BSTS employing purposedly spurious regressors for causal impact analysis

Question

I'm employing Google Correlate time series to evaluate the causal impact of an intervention on a variable of interest y. I made sure that the Google series are highly correlated with y during the pre-treatment period, and that their relationship with y is merely spurious. Because of this, the probability of these series being affected by the intervention can be thought to be very low.

The causal impact analysis reveals a significant impact in the expected direction.

When employing a placebo treatment period (I divide the pre-treatment period into two: placebo pre-treatment and placebo treatment), and obtaining Google Correlate variables that are good predictors for the placebo pre-treatment period (to avoid a downwards bias), I find that the model fails to find a significant impact where there was no intervention.

So it seems like the spurious variables behave as good predictors would. Given this, is it a bad practice to employ such variables for causal impact analysis because of the spurious nature of their correlation?

Answer 1

This is a good approach (both using spurious variables and the placebo treatment you describe).

As you write, it's important to make sure the control time series are not affected by the intervention. This is the case if

1. the intervention does not does not directly affect the control time series, and
2. the response does not (causally) influence the control time series.

Using spurious variables makes sure 2 is not the case. To make sure also 1 is not the case, you could fit an additional CausalImpact model using one of the control time series as response, and the remaining ones as covariates (and repeating this for each control time series): if the control time series are indeed not affected by the intervention, CausalImpact should fail to find a significant impact here.