Journal of the Academy of Marketing Science

, Volume 19, Issue 4, pp 333–340 | Cite as

Confidence interval for the total advertising impact and its mean duration under Koyck models

  • John M. McCann
  • Richard C. Morey
  • Amitabh S. Raturi


The estimates of total advertising impact and of its mean duration in distributed lag models are important in budgeting and planning decisions. The typical approach to assessing the short and long term impact of advertising is to perform a sequential test, one on the short term coefficient and one on the lag parameter. However, estimate of the effect of advertising on sales involves the ratio of estimated regression parameters. The estimates of these parameters are known to be correlated. Generation of confidence intervals on such key estimates is possible, using information that is typically discarded. This paper develops and illustrates a method for developing these confidence intervals which specifically accounts for the correlation between the standard regression estimates. Examples are used to illustrate that the conclusion from standard sequential testing procedures can be erroneous. An empirical application then demonstrates the application of the suggested procedure. Finally, we provide insights on the length of this interval as the sample size and other characteristics are varied.


Ordinary Little Square Duration Interval Advertising Expenditure Standard Normal Random Variable Naval Research Logistics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Bass, Frank M. and Robert Leone. 1981. “Temporal Aggregation, the Data Interval Bias and Empirical Estimation of Bi-monthly Relations from Annual Data.” Working Paper. West Lafayette, IN: Krannert Graduate School of Management, Purdue University.Google Scholar
  2. Bultez, A. V. and P. A. Naert. 1979. “Does Lag Structure Matter in Optimizing Advertising Expenditures?”Management Science 25: 454–465CrossRefGoogle Scholar
  3. Clarke, Darral G. 1976. “Econometric Measurement of the Duration of Advertising Effects on Sales.”Journal of Marketing Research 13: 345–357.CrossRefGoogle Scholar
  4. Crane, M. A. and A. J. Lemoine. 1974.An Introduction to the Regenerative Method for Simulation Analysis. New York: Springer-Verlag.Google Scholar
  5. Dhrymes, P. J. 1971.Distributed Lags: Problem of Estimation and Formulation. Holden Day.Google Scholar
  6. Hayduk, L. A. 1987.Structural Equation Modelling with LISREL. Baltimore: The John Hopkins University Press.Google Scholar
  7. Hansen, Morris H., W. N. Hurwitz, and W. G. Madow. 1953.Sample Survey Methods and Theory. New York: John Wiley & Sons.Google Scholar
  8. Helwig, Jane T. and Kathrun A. Council. 1979.SAS User’s Guide. SAS Institute.Google Scholar
  9. Johnson, R. M. and D. W. Wichern 1982.Applied Multivariate Statistical Analysis. Engelwood Cliffs, NJ: Prentice Hall.Google Scholar
  10. Johnston, J. 1972.Econometric Methods. New York: McGraw Hill.Google Scholar
  11. Koyck, L. M. 1954.Distributed Lags and Investment Analysis. Amsterdam: North Holland Publishing.Google Scholar
  12. Lambin, Jean Jacques. 1972. “Is Gasoline Advertising Justified.”Journal of Business 45: 505.Google Scholar
  13. Lambin, Jean Jacques. 1976.Advertising, Competition and Market Conduct in Oligopoly Over Time. Amsterdam: North-Holland.Google Scholar
  14. Maddala, G. S. 1977.Econometrics. McGraw-Hill.Google Scholar
  15. Magat, W. A., J. M. McCann, and R. C. Morey. 1986. “When Does Lag Structure Really Matter in Optimizing Advertising Expenditures?”Management Science 32: 182–193.Google Scholar
  16. Morey, R. C. and J. M. McCann. 1983. “Estimating the Confidence Interval for the Optimal Marketing Mix: An Application to Lead Generation.”Marketing Science 2: 193–202.Google Scholar
  17. Moriarty, M. M. and J. L. Lastovicka. 1985. “Time Interval Bias: Its Impact on Advertising Budgeting.” InCurrent Issues and Research in Advertising, 1985, Volume 1: Original Research and Theoretical Contributions, pp. 115–128. Eds. J. L. Leigh and C. R. Martin. The University of Michigan.Google Scholar
  18. Roy, S. N. and R. F. Potthoff. 1958. “Confidence Bounds on Vector Analogues of the ‘Ratio of Means’ and the ‘Ratio of Variances’ for Two Correlated Normal Variates and Some Associated Tests.”Annals of Mathematical Statistics 29: 829–841.Google Scholar
  19. Simon, Julian. 1969. “The Effect of Advertising on Liquor Brand Sales.”Journal of Marketing Research 6.Google Scholar
  20. Weiss, Doyle L. and Pierre M. Windal. 1980. “Testing Cumulative Advertising Effects: A Comment on Methodology.”Journal of Marketing Research 17:371–378.CrossRefGoogle Scholar

Copyright information

© Academy of Marketing Science 1991

Authors and Affiliations

  • John M. McCann
    • 1
  • Richard C. Morey
    • 2
  • Amitabh S. Raturi
    • 3
  1. 1.Duke UniversityDurhamUSA
  2. 2.Tulane UniversityUSA
  3. 3.University of CincinnatiCincinnatiUSA

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