*! version 1.0.1 7Feb2011
help multipurt

Title

multipurt -- Running 1st and 2nd generation panel unit root tests for multiple variables and lags

Syntax

multipurt varname [if] [in] [, lags(numlist)]

Description

multipurt runs the Maddala and Wu (1999) as well as the Pesaran (2007) panel unit root tests for multiple
variables and lags. This is not a new command for these panel unit root tests but a convenient tool using the existing
xtfisher (if installed) and pescadf (if installed) commands written by Scott Merryman and Piotr Lewandowski
respectively. The maximum number of variable or residual series to be tested is set to 9.

The multipurt routine implements these two panel unit root tests building on Dickey-Fuller and Augmented
Dickey-Fuller regressions for models with and without a trend term.

Details

The Maddala and Wu (1999) test assumes/allows for
heterogeneity in the autoregressive coefficient of the Dickey-Fuller regression and ignores cross-section dependence in
the data. Building on the Fisher-principle it constructs a chi-squared statistic, whereby the p-values of country-specific
(A)DF tests are transformed into logs and summed across panel members. Multiplied by -2 this sum is then distributed
chi-squared with 2N degrees of freedom under the null of nonstationarity in all panel members/series.

The Pesaran (2007) CIPS test allows for assumes/allows for heterogeneity in the autoregressive coefficient of the
Dickey-Fuller regression and
allows for the presence of a single unobserved common factor with heterogeneous factor loadings in the data. The statistic
is constructed from the results of panel-member-specific (A)DF regressions where cross-section averages of the dependent
and independent variables (including the lagged differences to account for serial correlation) are included in the model (referred
to as CADF regressions). The averaging of the group-specific results follows the procedure in the Im, Pesaran and Shin (2003) test.
Under the null of nonstationarity the test statistic has a non-standard distribution.

The pescadf command used in this procedure will report an error message if there are gaps in
the data. However, unless the number of observations missing in this fashion is large the Z-tbar test statistic can still be computed.

Required options

lags(numlist) identifies the maximum number of lagged differences to be included in the group-specific
Augmented Dickey Fuller regressions. The routine begins by omitting these augmentations (Dickey-Fuller regression: lags(0)),
which are intended to capture the serial correlation in the data.

Return values

Scalars
r(N_g) Number of panel groups
r(maxlags) Maximum number of lags to be included in the ADF regressions
r(N) Number of observations (evaluated before testing, i.e. does not
represent the number of observations in the DF and ADF regressions,
which depends on lag-length selection)
r(avgobs) Average number of time series observations across panel members
(same comment as above applies)

Matrices
r(mw) Matrix containing the results for the Maddala and Wu (1999) test
without trend. The column order is as follows: # of lags,
chi-sq statistic for variable 1, implied p-value for variable 1,
chi-sq statistic for variable 2, etc.
r(mw_trend) Matrix containing the results for the Maddala and Wu (1999) test
with trend. Same column order as above.
r(cips) Matrix containing the results for the Pesaran(2007) test
without trend. The column order is as follows: # of lags,
Z-tbar statistic for variable 1, implied p-value for
variable 1, t-bar statistic for variable 1, Z-tbar statistic
for variable 2, etc.
r(cips_trend) Matrix containing the results for the Pesaran(2007) test
with trend. Same column order as above.

Macros
r(varname) Names of variables or residual series tested

Example

Download FAO production data (zipped file)
for the agriculture sector in 128 countries (1961-2002, unbalanced). See Eberhardt and Teal (2010) for details on data construction and deflation.
Cross-country growth empirics are reviewed in Eberhardt and Teal (2011).

Variables used in illustration: ly log value-added per worker, ltr log tractors per worker,
llive log livestock per worker, lf log fertilizer per worker, ln log land per worker
(all with reference to the agricultural sector). Note that the dataset is quite large, such that it may be advisable (but not required) to
increase the memory and matsize before loading the data (e.g. .set mem 100m, .set matsize 8000). The
routine also works with a much more modest memory and matsize allocation.

Once the dataset is loaded into the program, set the panel dimensions: time variable - year, country identifier - clist2.

.tsset clist2 year

Investigate stationarity in the production function variables. We limit the analysis to the first 20 countries (results for the full N=128 sample
-if !missing(clist2) & sample==1- can take several minutes to compute)

.multipurt ly ltr llive lf ln if clist2<21 & sample==1, lags(4)

References

Eberhardt, Markus and Francis Teal (2011) 'Econometrics for Grumblers: A New Look at the Literature
on Cross-Country Growth Empirics', Journal of Economic Surveys, Vol.25(1), pp.109–155.

Eberhardt, Markus and Francis Teal (2010) 'Mangos in the Tundra? Spatial Heterogeneity in
Agricultural Productivity Analysis', Centre for the Study of African Economies, University of Oxford,
unpublished working paper, available here.

Im, K, Hashem Pesaran and Yeongchol Shin (2003) 'Testing for unit roots in heterogeneous panels',
Journal of Econometrics, Vol.115(1), pp.53-74.

Maddala, G.S. and S. Wu (1999) 'A comparative study of unit root tests with panel data and a new simple test',
Oxford Bulletin of Economics and Statistics, Vol.61(Special Issue), pp.631-652.

Acknowledgements and Disclaimer

This routine uses some clever practices for data handling taken from Damiaan Persyn's xtwest (if installed) command.
It furthermore employs the panel unit root tests implemented in Stata by Scott Merryman xtfisher (if installed) and Piotr
Lewandowski pescadf (if installed) and also uses some of these authors' data handling routines. Users should refer to these help files for more details and acknowledge the authors of the
commands. Thanks to Kit Baum for help and support. Any errors are of course my own.

Author

Markus Eberhardt
Centre for the Study of African Economies
Department of Economics
University of Oxford
Manor Road, Oxford OX1 3UQ
markus.eberhardt@economics.ox.ac.uk

Also see

Online: help for xtfisher (if installed), pescadf (if installed), ipshin (if installed)