Say I have the following treatment:
\begin{array}{cccccccccc} \hline unit & year & treatment & d^{-3} & d^{-2} & d^{-1} & d^{0} & d^{+1} & d^{+2} & d^{+3} \\ \hline 1 & 2000 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 1 & 2001 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 1 & 2002 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 1 & 2003 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 1 & 2004 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 1 & 2005 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ 1 & 2006 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\ 1 & 2007 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 or 1? \\ 1 & 2008 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 1 & 2009 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 1 & 2010 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 1 & 2011 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline 2 & 2000 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 2 & 2001 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 2 & 2002 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 2 & 2003 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 2 & 2004 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ 2 & 2005 & 1 & 0 or 1? & 0 & 0 & 0 & 0 & 1 & 0 \\ 2 & 2006 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 or 1? \\ 2 & 2007 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 2 & 2008 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 2 & 2009 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ 2 & 2010 & 0 & 0 & 0 & 0 & 0 & 0 & 0 or 1? & 0 \\ 2 & 2011 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 or 1? \\ \hline 3 & 2000 & 1 & 0 & 0 & 0 & 0 & . & . & . \\ 3 & 2001 & 1 & 0 & 0 & 0 & 0 & . & . & . \\ 3 & 2002 & 1 & 0 & 0 & 0 & 0 & . & . & . \\ 3 & 2003 & 1 & 0 & 0 & 0 & 0 & . & . & . \\ 3 & 2004 & 1 & 0 & 0 & 0 & 0 & . & . & . \\ 3 & 2005 & 1 & 0 or 1? & 0 & 0 & 0 & . & . & . \\ 3 & 2006 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 3 & 2007 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 3 & 2008 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 3 & 2009 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ 3 & 2010 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\ 3 & 2011 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ \hline \end{array}
The treatment effect is self-explanatory. Just think of it as some kind of regulation. For unit 1, it turns on in year 2004, but is repelled in 2007 onwards. For unit 2, it comes into effect in 2003, repelled in 2006 to 2007, comes back in 2008, but repelled in 2010.
For unit 3, the same applies but the regulation is already in place at the start of the sample period. Another key detail is that we don't know when the regulation came into effect, i.e., it could be 1999 or it could be 1979, we do not know any information outside the sample period.
Estimating the generalized diff-in-diff here is also pretty straightforward, there have been many discussions on this, one particular example similar to mine is here. However, my question is how can I estimate a dynamic (i.e., event study) version of this non-staggered diff in diff when the treatment can turn on and off? That is, what should the dummy variables $d^{-3}$ to $d^{+3}$ be? I have filled in the matrix as best as I can, but there are a few question marks as follows:
For unit 1 year 2007: Should $d^{+3}$ be 0 or 1 here? The regulation is already repelled in 2007, meaning technically $d^{+3}$ should be 0 right? If the regulation was still in place until 2008, then $d^{+3}$ should be 1, am I correct?
For unit 2 year 2005. Should $d^{-3}$ be 0 or 1 here? I am leaning towards it being 0 since this is still two years after 2003, meaning it is still the "post" period relative to the 2003 introduction of the regulation. How about the other question marks for unit 2?
For unit 3, since we don't know when the regulation came into effect then $d^{+1}$, $d^{+2}$, and $d^{+3}$ should all be missing from 2000 to 2005 right? If we had information outside the sample period, for example, the regulation came into effect in 1999, then we could fill in $d^{+1}$, $d^{+2}$, and $d^{+3}$. But as it stands, we can't. Am I correct?
