What's the convention for indices that are not specified?

[amrods]

In the paper you index beta and delta with negative indices for pre-treatment periods, and with positive indices for post-treatment periods. So, when constructing Delta^{SD}(M) for example, which includes expressions with delta_{t-1}, and delta_{t+1}, what is the convention for indices that are not defined? ie, how do I interpret expressions like delta_0, delta_(upperT+1), or delta_{lowerT-1}?

[asheshrambachan]

The number of pre-periods (lowerT) and number of post-periods (upperT) are given by the user/application. So, in Section 2.4 of the draft, we define delta = (deltapre, deltapost) with delta_0 normalized to zero.

[amrods]

I'm just skipping restrictions that involve periods outside [lowerT, upperT].