Fisher-type unit-root test: P-value

[Tina Samuel]

Hi all, I am doing a panel analysis with 20 years and 114 countries. I wanted to check for stationarity to avoid having a spurious regression. I checked for all variables and one of the variables had mixed results for the p-value. Both the "Inverse chi-squared" & "Modified inv. chi-squared" were less than 0.05 but the "Inverse normal" & "Inverse logit" were greater than 0.05. I am not sure if I should accept or reject the null hypothesis in this case. Thank you!

[Scott Merryman]

From Choi, In. 2001. “Unit Root Tests for Panel Data.” Journal of International Money and Finance 20 (2): 249–72.

Major findings of our experiments can be summarized as follows
....
5. The simulation results do not provide a definitive guideline on how large N should be for the
Pm test to be used instead of the P test. At least, N=100 seems to be too small for the Pm test
to have its asymptotic distribution.

6. Considering the trade-off between size and power, the Z test seems to outperform the other
tests, and hence is recommended for empirical applications. Furthermore, another advantage
of the Z test is that it can be used for both finite and infinite N (page 268)

See also page 18: https://www.stata.com/manuals/xtxtunitroot.pdf

[Tina Samuel]

Dear Scott,
Thank you for sharing this reference with me. Now that I can conclude that this variable is not stationary. I am not sure how to proceed.
I was thinking of demeaning it or detrending it. However, I am not sure how to do this for a panel analysis.
Any suggestions?

Thank you.

[Scott Merryman]

Differencing or de-trending are common ways to proceed. Here is an example testing after first differencing.

.  webuse pennxrate

.  xtunitroot fisher xrate if g7 ==1, dfuller lag(1)

Fisher-type unit-root test for xrate
Based on augmented Dickey–Fuller tests
--------------------------------------
H0: All panels contain unit roots           Number of panels  =      6
Ha: At least one panel is stationary        Number of periods =     34

AR parameter: Panel-specific                Asymptotics: T -> Infinity
Panel means:  Included
Time trend:   Not included
Drift term:   Not included                  ADF regressions: 1 lag
------------------------------------------------------------------------------
                                  Statistic      p-value
------------------------------------------------------------------------------
 Inverse chi-squared(12)   P        14.9798       0.2425
 Inverse normal            Z        -1.0440       0.1483
 Inverse logit t(34)       L*       -1.0047       0.1611
 Modified inv. chi-squared Pm        0.6082       0.2715
------------------------------------------------------------------------------
 P statistic requires number of panels to be finite.
 Other statistics are suitable for finite or infinite number of panels.
------------------------------------------------------------------------------

.  xtunitroot fisher d.xrate if g7 ==1, dfuller lag(1)
(151 missing values generated)

Fisher-type unit-root test for D.xrate
Based on augmented Dickey–Fuller tests
--------------------------------------
H0: All panels contain unit roots           Number of panels  =      6
Ha: At least one panel is stationary        Number of periods =     33

AR parameter: Panel-specific                Asymptotics: T -> Infinity
Panel means:  Included
Time trend:   Not included
Drift term:   Not included                  ADF regressions: 1 lag
------------------------------------------------------------------------------
                                  Statistic      p-value
------------------------------------------------------------------------------
 Inverse chi-squared(12)   P        79.1646       0.0000
 Inverse normal            Z        -7.2629       0.0000
 Inverse logit t(34)       L*       -9.0419       0.0000
 Modified inv. chi-squared Pm       13.7099       0.0000
------------------------------------------------------------------------------
 P statistic requires number of panels to be finite.
 Other statistics are suitable for finite or infinite number of panels.
------------------------------------------------------------------------------

.

[Tina Samuel]

Thank you. first differencing worked perfectly