**[XT] xtunitroot** -- Panel-data unit-root tests

__Syntax__

Levin-Lin-Chu test

**xtunitroot llc** *varname* [*if*] [*in*] [**,** *LLC_options*]

Harris-Tzavalis test

**xtunitroot ht** *varname* [*if*] [*in*] [**,** *HT_options*]

Breitung test

**xtunitroot breitung** *varname* [*if*] [*in*] [**,** *Breitung_options*]

Im-Pesaran-Shin test

**xtunitroot ips** *varname* [*if*] [*in*] [**,** *IPS_options*]

Fisher-type tests (combining p-values)

**xtunitroot fisher** *varname* [*if*] [*in*]**,** {__df__**uller** | __pp__**erron**} __l__**ags(***#***)**
[*Fisher_options*]

Hadri Lagrange multiplier stationarity test

**xtunitroot hadri** *varname* [*if*] [*in*] [**,** *Hadri_options*]

*LLC_options* Description
-------------------------------------------------------------------------
__t__**rend** include a time trend
__nocons__**tant** suppress panel-specific means
**demean** subtract cross-sectional means
__l__**ags(***lag_spec***)** specify lag structure for augmented Dickey-Fuller
(ADF) regressions
__ker__**nel(***kernel_spec***)** specify method to estimate long-run variance
-------------------------------------------------------------------------
*lag_spec* is either a nonnegative integer or one of **aic**, **bic**, or **hqic**
followed by a positive integer.
*kernel_spec* takes the form *kernel* *maxlags*, where *kernel* is one of
__ba__**rtlett**, __pa__**rzen**, or __qu__**adraticspectral** and *maxlags* is either a positive
number or one of **nwest** or **llc**.

*HT_options* Description
-------------------------------------------------------------------------
__t__**rend** include a time trend
__nocons__**tant** suppress panel-specific means
**demean** subtract cross-sectional means
**altt** make small-sample adjustment to T
-------------------------------------------------------------------------

*Breitung_options* Description
-------------------------------------------------------------------------
__t__**rend** include a time trend
__nocons__**tant** suppress panel-specific means
**demean** subtract cross-sectional means
__r__**obust** allow for cross-sectional dependence
__l__**ags(***#***)** specify lag structure for prewhitening
-------------------------------------------------------------------------

*IPS_options* Description
-------------------------------------------------------------------------
__t__**rend** include a time trend
**demean** subtract cross-sectional means
__l__**ags(***lag_spec***)** specify lag structure for ADF regressions
-------------------------------------------------------------------------
*lag_spec* is either a nonnegative integer or one of **aic**, **bic**, or **hqic**
followed by a positive integer.

*Fisher_options* Description
-------------------------------------------------------------------------
* __df__**uller** use ADF unit-root tests
* __pp__**erron** use Phillips-Perron unit-root tests
* __l__**ags(***#***)** specify lag structure for prewhitening
**demean** subtract cross-sectional means
*dfuller_opts* any options allowed by the **dfuller** command
*pperron_opts* any options allowed by the **pperron** command
-------------------------------------------------------------------------
* Either **dfuller** or **pperron** is required.
* **lags(***#***)** is required.

*Hadri_options* Description
-------------------------------------------------------------------------
__t__**rend** include a time trend
**demean** subtract cross-sectional means
__r__**obust** allow for cross-sectional dependence
__ker__**nel(***kernel_spec***)** specify method to estimate long-run variance
-------------------------------------------------------------------------
*kernel_spec* takes the form *kernel* [*#*], where *kernel* is one of __ba__**rtlett**,
__pa__**rzen**, or __qu__**adraticspectral** and *#* is a positive number.

*varname* may contain time-series operators; see tsvarlist.

__Menu__

**Statistics > Longitudinal/panel data > Unit-root tests**

__Description__

**xtunitroot** performs a variety of tests for unit roots (or stationarity)
in panel datasets. 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. The top of the output for each test makes explicit the null
and alternative hypotheses. Options allow you to include panel-specific
means (fixed effects) and time trends in the model of the data-generating
process.

__Options__

__LLC_options__

**trend** includes a linear time trend in the model that describes the
process by which the series is generated.

**noconstant** suppresses the panel-specific mean term in the model that
describes the process by which the series is generated. Specifying
**noconstant** imposes the assumption that the series has a mean of zero
for all panels.

