How to estimate the "effect of an effect" identified through regression? Suppose I estimate the effect of some variable $X_t$ on $Y_t$. Let's say that $X_t$ is some firm variable (age of CEO in year $t$ or something like that), and $Y_t$ is a firm's change in investment in year $t$ (so, we are trying to see how $X_t$ influences investment in firms). Suppose that this analysis is done properly, and all the correct variables are controlled for etc. etc.
Now, suppose I find that $X_t$ has a positive effect on $Y_t$, on average. I want to find out whether this increase in $Y_t$ increases firm value, $Z_t$. That is, I want to estimate how $Z_t$ changes through the change in $Y_t$ caused by $X_t$.
How do I go about doing this? Is it sufficient to regress $Z_t$ against $X_t$? What if there are other channels through which $X_t$ impacts $Z_t$? 
I apologize if this is a very basic question, or if it is not well-defined/too broad. Please let me know if I can clarify this further.
 A: Given what you want to estimate (the effect of $Y$ and $Z$) and how you want to estimate it (by using the variation of $Y$ induced by another variable $X$), you are actually quite close to the instrumental variable (IV) framework. A canonical reference to this framework is Angrist, Imbens and Rubin (1996). 
In the IV framework, you assume that $X$ (using your notations) is an instrumental variable, and is only acting on the outcome $Z$ through the treatment variable $X$. It is an assumption, and it is an untestable one. Another assumption, testable this one, is that $X$ is indeed correlated with $Y$ (which you mention you are ready to assume in this case). Under these two assumptions, you can compute an IV estimator of the effect of $Y$ on $Z$. The simplest one, conceptually, is the two-stage least-square estimator. In the first stage, you regress the treatment $Y$ on the instrument $X$. You collect the predicted values $\bar Y$ from this first regression. In the second stage, you regress $Z$ on the predicted $\bar Y$. The idea is that you only use the variability in the treatment that comes from the instrument. 
