Specification bias - estimated variance is biased estimator of true variance of error term Consider the two models $ (a)  y = X\beta + u $ where $X$ is $n \times K$ and (b) $y = Z\gamma + \omega $ where $Z$ is $n \times r$.
Under classical assumptions (and $Z$ and $X$ are non-stochastic) if model (a), that is $y = X\beta + u$ is the true model, show that $E(\sigma^{2}_{\omega}) \geq \sigma^2_u$ and explain the implication of your result.

I can do it in two cases when $r&gt;k$ (overfitting) or when $r&lt;k$ (underfitting). 

Is there any short way of doing this, without cases (because for both overfitting and underfitting variance is biased)? So, what I am asking is that can they be clubbed so that result doesn't depend on relationship between $r$ and $k$?
If the model $ (a)  y = X\beta + u $ is true, then $\omega = u + X\beta - Z\gamma $ in $(b)$, and the claim follows.