**demean** requests that **xtunitroot** first subtract the cross-sectional
averages from the series. When specified, for each time period
**xtunitroot** computes the mean of the series across panels and
subtracts this mean from the series. Levin, Lin, and Chu suggest
this procedure to mitigate the impact of cross-sectional dependence.

**lags(***lag_spec***)** specifies the lag structure to use for the ADF regressions
performed in computing the test statistic.

Specifying **lags(***#***)** requests that *#* lags of the series be used in the
ADF regressions. The default is **lags(1)**.

Specifying **lags(aic ***#***)** requests that the number of lags of the series
be chosen such that the Akaike information criterion (AIC) for the
regression is minimized. **xtunitroot llc** will fit ADF regressions
with 1 to *#* lags and choose the regression for which the AIC is
minimized. This process is done for each panel so that different
panels may use ADF regressions with different numbers of lags.

Specifying **lags(bic ***#***)** is just like specifying **lags(aic ***#***)**, except
that the Bayesian information criterion (BIC) is used instead of the
AIC.

Specifying **lags(hqic ***#***)** is just like specifying **lags(aic ***#***)**, except
that the Hannan-Quinn information criterion is used instead of the
AIC.

**kernel(***kernel_spec***)** specifies the method used to estimate the long-run
variance of each panel's series. *kernel_spec* takes the form *kernel*
*maxlags*. *kernel* is one of **bartlett**, **parzen**, or **quadraticspectral**.
*maxlags* is a number, **nwest** to request the Newey and West (1994)
bandwidth selection algorithm, or **llc** to request the lag truncation
selection algorithm in Levin, Lin, and Chu (2002).

Specifying, for example, **kernel(bartlett 3)** requests the Bartlett
kernel with 3 lags.

Specifying **kernel(bartlett nwest)** requests the Bartlett kernel with
the maximum number of lags determined by the Newey and West bandwidth
selection algorithm.

Specifying **kernel(bartlett llc)** requests the Bartlett kernel with the
maximum number of lags determined by the method proposed in Levin,
Lin, and Chu's (2002) article:

*maxlags* = int(3.21*T^(1/3))

where T is the number of observations per panel. This is the
default.

__HT_options__

**trend** includes a linear time trend in the model that describes the
process by which the series is generated.

**noconstant** suppresses the panel-specific mean term in the model that
describes the process by which the series is generated. Specifying
**noconstant** imposes the assumption that the series has a mean of zero
for all panels.

**demean** requests that **xtunitroot** first subtract the cross-sectional
averages from the series. When specified, for each time period
**xtunitroot** computes the mean of the series across panels and
subtracts this mean from the series. Levin, Lin, and Chu suggest
this procedure to mitigate the impact of cross-sectional dependence.

**altt** requests that **xtunitroot** use T-1 instead of T in the formulas for
the mean and variance of the test statistic under the null
hypothesis. When the number of time periods, T, is small (less than
10 or 15), the test suffers from severe size distortions when fixed
effects or time trends are included; in these cases, using **altt**
results in much improved size properties at the expense of
significantly less power.

__Breitung_options__

**trend** includes a linear time trend in the model that describes the
process by which the series is generated.

**noconstant** suppresses the panel-specific mean term in the model that
describes the process by which the series is generated. Specifying
**noconstant** imposes the assumption that the series has a mean of zero
for all panels.

**demean** requests that **xtunitroot** first subtract the cross-sectional
averages from the series. When specified, for each time period
**xtunitroot** computes the mean of the series across panels and
subtracts this mean from the series. Levin, Lin, and Chu suggest
this procedure to mitigate the impact of cross-sectional dependence.

**robust** requests a variant of the test that is robust to cross-sectional
dependence.

**lags(***#***)** specifies the number of lags used to remove higher-order
autoregressive components of the series. The Breitung test assumes
the data are generated by an AR(1) process; for higher-order
processes, the first-differenced and lagged-level data are replaced
by the residuals from regressions of those two series on the first *#*
lags of the first-differenced data. The default is to not perform
this prewhitening step.

__IPS_options__

**trend** includes a linear time trend in the model that describes the
process by which the series is generated.

**demean** requests that **xtunitroot** first subtract the cross-sectional
averages from the series. When specified, for each time period
**xtunitroot** computes the mean of the series across panels and
subtracts this mean from the series. Levin, Lin, and Chu suggest
this procedure to mitigate the impact of cross-sectional dependence.

