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Estimating Continuous Time Advertising-Sales Models

Author

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  • Ram C. Rao

    (The University of Texas at Dallas)

Abstract

This paper develops the advertising-sales model in continuous time with a view to studying the consequences of temporal aggregation for estimation. Difficulties arising from temporal aggregation are shown to correspond to the problem of unobservables. Two previously suggested ways of treating these unobservables due to Blattberg and Jeuland and Bass and Leone are studied in detail focusing on the nature of errors due to each approximation and the aggregation of underlying continuous time stochastic processes. The latter determine the properties of the disturbance terms in the estimating equations. Analytical results are presented and these are examined in light of an empirical application.

Suggested Citation

  • Ram C. Rao, 1986. "Estimating Continuous Time Advertising-Sales Models," Marketing Science, INFORMS, vol. 5(2), pages 125-142.
    • Handle: RePEc:inm:ormksc:v:5:y:1986:i:2:p:125-142
    DOI: 10.1287/mksc.5.2.125
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    Cited by:

    1. Sridhar Narayanan & Harikesh S. Nair, 2011. "Estimating Causal Installed-Base Effects: A Bias-Correction Approach," Working Papers 11-22, NET Institute.
    2. Keita Kinjo & Takeshi Ebina, 2016. "An Advertising Strategy Using Consumption Externality and Forgetting in the Case of Japanese Electronic Books," The Review of Socionetwork Strategies, Springer, vol. 10(2), pages 55-71, December.
    3. Michele Giordano & Anton Yurchenko-Tytarenko, 2024. "Optimal control in linear-quadratic stochastic advertising models with memory," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 47(1), pages 275-298, June.
    4. Prasad A. Naik & Murali K. Mantrala & Alan G. Sawyer, 1998. "Planning Media Schedules in the Presence of Dynamic Advertising Quality," Marketing Science, INFORMS, vol. 17(3), pages 214-235.
    5. Nolan Miller & Amit Pazgal, 2007. "Advertising budgets in competitive environments," Quantitative Marketing and Economics (QME), Springer, vol. 5(2), pages 131-161, June.
    6. Chan, Tat Y. & Narasimhan, Chakravarthi & Yoon, Yeujun, 2017. "Advertising and price competition in a manufacturer-retailer channel," International Journal of Research in Marketing, Elsevier, vol. 34(3), pages 694-716.
    7. Ganesh Iyer & David Soberman & J. Miguel Villas-Boas, 2005. "The Targeting of Advertising," Marketing Science, INFORMS, vol. 24(3), pages 461-476, May.
    8. Raman Kalyan & Naik Prasad A., 2004. "Long-term Profit Impact Of Integrated Marketing Communications Program," Review of Marketing Science, De Gruyter, vol. 2(1), pages 1-23, October.
    9. Fred M. Feinberg, 2001. "On Continuous-Time Optimal Advertising Under S-Shaped Response," Management Science, INFORMS, vol. 47(11), pages 1476-1487, November.
    10. Kiygi Calli, M. & Weverbergh, M. & Franses, Ph.H.B.F., 2010. "To Aggregate or Not to Aggregate: Should decisions and models have the same frequency?," ERIM Report Series Research in Management ERS-2010-046-MKT, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    11. Du, Rong & Hu, Qiying & Ai, Shizhong, 2007. "Stochastic optimal budget decision for advertising considering uncertain sales responses," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1042-1054, December.
    12. Weiss, Kenneth R. & Green, Richard D. & Havenner, Arthur M., 1996. "Walnuts in Japan: A Case Study of Generic Promotion Under the USDA's Market Promotion Program," Agricultural Commodity Promotion Policies and Programs in the Global Agri-Food System, May 26-27, 1996, Cancun, Mexico 279647, Regional Research Projects > NECC-63: Research Committee on Commodity Promotion.
    13. Milan Bradonjić & Matthew Causley & Albert Cohen, 2015. "Stochastic Optimal Control for Online Seller under Reputational Mechanisms," Risks, MDPI, vol. 3(4), pages 1-20, December.
    14. Marinelli, Carlo, 2007. "The stochastic goodwill problem," European Journal of Operational Research, Elsevier, vol. 176(1), pages 389-404, January.
    15. Mesak, Hani I., 1999. "On the generalizability of advertising pulsation monopoly results to an oligopoly," European Journal of Operational Research, Elsevier, vol. 117(3), pages 429-449, September.
    16. Huang, Jian & Leng, Mingming & Liang, Liping, 2012. "Recent developments in dynamic advertising research," European Journal of Operational Research, Elsevier, vol. 220(3), pages 591-609.
    17. Gerard J. Tellis & Philip Hans Franses, 2006. "Optimal Data Interval for Estimating Advertising Response," Marketing Science, INFORMS, vol. 25(3), pages 217-229, 05-06.
    18. David Paton, 2002. "Advertising, quality and sales," Applied Economics, Taylor & Francis Journals, vol. 34(4), pages 431-438.
    19. Olivier Rubel & Prasad A. Naik & Shuba Srinivasan, 2011. "Optimal Advertising When Envisioning a Product-Harm Crisis," Marketing Science, INFORMS, vol. 30(6), pages 1048-1065, November.
    20. Zhang, Jing & Lee, Eun-Ju, 2022. "“Two Rivers” brain map for social media marketing: Reward and information value drivers of SNS consumer engagement," Journal of Business Research, Elsevier, vol. 149(C), pages 494-505.
    21. Mesak, Hani I. & Calloway, James A., 1995. "A pulsing model of advertising competition: A game theoretic approach, part A -- Theoretical foundation," European Journal of Operational Research, Elsevier, vol. 86(2), pages 231-248, October.

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