Difference-In-Difference's control group I have a problem with the Difference-In-Differences' control group.
In particular I have data from 2001 to 2015 and the problem rises because the timings of the treatment period can start from 2006 (till 2015) but is different for the different treatment group's elements. In this case the dummy variable that represent the treatment period can vary in the treatment group (in my case, it will be 1 for each firm (i) that does IFRS reporting in year (t), but what happens to the same time variable for the control group?
I don't think that it could be right if the time variable will always be zero for the control group, but I could be wrong... so, should the time variable (for the control group) be 1 from 2006 to 2015 (the represent the period when the treatment starts, even if not for the whole treatment group?
Please help me and thank you.
 A: Your basic model is the standard DID setup, so it is fine I think. Your actual question and therefore this answer focusses on the timings of the treatment period being different for different companies. 
This is doable if you specifiy the interaction term for the treatment effect to use a year indicator for the actual year of the IFRS implementation for a given firm, instead of just an interaction between year and firm. Let $D_{it}$ be an indicator variable for when firm $i$ does IFRS reporting in year $t$. You get the following (in your notation):
$Y_{it}=\beta_0+\beta_1 IFRS_{it} + \beta_2 Time_{it} +\beta _3 (IFRS_{it} * D_{it} ) + Variables + \epsilon_{it}.$
Note that (despite notation) the variable $IFRS_{it}$ is time invariant, $Time_{it}$ is only time variant, $D_{it}$ is both time and firm variant and thus $D_{it} * Time_{it}$ is as well. 
Another option might be
$Y_{it}=\beta_0+\beta_1 IFRS_{it} + \beta_2 D_{it} +\beta _3 (IFRS_{it} * D_{it} ) + Variables + \epsilon_{it},$
in which we replaced the time period variable to conincide with $D_{it}$. This assumes that all years leading up to IFRS are similar for the firms, which be what you want, or maybe not. 
If you have enough data, you could perhaps also combine time periods such that all firms which eventually adopt IFRS do so in the same year. This avoids the problem of different treatment timings altogether.