**lags(***lag_spec***)** specifies the lag structure to use for the ADF regressions
performed in computing the test statistic. With this option,
**xtunitroot** reports Im, Pesaran, and Shin's (2003) W_t-bar statistic
that is predicated on T going to infinity first, followed by N going
to infinity. By default, no lags are included, and **xtunitroot**
instead reports Im, Pesaran, and Shin's t-tilde-bar and Z_t-tilde-bar
statistics that assume T is fixed while N goes to infinity, as well
as the t-bar statistic and exact critical values that assume both N
and T are fixed.

Specifying **lags(***#***)** requests that *#* lags of the series be used in the
ADF regressions. By default, no lags are included.

Specifying **lags(aic ***#***)** requests that the number of lags of the series
be chosen such that the AIC for the regression is minimized.
**xtunitroot llc** will fit ADF regressions with 1 to *#* lags and choose
the regression for which the AIC is minimized. This process is done
for each panel so that different panels may use ADF regressions with
different numbers of lags.

Specifying **lags(bic ***#***)** is just like specifying **lags(aic ***#***)**, except
that the BIC is used instead of the AIC.

Specifying **lags(hqic ***#***)** is just like specifying **lags(aic ***#***)**, except
that the Hannan-Quinn information criterion is used instead of the
AIC.

If you specify **lags(0)**, then **xtunitroot** reports the W_t-bar statistic
instead of the Z_t-bar, Z_tilde-t-bar, and t-bar statistics.

__Fisher_options__

**dfuller** requests that **xtunitroot** conduct ADF unit-root tests on each
panel by using the **dfuller** command. You must specify either the
**dfuller** or the **pperron** option.

**pperron** requests that **xtunitroot** conduct Phillips-Perron unit-root tests
on each panel by using the **pperron** command. You must specify either
the **pperron** or the **dfuller** option.

**lags(***#***)** specifies the number of lags used to remove higher-order
autoregressive components of the series. The Fisher test assumes the
data are generated by an AR(1) process; for higher-order processes,
the first-differenced and lagged-level data are replaced by the
residuals from regressions of those two series on the first *#* lags of
the first-differenced data. **lags(***#***)** is required.

**demean** requests that **xtunitroot** first subtract the cross-sectional
averages from the series. When specified, for each time period
**xtunitroot** computes the mean of the series across panels and
subtracts this mean from the series. Levin, Lin, and Chu suggest
this procedure to mitigate the impact of cross-sectional dependence.

*dfuller_opts* are any options accepted by the **dfuller** command, including
**noconstant**, **trend**, **drift**, and **lags()**. Because **xtunitroot** calls
**dfuller** **quietly**, the **dfuller** option **regress** has no effect.

*pperron_opts* are any options accepted by the **pperron** command, including
**noconstant**, **trend**, and **lags()**. Because **xtunitroot** calls **pperron**
**quietly**, the **pperron** option **regress** has no effect.

__Hadri_options__

**trend** includes a linear time trend in the model that describes the
process by which the series is generated.

**demean** requests that **xtunitroot** first subtract the cross-sectional
averages from the series. When specified, for each time period
**xtunitroot** computes the mean of the series across panels and
subtracts this mean from the series. Levin, Lin, and Chu suggest
this procedure to mitigate the impact of cross-sectional dependence.

**robust** requests a variant of the test statistic that is robust to
heteroskedasticity across panels.

**kernel(***kernel_spec***)** requests a variant of the test statistic that is
robust to serially correlated errors. *kernel_spec* specifies the
method used to estimate the long-run variance of each panel's series.
*kernel_spec* takes the form *kernel* [*#*]. Three kernels are supported:
**bartlett**, **parzen**, and **quadraticspectral**.

Specifying, for example, **kernel(bartlett 3)** requests the Bartlett
kernel with 3 lags.

If *#* is not specified, then 1 lag is used.

__Remarks__

**xtunitroot** implements a variety of tests for unit roots (or stationarity)
in panel datasets. Consider the autoregressive model

y_it = a_it + rho_i * y_i,t-1 + e_it

where e_it is a mean-zero regression error term and a_it represents the
deterministic part of the model. i=1, ..., N indexes panels, and t=1,
..., T indexes time. a_it may include panel-specific intercepts (fixed
effects), a panel-specific time trend, or nothing, in which case y_it is
predicated to have mean zero for all panels.

All the tests except for the Hadri LM test investigate null hypotheses of
the general form Ho: rho_i = 1 versus Ha: rho_i < 1, though they differ
in precisely how Ha is specified. The Hadri LM test, rather than
assuming a unit root under the null hypothesis, assumes that the data are
stationary (rho_i < 1) versus the alternative that the data contain a
unit root.

