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  • 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.

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