I know that linear regression is used for calculating price elasticity. If my objective is to estimate the parameters of a causal relationship, can i use machine learning techniques like Random Forest or lets say ARIMA with regressors? Has anyone done this before? I tried searching in jstor.org but didn't find any.
There are typically two ways to go about estimating causal relationships in the data: by using exogenous variation in the "right-hand-side" variable, or by using structural estimation.
Unless there's an experiment or a quasi-experiment of some sort, the technique economist's apply is instrumental variable (IV) estimation. The idea is that to find the causal impact of x on y in a situation in which x is partly determined by y itself or by a third variable that also affects y, is to find a source of variation that only has a direct effect on x.
Machine learning techniques are not typically used to estimate causal relationships. Instead, they are often used for forecasting.
Mixing the two: machine learning and causal inference is a focus of current research, but apparently there are no solid, off-the-shelf methods to use. Intuitively, the issue is that in the example above, you will need all of x to produce the best forecast of y, but you want only the exogenous par of x to get a sense of the causal relationship between x and y.