Fisher-type unit-root test for panel data. Results interpretation in Stata

As part of my master thesis, I'm performing several tests on panel data. One of these is a Fisher-type unit-root test, which works well with an unbalanced panel. I have performed the test, but I haven't managed to find an explanation of how to interpret the results.

This is the setup:

• Fisher-type test
• Time-trend included
• Cross-sectional mean removed
• Variables are being lagged once

The code that makes this happen is:

. xtunitroot fisher beta, dfuller trend demean lags(1)

The output for variable beta is:

Fisher-type unit-root test for beta
Based on augmented Dickey-Fuller tests

Ho: All panels contain unit roots           Number of panels  =      5
Ha: At least one panel is stationary        Number of periods =     61

AR parameter: Panel-specific                Asymptotics: T -> Infinity
Panel means:  Included
Time trend:   Included                      Cross-sectional means removed
Drift term:   Not included                  ADF regressions: 1 lag

Statistic      p-value

Inverse chi-squared(10)   P        77.8047       0.0000
Inverse normal            Z        -7.2246       0.0000
Inverse logit t(29)       L*       -9.7556       0.0000
Modified inv. chi-squared Pm       15.1616       0.0000

P statistic requires number of panels to be finite.
Other statistics are suitable for finite or infinite number of panels.

Questions:

1. Based on the results, does my data contain a unit-root, or is it stationary?
2. How do I know the confidence level at which I can accept/reject H0?
• This is probably a bit too late, but if anyone else is still puzzled by this question, in the link Example 6 there is explanation of all the statistics of the panel data ADF test and which should be taken into consideration in different cases. stata.com/manuals13/xtxtunitroot.pdf – user113465 Apr 25 '16 at 17:35

The null hypothesis of this test is that all panels contain a unit root. Given your results we reject this hypothesis. If you look at your tests P, Z, L* and Pm, you get a value for these test statistics (77.8047, -7.2246, and so on) and in the next column you see the p-value. Since they are all smaller than 0.01, you can reject the null hypothesis at the 1% level of statistical significance. This means there are no unit roots in your panels under the given test conditions (included panel mean and time trend). This should also answer your second question because the p-value tells you at which level of statistical significance you can reject the null. If you would like some more details on p-values have a look at these notes (lecture1, lecture2).

• Thank you very much Andy! One last question, how do I determine whether I reject the null or not all the statistics are significant? Which one would actually be the one to look at? – Herman Haugland Jul 27 '13 at 8:04
• Since all the tests give you the same result it does not matter a lot which one you look at exactly. All of them reject the null of having a unit root at the 1% significance level. In your thesis you can either report those underneath the regression results or simply put them in the appendix. – Andy Jul 27 '13 at 8:31
• Yes, I understood that in this case doesn't matter really, but my question is about which one should I look at in the case that they were not the same, for another set of variables, for example, in which some statistics are < 0.05 and other higher than that. – Herman Haugland Jul 27 '13 at 8:39
• Can you provide more information on this in the question? For instance the values of the tests. If it is only the Pm statistic which gives a different result you can discard this one because it is for large T, large N (you only have large T). Also p-values below 0.1 are fine, i.e. rejection of the null at the 10% significance level. Also try the "pperron" option instead of dfuller because the Phillips-Perron test is robust to serial correlation (if you have serial correlation in your data). – Andy Jul 27 '13 at 9:02
• Thank you very much Andy. I have tried your suggestion and I get highly significant values for my data, so I'll just stop it there for now. I have other problems with my data though, one of them seems to be some mild autocorrelation, and the fact that one of my variables is U-shaped, but I'll keep that for another question. Thank you for answering this, I was very puzzled trying to figure out what each of the 4 statistics mean. Do you have a source for understanding each of the 4 statistics, for future reference? – Herman Haugland Jul 27 '13 at 9:22

protected by Community♦Dec 10 '16 at 15:27

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