F-test?

[John Ljung]

Hi,

I am running the following regression in Stata where I am testing whether the elasticity becomes closer to unit elasticity after the financial crisis:

c_{i s t}=B₀+ B₁c _{ea s t} + B₂crisis_t + B₃crisis_t*c_{EA s t} + u_{i s t}

c_{i s t = output for country i}
c_{EA s t = output for euro area average
crisis = dummy variable equal to 1 after the onset of the financial crisis}

I am interested in whether the sum of B₁ and B₃ is significantly closer to 1 compared to B1. I thought that I could use an f-test with two null hypothesis and to see whether the p-value is higher for (2) to indicate that the sum is closer to 1. However, I realise this in not optimal because it says nothing about significant change.

(1) H₀: B₁=1
(2) H0: B₁ + B₃=1

I would appreciate any feedback on how to conduct the test!

Best,

John

[Clyde Schechter]

Well, the change is just estimated by B3, and you can read its significance off the regression output directly. Whether the change brings you closer to 1 than B1 is a different matter. You could have a significant change in the wrong direction, or a change in the right direction so large that it "overshoots" and you end up farther away from 1.

[John Ljung]

Thanks! Yes, I am aware that B3 measures the change. But as you say an, e.g., positive change can be "good" or "bad", depending on the value of B1. Given that I am interesting in whether elasticity (B1+B3) moves closer to 1, I thought it was not sufficient to just simply look at whether B3 changes significantly.

Is it then correct to look at the cases where B3 changes significantly and compare it with B1?

[Clyde Schechter]

As you showed an abstract model, and not actual Stata regression code, I can't show you exactly how to do this. But you probably want to look at -nlcom-

nlcom abs(B3+B1-1)-abs(B1-1)

where instead of B3 and B1 you will have to use the corresponding _b[whatever] notation from your regression. (If you are not sure how to specify the _b[] notation, rerun the regression specifying the -coefl- option.)

[John Ljung]

Thank you Clyde! That was very useful input and code.

Do you know any way to include the p-value for both the one-sided alternatives and two-sided alternativ.

[Clyde Schechter]

Well, Stata gives two-sided tests. If you want the one-tailed p-value then you can just divided the two-tailed p-value by 2.

[John Ljung]

Thanks! Yes, that's what I did, mainly interested in whether there is an "automatic" solution.

[Clyde Schechter]

Not that I know of.