Marketing Mix Modeling and Adstock Elasticity Analysis

Role: Lead Econometrician and Quantitative Marketing Scientist specializing in time-series regression and marketing mix modeling.

Context

• Historical Channel Spend Data: {{channel_spend_dataset}}
• Historical Sales and Revenue Series: {{historical_sales_series}}
• Adstock Decay and Lag Assumptions: {{adstock_decay_parameters}}
• Macroeconomic and Seasonality Covariates: {{macroeconomic_covariates}}
• Target Revenue Objective: {{target_revenue_objective}}
• Budget Reallocation Constraints: {{budget_reallocation_ceiling}}

Task

Deliver an advanced econometric Marketing Mix Model (MMM) analysis that estimates marketing channel elasticity, isolates baseline sales from marketing lift, measures adstock saturation curves, and prescribes budget shifts to hit the revenue target.

Method

1. Normalize and align the time-series datasets from {{channel_spend_dataset}} and {{historical_sales_series}} across uniform weekly intervals.
2. Apply Weibull and geometric transformation functions using {{adstock_decay_parameters}} to model carryover effects for each channel.
3. Fit Hill saturation functions to calculate diminishing marginal return thresholds for individual marketing touchpoints.
4. Control for exogenous baseline variation, trend, and seasonal volatility using {{macroeconomic_covariates}}.
5. Estimate multivariate ridge/Bayesian regression coefficients to evaluate individual channel elasticities and Return on Marketing Investment (ROMI).
6. Decompose total revenue into organic baseline volume versus paid channel contribution percentages.
7. Execute a non-linear optimization routine subject to {{budget_reallocation_ceiling}} to solve for {{target_revenue_objective}}.
8. Produce a sensitivity stress-test analyzing model parameter stability against sudden spend shifts.

Constraints

• MUST account for collinearity and carryover decay across all simultaneous media channels.
• MUST NOT treat organic baseline demand as paid media conversion volume.
• Spend adjustments MUST strictly respect the limits defined in {{budget_reallocation_ceiling}}.
• Detail parameter confidence bounds (standard errors and t-statistics) for all regression coefficients.

Output format

Generate an in-depth econometric report structured as follows:

1. Model Diagnostics & Fit: R-squared, MAPE, Durbin-Watson statistics, and collinearity VIF scores.
2. Channel Elasticity & Saturation Breakdown: Markdown table with Channel, Estimated Alpha/Adstock Half-life, Current Marginal ROMI, and Saturation Inflection Point.
3. Revenue Decomposition: Percentage breakdown of organic baseline vs. channel-attributed revenue.
4. Budget Optimization Matrix: Current vs. Recommended spend allocation by channel with projected uplift.

Self-review

• Ensure all exogenous factors in {{macroeconomic_covariates}} are integrated into baseline decomposition.
• Validate that sum of budget reallocations equals total allowable spend per {{budget_reallocation_ceiling}}.
• Check that saturation curves logically reflect diminishing returns at high spend volumes.