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Please help me word exactly what is wrong with using total spends (split by different media) as variables in regression analysis, with sales/store traffic or something similar as the dependant variable

I work in advertising and everyone in the industry is building a lot of models like this (mostly to rationalize increasing ad spends to clients), which seems very wrong from a theoretical point of view

My own thoughts: 1) Multicollinearity makes it impossible to interpret coefficients for each media, so it would be wrong to say "Spends in X media increase sales by -coefficient- units" 2) Endogenity between advertising and sales (for example similar seasonality due to advertisers increasing activity during high sales season)

Please feel free to add to this or correct me if i'm wrong

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Using ad spend (or any marketing instrument) in a model predicting unit sales is pretty standard. To your very good point, it is almost always endogenous, e.g., ad spend is frequently a percentage of sales revenue as in the A/S ratio. The statistical solutions are to create and model HAC residuals for the DV and then run the usual tests for endogeneity, e.g., Durbin-Wu-Hausman or simply correlate the model residuals with the predictors (Wooldridge's test). If the tests suggest that endogeneity is still a problem, then the next step would be to run a 2SLS to further control for it.

That said, these solutions are far from perfect as endogeneity can be very difficult, if not impossible, to eliminate.

Lots of references out there about it, e.g., Wooldridge's Econometric Analysis of Cross Section and Panel Data or Hanssen and Parsen's Market Response Models: Econometric and Time Series Analysis.

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If you are saying that the spending falls into different groups or categories (e.g. different seasons) then lumping them all together breaks the assumption of independence of observations. E.g. if the observations for spring constitute one group of observations, and the observations for Christmas constitute a different group, the relationship between spend and outcome might be quite different in the different groups.

This doesn't necessarily just give you some kind of average between the groups. To see how badly this can go wrong, read up on Simpson's paradox, e.g. http://www.theregister.co.uk/2014/05/28/theorums_3_simpson/.

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