I have regression results about the effect of a treatment on two outcome variables, $N$ and $D$.

The coefficient on $N$ is positive. The coefficient on $D$ is negative.

These results suggest that the effect on $\frac{N}{D}$ should be positive. The treatment increases the numerator, and decreases the denominator.

However, when I create a new variable $\frac{N}{D}$ and use this as an outcome variable, I get an negative coefficient on $\frac{N}{D}$.

I don't understand why this is happening. Full setup below.

I have an experiment in a panel data setting. All subjects are viewed twice (once pre- and once post- treatment). Between the two periods, randomly selected subjects are treated with a binary variable. The control group remains untreated.

I have two outcome variables, $N_{i,t}$ and $D_{i,t}$. Both underlying $N$ and $D$ variables are strictly positive.

I'm estimating regressions as:

$Outcome_{i,t}=\beta_{T}\times Treatment + TimeFEs + SubjectFEs+\epsilon$

Where:

- TimeFEs = Time Fixed Effects (binaries variables for before/after)
- SubjectFEs = Subject Fixed Effects (binaries for each subject).

The treatment coefficient ($\beta_{T}$) is positive for $N$, and negative for $D$.

However, when I create a new variable for each observation (call it "$R_{i,t}$" = $\frac{N_{i,t}}{D_{i,t}}$) and use it as the outcome, I get a negative treatment coefficient.

- Serverfault Help
- Superuser Help
- Ubuntu Help
- Webapps Help
- Webmasters Help
- Programmers Help
- Dba Help
- Drupal Help
- Wordpress Help
- Magento Help
- Joomla Help
- Android Help
- Apple Help
- Game Help
- Gaming Help
- Blender Help
- Ux Help
- Cooking Help
- Photo Help
- Stats Help
- Math Help
- Diy Help
- Gis Help
- Tex Help
- Meta Help
- Electronics Help
- Stackoverflow Help
- Bitcoin Help
- Ethereum Help