What happens when you increase prices? More sales or less?

Economists tend to think that increasing price will cause a corresponding decrease in sales. Can we measure this by looking at data?

If you looked at petrol sales last weekend you would see an increase in price and a massive increase in sales - does that mean that the price increases caused the sales increase? Or is there some other factor driving both the price increase and the sales increase? How would you know what was going on from a dataset of sales and price data?

We would love to be able to learn about causal relationships just by observing the world via big datasets. Unfortunately, this is hard due to the presence of confounders and mediation. Even when we try to measure these confounders (eg mentions of 'panic buying' in the media), we won't be able to do it perfectly.

I recently went to a talk at the RSS conference by Prof Eric J Tchetgen Tchetgen on proximal causal learning, that gives some methodological improvements in how we can model these relationships by using proxy measurements of confounding effects. Using his approach, we can quantify causal effects even when we have imperfect measurements of all external factors.