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 regressi
> ons
       r(N)           Number of observations (evaluated before testing, i.e. do
> es 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 m
> embers
                         (same comment as above applies)

   Matrices
       r(mw)          Matrix containing the results for the Maddala and Wu (199
> 9) test 
                         without trend. The column order is as follows: # of la
> gs,
                         chi-sq statistic for variable 1, implied p-value for v
> ariable 1, 
                         chi-sq statistic for variable 2, etc.
       r(mw_trend)    Matrix containing the results for the Maddala and Wu (199
> 9) 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 la
> gs,
                         Z-tbar statistic for variable 1, implied p-value for 
                         variable 1, t-bar statistic for variable 1, Z-tbar sta
> tistic 
                         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)