Simple Question About Control Variables Should you include a specific control variable in your regression if the only basis for doing so is that it is correlated significantly (positively or negatively) with other controls?
There is no economic theory to suggest it is related to the dependent or independent variable. However, the other control variables already within the regression are supported by economic theory.
What would be the theoretical reasoning for including or excluding the control variable in question?
 A: This is a question best answered with the new revolution in causality. The short answer is that correlation is not sufficient to justify conditioning (i.e., including in your regression). Indeed, sometimes you need to exclude variables from your regression! What you want to include in your regression are causal variables, as well as variables such that, when you condition on them, they shut backdoor paths. Here are a few examples. First, though, we need a definition or two. 
We draw the graph $X\to Y$ if $X$ causes $Y.$ A "backdoor path" is a path from $X$ (typically our cause of interest) to $Y$ (typically the effect of interest) that begins with an arrow into $X.$ 

In this figure, $M$ is a confounding variable, and the path $X\leftarrow M\to Y$ is a backdoor path. You would want to include $M$ in your regression here, in order to block the backdoor path.
In this example,

there is no backdoor path from $X$ to $Y$, and $M$ is what we call a mediator. There is no need to include $M$ in your regression; indeed, you will not get the true causal effect of $X$ on $Y$ if you do. In this case, there are subtle "mediation analysis" techniques you can use, such as finding the Total Effect, the Natural Indirect Effect, the Natural Direct Effect, etc. See Causal Inference in Statistics: A Primer, by Pearl, Glymour, and Jewell for more information (Chapter 4 on counterfactuals is the most relevant.)
In your case, you're considering a situation more like this:

You've already got $X,S,$ and $T$ in your regression, and you're wondering if you should include $M.$ In this case, you certainly don't need to include $M;$ its coefficient should be $0,$ anyway, because $M$ and $Y$ are independent, given the variables you're already regressing on.
On the other hand, suppose you have a situation like this:

Let's say you've only included $T$ in your regression until now. That's actually bad, because it opens up the backdoor path (conditioning on $B$ in a collider like $A\to B\leftarrow C$ allows information to flow from $A$ to $C$). So you would want to include something else in your regression to stop the backdoor path. 
