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st: Re: interpreting ipshin results

From   Kit Baum <>
Subject   st: Re: interpreting ipshin results
Date   Fri, 19 Nov 2004 09:31:41 -0500

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

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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