Linear regression / correlation question

Question

Thinking about the following problem this morning:

Suppose $X(n) = a_0 + a_1 * Y(n) + e(n)$, basic linear causation with some iid noise $e(n)$.

Also suppose $Z(n) = b_0 + b_1 * Y(n) + f(n)$, that Y is correlated with $Z$.

Now... suppose you just want to get $X$ and $Z$ together and try an OLS: $X(n) = g_0 + g_1 * Z(n) + r(n)$.

So what I'm wondering is:

1. What information is lost in ignoring $Y$? i.e., are any statistical crimes being committed here?
2. How would I estimate $g_1$?