# Difference-in-Difference regression model for sensitivity analysis

I have 5-year sales information from a grocery store in Canada. I want to check whether an event that happened in 2017, affected the effect of the price of a product on its sales.

For example, imagine that before treatment price elasticity (i.e. the degree to which changes in price impact the unit sales of a product) for diary goods was -0.05, I am eager to know whether my treatment changed it or not. Actually, I already know that price influences sales, but I suspect that the imposition of the treatment might alter the consumers' price sensitivity.

The standard DiD model only investigates the impact of treatment on the outcome variable. While I need to see whether the treatment has affected the coefficient of the regression model (Sales ~ Price) or not. In other words, I need to check whether the treatment affected the relationship between my independent variable (Price) and dependent variable (Sales). Would you please guide me on what formula should I use as the standard difference-in-difference model does not seem to be working here?

$$log(Outcome_{it})= \beta_1 + \beta_2Treat_{i} + \beta_3 Post_{t} + \beta_4 (Treat \times Post)_{it} + \epsilon_{it}$$

can I use the below model instead?

$$log(Sales_{it})= \beta_1 + \beta_2Treat_{i} \times Price_{it} + \beta_3 Post_{t} \times Price_{i} + \beta_4 DiD_{it} \times Price_{it} + \epsilon_{it}$$

where DiD is:

$$DiD = Treat \times Post$$

• Is this a duplicate of your previous question? Jan 10, 2021 at 22:41
• I deleted that one and merged all the data into this one. I'm sorry it seems that one still exists. Is it against the rule and should I remove the new one? Jan 11, 2021 at 12:19
• Your previous post included additional clarification and has been upvoted more than once. I would edit the original post. But then again, it isn’t up to me which question is removed. Jan 15, 2021 at 19:15