Interacting an independent variable with fixed effects

Dear Statalist members,

Thank you so much for reading this post and helping me answer my question! In short, my question is how I can run a regression in Stata which contains not only fixed effects, but also the interaction of an independent variable with the fixed effects. I will explain the details below.

I am trying to replicate a paper which examines how the stock price reaction to earnings (a.k.a. earnings response coefficient) changes after a certain regulation was introduced. It is a classic difference-in-differences design complicated by the fact that the variable of interest is not a stand-alone variable but the coefficient obtained from a regression.

Specifically, the earnings response coefficient is the "b₁" coefficient in the regression below:
CAR _i,t = b₀ + b₁* UE i,t + bm* Controls i,t + e_i,t
where
CAR _i,t is the stock return around earnings announcement, for company i and year-quarter t;
UE i,t is the earnings being announced, for company i and year-quarter t;
Controls i,t is a list of control variables.

The regression I am trying to run is specified as follows (Table 3 in the attached paper https://www.sciencedirect.com/scienc...300417#bib0026):
CAR= b₀ + b₁* UE*Post*Treat + b2* UE + b3* Treat + b4* Post + b5* Treat*Post + b6* UE*Post + b7* UE*Treat
+ bm* Controls + bn* UE*Controls + Year-quarter fixed effect + Industry fixed effect + UE*Year-quarter fixed effect + UE*Industry fixed effect

In Stata 14, I tried to run the following code:
reghdfe car ue_post_treat ue ue_treat ue_post controls ue_controls, ///
absorb(industry yearquarter ue_industry ue_yearquarter) vce (cluster announcement_date)

The regression ran, but "ue" was omitted due to collinearity. This is expected because "ue_industry" = ue*i.industry and "ue_yearquarter" = ue*yearquarter are obviously collinear with "ue". This brings me to my questions:

1. Is my regression correctly specified? The paper cited above mentioned that they included the "interactions of UE with year-quarter fixed effect and industry fixed effects" and Table 3 also shows "UE*fixed effects", but does that actually mean taking the product of the year-quarter (or industry) dummy and UE? I am really confused as that seems to inevitably result in collinearity problems.

2. Suppose my specifications are correct, how should I run this regression in Stata (or other softwares)? In the paper, none of variables were omitted due to collinearity, so it is definitely achievable. Is there any other command I should use to run this regression?

Again, thank you so much for your help, I truly appreciate any suggestions or reference to any post or paper that addresses a similar problem.