xtunitroot fisher - Interpretation of different statistics

[Louisa Krekel]

Hey everyone,

I do have difficulties interpreting the different statistics of the xtunitroot fisher test

Inverse chi-squared
Inverse normal
Inverse logit t
Modified inv. chi-squared Pm

What happens, when some statistics reject the null and other fail to reject the null - as in the following two expamples:


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

Ho: All panels contain unit roots Number of panels = 28
Ha: At least one panel is stationary Avg. number of periods = 22.14

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(56) P 69.9783 0.0991
Inverse normal Z -0.6253 0.2659
Inverse logit t(144) L* -0.7698 0.2213
Modified inv. chi-squared Pm 1.3208 0.0933






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

Ho: All panels contain unit roots Number of panels = 29
Ha: At least one panel is stationary Avg. number of periods = 22.97

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(58) P 83.7923 0.0150
Inverse normal Z -0.3887 0.3487
Inverse logit t(149) L* -0.5619 0.2875
Modified inv. chi-squared Pm 2.3948 0.0083

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




Really appreciate your help!

Thanks,
Louisa

[Scott Merryman]

Choi’ s (2001) simulation results suggest that the inverse normal Z statistic offers the best trade-off between
size and power, and he recommends using it in applications. .... For large panels, Choi (2001) therefore proposes the modified inverse chi_2 Pm test which converges to a standard normal distribution;

Page 522 xtunitroot — Panel-data unit-root tests

When the number of panel is finite the inverse chi-square is applicable. The inverse normal can be used when N is finite or infinite.

Choi, I. 2001. Unit root tests for panel data. Journal of International Money and Finance 20: 249–272.