Schmittlein and Mahajan (Marketing Science 1982) made an important improvement in the estimation of the Bass (1969) diffusion model by appropriately aggregating the continuous time model over the time intervals represented by the data. However, by restricting consideration to only sampling errors and ignoring all other errors (such as the effects of excluded marketing variables), their Maximum Likelihood Estimation (MLE) seriously underestimates the standard errors of the estimated parameters. This note uses an additive error term to model sampling and other errors in the Schmittlein and Mahajan formulation. The proposed Nonlinear Least Squares (NLS) approach produces valid standard error estimates. The fit and the predictive validity are roughly comparable for the two approaches. Although the empirical applications reported in this paper are in the context of the Bass diffusion model, the NLS approach is also applicable to other diffusion models for which cumulative adoption can be expressed as an explicit function of time.
-
Faculty
- Academic Areas
- Awards & Honors
- Seminars
-
Conferences
- Accounting Summer Camp
- California Econometrics Conference
- California Quantitative Marketing PhD Conference
- California School Conference
- China India Insights Conference
- Homo economicus, Evolving
-
Initiative on Business and Environmental Sustainability
- Political Economics (2023–24)
- Scaling Geologic Storage of CO2 (2023–24)
- A Resilient Pacific: Building Connections, Envisioning Solutions
- Adaptation and Innovation
- Changing Climate
- Civil Society
- Climate Impact Summit
- Climate Science
- Corporate Carbon Disclosures
- Earth’s Seafloor
- Environmental Justice
- Finance
- Marketing
- Operations and Information Technology
- Organizations
- Sustainability Reporting and Control
- Taking the Pulse of the Planet
- Urban Infrastructure
- Watershed Restoration
- Junior Faculty Workshop on Financial Regulation and Banking
- Ken Singleton Celebration
- Marketing Camp
- Quantitative Marketing PhD Alumni Conference
- Rising Scholars Conference
- Theory and Inference in Accounting Research
- Voices
- Publications
- Books
- Working Papers
- Case Studies
- Postdoctoral Scholars
-
Research Labs & Initiatives
- Cities, Housing & Society Lab
- Corporate Governance Research Initiative
- Corporations and Society Initiative
- Golub Capital Social Impact Lab
- Policy and Innovation Initiative
- Rapid Decarbonization Initiative
- Stanford Latino Entrepreneurship Initiative
- Value Chain Innovation Initiative
- Venture Capital Initiative
- Behavioral Lab
- Data, Analytics & Research Computing