What statistical test method is most suitable for testing how variable A affects variable B over time?

Question

I'm doing an analysis on how one variable affects another variable over time and I am not sure how I should test this. Our more exactly, I don't know which type of statistical test method I should use. The data looks like this

SO... I want to test IF and HOW the variable "sweibr" is affecting the variable "swedendebt" over time. Further,I also want to test how the relationship between the variables changes when sweibr goes from positive to negative. ( I have made a dummyvariable on sweibr for this).

I would be thankful if someone could help me solve this.

Answer 1

Let's call your variables $x$ and $y$. You want to know if $y$ causally depends on $x$.

Just to recapitulate that standard approaches like regressions look for correlations between $x$ and $y$. If we have a correlation, it is not clear in which direction the causality goes, or even if causality exists at all. There could be a third variable (confounder) that controls $x$ and $y$.

There are basically two routes to address this problem:

a) For static situations, the idea is to control confounders and re-build / test the causal structure that controls the variables. Keywords are path analysis, structural equation models, Pearl et al.'s book Causal inference

b) For time-series, however, the situation is much more convenient because one can use a (presumed) property of causality, which is that the cause precedes the effect. There are a number of methods that test for temporal precedence, i.e. if $y_t$ depends on $x_{t-1}$. The most basic approach is Granger causality (see discussion here), which is implemented, e.g., in R here.