Happy New Year to everyone once again. Here is a quick ‘Metrics Monday post to start the year on the right foot.
Dave Giles had a neat post, sandwiched between Christmas and New Year, titled “Correlation Isn’t Necessarily Transitive.” If you are not familiar with the concept of transitivity,* what this means is that when Y is correlated with D, and D is correlated with Z, Y isn’t necessarily correlated with Z.
From my choice of labels for those variables, you have probably guess why this is matters for applied econometrics: It is perfectly possible that in a regression of Y on D where you are interested in the causal relationship flowing from D to Y, you have an otherwise valid instrument Z (i.e., a variable that is plausibly exogenous to outcome Y and which is also relevant in explaining D). Obviously, Z being relevant means that it is correlated with D. Assuming that D is also correlated with Y, the fact that correlation isn’t necessarily transitive means that the IV is not necessarily correlated with the outcome.