Here we provide a brief overview of the salient features of each test;
see **[XT] xtunitroot** for additional information.

Remarks are presented under the following headings:

Levin-Lin-Chu test
Harris-Tzavalis test
Breitung test
Im-Pesaran-Shin test
Fisher-type tests
Hadri LM stationarity test

__Levin-Lin-Chu test__

The Levin-Lin-Chu (LLC) (2002) test assumes that all panels have the same
autoregressive parameter, that is, that rho_i = rho for all i. Then the
alternative hypothesis is simply that rho < 1.

The LLC test requires that the panels be strongly balanced.

The LLC test is based on a regression t statistic, but because the data
are nonstationary under the null hypothesis, the asymptotic mean and
standard deviation of the t statistic depend on the specification of the
deterministic part of the model.

Levin, Lin, and Chu recommend using their procedure for moderate-sized
panels, with perhaps between 10 and 250 individuals and 25 to 250
observations per individual. If the time-series dimension of the panel
is very large, then standard unit-root tests can be applied to each
panel, because the gains from aggregation are likely to be small.

Formally, if there is no deterministic term in the model (a_it = 0), then
the test allows the number of time periods, T, to tend to infinity at a
slower rate than the number of cross-sectional units, N, though T must go
to infinity sufficiently fast that sqrt(N)/T tends to 0. If fixed
effects or time trends are included in the deterministic part of the
model, then T must tend to infinity at a rate faster than N so that N/T
tends to 0.

__Harris-Tzavalis test__

The Harris-Tzavalis (HT) (1999) test is similar to the LLC test in that
it assumes that all panels have the same autoregressive parameter so that
the alternative hypothesis is simply rho < 1. Differing from the LLC
test, the HT test assumes that the number of time periods, T, is fixed.

Like the LLC test, the HT test requires that the panels be strongly
balanced.

Baltagi (2008, 278) mentions that T being fixed is the typical case in
micropanel studies. Here you may have a panel dataset of firms, and it
may be more natural to think that if you could increase the sample size
of your dataset, you would do so by collecting data on more firms, though
the number of time periods available for each firm is fixed.

__Breitung test__

The LLC and HT tests are based on regression t statistics that are
subsequently adjusted to reflect the fact that under the null hypothesis,
the t statistics have a nonzero mean because of the inclusion of
panel-specific means or trends. The Breitung (2000) test takes a
different approach, transforming the data before computing the
regressions so that the standard t statistics can be used.

The Breitung test requires that the panels be strongly balanced.

When the **robust** option is specified, a version of the t statistic that is
robust to cross-sectional correlation of the error terms is reported.
This statistic has an asymptotically normal distribution when first T
tends to infinity followed by N tending to infinity.

The Breitung test assumes that all panels have a common autoregressive
parameter. The null hypothesis is that all series contain a unit root.
The alternative hypothesis is that rho < 1 so that the series are
stationary. Breitung and Das (2005) remark that the test also has power
in the heterogeneous case, where each panel is allowed to have its own
autoregressive parameter, though the test is optimal in the case where
all panels have the same autoregressive parameter.

The Breitung (2000) Monte Carlo simulations suggest that his test is
substantially more powerful than other panel unit-root tests for the
modest-size dataset he considered (N=20, T=30).

__Im-Pesaran-Shin test__

A major limitation of the LLC, HT, and Breitung tests is the assumption
that all panels have the same value of rho. The Im-Pesaran-Shin (IPS)
(2003) test relaxes the assumption of a common rho and instead allows
each panel to have its own rho_i. The null hypothesis is that all panels
have a unit root (Ho: rho_i = 0 for all i). The alternative hypothesis
is that the fraction of panels that are stationary is nonzero.
Specifically, if we let N_1 denote the number of stationary panels, then
the fraction N_1/N tends to a nonzero fraction as N tends to infinity.
This allows some (but not all) of the panels to possess unit roots under
the alternative hypothesis.

The IPS test does not require strongly balanced data, but there can be no
gaps in each individual time series.

When the errors are assumed to be serially uncorrelated, imposed by
either specifying the **lags(0)** option or not specifying the **lag()** option
at all, **xtunitroot ips** reports IPS's t-bar, t-tilde-bar, and
Z_t-tilde-bar statistics. These statistics assume that the number of
time periods, T, is fixed. When there are no gaps in the data,
**xtunitroot ips** reports exact critical values for the t-bar statistic that
are predicated on the number of panels, N, also being fixed. The other
two statistics assume N tends to infinity.

