F-test interpretation

[Jack Benhayon]

I am running restricted F tests on diff-in-diff regressions to evaluate the effect of a government health initiative. I am using the testparm command and I am trying to understand how the tests should be interpreted when I use the command

testparm educ#postt

( 1) 13.educ#1.postt = 0
( 2) 13.educ#2.postt = 0
( 3) 14.educ#1.postt = 0
( 4) 14.educ#2.postt = 0
( 5) 15.educ#1.postt = 0
( 6) 15.educ#2.postt = 0
( 7) 16.educ#1.postt = 0
( 8) 16.educ#2.postt = 0

F( 8, 55986) = 1.09
Prob > F = 0.3696

versus

testparm educ##postt

( 1) 1.postt = 0
( 2) 2.postt = 0
( 3) 13.educ = 0
( 4) 14.educ = 0
( 5) 15.educ = 0
( 6) 16.educ = 0
( 7) 13.educ#1.postt = 0
( 8) 13.educ#2.postt = 0
( 9) 14.educ#1.postt = 0
(10) 14.educ#2.postt = 0
(11) 15.educ#1.postt = 0
(12) 15.educ#2.postt = 0
(13) 16.educ#1.postt = 0
(14) 16.educ#2.postt = 0

F( 14, 55986) = 2.28
Prob > F = 0.0040

. Using 2 hashtags tests not only the interaction terms (12.education#1.post, 13.eduction#1.post, and so on) but also the coefficients on education and post themselves. How should my interpretation of the results change based on whether or not these additional coefficients are included in F-test, and which is likely a better test to run? Thank you.

[Clyde Schechter]

The test with the single # tests the hypothesis that there is interaction educ and postt. Otherwise put, it tests the hypothesis that the effect of educ on whatever your outcome variable is, varies according to the value of postt, and vice versa.

The test with the double ## tests the hypothesis that your outcome variable is independent of any joint effects of educ and postt.

As for which is better, these are tests of two different hypotheses. So it depends on what your research question is. Pick the one that matches your research question.