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On the Econometrics of the Bass Diffusion Model


  • Boswijk, H. Peter
  • Franses, Philip Hans


We propose a new empirical representation of the Bass diffusion model, in order to estimate the three key parameters, concerning innovation, imitation and maturity. The representation is based on the notion that the observed data may temporarily deviate from the mean path determined by the underlying hazard rate. Additionally, it rests on the idea that uncertainty about the cumulative process should be smaller, the closer it is to the start of the process and to the level of maturity. Taking this into account, we arrive at an extension of the basic representation proposed in Bass (1969), with an additional heteroskedastic error term. The type of heteroskedasticity can be set by the modeler, as long as it obeys certain properties. Next, we discuss the asymptotic theory for this new empirical model, that is, we focus on the properties of the estimators of the various parameters. We show that the parameters, upon standardization by their standard errors, do not have the conventional asymptotic behavior. For practical purposes, it means that the t-statistics do not have an (approximate) t-distribution. Using simulation experiments, we address the issue how these findings carry over to practical situations. In a next set of simulation experiments, we compare the new representation with that of Bass (1969) and Srinivasan and Mason (1986). We document that these last two approaches often seriously overestimate the precision of the parameter estimators. We also shed light on the effects of temporal aggregation and on the effects of a serious and persisent deviation between the actual data and their mean. Finally, we consider the various empirical representations for a monthly series on installed ATMs.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Boswijk, H. Peter & Franses, Philip Hans, 2005. "On the Econometrics of the Bass Diffusion Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 255-268, July.
  • Handle: RePEc:bes:jnlbes:v:23:y:2005:p:255-268

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    Cited by:

    1. Marc Fischer & Peter Leeflang & Peter Verhoef, 2010. "Drivers of peak sales for pharmaceutical brands," Quantitative Marketing and Economics (QME), Springer, vol. 8(4), pages 429-460, December.
    2. Jacob Grazzini & Matteo Richiardi & Lisa Sella, 2012. "Indirect estimation of agent-based models.An application to a simple diffusion model," LABORatorio R. Revelli Working Papers Series 118, LABORatorio R. Revelli, Centre for Employment Studies.
    3. Torben Klarl, 2014. "Knowledge diffusion and knowledge transfer revisited: two sides of the medal," Journal of Evolutionary Economics, Springer, vol. 24(4), pages 737-760, September.
    4. Jonathan Beck, 2007. "The sales effect of word of mouth: a model for creative goods and estimates for novels," Journal of Cultural Economics, Springer;The Association for Cultural Economics International, vol. 31(1), pages 5-23, March.
    5. Beck, Jonathan, 2008. "Diderot´s rule," Discussion Papers, Research Unit: Competition and Innovation SP II 2008-13, WZB Berlin Social Science Center.
    6. Boswijk, H. Peter & Franses, Philip Hans & van Dijk, Dick, 2010. "Cointegration in a historical perspective," Journal of Econometrics, Elsevier, vol. 158(1), pages 156-159, September.
    7. Jacob Goldenberg & Oded Lowengart & Daniel Shapira, 2009. "Zooming In: Self-Emergence of Movements in New Product Growth," Marketing Science, INFORMS, vol. 28(2), pages 274-292, 03-04.
    8. Chihyun Jung & Dae-Eun Lim, 2016. "Development of an Adaptive Forecasting System: A Case Study of a PC Manufacturer in South Korea," Sustainability, MDPI, Open Access Journal, vol. 8(3), pages 1-12, March.
    9. Yuri Peers & Dennis Fok & Philip Hans Franses, 2012. "Modeling Seasonality in New Product Diffusion," Marketing Science, INFORMS, vol. 31(2), pages 351-364, March.
    10. repec:gam:jsusta:v:8:y:2016:i:3:p:263:d:65516 is not listed on IDEAS
    11. Fok, Dennis & Franses, Philip Hans, 2007. "Modeling the diffusion of scientific publications," Journal of Econometrics, Elsevier, vol. 139(2), pages 376-390, August.
    12. Don M. Chance & Eric Hillebrand & Jimmy E. Hilliard, 2008. "Pricing an Option on Revenue from an Innovation: An Application to Movie Box Office Revenue," Management Science, INFORMS, vol. 54(5), pages 1015-1028, May.
    13. Massiani, Jérôme & Gohs, Andreas, 2015. "The choice of Bass model coefficients to forecast diffusion for innovative products: An empirical investigation for new automotive technologies," Research in Transportation Economics, Elsevier, vol. 50(C), pages 17-28.
    14. Franses,Philip Hans & Dijk,Dick van & Opschoor,Anne, 2014. "Time Series Models for Business and Economic Forecasting," Cambridge Books, Cambridge University Press, number 9780521817707.
    15. Franses, Ph.H.B.F., 2009. "Forecasting Sales," Econometric Institute Research Papers EI 2009-29, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    16. Klarl, Torben, 2009. "Knowledge diffusion and knowledge transfer: two sides of the medal," ZEW Discussion Papers 09-080, ZEW - Leibniz Centre for European Economic Research.
    17. Hong, Jungsik & Koo, Hoonyoung & Kim, Taegu, 2016. "Easy, reliable method for mid-term demand forecasting based on the Bass model: A hybrid approach of NLS and OLS," European Journal of Operational Research, Elsevier, vol. 248(2), pages 681-690.
    18. Meade, Nigel & Islam, Towhidul, 2006. "Modelling and forecasting the diffusion of innovation - A 25-year review," International Journal of Forecasting, Elsevier, vol. 22(3), pages 519-545.
    19. repec:eee:ijrema:v:27:y:2010:i:2:p:91-106 is not listed on IDEAS
    20. Fernández-Durán, J.J., 2014. "Modeling seasonal effects in the Bass Forecasting Diffusion Model," Technological Forecasting and Social Change, Elsevier, vol. 88(C), pages 251-264.
    21. H.P. Boswijk & D. Fok & P.-H. Franses, 2006. "A New Multivariate Product Growth Model," Tinbergen Institute Discussion Papers 06-027/4, Tinbergen Institute.

    More about this item

    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • M - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics
    • M31 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Marketing and Advertising - - - Marketing


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