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I am trying to determine the rate of cannibalization of product sales for A with product B. I am using ~ 2 years of daily sales data for product A and then ~8 months of data for product B. That is, product B launched 8 month ago. I am using the longer series for A to capture trend effects in the business (natural or industry rate of decline or growth). I also control for seasonality by using a weekday variable (= day of week 1-7) and a week number variable (1-52).

If I use the log-log regression to determine the elasticity of A to B, then I can use that to estimate cannibalization. By regressing the log (A) daily sales as the Y variable against the Log (X) i.e. products B's daily sales I get an equation in the terms of:

log (A)=Bo +B(log(X)) + error and this tells me the % change in A given a 1 % change in X. However, I want to express this in terms of dollars. Therefore, I have to transform the logs back into the original sales values (I do not use any smearing transformations).

Question: Is the equation below correct? If not please advise. Furthermore, is it proper to take the log coefficient of product B and do the following to estimate the % sales lost to B:

% cannibalization of year to date sales = [(EXP(B1)-1) x (year-to-date sales of B)] / (year-to-date sales of A); where B1 = coefficient from log-log regression Say the above equation gives me a % cannibalization of year to date sales of 87 %, how should I interpret it?

Thanks alot for helping me out

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  • $\begingroup$ What are you doing when B is not available, so log(X) is undefined? Also, I believe the coefficient B should be interpreted as the % change in A's sales for a 1% increase in sales of B. $\endgroup$ – Dimitriy V. Masterov Jan 28 '13 at 19:19
  • $\begingroup$ You are right, just edited that:) $\endgroup$ – Tom Jan 29 '13 at 9:19
  • $\begingroup$ It's not good practice to destroy your post and repost just after. Better to update your question so that this thread remains self-contained. Thanks. $\endgroup$ – chl Jan 31 '13 at 22:47
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If you wish to determine the impact of sales of product B on Product A , you must look at the conditional effect. The conditions that you might need to consider are 1) day-of-the-week ; 2) week-of-the-year ; 3) month-of-the-year 4) specific days-of-the-month ; 5) lead and lag effects around each holiday/event 5) Monday-after-a Friday event ; 6) Friday-before a Monday event ; 7) particular-weeks-in-the-month ; 8) ARIMA structure ; 9) Level Shifts, Local Time Trends , Seasonal Pulses, Pulses ; 9) changes in parameters over time; 10) changes in variance over time ; 11) impact of price/promotions ...... to name a few. I have written a paper on this subject, please see http://www.autobox.com/cms/index.php/news/131-102706-white-paper-on-cannibalization-qtesting-market-hypothesisq-by-john-c-pickett-david-p-reilly-view

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  • $\begingroup$ I have actually read your article prior to posing my question. I am still confused with regards to the equation where lost sales are calculated: % cannibalization of year to date sales = [(EXP(B1)-1) x (year-to-date sales of B)] / (year-to-date sales of A); where B1 = coefficient from log-log regression..is this correct? $\endgroup$ – Tom Jan 29 '13 at 9:22

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