Price Elasticity for a group of products

I am given a list with items and corresponding prices and units sold. Those items can be clustered into product groups. For most of the items, between 2 and 3 different prices can be observed. This seems to be very little information to calculate a price elasticity of demand for the different items. An idea I had is to take all of a groups' items, normalize the prices and use all the data points to calculate the elasticity of demand. Since this topic is new to me, I would very much appreciate some feedback whether this approach makes sense or not.

It would make sense if the products/items are homogenous (same) eg. different brands of milk, bottled water etc.

If they are heterogenous then each product demand will have different elasticity so trying to calculate elasticity out of multiple heterogenous products does not make sense.

Also, do not forget price and quantity demanded are endogenous, so when you are estimating your demand function to get the elasticity you need to account for reverse causality.

• Thank you very much for your answer. Regarding your comment about reverse causality. When I observe a price increase of a retailer aiming on increasing the margin and not due to higher (marginal) costs or due to a competitor increasing its price, I supply is supposed to be constant and I am not facing this issue, right? Thanks Aug 28, 2022 at 14:17
• @PatrickBalada there is also problem of demand not being constant across time (unless you have just cross-section data all collected at the same point of time). In that case you can observe increase in price together with increased quantity sold even if in fact what was that demand shifted left so it was not effect of price on quantity but shift in demand. If you have cross-sectional data it would be easier to justify but there you still have problems with expectations -marginal costs did not changed now but maybe the seller expected them to change next time period so they already hiked prices
– 1muflon1
Aug 28, 2022 at 15:19
• Thank you! I accepted your answer :-) One last question. From your experience, how bad is ignoring the reverse causality and simply fit a regression model on historic data (price, number of sold items, ...). I have the impression that a lot of companies do not use instrumental variables or simultaneous equations to infer price elasticities and set optimal prices. Sep 1, 2022 at 8:18
• @PatrickBalada it’s extremely bad. Ignoring reverse causality means you will not be able to discover true relationship between price and sales. Ignoring reverse causality could only make sense when you do short run forecasting (although even there state of the art structural model may perform better especially when you forecast more than just few days/weeks ahead). If you want to use the model for strategic pricing decisions then don’t even bother if you ignore this issue. I know many business are not aware of this - consequently many business make poor strategic decisions based on the model
– 1muflon1
Sep 1, 2022 at 8:37
• But times are changing, for example one of the professors that taught my PhD econometrics now set up a consulting business in amsterdam where he offers to do this sort of more complex data analysis for business and he always says his business is booming and before he gets involved business usually use bad models as you say so there is a lot of money to be made in this industry because estimating demand is important for optimal pricing decisions and those are important for profitability.
– 1muflon1
Sep 1, 2022 at 8:40