# Finding SSE when ignoring a parameter in estimation

The model is $$Y=XB+Zy+e$$ where $$B$$ and $$y$$ are unknown parameters and $$e\sim \text{N}(0,σ^2 I)$$.

Using ordinary least squares and ignoring $$Z$$ in parameter estimation, I need to find the distribution of SSE obtained from the misspecified model. Can anyone show me the process? I am struggling with how to set up the problem or go about solving it.

We know that SSE/$$\sigma^2$$ follows chi square distribution when the model is specified correctly. It is hard or impossible to derive the distribution of SSE obtained from the misspecified model.