Hi
I have a panel of roughly 1000 firms across 10 years (2004-2013) in 2 states in the US (CA and PA). These firms adopt a technology at different years during the panel. However, firms in CA start getting audited in 2006 and in PA in 2009. Firms can adopt the technology either before the audit or after the audit.

In our analysis, we are trying to study if the technology and the audit have any impact on the output. The model that we are running is as follows:

reghdfe output 1.technology##1.audit , absorb(firm_id year)

We are interested in the effect of technology on output both before and after the audit (and posit that the technology may be used in different ways under and outside the audit - hence the interaction term). So one way to get the econometric effect is to examine the interaction term in the above model. Can we also run the following code:

reghdfe output 1.technology if audit ==0 , absorb(firm_id year)
reghdfe output 1.technology if audit ==1 , absorb(firm_id year)

This will also give us the effect of technology both before and under the audit. However, what would be the difference in the interpretation of the coefficients between the two approaches?