<p>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 <span class="math-container">$H_0$</span> is correct. So in your case 0.0013.</p>
<p>Consequently, you should reject the null of your test and thus the parallel trend assumption is clearly violated and you should not use DiD.</p>

CC BY-SA 4.0
2021-08-09T08:39:38.950Z
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?
Phil Nguyen
CC BY-SA 4.0
2021-08-09T08:50:44.870Z
@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
1muflon1
CC BY-SA 4.0
2021-08-09T08:52:10.347Z
I got it, thanks a heap, @1muflon1
Phil Nguyen
CC BY-SA 4.0
2021-08-09T21:55:39.240Z
@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.
Thomas Bilach
CC BY-SA 4.0
2021-08-09T23:58:49.353Z
Thanks a lot, @ThomasBilach . so do you mean that the way I conduct the test as above still correct ? (testing joint null hypothesis that average of coefficients of dkt_i equal to 0) ?
Phil Nguyen
CC BY-SA 4.0
2021-08-10T20:39:04.373Z
It's still correct.
Thomas Bilach
CC BY-SA 4.0
2021-08-09T08:30:02.080Z
2021-08-09T08:30:02.080Z
1muflon1
<p>When trying to satisfying the paralell assumption in Difference-in-Differences setting, I have the equation:</p>
<p><span class="math-container">$$
y_{kt} = \alpha_k + \lambda_t + + \delta_{-4} d_{k,t-4} + \delta_{-3} d_{k,t-3} + \delta_{-2} d_{k,t-2} + \delta_{-1} d_{k,t-1} + \delta d_{kt} + \delta_{+1} d_{k,t+1} + \delta_{+2} d_{k,t+2} + \delta_{+\bar{3}} d_{k,t+\bar{3}} + \epsilon_{kt},
$$</span></p>
<p>So, to satisfy the parallel equation, as suggested by <a href="https://link.springer.com/article/10.1007%2Fs10940-021-09513-w" rel="nofollow noreferrer">Miller, 2021, Table 3</a>, we can do a joint test that <span class="math-container">$d_{k,t-i}$</span> {i=1;4} equal to 0.</p>
<p>What I tried is:
From my understanding, if <strong>p-value</strong> of joint test is higher than 0.1, we can say that there is no significant difference between treatment and control value in average.</p>
<p>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.</p>
<pre><code>    . 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 &gt; F =    0.0013
</code></pre>

<econometrics><stata>
What are the hypothesis and results explaination of joint null test?
Phil Nguyen
# What are the hypothesis and results explaination of joint null test?

(Asked by: username_0 on 2021-08-09)

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](https://link.springer.com/article/10.1007%2Fs10940-021-09513-w), 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

```

**Tags:** econometrics, stata


---

## 1 answers

### Answer by username_1 on 2021-08-09. Score: 2 | Accepted answer

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.

> **Comments:**
> **username_0**: Thanks a lot , @username_1. 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?  
> **username_1**: @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  
> **username_0**: I got it, thanks a heap, @username_1  
> **username_2**: @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 username_1 (+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.  
> **username_0**: Thanks a lot, @username_2 . so do you mean that the way I conduct the test as above still correct ? (testing joint null hypothesis that average of coefficients of dkt_i equal to 0) ?  
> **username_2**: It's still correct.  

---

