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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