Stacking up panel data to use OLS over it

Question

I'm posting this question for someone. He has the model:

(1) $Y_{it} = a + b X_{1,it} + c X_{2,it} + d X_{3,it} + e_{it}$

$i = 1,2,...,N;\phantom{...} t = 1,2,3,4,5,6,7$

Variables are approximately normal and we suspect no violation in OLS assumptions. The coefficient estimates are not subscripted with $i$ because the intention is to get panel-like estimates. $t$ represents a year and $i$ represents a company. Instead of using pooled OLS he wants to stack up the data. So, if we consider the matrix $\bf{Y}$ with number of rows $N$ and number of columns $7$ where $Y_{it}$ is some element in $\bf{Y}$ $\forall i \wedge \forall t$, he wants to stack this such that it's a $7*N$ row, $1$ column vector as the response variable to be estimated in usual cross-sectional OLS (after doing the same for the design matrix, of course).

Is this bad? (Looking for general answers on its weaknesses, or whether it's fine).

Answer 1

Standard panel data representation assumes $Y=[y_{it}]_{i=1,...N,t=1,...,T}$ this is a $NT $ rows vector. So your representation is an orthodox one. As long as your matrix representation retrieves your NT equations, then it's ok.