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

panel datastataunit root

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?

Best Answer

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).

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