I have data on
- gross prices
- discounts (like coupons)
- net prices (i.e. gross price - discounts)
- number of leads (potential customers at any given time)
- conversion rates (# purchases / # leads) over time
A business wants to know how price elastic its consumers are and to use this information in part to set their net price by changing either gross price and/or discounts.
The problem is that there's some endogeneity (or recursion) in the system - when the business predicted higher conversion rates it raised prices. The business also varied the discount levels based on the conversion rates and gross price.
While the business is clearly selling a normal good, the endogeneity/recursion makes it looks like higher prices are associated with more sales and higher conversion rates. I need to disentangle these effects. Perhaps there's some great IV I'm not thinking of, but barring that, is there any other strategy to address this situation?
We can think of this as a single good case (I can add complexity later, but based on my subject matter knowledge it would be safe to ignore other goods and cross-price effects, etc).