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## Panel-data unit-root tests

**. xtunitroot llc lnrxrate if g7, lags(aic 10)**

Ho: Panels contain unit roots Number of panels = 6
Ha: Panels are stationary Number of periods = 34
AR parameter: Common Asymptotics: N/T -> 0
Panel means: Included
Time trend: Not included
ADF regressions: 1.00 lags average (chosen by AIC)
LR variance: Bartlett kernel, 10.00 lags average (chosen by LLC)

**. xtunitroot ht lnrxrate**

Ho: Panels contain unit roots Number of panels = 151
Ha: Panels are stationary Number of periods = 34
AR parameter: Common Asymptotics: N -> Infinity
Panel means: Included T Fixed
Time trend: Not included

### References

Stata implements a variety of tests for unit roots or stationarity in panel
datasets with **xtunitroot**. The Levin–Lin–Chu (2002),
Harris–Tzavalis (1999), Breitung (2000; Breitung and Das 2005),
Im–Pesaran–Shin (2003), and Fisher-type (Choi 2001) tests have as the
null hypothesis that all the panels contain a unit root. The Hadri (2000)
Lagrange multiplier (LM) test has as the null hypothesis that all the panels
are (trend) stationary. Options allow you to include fixed effects and time
trends in the model of the data-generating process.

The assorted tests make different asymptotic assumptions regarding the
number of panels in your dataset and the number of time periods in each
panel. **xtunitroot** has all your bases covered, including tests
appropriate for datasets with a large number of panels and few time periods,
datasets with few panels but many time periods, and datasets with many
panels and many time periods. The majority of the tests assume that you
have a balanced panel dataset, but the Im–Pesaran–Shin and
Fisher-type tests allow for unbalanced panels.

We have data on the log of real exchange rates for a large panel of
countries for 34 years. Here we apply the Levin–Lin–Chu test to
a subset of data for the G7 countries to examine whether the series
**lnrxrate** contains a unit root. Because we use the United States as
the numeraire when computing the **lnrxrate** series, this subset of data
contains six panels.

Levin-Lin-Chu unit-root test for lnrxrate |

Statistic p-value |

Unadjusted t -6.7538 |

Adjusted t* -4.0277 0.0000 |

The header of the output summarizes the test. The null hypothesis is that
the series contains a unit root, and the alternative is that the series is
stationary. As the output indicates, the Levin–Lin–Chu test
assumes a common autoregressive parameter for all panels, so this test does
not allow for the possibility that some countries’ real exchange rates
contain unit roots while other countries’ real exchange rates do not.
Each test performed by **xtunitroot** also makes explicit the assumed
behavior of the number of panels and time periods. The
Levin–Lin–Chu test with panel-specific means but no time trend
requires that the number of time periods grow more quickly than the number
of panels, so the ratio of panels to time periods tends to zero. The
test involves fitting an augmented Dickey–Fuller regression for each
panel; we requested that the number of lags to include be selected based on
the AIC with at most 10 lags. To estimate the long-run variance of the
series, **xtunitroot** by default uses the Bartlett kernel using 10 lags
as selected by the method proposed by Levin, Lin, and Chu.

The Levin–Lin–Chu bias-adjusted *t* statistic is −4.0277,
which is significant at all the usual testing levels. Therefore, we reject
the null hypothesis and conclude that the series is stationary. When we use the
**demean** option to **xtunitroot** to remove cross-sectional means from
the series to mitigate the effects of cross-sectional correlation, we obtain
a test statistic that is significant at the 5% level but not at the 1% level.

Because the Levin–Lin–Chu test requires that the ratio of the
number of panels to time periods tend to zero asymptotically, it is not well
suited to datasets with a large number of panels and relatively few time
periods. Here we use the Harris–Tzavalis test, which assumes that the
number of panels tends to infinity while the number of time periods is
fixed, to test whether **lnrxrate** in our entire dataset of 151
countries contains a unit root:

Harris-Tzavalis unit-root test for lnrxrate |

Statistic z p-value | ||

rho 0.7534 -22.0272 0.0000 | ||

Here we find overwhelming evidence against the null hypothesis of a unit
root and therefore conclude that **lnrxrate** is stationary.

- Breitung, J. 2000.
- The local power of some unit root tests for panel
data.
*Advances in Econometrics, Volume 15: Nonstationary Panels, Panel Cointegration, and Dynamic Panels*, ed. B. H. Baltagi, 161–178. Amsterdam: JAY Press.

- Breitung, J., and S. Das. 2005.
- Panel unit root tests under
cross-sectional dependence.
*Statistica Neerlandica*59: 414–433.

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

- Hadri, K. 2000.
- Testing for stationarity in heterogeneous panel data.
*Econometrics Journal*3: 148–161.

- Harris, R. D. F., and E. Tzavalis. 1999.
- Inference for unit roots in
dynamic panels where the time dimension is fixed.
*Journal of Econometrics*91: 201–226.

- Im, K. S., M. H. Pesaran, and Y. Shin. 2003.
- Testing for unit roots in
heterogeneous panels.
*Journal of Econometrics*115: 53–74.

- Levin, A., C.-F. Lin, and C.-S. J. Chu. 2002.
- Unit root tests in panel
data: Asymptotic and finite-sample properties.
*Journal of Econometrics*108: 1–24.