Automatic lag length selection - Panel Unit Roots

[j.galimberti]

Hi!

Is the information criteria used in Panel Unit Root Tests (like the Fisher ADF) to select the lag length calculated by the formulas given in the Eviews help file?

E.g.:
In the help I found the following Akaike definition:

AIC = -2*(l/T) + 2*(k/T)

where l is the value of the log of the likelihood function with k parameters estimated using T observations.

However, I was checking some lags selected using the Fisher ADF Panel Unit Root test, and I found that the selected lag isn't the one that minimizes the AIC obtained by estimating the individual ADF's with lags between the pre-determined bounds. The lag selection discrepance was not found at all the individual estimations. Anyway, I would like to know if the AIC is calculated by a different definition than that above for panel unit roots.

Thanks.

[EViews Glenn]

I can take a look at this one for you, but before I do, I want to make certain that when you computed the information criteria, you used a common sample for all comparisons...

[j.galimberti]

Yes, I used a common sample. Actually, I have just found that this problem(*) also happens with unit root tests on time series. If you would like to replicate the problem here goes:

(*) I'm not sure if it is really a problem, yet.

-Given the two series:
y1t:
-0.02889473846674593
-0.006565018033503783
0.03004759186034071
-0.0001618734848641817
0.0898586400535514
0.06130508519277453
0.08773559889243597
0.1382613389304532
0.1624226784562256
0.2822257474139977
0.2486000178518115
0.2385815025999889

y2t:
0.07548934150818366
0.003133977539827632
0.01055709230440629
0.003067647093354661
0.1050570372750643
0.1723446888700069
0.08705645167566592
0.1358770813391564
0.1679361296341792
0.1500609010104193
0.1275790391774584
0.1281819586681591

- If you run the ADF Unit Root test on y1t with automatic lag length selection based on AIC (with MAXLAG=1), the lag length selected is 0. Running the same unit root test with fixed lag lengths 0 and 1, you will find that the 0 lag length is the one that has lower AIC. So, this is right.

- However, if you run the same tests on y2t, the automatically selected lag length is 0. But with the lag length of 1, you will find a lower AIC.

I wonder if this selection has something to do with the statiscal significante of the lagged variable.

[EViews Gareth]

Are you sure you're using a common sample?

When I ran the unit root test on Y2t, I got the following results:

Lag 0 AIC: -3.088014143801401
Lag 1 AIC: -2.908717172846197

Thus Lag 0 is clearly the lowest.

[j.galimberti]

Finally, the answer!

I was running the unit root test over the same series, and with this, the AIC obtained with lag 0 was -2.855214. However, this unit root used 11 obs, while with the lag 1 we have only 10 obs. Now, if I restrict the first unit root to use only 10 obs I get the same result as you, and so, lag 0 is the best one. Now I see how Eviews does the automatic lag selection by the information criterias. These statistics are calculated adjusting for the sample size, and I agree with that.

I'm not sure if this is the theorethically right choice. After all, the criterias are adjusted by the sample size.

Thank you for the helpful answers!

Best regards.

[EViews Glenn]

Ng and Perron, "A Note on the Selection of Time Series Models,"
Oxford Bulletin of Economics and Statistics, 67, 1 (2005), 115-134.