Marketing Promotion modelling, effects of a competitor's promotions I am modelling the impact of a manufacturer's promotions onto it's sales using a regression model. Furthermore, I intend to include the effects of competitor A's promotions onto the manufacturer's sales. In that given market, there are only those two competitors and the market is fairly split between the two, you could think of laundry detergent, where in some countries, there is only Persil vs. Ariel. In one week, Persil will run a promotion and in the other, Ariel. It does not happen, that two promotions run at the same time.
The model would look something like this:
sales(manufacturer) ~ promo(manufacturer) + promo(competitor A)

What is your take on it? Would you include some form of interaction / cannibilization? Is it reasonable the way I take the competitor's effect into account? Interessted to hear your opinion!
 A: It's a reasonable approach in my opinion. A couple of things to keep in mind:

*

*If there is always a promotion running, then you won't be able to get a good "baseline" estimate, so it will be hard-to-impossible to disentangle the cannibalization effect from baseline sales. I have seen this in a slightly different context (bakery, where there was always a promotion on one type of bread, though a different type each week).


*How good are your data? You probably have data on your own promotions. (Though, surprisingly enough, people don't keep historical information on their own promotions.) But your competitor will likely enough not be so kind to supply you with historical data on their promotions, so you will have to rely on keeping your own records.
And of course, if you want to forecast using your model, it will be pretty impossible to get information about future promotions your competitor plans to run.


*If there are multiple products that are possible substitutes for one another, then things can get complicated. Product X from manufacturer A may be very similar to product Y from manufacturer B, so if X is promoted, we expect a cannibalization effect on Y. But what about product Z, which is not very but somewhat similar to X? For instance, Z might be the very same product as Y, just in a larger or smaller size, or they may differ in some other way. We might be tempted to just model all possible cannibalization interactions, but depending on your assortment, that might turn into a hugely overparameterized model, with effects that get smaller and smaller.
Plus, we typically don't have a promotion on a single product, but on an entire brand, or part of it. So we really don't have a 1:1 relationship, and not even a 1:n one, but an n:m one.
