BIAS AND INSTRUMENT INSTABILITY
INSTRUMENT INSTABILITY AND SYSTEM DYNAMICS
G, is very stable for most endogenous variables, allowing of course for
a small adjustment at the beginning of the planning period due to the
influence of the initial conditions. The reaction of G, when both
instruments are permitted to adjust freely, when the target is the total
base is one of damped behaviour. This is most likely due to the
influence of FR on MB with FR being the most potentially unstable
variable in the system due to the term which appears in the
identity for FR . The influence of FR on the monetary variables
period. Of course it cannot be concluded that instrument instability
does not exist but G is at least stable over the twenty periods of the
policy interval. The only target which produces cause for concern is
CF. The achievement of a constant CF target requires that G
fluctuates between positive and negative values although the severe
movements are not part of regular oscillary behaviour and would perhaps
not be classified as instrument instability in the strict positive semi-
definite cost matrix case. The behaviour of G is due largely to the
time path of Y which fluctuates severely and feeds back into CF via
CB and (Y^-Y^ • T^e movement of G to offset this influence produces
further severe movements in Y which require further adjustment in G.
This result illustrates an important aspect of instrument stability in
that the impact of a stable variable (stable in the strict dynamic sense)
on a target can generate excessive movement in the instruments,
particularly if there is a close trade-off involved as there is between
G and Y.15 Perhaps what is required is a redefinition of instrument
instability to concompass the type of behaviour mentioned above and which
may not fall into the category of "pure" instability which is essentially
the type discussed by the abovementioned authors.
The behaviour of the monetary instrument when both instruments
are allowed to adjust is similar to that of G, that is, stable but
exhibiting slightly damped behaviour for MB and the other monetary
variables. Like G, the only "unstable" behaviour occurs when CF is
treated as a target and occurs for similar reasons to those given above.
DM must move to offset the influence of Y and CB and in doing so
generates greater movements in these variables requiring more adjustment
in later periods. Note that if Y,CB and the other endogenous variables
removed as the severe fluctuations in variables would be largely,
although not completely, removed.
The remaining instrument experiments with G and DM
alternatively fixed and free provide the most interesting and revealing
insight into the behaviour of the system. The requirement that only one
instrument can adjust in a free manner would suggest that the behaviour
of the free instrument would be significantly more severe than
corresponding behaviour of the fixed instrument. The general indicative
results are given in Table 5. The heading "stable" refers to a time path
which does not exhibit any tendency to explode upwards or downwards
(columns three and four) or exhibits severe oscillatory type fluctuations
which are covered by the second heading "severe movements". It can be
seen that for the majority of endogenous variables, the monetary
instrument is characterised by severe fluctuating behaviour or explosive
type movements. Only the rates of interest are compatible with a
relatively stable time path and even then some fluctuations do exist in
the instrument time path but at a level far removed from the fluctuations
contained in the time paths included in the second column. On the other
hand the behaviour of the fiscal instrument presents a more uniform
distribution between stable and significant downward movements. The
stability of the fiscal instrument in relation to the income variables
is not surprising and reflects the historical behaviour of G, if we
assume that G was historically aimed at income targets rather than
open or monetary sector targets. The indications are that an incorrect
assignment of fiscal policy could produce an unstable time path for the
fiscal instrument while the assignment of monetary policy to a particular
target without the assistance of fiscal policy, will most likely result
Table 5
Instrument Behaviour - One Instrument Fixed
Target Y MB FR CB YD Try C I IM M RS RL CF T Y MB FR CB YD TPY C I IM M RS RL CF T
Note: Table headings refer to the behaviour of the freely adjusting instrument.
important point to come out of the above analysis is that unstable
instrument behaviour is possible within the constraints of the model
and the analysis will assist in later experiments to ascertain whether
or not severe fluctuations in the instruments, if there are any, are
purely a function of any perturbations in the exogenous variables or
are a result of the underlying structure of the model. It is likely
that a combination of the two causes will be important but at least the
preceding experiments will help to disentangle the problem. The results
of the experiments also suggest that a combination of targets may remove
instability, particularly if one target is compatible with a stable time
path for one or both instruments. A further important aspect of
stabilisation is suggested by the experiments and that is that it may not
be possible to rely on one instrument or instruments of a similar nature
to stabilise a given target or targets when the other instruments are
specifically directed away from the desired targets. Further insight on
this aspect will be gained from the following experiments.
The brief analysis of instrument instability carried out in this
section not only gives insight into the particular dynamic instrument
characteristics of the model but also presents a simple technique for
detecting instability for particular targets when the time span is of
concern and a formal analysis is prohibitive. A formal dynamic analysis
would have been possible in this case but as it has already been pointed
out even if instability had been present, if it did not become a problem
until after the end of the policy interval then it would be of little
concern. It may be of concern in the next policy interval but by then
a structural shift may have occurred which would reverse the process.
A more exhaustive approach to the problem would have been to test all
endogenous variables in the cost function as the latter case would fall
directly into the Turnovsky framework. Testing all combinations would
be a computationally prohibitive process so only selected sets of
targets were chosen. The limited results obtained largely confirmed the
above assertions. An experiment was conducted within the Turnovsky
framework with zero costs on the monetary instrument with the result that
the time path for DM did exhibit a tendency to increase over time,
although not in an excessively severe manner, suggesting that instrument
instability of the more conventional analysis of stabilisation policy.
It should be noted that the problem of instrument instability in a fixed
target framework has been ignored mainly because at the time of writing
no general theory had been developed in this context and was beyond the
scope of this study to pursue such an investigation. Two observations
can be made, however, concerning the fixed target approach. First of
all it should be recognised that Holbrook's example is of a fixed target
path problem (one instrument one target) and can be extended to include
all strongly-Tinbergen dynamic stabilisation problems. Secondly, the
situation in which the number of targets exceeds the number of
instruments and a policy lead is required cannot be directly analysed in
Holbrook's framework or the fixed target framework,but the results of
the linear/quadratic experiments will give some indication of whether
or not instrument instability may be a problem. The unsatisfactory
nature of this approach can be counter-balanced by the fact that an
alternative rigorous analysis within the fixed target, policy lead