Price elasticity of demand estimation with single store level data

Question

I have weekly data per single SKU and for more than 500 point of sales. Data embeds base price, quanity sold, holidays, temperature, market activities (cut-price, display, leaflets) and so on.

I want to run a regression model (OLS) to capture the effect of changes of base price on sellout controlling for all the other exogenous factors. I am thinking of running a regression using all the data from my point of sales but of course the higher the dimension and potential of a shop, the higher the sellout of that product. As of now, I have added as a avariable in the regression model the potential of the point os sales (share of volume of sellout amon all the population of shops) to capture the different potentiality but I am not shure about this method.

I also cannot aggregate data per week because i would lost all the in store activities (i.e. cut-price) that of course have a great impact o sales.

How can I proceed?

Answer 1

You cannot use OLS to estimate a demand equation, unless you have good reason to believe that all the movement in prices that you see in your data come from shifts in the supply side (in other words, you have to assume that price is exogenous in your demand equation). The best way to circumvent this problem is to find an instrument for price, which would essentially be some variable that captures changes in the supply side (this is often called a cost-shifter) and use that to run an IV regression.

With regards to the heterogeneity across shops, since you have a panel of data, you can use shop fixed-effects to take out all the unobserved differences (perhaps what you label as "potential") across shops that stay fixed over time. There still might be other things you wish to control for, but IV and shop fixed effects would get you closer to recovering the correct demand parameters.