TITLE: How to interpret a sum with two indices?
QUESTION [9 upvotes]: Could anyone please break the following down for me? 
$$\sum_{i,t}y_{i,t-2}e_{it}=0$$
I am familiar with $\sum_{i}$ and also $\sum_i\sum_t$. But I have not seen the above before. I will appreciate if someone could explain the first equation. Thanks in advance.

REPLY [4 votes]: While Klirk offers a definition that is useful for this particular case, I think it is more instructive to interpret this more generally:
$\displaystyle\sum_{i,j}$ essentially means is shorthand for $\displaystyle\sum_{(i,j)\in D\times D'}$ where $D$ and $D'$ are the 'omitted' domains over which the summation is performed (often, $D=D'$), i.e. there is a term for each pair from $D\times D'$. 
This more general interpretation becomes useful when $D$ and $D'$ are defined depending on each-other in a non-trivial way. While that can still be reduced to a form of $\displaystyle\sum_i \sum_j$, the latter form can become 'ugly', compare: $\displaystyle\sum_{i,j: \text{$i+j>0$}}$ with $\displaystyle\sum_{i}\sum_{j: i+j>0}$. The first is clearer, as it directly shows what domain we work on and doesn't require the convention that empty sets sum to $0$ (which can occur if the domain for $i,j$ is $\{-2,-1,0,1,2\}$, for instance).