Problem with Kao cointegration test

[Fructuoso]

Dear all,

I have run a Kao Panel Cointegration Test in Eviews 8. I have seen on the help the formula used to do the calculation, which is I think the 46.18 in the link:

http://www.eviews.com/help/helpintro.ht ... 060.4.html

When I run the cointegration test, I get the Kao t statistic, residual variance (sigma squared of "v" in the formula), hac variance (sigma squared of "0v" in the formula") and what I think is the t_p from the formula, the t statistic in the auxiliary regression. However, when I try to make the calculation appliying the formula "by hand", I get a quite different result.

My question is if the output that anyone can get from the Kao cointegration test (the residual variance, HAC variance and the t statistic in the auxiliary regression) is supposed to be coincident with the elements used to do the calculation of the Kao t statistic.

Kind regards,

Fructuoso



P.D. In the case it is necessary to clarify my question, this is the output that I get from Eviews:

t-Statistic Prob.
ADF -7.432208 0.0000
Residual variance 0.014640
HAC variance 0.003992

With auxiliary regression:
Variable Coefficient Std. Error t-Statistic Prob.
RESID(-1) -0.553640 0.044463 -12.45184 0.0000

[EViews Glenn]

You'll have to provide a lot more detail for us to comment.

[Fructuoso]

Dear Glenn,

I am running a Kao panel cointegration test, with N=10, T=43. I get that the t ADF statistic (the Kao statistic) is -7.432208. Then, Eviews offers me more information: the residual variance, which is 0.014640, and the HAC variance, which is 0.003992. Then, in the auxiliary regression (the ADF regression of the test) I get that the t statistic of resid(-1) is -12.45.

Now, I take a look to the formula that I attach below (which I have taken from the Eviews help, the ADF formula, 46.19)

I asume, then, that tp = -12.45, squared sigma v is 0.01464 and squared sigma 0v is 0.003992. If N =10, then the Kao statistic is computed in this way:

Kao t statistic = (tp + (6*N)^(1/2)*sigma v /(2 * sigma 0v))/(squared sigma 0v/(2* squared sigma v) + 3*squared sigma v /(10*squared sigma 0v)) ^(1/2) =
(-12.45 + (6*10)^(1/2) * (0.01464)^(1/2)/(2*(0.003992)^(1/2))) / (0.003992/(2*0.01464)+3*0.01464/(10*0.003992))^(1/2)=
= -5.033/1.11 = -4.53

So if I use the information provided by the program, the Kao t statistic is -4.53, but the program says it is -7.43, and there is a huge difference between both.
What I am wondering is if the information that Eviews provides, the HAC variance and the residual variance, is coincident with the squared sigma 0v (the long run variance) and squared sigma v (the variance) of the Kao t statistic formula. If they are supposed to be, then I asume that Eviews is computing the Kao t statistic in another way,.

I apologize if the previous post was not very clear.

Kind regards,

Fructuoso Borrallo

[EViews Gareth]

Typo in the documentation. The sigma_0v in the numerator should be sigma_0u. Unfortunately we do not report sigma_0u on our output.

[Fructuoso]

Thank you Gareth. That helps me a lot!