Re: On trend stationarity and unit roots.

[BILL MITCHELL <ECWFM@xxxxxxxxxxxxxxxxxxx>]

John Irons comments on our recent "debate":

>A useful way of thinking about a series that may be either
>TS or I(1) is to think of the series as non-stationary
>but ``cointegrated'' with the trend. This follows
>naturally from the idea that the series itself is non-
>stationary, yet a linear combination of the series and
>another (namely the trend) is stationary. With this
>interpretation the distinction between a TS series and
>an integrated series with a drift (and which
>looks like it may be TS) is nearly
>meaningles as the quarrel is merely over where the
>non-stationarity lies.


well I don't entirely agree. If we model a process under two
assumptions - that it is TS and then as if it is a DS - then
express both in a moving average form and shock them by a unit
innovation, the cumulative response functions of each behave
entirely differently, even though the respective representations
are not differentiable by conventional tests (they both have
similar s.errors for example).

a near unit process is best thought of as a long memory ARMA process
sometimes referred to in the economics literature as a persistent
process (not to be mistaken, although it usually is with a hysteretic
process which is not autoregressive, but a unit root process).

the reason why it matters is that the persistence may be shorter than
political cycle. if the persistence is longer than the political cycle,
then an activist government policy can attenuate the results of the last
shock before the next one hits and thus improve outcomes (typically for
the unemployed). However, if there is low memory, the policy may just add
new shocks.

this is a very significant debate in macro. and (putting on my missionary
cap once again today), is a way in which econometric research can help us
to design policy. if anyone is interested in some actual work on modelling
persistence (half lives, full lives after a unit shock) in OECD countries
along the lines of the previous few points see my Applied Economics articles
in December 1993.

I found that in almost every OECD country, the UR exhibits very long memory
characteristics even though it is difficult to actually guage whether it is TS
or DS (although by definition it must be the former, despite the ADFs saying it
is the latter). the persistence clearly means that well designed policy can
attentuate and have permanent effects.

Now Paul how would you provide the same advice to the governments of the
countries concerned. How would you guage how long the time series seemed to
cumulatively respond to past shocks? How would you be able to advice them of
the likely magnitude of the attenuations for a given $ injection (at least
within 2 standard errors)?

kind regards
bill
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