F-test / Wald Test discrepancy

[phoenix1914]

Hello all

I have one question regarding the Wald Test in Eviews. I have the following regression: Y = β1 + β2Χ2 + β3Χ3 + β4Χ4 + β5Χ5 + β6Χ6 +u , and 145 observations .

I want to test the hypothesis that β3=β4=β5=β6=0 .

When I do manual calculation of F statistic (for 4,139 df) my result is ~2.77 . I calculating it using the R-square from the unrestricted equation and the R-square from the restricted.

But when I use the built-in Wald Test in Eviews my result is 2.11 . Do you know why there is this discrepancy?


Interestingly enough when I run a different regression (different sample and variables) and I test the hypothesis β2=β3=0 I get same results using the manual calculation and Wald Test.

[startz]

You'd have to post both sets of information for anyone to compare them.

As a wild guess, the sample changed when you did it manually.

[phoenix1914]

Thank you Startz. Let's ignore the second example I mentioned, since it might complicate the matters. I will provide more details on the issue I have.

In the first screenshot below I run a multiple regression, let's consider it as the unrestricted one. The r-square is 0.432632 . What I want then is to test the hypothesisβ3=β4=β5=β6=0 . One way is to run the Wald-test and the result of the F statistic is what I posted above.



The second way is to calculate manually the following statistic F= [(Rsquare-unrestricted - Rsquare-restricted)/ (k-1)] / [Rsquare-unrestricted/(n-k)]

where Rsquare unrestricted can be found above. The r-square restricted can be obtained by running another regression keeping only β1 and β2 and can be found here, Rsquare = 0.398089.




If I use the R-squared from the above outputs and use the manual formula, for 4,139 d.f., the result I obtain is 2.774573. Which is very different from the result of the Wald-test.

Let me know if you need further clarifications and many thanks in advance for any help!

[phoenix1914]

I found it..my manual formula had an error. The denominator is (1-R-square) and not purely R-square.

[startz]

I think your R^2 formula is wrong. Maybe the k-1 should be the number of restrictions, r