general models

[ECWFM@xxxxxxxxxxxxxxxxxxx]

Wednesday 6/4/94

Noting the recent interchange between Paul Davidson and Barklet Rosser, I make
the following points. I essentially agree with Barkley that a
multiple-equilibrium framework encompasses the single (unique) equilibrium
model and is more general. I suppose it all depends on what we mean by general.
But to me, general means the ability to embrace the results of other competing
models and offer more. Note I have not necessarily included non-linearity in my
concept of a general model, more about which later.

Barkley claimed that the evidence is strongly indicative of non-linear
stochastic behaviour in our time-series. Possibly. The evidence is somewhat
mixed. What cannot be substantiated is a view that the macro data behaves in
accordance with a natural rate world (one of unique equilibrium).

The problem is that the tests we have available are still sample dependent and
sensitive to the way we pose the null. My own feeling is that the macro data
probably contains both sources of non-stationarity (deterministic and
stocastic), rendering a view of the world which says that the business cycle is
a transitory (and random - mean zero) fluctuation around a deterministic trend
rather dubious. I note that the majority of macro texts are built on this view
of the relationship between the long-term growth path and the short-term cycle.

>From this type of model one gets a unique equilibrium. It is the basis of the
claim that the unique equilibrium is deterministic (set up by structural micro
parameters) and is resistant over the longer-term to aggregate government
policy. Hence the anti activist view of new classical economics, for example.

I would call this a very specific model. A unique equilibrium with no
government influence at macro level in longer term. If the time series do
contain stochastic non-stationarities (with or without deterministic
components), a more general model emerges. Because then, the non-deterministic
component(s) of the series cannot be considered mean-zero transitions around a
trend. The trend itself has stochastic elements capable of being shocked by
exogenous factors (perhaps government aggregate policy).

In this case, a range of equilibria occurs depending on historical evolution.
There is no unique equilibrium specified in this type of framework (model). It
all depends. The path the economy takes then depends on the shocks it receives
and the equilibrium it is heading to can change as the path ensues. So the
dynamic model in this case may contain an error correcting component, the
specification of which depends on the historical shocks that the process has
been subjected to. The target of the error correction is dependent on the
history, rather than being unique and ahistorical.

That is a much more general model than the former. Under certain conditions
regarding the dynamics and the form of the error correction, this general
framework can embrace a unique stable equilibrium. But it is likely that the
conditions would be very restrictive such that the real world would be
forgotten and we would be counting angels of the pin head (a sort of quote from
Paul in a great piece of his some time ago). I would have thought this is where
we (PKs) can effectively make our break from N/C economic thinking. The
multiple equilibrium world represents a building block to develop a paradigm
shift in the future.

As to non-linearity vs linearity. The evidence is also mixed there. It cannot
be clearly shown that the seeming non-linearities are not just mean shifts. But
I would not push the claim myself. For me, I simply approximate non-linearity
in some neighbourhood and proceed in the linear world. Clearly, this is a very
partial approach. The non-linear approach allows is to use linear approximation
for tractability and computation, but a linear approach could never recurse
back into a non-linear world (I don't think). In that sense, the non-linear
model encompasses the linear world and is in my view more general.

I would say that this part of the story is less important to me than the issue
of unique or multiple equilibrium(a)

hope my thoughts help a bit.

kind regards bill mitchell department of economics university of newcastle nsw
australia ecwfm@xxxxxxxxxxxxxxxxxxx