I am not sure if the title makes sense. Here is my situation.
I am running a regression as below:
$$ y = \alpha_0 + \alpha_1 T_1 + \alpha_2 Z + \epsilon $$
Where $T_1$ is my interested covariate: a binary variable of whether the company listed volunteer as an activity in 2008.
I am interested to see if introducing volunteer since 2002 to 2008 will affect the outcome $y$.
I want to break $T_1$ into two variables (and I have the data): $T_2$: whether the company has introduced volunteer activity since 2002 to 2008, and $T_3$: whether the company had volunteer at the beginning.
So basically $T_2 + T_3 = T_1$. So I am worried that $T_2$, $T_3$ and $T_1$ are correlated each other (but when I run correlation test, the correlation coefficient is very small at about $-0.1$)
What happen if I do that? Does this cause collinearity? Can you please tell me if any of these regressions will have problem?
$$ y = \alpha_0 + \beta_1 T_2 + \beta_2 T_3 + \alpha_2 Z + \epsilon \ \ \ \ \ \ \ \ (1)$$ $$ y = \alpha_0 + \beta_1 T_2 + \alpha_1 T_1 + \alpha_2 Z + \epsilon \ \ \ \ \ \ \ \ (2)$$
Edited: As suggested by @EdM I posted my regressions after the answer.
I use Stata 13. numbacty is my outcome of interest and I use nbreg (negative binomial regression) as my estimator.
Which one is better? And can someone please give me some interpretation?
The picture below is my Equation 1. initialhiv is $T_3$, that is, having volunteer from the beginning. introhivservice is $T_2$, that is, having introduced volunteer since 2002 to 2008
The picture below is the regression after using 3-level categorical factor. Here levelactyhiv takes the values of 0, 1, 2 if the company has no volunteer, has volunteer from the beginning and having introduced volunteer since 2002 to 2008.