F-test after regression with FEs and clustered standard errors

[David Tsu]

Hi,

I run an OLS regression with firm-year panel dataset:

reghdfe y x1 x2 x3 controls, a(firm year) vce(cluster industry)

After running the regression, I use a F-test to test null hypothesis H0: x1=x3=x3=0

testparm x1 x2 x3

Since standard errors are clustered at industry level, compared with the case of no clustering, the F-test has a very small DoF. In some case, this F-statistic is way larger than the version without clustering. How should we interpret these results, and which version should I use?