Why doesn't correlation mean that one thing causes another?
I've been learning more about econometrics recently, and one concept I'm still trying to fully understand is the difference between correlation and causation.
I understand the basic idea: if two variables are correlated, it means they tend to move together, but that doesn't necessarily mean that a change in one variable causes a change in the other.
The classic example is ice cream sales and drowning deaths. Both increase during summer, but buying ice cream obviously doesn't cause people to drown. A third variable, temperature or season, affects both.
What I'm more interested in is how this works in real economic research, where there are usually many variables changing at the same time.
For example, suppose we find that countries with higher education spending also have higher GDP. How would an economist determine whether higher education spending actually causes higher GDP?
Could someone explain this =, but also go a little beyond the basic "correlation ≠ causation" explanation?
Specifically, how do methods such as control variables, experiments, natural experiments, instrumental variables, or difference-in-differences help economists get closer to identifying a causal relationship?
I'm especially interested in understanding what makes us confident that X caused Y rather than simply being correlated with Y.