Calculate optimal discount for product bundling

Question

So recently I made some rules with my transaction data. Based on it I can determine which products are profitable to bundle it together.

But even though I know e.g. product A→ product B, are there any ways to determine how many bundles will be sold based on the discount value?

E.g. out of the 100 transactions with product A for price X and there are 40 transactions with product B for price Y(I know lift value might be better but let's keep it easy for now), if product A and B are bundled together, what is the discount rate to increase the optimal short term sales?

I do have products sold for product A and B for different kind of discount, so I was thinking using price elasticity to determine the discount for the bundle because if you know the price you know the quantity, but I dont think it is the right way of thinking and there is no price elasticity for both products.

The data I have:

Price of the product

Lift, support, confidence values and other values related to rules.

sold product per month

Discount value per product

I think these variables are more crucial.

Any suggestions would be appreciated.

Thanks in advance!

Answer 1

Do you have price elasticity figures at your disposal from other sources or were you planning on trying to estimate elasticities yourself using the data? If you are planning on estimating elasticities using the data, you need to be very careful. Running a simple log-log OLS regression will give you poor estimates because your data points are all market equilibrium points and are not a representative sample of points along a static demand curve. You have serious endogeneity issues there.

I have tried undertaking similar projects so I know the pitfalls well. If you still want to back out sales using elasticities, you could try an instrumental variables approach using some of your other variables as instruments to try and circumvent the endogeneity problem via supply-side identification. Another option is to use a simultaneous equations model where you posit functional forms for supply and demand separately and then estimate the reduced form using, say, two-stage least squares (2SLS).

If you are strictly interested in forecasting sales well and not really concerned with understanding causal channels, you can look into machine learning algorithms. Depending on how many data points and how many variables you have at your disposal, there are various models that may suit your needs. You should understand these models well before running them, however, because most of them are not like the models in your standard econometrics toolkit. For instance, the more "flexible" models (such as unpruned decision trees, multilayer perceptrons, etc.) are very susceptible to overfitting the data by essentially modeling noise, leading to higher mean squared errors than anticipated due to high variance.

If you're interested in learning more, I found this to be an outstanding, easy-to-understand introduction into statistical learning.