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When trying to satisfying the paralell assumption in Difference-in-Differences setting, I have the equation:

$$ y_{kt} = \alpha_k + \lambda_t + + \delta_{-4} d_{k,t-4} + \delta_{-3} d_{k,t-3} + \delta_{-2} d_{k,t-2} + \delta_{-1} d_{k,t-1} + \delta d_{kt} + \delta_{+1} d_{k,t+1} + \delta_{+2} d_{k,t+2} + \delta_{+\bar{3}} d_{k,t+\bar{3}} + \epsilon_{kt}, $$

So, to satisfy the parallel equation, as suggested by Miller, 2021, Table 3, we can do a joint test that $d_{k,t-i}$ {i=1;4} equal to 0.

What I tried is: From my understanding, if p-value of joint test is higher than 0.1, we can say that there is no significant difference between treatment and control value in average.

However, when using STATA, I have the joint test code andthe result is as below, I do not know how to read the result because there is no t-stat or p-value here.

    . test (dkt_4=0) (dkt_3=0) (dkt_2 = 0) (dkt_1 = 0)

 ( 1)  dkt_4 = 0
 ( 2)  dkt_3 = 0
 ( 3)  dkt_2 = 0
 ( 4)  dkt_1 = 0

       F(  4, 25334) =    4.48
            Prob > F =    0.0013
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1 Answer 1

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There is no t-statistics because you are using F-test, with F-statistics. Also you do get p-value, p-value is the probability value of obtaining test results at least as large as the results actually observed, under the assumption that the $H_0$ is correct. So in your case 0.0013.

Consequently, you should reject the null of your test and thus the parallel trend assumption is clearly violated and you should not use DiD.

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  • $\begingroup$ Thanks a lot , @1muflon1. So, form my understanding here (1) Does Prob >F equal to p-value? and (2) The null hypothesis is that coefficients of dkt_i are jointly equalling to 0, so in this case, the p-value is smaller than 0.01 (0.0013), therefore, the null hypothesis cannot be rejected in this case, leading to that the joint test failed, so the parallel trend assumption is violated here? $\endgroup$ Commented Aug 9, 2021 at 8:39
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    $\begingroup$ @NoviceMindset 1. yes, that’s the p value. No if p-value is smaller than 0.01 you can not only reject the null but you already reject it at 1% level (e.g. equivalent of $^{***}$). So the null is rejected. Also as I understood from your text when null is rejected parallel trend is violated $\endgroup$
    – 1muflon1
    Commented Aug 9, 2021 at 8:50
  • $\begingroup$ I got it, thanks a heap, @1muflon1 $\endgroup$ Commented Aug 9, 2021 at 8:52
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    $\begingroup$ @NoviceMindset In Table 3, they use a joint null test in the “post-treatment” period, not the pre-treatment period. The “leads” refer to the periods after body-worn camera acquisition, at least it is according to the description provided in the paper. It doesn’t affect the answer given by 1muflon1 (+1), but make sure you know whether you’re using the test in the pre-period or the post-period. The difference isn’t trivial. $\endgroup$ Commented Aug 9, 2021 at 21:55
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    $\begingroup$ It's still correct. $\endgroup$ Commented Aug 10, 2021 at 20:39

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