Unintuitive Wald Test Results

[Dave_the_Forecaster]

Hi,

I have estimated an equation with the following results:

Variable | Coefficient | Std. Error | t-Statistic | Prob.

C(1) | 0.125698 | 0.157044 | 0.800397 | 0.423700
C(2) | 0.765549 | 0.851063 | 0.899522 | 0.368700
C(3) |-0.163058 | 0.320517 |-0.508735 | 0.611100
C(4) |-0.003991 | 0.106239 |-0.037570 | 0.970000
C(5) |-0.464766 | 0.245652 |-1.891971 | 0.058900
C(6) | 8.757433 | 10.08753 | 0.868144 | 0.385600

To me, this means that all of the variables are effectively zero except for variable 5.

I want to test the hyposthesis that all of the variables are zero.
So, when I perform a Wald test with the restriction c(1)=c(2)=c(3)=c(4)=c(5)=c(6)=0, I get a p-value from the F-test of 0.064 (as expected)

However, if I exclude variable 5 from the Wald test restriction (ie. test the statment c(1)=c(2)=c(3)=c(4)=c(6)=0) I get a p-value of 0.05

Basically, by excluding each variable in turn I discovered that it is variable 4 (the variable which seems closest to zero in the estimation) which is causing the rejection of the null-hypothesis in the Wald test.

Can somebody with better stats knowledge than me explain why this is happening?

[startz]

You probably have substantial multicollinearity. The regression knows that the variables collectively matter, but can't separately tell which one(s) are really nonzero.

[Dave_the_Forecaster]

Thanks for replying.

So I shouldn't be drawing any conclusions from the individual t-statistics, rather, I should only trust the 'collective' results of the Wald test?

[startz]

Thanks for replying.

So I shouldn't be drawing any conclusions from the individual t-statistics, rather, I should only trust the 'collective' results of the Wald test?

That's probably right. At least if the variables you have are all measures related to some common phenomenon.

[EViews Gareth]

One of those cases where "Non-normality and collinearity are problems!"