Suppose I want to model the sales of Coke sold at WalMart for a particular state in the U.S. Suppose I only have access to a year's worth of weekly sales data for that particular store. I want to model the sales of Coke. My question pertains to the modeling of catastrophic events or rare events. For example, suppose I want to model the effect of Hurricane Sandy on the sales of Coke for the particular WalMart. Also, I would like to model the effect of President Obama's re-election on the sales of Walmart. Intuitively, I feel I cannot model these directly. For modeling the influence of Hurricane Sandy, would it make sense to partition the data into two subsets where one subset includes the influence of Hurricane Sandy and the subset does not? Would an approval rating regarding the president's handling of Hurricane Sandy be a good variable that encapsulates the influence of Hurricane Sandy on the sales of Coke at that particular Walmart?
As a side note, are there any good resources/books about market mix modeling?
Best Answer
I think the hurricane model is possible, though it is not trivial and you will need panel data. The basic idea is that you get sales and demographics data from other Walmarts, from which you can construct a synthetic control group to compare with the affected store. Here's an example of this approach where the treatment was smoking control program in California from Prop 99, and a weighted combination of other states served as the untreated comparison group.
The approach you outline is not likely to work since there are seasonal effects in soft drink consumption. Saying that the end of September is just like the end of October, except for the hurricane is not quite right. The average temperature is October is lower, so that the reduction in sales from cooler weather is conflated with the effect of the hurricane.
The re-election model is not possible since you have no variation: Obama was reelected everywhere. There's no control group that you can construct.
The approval rating method is likely to suffer from spurious correlation. Both ratings and sales are likely to plummet and go back up, but that would hardly indicate a causal relationship (though that might be part of the story). Here's an example of regression of two series with a common trend going awry: