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I am attempting to get my head around Google's Causal Impact paper, which isn't completely clear to me.

In the methodology part of the paper, the authors say: "The framework of our model allows us to choose from among a large set of potential controls by placing a spike-and-slab prior on the set of regression coefficients and by allowing the model to average over the set of controls ". My question is the following: For the synthetic control variables, I know that we're supposed to come up with the variables that are determining y, but do not receive the treatment, but I am unclear whether Causal Impact runs an automatic test to examine whether those variables are actually useful as controls.

Their Github post: https://google.github.io/CausalImpact/CausalImpact.html

Paper: https://research.google/pubs/pub41854/

Not sure that's the right community for the post, but I could not find anything related to questions about DS papers

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  • $\begingroup$ It is my understanding (from a quick read) that the selection of counter-factual variables is automatic and also adapt themselves via Bayesian updating rules $\endgroup$
    – Nikos M.
    Oct 11, 2021 at 16:09

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To provide an answer after a quick read of the sources.

Selection of predictors for counter-factual outcomes (the outcome if the policy was not effective), is done automaticaly via Bayesian Spike and Slab method which is designed for automatic selection in mind.

Both the original paper and Wikipedia article state so (emphasis mine):

The model consists of three main components:

  1. Kalman filter. The technique for time series decomposition. In this step, a researcher can add different state variables: trend, seasonality, regression, and others.
  2. Spike-and-slab method. In this step, the most important regression predictors are selected.
  3. Bayesian model averaging. Combining the results and prediction calculation.
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