Hi Statalist,
I am having a hard time interpreting the results of the xtunitroot command, i.e. the test of whether a not a variable has a unit root.
The setup is a standard micro-panel, N is about 400 and T is 8. Thus, the Harris–Tzavalis and the Im-Pesaran-Shin test appear most appropriate to me.
When I run the Harris–Tzavalis test, I get the following:
. xtunitroot ht my_variable, altt demean trend
Harris-Tzavalis unit-root test for my_variable
--------------------------------------------
Ho: Panels contain unit roots Number of panels = 393
Ha: Panels are stationary Number of periods = 8
AR parameter: Common Asymptotics: N -> Infinity
Panel means: Included T Fixed
Time trend: Included Cross-sectional means removed
Small-sample adjustment to T applied
------------------------------------------------------------------------------
Statistic z p-value
------------------------------------------------------------------------------
rho 0.3110 6.3600 1.0000
------------------------------------------------------------------------------
I understand that the Ho cannot be rejected. However, the estimate of rho=0.3110 seems to lie well below a a value of 1. Can you help me with interpretation? Does it make sense to get a p-value of basically 1.0, if the rho-statistic is so little? Moreover, when leaving out the "altt"-option (which I think I should include due to the low number of time periods), the Z-value diminishes strongly and the p-value consequently decreases as well, even though the rho-estimate remains the same. The p-value is very sensitive to the value of Z, independent of rho?
I get more puzzled when allowing the individual rho's to differ, using the Im-Pesaran-Shin test. The my result is
. xtunitroot ips my_variable , demean trend
Im-Pesaran-Shin unit-root test for my_variable
--------------------------------------------
Ho: All panels contain unit roots Number of panels = 393
Ha: Some panels are stationary Number of periods = 8
AR parameter: Panel-specific Asymptotics: T,N -> Infinity
Panel means: Included sequentially
Time trend: Included Cross-sectional means removed
ADF regressions: No lags included
------------------------------------------------------------------------------
Fixed-N exact critical values
Statistic p-value 1% 5% 10%
------------------------------------------------------------------------------
t-bar -3.0995 -2.420 -2.340 -2.300
t-tilde-bar -1.4000
Z-t-tilde-bar -5.1825 0.0000
------------------------------------------------------------------------------
Now the t-bar statistic lies below the 1% critical value, and the Z-t-tilde-bar's p-value is essentialy 0 - so the Ho of unit-roots is rejected!?
I would greatly appreciate your help. Thanks a lot in advance!
Jack
I am having a hard time interpreting the results of the xtunitroot command, i.e. the test of whether a not a variable has a unit root.
The setup is a standard micro-panel, N is about 400 and T is 8. Thus, the Harris–Tzavalis and the Im-Pesaran-Shin test appear most appropriate to me.
When I run the Harris–Tzavalis test, I get the following:
. xtunitroot ht my_variable, altt demean trend
Harris-Tzavalis unit-root test for my_variable
--------------------------------------------
Ho: Panels contain unit roots Number of panels = 393
Ha: Panels are stationary Number of periods = 8
AR parameter: Common Asymptotics: N -> Infinity
Panel means: Included T Fixed
Time trend: Included Cross-sectional means removed
Small-sample adjustment to T applied
------------------------------------------------------------------------------
Statistic z p-value
------------------------------------------------------------------------------
rho 0.3110 6.3600 1.0000
------------------------------------------------------------------------------
I understand that the Ho cannot be rejected. However, the estimate of rho=0.3110 seems to lie well below a a value of 1. Can you help me with interpretation? Does it make sense to get a p-value of basically 1.0, if the rho-statistic is so little? Moreover, when leaving out the "altt"-option (which I think I should include due to the low number of time periods), the Z-value diminishes strongly and the p-value consequently decreases as well, even though the rho-estimate remains the same. The p-value is very sensitive to the value of Z, independent of rho?
I get more puzzled when allowing the individual rho's to differ, using the Im-Pesaran-Shin test. The my result is
. xtunitroot ips my_variable , demean trend
Im-Pesaran-Shin unit-root test for my_variable
--------------------------------------------
Ho: All panels contain unit roots Number of panels = 393
Ha: Some panels are stationary Number of periods = 8
AR parameter: Panel-specific Asymptotics: T,N -> Infinity
Panel means: Included sequentially
Time trend: Included Cross-sectional means removed
ADF regressions: No lags included
------------------------------------------------------------------------------
Fixed-N exact critical values
Statistic p-value 1% 5% 10%
------------------------------------------------------------------------------
t-bar -3.0995 -2.420 -2.340 -2.300
t-tilde-bar -1.4000
Z-t-tilde-bar -5.1825 0.0000
------------------------------------------------------------------------------
Now the t-bar statistic lies below the 1% critical value, and the Z-t-tilde-bar's p-value is essentialy 0 - so the Ho of unit-roots is rejected!?
I would greatly appreciate your help. Thanks a lot in advance!
Jack
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