Wald-test & T-test confusion

#1
Hi,
I'm trying to test the linear restriction b1-b2=0 in my MNL-Modell to find if the coefficients b1 and b2 are equal or not.
My Wald-statistic has a value of 30.46 and my text-book tells me that with Wald-values exceeding the critical chi-squared value (here 3.84) I can assume that the coefficients are equal.
This confuses me because with the T-test values exceeding the critical t-value result in rejecting the Ho (which is b1-b2=0) and I have to assume that b1 and b2 are different.
Can anybody pitch me his ideas and thoughts on this?

alex
 
#2
Hi alex,

In order to test for Ho: β1 -β2=0 you cannot use the individual t statistics for β1 and β2 (estimates). The t statistic is calculated like this t=(β1-β2)/se(β1-β2). The βi used in the t statistic are all estimates and not actual β. Hope this helps!
 

fed1

TS Contributor
#3
I cant remember the details, but the wald test is less efficient(not as good) because of the way it estimates the variance.

Wald is asymptotically efficient.

Do you know what exact formula is for denominator of wald in this case?

I cant remember/too lazy to look up.
 

Dragan

Super Moderator
#4
Hi,

My Wald-statistic has a value of 30.46 and my text-book tells me that with Wald-values exceeding the critical chi-squared value (here 3.84) I can assume that the coefficients are equal.

Can anybody pitch me his ideas and thoughts on this?

alex
Well, yes I can.

Either you are misinterpreting the (perhaps entire) discussion in your textbook or the authors of this textbook are wrong.

So, which is it?...you tell me.