For the asymptotic normal distribution of Z_t-tilde-bar to hold, T must
be at least 5 if the dataset is strongly balanced and the deterministic
part of the model includes only panel-specific means, or at least 6 if
time trends are also included. If the data are not strongly balanced,
then T must be at least 9 for the asymptotic distribution to hold. If
these limits on T are not met, the p-value for Z_t-tilde-bar is not
reported.

When serial correlation in the error terms is accommodated by using the
**lags()** option with **xtunitroot ips**, then IPS's W_t-bar statistic is
reported. This statistic is asymptotically normally distributed when
first T tends to infinity followed by N tending to infinity.

__Fisher-type tests__

Fisher-type tests approach testing for panel-data unit roots from a
meta-analysis perspective. That is, these tests conduct unit-root tests
for each panel individually, and then combine the p-values from these
tests to produce an overall test. **xtunitroot fisher** supports ADF tests
with the **dfuller** option and Phillips-Perron tests with the **pperron**
option. Any options allowed by **dfuller** or **pperron** can be specified
(except the **regress** option has no effect).

**xtunitroot fisher** does not require strongly balanced data, and the
individual series can have gaps.

These tests assume that T tends to infinity. If the number of panels, N,
is fixed, then these tests are consistent against the alternative that at
least one panel is stationary. If we allow N to tend to infinity, then
the number of panels that do not have a unit root must grow at the same
rate as N for the tests to be consistent.

**xtunitroot fisher** combines p-values using the inverse chi-squared,
inverse-normal, and inverse-logit transformations. Also a modified
version of the inverse chi-squared transformation proposed by Choi (2001)
is reported for use when N is believed to tend to infinity, because here
the standard inverse chi-squared test statistic goes to infinity.

__Hadri LM stationarity test__

All the tests discussed thus far have as the null hypothesis that the
data contain a unit root. As Hadri (2000) notes, classical hypothesis
testing requires strong evidence to the contrary to reject the null
hypothesis. Thus we may also want to conduct a test in which the null
and alternative hypotheses are reversed, to help confirm or deny
conclusions based on tests with the null hypothesis being
nonstationarity.

The Hadri LM test requires that the panels be strongly balanced.

The Hadri LM test has as the null hypothesis that all the panels are
stationary, perhaps around a linear trend if the **trend** option is
specified. The alternative hypothesis is that at least some of the
panels contain a unit root. The test assumes that the model error terms
are normally distributed. The test is justified asymptotically as T
tends to infinity followed by N tending to infinity. Hadri states that
his tests are appropriate for panel datasets in which T is large and N is
moderate, such as the Penn World Tables frequently used for cross-country
comparisons.

__Examples__

Setup
**. webuse pennxrate**

LLC test, using the AIC to choose the number of lags for regressions and
using an HAC variance estimator based on the Bartlett kernel and the
number of lags chosen using Newey and West's method
**. xtunitroot llc lnrxrate if oecd, demean lags(aic 10)**
**kernel(bartlett nwest)**

HT test, removing cross-sectional means from data
**. xtunitroot ht lnrxrate, demean**

Robust version of the Breitung test on a subset of OECD countries, using
3 lags for the prewhitening step
**. xtunitroot breitung lnrxrate if g7, lags(3) robust**

IPS test, using the AIC to choose the number of lags for regressions
**. xtunitroot ips lnrxrate, lags(aic 5)**

Fisher-type test based on ADF tests with 3 lags, allowing for a drift
term in each panel
**. xtunitroot fisher lnrxrate, dfuller lags(3) drift**

Hadri LM test of stationarity, using an HAC variance estimator based on
the Parzen kernel with 5 lags
**. xtunitroot hadri lnrxrate, kernel(parzen 5)**

__Stored results__

**xtunitroot llc** stores the following in **r()**:

Scalars
**r(N)** number of observations
**r(N_g)** number of groups
**r(N_t)** number of time periods
**r(sig_adj)** standard deviation adjustment
**r(mu_adj)** mean adjustment
**r(delta)** pooled estimate of delta
**r(se_delta)** pooled standard error of delta hat
**r(Var_ep)** variance of whitened differenced series
**r(sbar)** mean of ratio of long-run to innovation standard
deviations
**r(ttilde)** observations per panel after lagging and
differencing
**r(td)** unadjusted t_delta statistic
**r(p_td)** p-value for t_delta
**r(tds)** adjusted t_delta_star statistic
**r(p_tds)** p-value for t_delta_star
**r(hac_lags)** lags used in HAC variance estimator
**r(hac_lagm)** average lags used in HAC variance estimator
**r(adf_lags)** lags used in ADF regressions
**r(adf_lagm)** average lags used in ADF regressions

