Dear all,

I have a panel dataset organised by cell and quarter. My main regression is the following
xi: reghdfe y x1 x2 x3, a(cell quarter) vce(cluster cell quarter)

I want to include an additional fixed effect, namely a postcode fixed effect. Therefore, I did
xi: reghdfe y x1 x2 x3, a(cell postcode quarter) vce(cluster cell quarter)
For comparison, I also performed the following:
xi: reghdfe y x1 x2 x3 i.postcode, a(cell quarter) vce(cluster cell quarter).
I get the same coefficient, the same number of observations and R-squared. However, I got a different level of significance.

I was not expecting this. What could explain this difference in the level of significance and which one is the more correct approach?

Thank you!