Re: Reply to B. Mitchell, P. Davidson

[ecwfm@xxxxxxxxxxxxxxxxxxx (bill mitchell)]

Paul asks the following question:

>Dear Bill: What if I believe in a NAIRU, won't there be a cointegration
>between the level of employment and the rate of acceleration of the change
>in the price level. Don't these involve different degrees of differencing
>from the original level of the data? Are you saying that I can not test for
a NAIRU by cointegration?

First of all the NAIRU is a property of a certain type of _economic_ model
and as such cannot be tested via CI or any econometric model which only
tests hypotheses about stochastic or _econometric_ models. But we may see it
as being useful (and certainly i have seen it useful) to build an
econometric model based upon economic categories and relations.

In technical terms the answer is simple. You can only seek CI b/tw variables
or groupings of variables if they are of the same order of integration,
irrespective of how many times they are differenced. So a level could be
I(1), a first diff I(1) - implying its level is I(2), a second diff I(1) -
implying its level is I(3) and so on and these combinations might CI (might
not).

Of-course, you would not test the CI possibility in the case above, unless a
steady state relation (that made economic sense or confronted a steady state
that some economic paradigm said made sense) existed b/tw the level, the
first diff, and the second diff in the example above.

So if the log UR was I(0) and the measure of the price level was I(1)
implying that pdot (first diff in logs of the price level) was I(0) then you
could model via a CI framework, the relation of long run proportionality
b/tw the level of the UR and the rate of change in the price level.

Here is the rub. It relates to how you interpret the CI regression. Some
practitioners have called it an equilibrium relation, and let themselves and
others slip easily without much fuss into the economic meaning of the term.
of-course, that is a con job. it may be but then again it may not be
commensurate with what economists call equil. all one can really say about
the CI regression is that if it passes the tests and we find CI b/tw the
variables, then there has been some proportionality b/tw the variables over
a lengthy period. the linear combination of them expressed as the residuals
are I(0) and are stationary. so while the variables themselves may have been
non-stationary (stochastically), the "difference" b/tw them has been stable
(using the word to mean I(0)).

whether that is equil in the economic model sense is another issue. one
might argue that proportionality is definately a pre-condition for a state
of rest. that is one line of argument which i might support. another problem
with the Engle-granger approach which we have been implicitly talking about
here is that it defines a unique steady state. of-course, we can normalise
on any of the variables in the model, and as such OLS will give different
estimates of the "equil surface" for each of the normalised variables. some
have said that this means we interpret the equil. to be a surface rather
than a point. bit dodgy. johansen's VAR method overcomes this problem but
adds others.

with all this in mind, one can look more directly to thinking about the
NAIRU in a CI framework.

I have published work using U as the normalised variable and then running a
CI regression with various structural variables, and also a capacity
utilisation variable. if you believe the regression "sort of" measures the
steady proportional relation, and the CU variable CI with U, then, mapping
this back to our economic model, you might conclude that U* (the
proportional or long run U - the NAIRU?) is cyclically sensitive, b/c its
level is dependent on the cycle. all of this is open to dispute.

but the point is that it cannot be proven either way that this is useless
information for us to consider and generate. and i am the sort of guy who
likes to get as much info as i can and then decide on how my religous system
orders it.

hope that answers your question, Paul.

kind regards
bill


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