First note that lngap is not the ratio of two variables; it is the
difference of two variables. The fact that the difference of logs is
the ratio of the unlogged variables is not relevant here. I agree,
though, that the difference of two variables is also likely to contain
a unit root if one of them does.
But a panel unit root test is in some sense a box score over units of
the panel; in the case of ipshin, it is an averaging of the
dickey-fuller values for your states' individual t-ratios. It would be
easy enough, as Nick suggests, to look at those values individually,
and see whether the null that they are all I(1) is sensible here.
ipshin is flexible in allowing for variations in lag length, etc. and
allowing a fraction of the units of the panel to be I(1) while others
are I(0). But it would be interesting to see what you get from the
individual states' tests of stationarity.
I really question whether it makes any sense to treat the (log of the)
minimum wage as a random variable. It is a policy variable, and to my
understanding is a step function. Most periods it does not change; some
periods, the legislature responds to pressure and increases it by a
substantial amount. In economic modelling terms, it is a jump process
(and only positive jumps are allowed in the nominal minimum wage).
Although one can certainly apply mechanical time series techniques to
such a variable, I wonder why it is sensible. I am not a labor
economist, but I would think that the interesting thing would be the
REAL (inflation-adjusted) minimum wage, using a state deflator, vs. the
5th REAL wage percentile. Now dividing each of those by the same price
deflator will cancel out of your ratio (or difference of logs), but it
makes more sense from the econometric standpoint to subject a real
minimum wage (which is not a policy variable, but an outcome) to a unit
root test than it does the series you are using.
I will add a message to ipshin indicating that the IPS tables are not
applicable for more than 8 lags. That is why missing values are
appearing in your output. I question whether 17 lags (almost 9 years)
makes sense--although again if you're doing unit root tests on a jump
process, any automatic lag selection procedure is likely to be fooled
by its trajectory.
Kit Baum, Boston College Economics
http://ideas.repec.org/e/pba1.html
On Nov 19, 2004, at 2:33 AM, Jeanette wrote:
When I create
a third variable (log of 5th wage percentile - log of minimum wage,
or"lngap"), the IPSHIN test indicates that it is stationary. How can
it be
that the ratio of a stationary and nonstationary variable is
stationary?
(Some background info: the panels in this dataset are US states -- all
50,
the time points are 6 month intervals over 20 years).
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