Dear Researchers,
Greetings,

I have quick questions about interaction variables, please.

At first, I am going to examine the effect of specific standards on the financial reporting quality in the same country for industrial firms for the period 2006-2018. The standards issued let’s say in 2006 and firms started adopting the standards voluntarily. In other words, firms that did not adopt in 2006, they adopt in 2007, and those that did not adopt in 2007 adopted in 2008 and so on. I’ve read a lot about the Difference in Differences method (DID) but it seems that this method will not work in my case as the DID approach require control sample (non-adopters), and in my case, all non-adopters become adopters during the period. Now I am confused about which methods I can use.
To illustrate:
Let us assume the following model:
This is the basic model before studying the effect of the standards.
  1. Financial Reporting quality = α0+ β1 size + β2 Audit + β3 Growth + €.
Where:
Financial Reporting quality, size, and growth are scales (ratio) variables while Audit is a binary variable.
Now, I want to examine the effect of the standards on the financial reporting quality as below:
Financial Reporting quality = α0+ β1size + β2 Audit + β3 Growth + β4 GG + β5GG*size + β6GG*Audit+ βGG*Growth+ €.
Where:
GG = are the standards adopted
Q (1) Can I code GG (1) for a firm (X) for the observations under the adoption period and (0) for the same firm but for observation under the old standard period.
Q(2) can I consider those observations that coded (0) under the old standards as a control?
Q(3) Do the following are correct:
β4 capture the effect of the standards on the financial reporting quality and if it is positive means that the average values of financial reporting quality are higher under the new standards than the old standards keeping other factors constant.
β1 Capture the effect of size before the adoption of the new standards
β5 Capture the effect of size after the adoption of the new standards
β1+ β5 Capture the overall effect (before and after).

Thank you very much in advance for your cooperation.