In general, it is very hard to identify causal effects from non-experimental data because correlation is not causality. Unless you run an experiment by randomly varying price, you cannot identify causality.
Preston solves this problem by "creating" an experiment:
What we do is first we build a model of ourselves, of how we set our prices. So our first model is going to not predict demand; it's just going to predict what decision-makers were doing in the past. It incorporates everything we know: prices of competing products, news stories, and lots of other data. That's the first ML [machine learning]. We're not predicting what demand or sales will look like, we're just modeling how we behaved in the past. Then we look at deviations between what happened in the market and what the model says we would have done. For instance, if it predicted we would charge $1,110, but we actually charged $1,000, that $110 difference is an experiment. Those instances are like controlled experiments, and we use them in the second process of machine learning to predict the actual demand. In practice, this has worked astoundingly well.
In other words, by predicting how price was normally set in the past, the Microsoft economists create a "control group" to which they compare current prices. The difference is the "experiment" that they use to identify causality.
BOTTOM LINE: study econometrics!