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I have the following model:

$Y_i=\beta_0 + \beta_1 X_i + \beta_2 D_i + \beta_3 (D_i*X_i) + \epsilon_i$

where $D_i$ is a dummy variable

I want to understand if it is desirable do keep the variable $D_i$ inside the model (if it has an effect on the $y$)

I would do the following test on parameters: $H_0: \beta_2= \beta_3=0$ vs $H_1$: at least one is not $0$

If I accept $H_0$, I remove $D_i$ from my model.

The test I just mentioned, is a test on a group of parameters (test F). Is it in some way different from the Chow test?

In other words, after doing the test previously mentioned, it is important to consider also the chow test? it would give me other / different information?

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    $\begingroup$ Hi: Here's an intro to the Chow-test. Note that the standard F-test in OLS regression is very different from the Chow test so I wouldn't try to relate them.. The only similarity is that you also look up the critical value using the F-distribution when making the decision in the Chow -test. statisticshowto.com/chow-test $\endgroup$
    – mlofton
    Apr 19 at 20:37
  • $\begingroup$ Ok probably I asked the question in a wrong way. Focus on the last part: I mentioned a test in my test: if I accept H0, I remove Di from the model. If I accept, instead, the H0 of the Chow Test, the conclusion is the same ( I remove Di from the model ) or the conclusion is another one? (practically speaking) @mlofton $\endgroup$ Apr 19 at 21:38
  • $\begingroup$ What you wrote may be an alternative formulation for how to do the Chow-test. I'm not familiar with that formulation but , according to the link I sent , you don't need a $D_{i}$. You just do two different regressions, calculate the statistic and compare it to the critical value. The result tells whether the coefficients are the same over the two periods. If they are, then one concludes that there is no structural change. $\endgroup$
    – mlofton
    Apr 20 at 20:17
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    $\begingroup$ Look at these lecture notes, there you could find derivation of Chow test from the F test statistics. $\endgroup$ Aug 31 at 11:10
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The test I just mentioned, is a test on a group of parameters (test F). Is it in some way different from the Chow test?

What you describe is precisely the Chow test. Indeed the Chow test can be viewed as an a particular case of usual F-test.

However, stating that I suppose that your dummy split the data around a relevant date, it is not a good idea to say something like "... [dummy] has an effect on $y$". What you are interested in is the presence of break in the data. The formalization of break is in the null hypothesis. Dummies are only auxiliary variables.

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