Index: Market Response Models

Market Response Models

Routing Summary

Empirical response models for marketing management using econometric and time series (ETS) analysis, plus modern Bayesian media mix modeling. Sources: Hanssens, Parsons & Schultz (2001) “Market Response Models,” 2nd Ed., and Jin et al. (Google, 2017) Bayesian MMM. Contains 31 notes organized across 6 subfolders.

• Need overview and management framework? → Introduction
• Need functional forms (linear, power, ADBUDG, MCI/MNL) with LaTeX + elasticities? → Static Response Models
• Need Koyck/ADL carryover, reaction functions, hysteresis? → Dynamic Response Models
• Need OLS/GLS/2SLS/Bayesian estimation, specification tests? → Estimation and Testing
• Need ARIMA, transfer functions, VAR, cointegration, ECM? → Time Series Analysis
• Need advertising/price/promotion empirical elasticities and optimal decisions? → Empirical Findings and Applications
• Need Bayesian MMM (adstock/carryover, Hill saturation, MCMC priors, ROAS/mROAS, optimal media mix, BIC selection)? → Bayesian Media Mix Modeling

Concept Map

Subfolder	Notes	Key Concepts
Introduction	3	MRM framework, simultaneous system, management tasks, scanner data, GRPs
Static Response Models	4	10 functional forms, MCI/MNL market share, aggregation bias, SCAN*PRO
Dynamic Response Models	4	Koyck, PDL, ADL, ratchet/hysteresis, reaction functions, S-shape, pulsing
Estimation and Testing	4	OLS, GLS, SUR, 2SLS, Bayes HB/EB, RESET, specification errors, AIC/BIC
Time Series Analysis	4	ARIMA, transfer functions, VAR, cointegration, ECM, Granger causality
Empirical Findings	5	Advertising elasticity ≈ 0.10, price ≈ −2.5, Dorfman-Steiner, DSS
Bayesian Media Mix Modeling	6	Adstock (geometric/delayed) carryover, Hill/logistic saturation, Bayesian MCMC + priors, ROAS/mROAS, optimal media mix, BIC model selection (Jin et al., Google 2017)

Key Equations Quick Reference

Equation	Description
$Q_t={\gamma }_{12}{A}_t+{\beta }_{11}{Y}_t+{\beta }_{12}{N}_t+{\beta }_{13}+u_{1t}$	Structural sales equation (Eq 1.1)
$Q=e^{{\beta }_0}{X}^{{\beta }_1}$; $\eta ={\beta }_1$	Power/log-log constant elasticity (Eq 3.x)
$Q_t=(1-\lambda ){\beta }_0+{\beta }_1(1-\lambda )X_t+\lambda Q_{t-1}+v_t$	Koyck transformation (Eq 4.10)
$\hat{\mathbf{\beta }}=({\mathbf{X}}^{\prime }\mathbf{X}{)}^{-1}{\mathbf{X}}^{\prime }\mathbf{q}$	OLS (Eq 5.5)
$\Phi (L)z_t=\Theta (L)w_t$	ARMA general form (Eq 6.11)
$y_t={\alpha }_0+V(L)x_t+n_t$	Transfer function impulse response (Eq 7.8)
$\Phi (L){\mathbf{z}}_t={\mathbf{\alpha }}_0+{\mathbf{w}}_t$	VAR model (Eq 7.22)
$\Delta Y_t={\alpha }_0+{\alpha }_1\Delta Y_{t-1}+{\alpha }_2\Delta X_{t-1}+{\alpha }_3{e}_{t-1}+u_t$	Error-correction model (Eq 7.29)
$A^/S^ = \eta_{QA} /	\eta_{QP}

Empirical Generalizations Summary

Marketing Instrument	Short-Run Elasticity	Long-Run Elasticity	Duration
Advertising	0.10–0.22	≈ 2× short-run	6–9 months (90%)
Price (own)	−2.5	Similar	Immediate
Price (cross)	+0.52	—	—
Coupon	+0.07	—	—
Display/Feature	Multiplier 1.5–2.6×	Low persistence	In-period
Distribution	High	High (sticky)	Long-run

Cross-Links to Existing Vault Notes

• Econometrics: Regression and the CEF, Omitted Variables Bias, Instrumental Variables, Differences-in-Differences
• Bayesian: Bayesian Workflow - Overview, Hierarchical Linear Models, Model Comparison
• Research Methodology: Garden of Forking Paths, Power Analysis and Sample Size, Multiple Testing Corrections
• Causal Inference: Activity Bias in Advertising, Directed Acyclic Graphs, Conditional Independence Assumption
• Consumer Behavior: Product Adoption and Diffusion Models, Logit Purchase Decision Model

Source

• Market Response Models Econometric and Time Series Analysis — Hanssens, Parsons & Schultz (2001), Kluwer Academic Publishers, 2nd Edition, 455 pp.
• Jin-2017-Bayesian-MMM-Carryover-Shape.pdf — Jin, Wang, Sun, Chan & Koehler (Google, 2017), “Bayesian Methods for Media Mix Modeling with Carryover and Shape Effects”: adstock, Hill saturation, MCMC estimation, ROAS/mROAS, optimal media mix, BIC selection, shampoo case study