- I have a market with three goods: PRODUCT_I,PRODUCT_II, PRODUCT_III.
- PRODUCT_I is banned by a policy, and its sales brought down to 0.
I want to estimate to what extent PRODUCT_II and/or PRODUCT_III act as a substitute for PRODUCT_I, in general and in a series of regions/sub-markets.
- Assume PRODUCT_II is the most likely substitute of PRODUCT_I.
- Assume pre-intervention parallel sales trends for the three goods, at least in general (in the markets/sub-regions not given). Growing.
- Assume substitution is simply defined by unchanged combined product revenue.
- Assume total revenues from a product as the dependent variable
The ban is likely to have changed the whole market environment so it is not clear to me how I should pick/construct a counterfactual. What is the best option to do so?
OPTION I: Using PRODUCT-III as a counterfactual for both PRODUCT_I and PRODUCT_II. If two separate diff-in-diff estimation produce two equal results (opposite sign) I have substitution. This appears demanding in terms of parallel assumptions, especially if I want to look into different regions/sub-markets.
OPTION II: I use PRODUCT_II and PRODUCT_III jointly to construct a synthetic control predicting where PRODUCT_I would have been were the ban not implemented. and measure the extent to the substitution by means of a standard diff-in-diff.
OPTION III: I simply use PRODUCT_II as a counterfactual and use a vanilla diff-in-diff. Any estimation larger than 0 is assumed as a (degree of) substitution: Higher results means higher substitution.