I am working with a dataset where the dependent variable is $y$ (level of use of a line of credit) and the key independent variables are $x_1$ and $x_2$ (two different types of interest rates).
Some lines of credit have both types of rates and, hence, $x_1$ and $x_2$ have values. Other lines of credit have just one of the rates (say, e.g., the first one) and $x_1$ has a value whereas the value in $x_2$ is missing. In addition, interest rates may occasionally be $0$.
Therefore, I have two problems:
If I regress y on $x_1$ and $x_2$, I lose those observations where, e.g., $x_1$ has value but $x_2$ has a missing value, although it is missing, not because I do not know the value, but because the line of credit does not include the second interest rate. Does anyone know a sound way of solving this problem? I have thought of replacing missing values with $0$. Would this be correct? Does it matter the fact that interest rates themselves can be $0$?
The second problem arises because I also use interaction terms of the form, e.g., $x_1d$, where $d$ is a dummy variable that is either $0$ or $1$. Since $x_1$ can be $0$, the interaction term can be $0$ not because $d = 0$, but because $x1 = 0$. Can anyone help me to solve this? I have thought of adding a small value (say, $0,001$) to $x_1$ and $x_2$. Does this affect the results?