Determine the effect on margins of a price increase I hope you can help guide me in the right direction! Any advice is appreciated!
Situation
I'm currently analyzing the effect of a price increase from a retailer on a few 100 products. I'm interested in understanding the effect of the price increase on volume, sales value, and margin. The data I have available is weekly product-level data in terms of sales value, volume, and margin for products that had a price increase and for products that did not have a price increase. The price was increased roughly 2 months ago, and I have data from the past couple of years.
Analysis so far
The way I have analyzed this so far is by:

*

*Comparing the sales data 7 weeks before the price increase to 7 weeks after the price increase.  The results are compared to a control group - i.e., last year for the same weeks where there were no price increases. This is done only for products that had a price increase. Edit: By compare, I mean calculating the following for the products that were increased in price: $$(sales_{this year, post increase}-sales_{this year, pre increase})-(sales_{last year, post increase}-sales_{last year, pre increase})$$

*Comparing the sales data 7 weeks after the price increase for two groups of products: 1 group of products that had a price increase and 1 group that didn't have a price increase Edit: By compare, I mean calculating the following for the pre- and post price increase period this year: $$(sales^{increased products}_{post increase}-sales^{increased products}_{pre increase})-(sales^{other products}_{post increase}-sales^{other products}_{pre increase})$$
Questions:

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*If I had to do some sort of regression, what type of regression would you suggest?

*Is the analysis I have conducted so far correct?

Thanks a lot!


If I had to do some sort of regression, what type of regression would you suggest?

Disclaimer: The following suggestions are only meant to give a short explanation of the methods and their requirements. For exact details, requirements and caveats I recommend to read the relevant (e.g. the linked) literature on them.
If your products are not vastly different (e.g. the same size screws, but from different producers), you could apply a Difference in Differences Design. The products which had no price increase can then serve as the control group. You would estimate the model:
$$
Y_{it} = \alpha + \beta Treated_{it} + \gamma Post_{it} + \delta Post_{it} \times Treated_{it}+ \varepsilon_{it}
$$
for products $i$ and time $t$. The $Treated$ dummy variable is $1$ for all products that had the price increase, while $Post$ is equal to one after the time of the price increase. Given that the parallel trends assumption holds (see linked reference for details), $\delta$ is the effect of the price increase.
If your products are vastly different, but you are confident that you have enough data points for a single product, a Regression Discontinuity Design (RDD) could be a useful approach. You basically estimate a "jump" of the outcome variable at the date of the price increase using the model
$$
Y_t = \alpha + \beta X_t + \delta D_i + \varepsilon_t
$$
The continuous "running variable" $X_t$ would be the time and the dummy variable $D_t$ is equal to $0$ before and equal to $1$ after the price increase, which occurs at a time $X_0$. The effect of the price increase is then given by $\delta$, if there were no other causes of the jump (see the linked reference for the details). However, since you mentioned that you have data from previous years, you could use those to construct a RDD Difference in Differences design as explained in e.g. Clark et al. (2020) which can control for this problem.
