Determine the effect on margins of a price increase

Question

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 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

Questions:

• 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!

Answer 1

What you have looks like a classic price elasticity model. Yes, you could do the analysis via regression. You can call the price increase group 'treatment' and the previous years products control: To compare the price increase group with the control group you could code some dummy variables in the regression equation. You would need to design this carefully since there are 3 different types of elasticity model, and some would require a few log transformations. Because you are not comparing current data, you would also need to account for the year lag, so I would also include 'year' as a time variant factor, and also include some interactions in the model.

Here are a few references to help you get started:

https://openstax.org/books/introductory-business-statistics/pages/13-5-interpretation-of-regression-coefficients-elasticity-and-logarithmic-transformation

https://economics.stackexchange.com/questions/19012/including-demand-price-elasticity-in-a-price-regression-model

https://stats.stackexchange.com/questions/207714/understanding-the-price-elasticity-interaction-in-a-regression-model