Macros
**r(test)** **llc**
**r(hac_kernel)** kernel used in HAC variance estimator
**r(hac_method)** HAC lag-selection algorithm
**r(adf_method)** ADF regression lag-selection criterion
**r(demean)** **demean**, if the data were demeaned
**r(deterministics)** **noconstant**, **constant**, or **trend**

**xtunitroot ht** stores the following in **r()**:

Scalars
**r(N)** number of observations
**r(N_g)** number of groups
**r(N_t)** number of time periods
**r(rho)** estimated rho
**r(Var_rho)** variance of rho under H_0
**r(mean_rho)** mean of rho under H_0
**r(z)** z statistic
**r(p)** p-value

Macros
**r(test)** **ht**
**r(demean)** **demean**, if the data were demeaned
**r(deterministics)** **noconstant**, **constant**, or **trend**
**r(altt)** **altt**, if **altt** specified

**xtunitroot breitung** stores the following in **r()**:

Scalars
**r(N)** number of observations
**r(N_g)** number of groups
**r(N_t)** number of time periods
**r(lambda)** test statistic lambda
**r(lrobust)** robust test statistic lambda_R
**r(p)** p-value for lambda
**r(p_lrobust)** p-value for lambda_R
**r(lags)** lags used for prewhitening

Macros
**r(test)** **breitung**
**r(demean)** **demean**, if the data were demeaned
**r(robust)** **robust**, if specified
**r(deterministics)** **noconstant**, **constant**, or **trend**

**xtunitroot ips** stores the following in **r()**:

Scalars
**r(N)** number of observations
**r(N_g)** number of groups
**r(N_t)** number of time periods
**r(tbar)** test statistic t-bar
**r(cv_10)** exact 10% critical value for t-bar
**r(cv_5)** exact 5% critical value for t-bar
**r(cv_1)** exact 1% critical value for t-bar
**r(zt)** test statistic Z_t-bar
**r(ttildebar)** test statistic t-tilde-bar
**r(zttildebar)** test statistic Z_t-tilde-bar
**r(p_zttildebar)** p-value for Z_t-tilde-bar
**r(wtbar)** test statistic W_t-bar
**r(p_wtbar)** p-value for W_t-bar
**r(lags)** lags used in ADF regressions
**r(lagm)** average lags used in ADF regressions

Macros
**r(test)** **ips**
**r(demean)** **demean**, if the data were demeaned
**r(adf_method)** ADF regression lag-selection criterion
**r(deterministics)** **constant** or **trend**

**xtunitroot fisher** stores the following in **r()**:

Scalars
**r(N)** number of observations
**r(N_g)** number of groups
**r(N_t)** number of time periods
**r(P)** inverse chi-squared P statistic
**r(df_P)** P statistic degrees of freedom
**r(p_P)** p-value for P statistic
**r(L)** inverse logit L statistic
**r(df_L)** L statistic degrees of freedom
**r(p_L)** p-value for L statistic
**r(Z)** inverse normal Z statistic
**r(p_Z)** p-value for Z statistic
**r(Pm)** modified inverse chi-squared P_m statistic
**r(p_Pm)** p-value for P_m statistic

Macros
**r(test)** **fisher**
**r(urtest)** **dfuller** or **pperron**
**r(options)** options passed to **dfuller** or **pperron**
**r(demean)** **demean**, if the data were demeaned

**xtunitroot hadri** stores the following in **r()**:

Scalars
**r(N)** number of observations
**r(N_g)** number of groups
**r(N_t)** number of time periods
**r(var)** variance of z under Ho
**r(mu)** mean of z under Ho
**r(z)** test statistic z
**r(p)** p-value for z
**r(lags)** lags used for HAC variance

Macros
**r(test)** **hadri**
**r(demean)** **demean**, if the data were demeaned
**r(robust)** **robust**, if specified
**r(kernel)** kernel used for HAC variance
**r(deterministics)** **constant** or **trend**

__References__

Baltagi, B. H. 2008. *Econometric Analysis of Panel Data*. 4th ed. New
York: Wiley.

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

Newey, W. K., and K. D. West. 1994. Automatic lag selection in
covariance matrix estimation. *Review of Economic Studies* 61:
631-653.