The topic of testing for unit roots in panel data came up here not
so long ago.

In CVS and the gretl snapshots for Windows and OS X there's now
code in place for doing such testing. It's not in the GUI yet (and
neither is it documented), but is implemented as an extension to
the existing "adf" command. If anyone's interested in testing, I'd
appreciate any comments.

Here's the story. If you issue the "adf" command with panel data
you get (a) a brief account of the test for each panel unit plus
(b) a joint test for al units, if possible. (The per-unit test
output should probably be suppressed if there's an excessive
number of units in the panel, but right now you always get it.)

A couple of restrictions. First, with the regular adf test for
time-series data you can supply a list containing more than one
series and get multiple tests, but with panel data we do only one
series per command; if the input list contains more than one
series we ignore all but the first one. Second, the regular adf
command defaults to performing 3 variants of the test -- with
constant, with linear trend, and with quadratic trend -- though
you can change that via the command options. With panel data we
only do one variant at a time, by default the test with constant.

Some details: The joint tests have the null hypothesis that the
selected series is non-stationary for all panel units; the
alternative is that the series is stationary for at least one
unit. The test statistics are taken from Im, Pesaran and Shin
(Journal of Econometrics, 2003) and Choi (Journal of International
Money and Finance, 2001).

The IPS test involves computing the average value of the
Dickey-Fuller t-statistic (t_bar). If the lag order for the test
is non-zero, t_bar is referred to the distribution that IPS call
W_tbar, which is asymptotically N(0,1). If the lag order is zero
but the time-series length differs across the units, we use the
IPS Z_tbar statistic, which again is N(0,1) asymptotically. If the
order is zero and T is the same for all units we report exact
critical values as tabulated in the IPS article.

(Note that the IPS test cannot be done if the --gls option to the
adf command is given. There are also constraints on the minimal
T for each unit.)

The other test reported (Choi) is based on the p-values from the
per-unit Dickey-Fuller tests. Three variants are given: the
inverse chi-square, inverse normal and logit tests. These differ
in how the p-values are "aggregated" and the distribution that the
resulting statistic follows. For the inverse chi-square test the
null is rejected if the chi-square value is big enough; for the
others it is rejected if the test statistic takes on a large
enough negative value (which is also the case for all variants of
the IPS test).

I've tested some of this against the ipshin.ado extension that's
available for stata. We're pretty close in the cases I've tried
but I'm not sure that ipshin gets everything right so I'm not
necessarily trying to replicate exactly it reports. If anyone can
test against other IPS or Choi test implementations that would be
of interest.

Allin Cottrell

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