Background:
I have the cross-sectional model:
$Y_{i} = a + b X_{1,i} + c X_{2,i} + d X_{3,i} + e X_{4,i} + \nu_i$.
The application is corporate finance. So each $Y_i$ is something like the change in return on assets over a 1 year period for firm $i$, and the regressors are typical corporate finance variables.
In corporate finance, very small values of $R^2$ are common, even sometimes $1\%$. My $R^2$ is around $1\%$ but my Adjusted $R^2$ is $-0.2\%$.
I have never seen papers report negative Adjusted $R^2$ but this could just be because they omit the publication of their adjusted $R^2$ when they see that it is negative.
Question
Is there some problem when the adjusted $R^2$ is negative?
Best Answer
The formula for adjusted R square allows it to be negative. It is intended to approximate the actual percentage variance explained. So if the actual R square is close to zero the adjusted R square can be slightly negative. Just think of it as an estimate of zero.