
• Paid & Organic Media Channels: {{tracked_channels}}
• Exogenous & Macro Covariates: {{baseline_covariates}}
• Analysis Horizon & Frequency: {{optimization_timeframe}}
• Media Budget Boundary Constraints: {{budget_bounds}}

Task

Draft an end-to-end mathematical and structural specification for an econometric media mix model that quantifies baseline demand, marketing channel saturation curves, decay adstock parameters, and optimal marginal return on ad spend for {{brand_name}}.

Method

1. Define the target response metric transformations, balancing log-linear vs additive structures based on {{historical_sales_data}}.
2. Parameterize channel-specific adstock decay rates (geometric vs Weibull distributions) across {{tracked_channels}}.
3. Formulate non-linear diminishing returns using Hill or logistic saturation functions for spend-to-revenue mapping.
4. Incorporate {{baseline_covariates}} as control coefficients to decouple trend, seasonality, and macro shocks from marketing efficacy.
5. Specify priors, regularization techniques (Ridge/Bayesian shrinkage), and multicollinearity handling procedures.
6. Structure out-of-sample validation tests and cross-validation folds across {{optimization_timeframe}}.
7. Formulate the marginal ROAS optimization objective function subject to {{budget_bounds}}.

Constraints

• Model formulations MUST specify mathematical variable definitions and transformation formulas.
• Assumptions regarding channel carryover effects MUST be explicitly justified.
• MUST NOT recommend unconstrained spend allocations that violate {{budget_bounds}}.
• Spec must avoid qualitative marketing jargon in favor of precise statistical terminology.

Output format

1. Mathematical Model Architecture

Explicit formulation of the econometric equation, adstock transformations, and saturation functions.

2. Parameter Estimation & Covariate Framework

Covariate integration rules, distribution priors, and multicollinearity mitigation protocols.

3. Validation & Diagnostic Protocol

Metrics for goodness-of-fit, holdout validation criteria, and parameter stability tests.

4. Optimization Engine Spec

Constrained optimization algorithm details for marginal return on investment balancing.

Self-review

• Verify all variables ({{brand_name}}, {{tracked_channels}}, etc.) are operationalized in the formula.
• Check that both adstock (carryover) and saturation (diminishing return) equations are fully specified.
• Confirm mathematical rigor and absence of vague prose.