<p>We develop a stochastic generalization of the Bass diffusion model that incorporates uncertainty directly into the adoption dynamics. The resulting stochastic diffusion captures innovation and imitation effects and yields a quasi-analytical solution via a martingale-based transformation. The framework delivers managerially relevant state-dependent probabilities, including the likelihood of attaining a target penetration conditional on current penetration, and characterizes how these probabilities vary with innovation, imitation, and diffusion variance coefficients. The stochastic formulation also implies a structured error process for discrete-time estimation: errors are heteroscedastic and may be serially correlated. Using standard consumer durable series, we find that inference is largely unchanged after applying heteroscedasticity and autocorrelation corrections, indicating that nonlinear least squares estimates from the deterministic Bass specification remain reliable in common applications. Finally, examining pre-Internet and Internet-era products, we find that diffusion curves continue to fit well and that imitation effects are stronger in the digital era, consistent with accelerated interpersonal influence through “word of mouse.” Collectively, our results show that introducing uncertainty improves managerial interpretation through state-dependent probabilities yet preserves the practical reliability of deterministic Bass estimation.</p>

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A Stochastic New Product Growth Model: Econometric Analysis and Managerial Insights

  • Dipak Jain,
  • Kalyan Raman

摘要

We develop a stochastic generalization of the Bass diffusion model that incorporates uncertainty directly into the adoption dynamics. The resulting stochastic diffusion captures innovation and imitation effects and yields a quasi-analytical solution via a martingale-based transformation. The framework delivers managerially relevant state-dependent probabilities, including the likelihood of attaining a target penetration conditional on current penetration, and characterizes how these probabilities vary with innovation, imitation, and diffusion variance coefficients. The stochastic formulation also implies a structured error process for discrete-time estimation: errors are heteroscedastic and may be serially correlated. Using standard consumer durable series, we find that inference is largely unchanged after applying heteroscedasticity and autocorrelation corrections, indicating that nonlinear least squares estimates from the deterministic Bass specification remain reliable in common applications. Finally, examining pre-Internet and Internet-era products, we find that diffusion curves continue to fit well and that imitation effects are stronger in the digital era, consistent with accelerated interpersonal influence through “word of mouse.” Collectively, our results show that introducing uncertainty improves managerial interpretation through state-dependent probabilities yet preserves the practical reliability of deterministic Bass estimation.