and I from the cost function would have allowed these variables to move
12 illustrates this proposition.)2^ If we believe that the model
reflects the economy in a reasonably accurate way then it could be
concluded that the government could have attained a more effective
stabilisation of the balance of payments position over a twenty-period
horizon beginning in the second quarter 1965. The historical results
suggest that while monetary policy was moving in the correct direction, it
was not manipulated sufficiently to produce results similar to those
obtained in the IEB1 experiment. How can we account for what appears to
be a historically cautious use of monetary policy (in terms of the linear
quadratic framework a "cautious" policy could be a policy resulting from a
reasonably heavily weighted control)? One answer is that the authorities
were unsure about the correct system structure but had a general idea of
the size of policy impacts and it is equally conceivable, and indeed most
likely, that it was not possible to obtain precise forecasts or current
information about the uncontrollable exogenous variables. This leads to the
not surprising result that, given better information about the system and
the exogenous variables, the easier it becomes to stabilise the system.
What is of interest however, is that even with a structurally estimated
model and exact information on the uncontrollable exogenous variables, it
may be possible to effectively fine tune the system within reasonable
bounds given costs on the controls. This suggests that a substantial
historical improvement in the performance of FR could have been obtained
if the authorities had been willing to allow monetary policy to adjust in
a more extensive manner. It cannot be emphasised too strongly that the
above analysis depends on initially having a fairly accurate model. The
model employed here obviously has weaknesses but if the policy multipliers
are close to the "true" multipliers then the results and conclusions
Nominal DM
$ Bil
Nominal FR
Historical IEB1 IEB2
performance.
The second experiment, IEB2, consisted of trying to exactly
achieve internal and external balance regardless of where the system
directs the other endogenous variables. In this situation we have two
targets and two controls and provided that the appropriate rank conditions
on the matrix of instrument impact multipliers is met, exact fine tuning
can take place. If the instrument impact multipliers have rank equal to
two then the problem collapses to a simple strongly-Tinbergen target path
problem whereby the authorities can hit the desired targets in every period
without resorting to anticipation or compromising the targets. The matrix
of instrument multipliers relevant to the targets of Y and FR is given
by
2.1984 0.1651~ 0.0512 -.2547
and p[tTq] = 2 hence the policy planner is indeed operating within a
strongly-Tinbergen framework and optimisation within the linear/quadratic
framework is redundant. As a point of comparison IEB2 was carried out in
two ways. Firstly, the problem was solved as a dynamic fixed target
problem with zero anticipation and secondly, it was solved within the
linear/quadratic framework. It has already been pointed out that the
linear/quadratic approach is unnecessary. However, it is of some interest
to compare the two results, particularly in light of the fact that in the
linear/quadratic framework some initial adjustment may take place as the
time paths of the targets react to the initial conditions (therefore even
with two targets and two instruments it may not be possible to exactly hit
the targets until the system settles down) while in the fixed target
framework the initial conditions are explicitly included in the solution.
quadratic control laws are solved initially over the entire planning
period and in this respect may be computationally more efficient than the
fixed target approach.
To enable the achievement of internal and external balance
within the linear/quadratic framework, both controls were allowed to adjust
freely. In terms of the cost function, G and DM were assigned zero
weights while FR and Y were weighted heavily using multiple weights to
maintain the exact desired trade-off between targets. The relative weights
assigned we re
Y FR G DM
1000 1000 0 0
All other state variables were allocated zero costs and allowed to adjust
freely. The results illustrate the fact that both solutions are identical
(allowing for some insignificant deviations in the linear/quadratic case)
which indicates that the optimally derived solution did not need to settle
down as a result of the initial conditions. Recall that the targets for
Y and FR are simple mappings of the initial conditions into target
vectors. Limited as the evidence is, a tentative conclusion can be drawn
along the lines that as long as the desired target paths' are non-extreme
mappings of the initial conditions, then the linear/quadratic solution
will be identical to the fixed target solution (provided the number of
targets and instruments are equal) for alX time periods of the planning period.21 The words "non-extreme" are very important qualifiers to the
above statement and are best interpreted as meaning that economically
meaningful targets are specified, for example, to specify a target of 10%
annual real growth in Y from the appropriate initial condition for Y
As the results of the two solutions are identical the discussion
that follows can be regarded as being applicable to either technique. The
results are graphed in Figures 8 to 11. To keep real Y on target
required an expansionary fiscal policy, particularly towards the end of
the planning period. This can be seen from Figure 10. Note that only the
latter part of the optimal G has been graphed. This procedure was
adopted to avoid confusion as the optimal G for the first part of the
planning period tracked between the optimal path of IEBl and the target.
The need for strong fiscal policy stems from the fact that the target level
of G is not sufficient to sustain the target level of real Y. In
addition, the optimal consumption path falls below its target. As
consumption is the largest component of the national income identity, it is
reasonable to expect that if it is declining then Y will tend to decline
also unless strong fiscal action is taken to offset the movement in C.
The divergent movement in the optimal paths of Y and C illustrates the
important problem for applied control theorists already mentioned above, and
that is the consistent specification of identities in terms of the
components of a particular identity. It will be remembered that the target
value of Y was consistently constructed from the targets of the
components of the national income identity. If all components are on
target then Y will be on target. However, as we have seen in the earlier
simple example and in IEBl and particularly IEB2, the value of Y that is
chosen as a target will not necessarily be able to be achieved
simultaneously with the target levels of its components. If policy
planners are concerned about achieving target levels for all their income
variables then high costs must be allocated to the appropriate variables
in the cost function.
the open and monetary sector variables (excluding FR of course) than the
corresponding movement in income variables in the achievement of internal
balance. The requirement that external balance be achieved implies that
capital flows and the current account balance are equal. This has been
achieved but at the expense of a stable total monetary base and a time
path for the supply of money which exhibits more severe expansions and
contractions from the path obtained in IEB1. To maintain external
balance, monetary policy has been used more extensively than it was in the
first experiment with the optimal path characterised by excessive expansions
and contractions. Severe changes in monetary policy are necessary in
order to maintain the equality between CF and CB and to ensure that FR
has a constant effect on the domestic economy. Even though FR is at its
target level throughout the planning period it does have a varying
indirect effect on the income sector through the excessive use of
monetary policy required to keep FR on target. The effect of the monetary
sector on Y does appear to be largely negated by fiscal policy with little
in the way of excessive counteractive fiscal policy required to offset the
monetary sector. This result is particularly encouraging as it indicates
that the internal balance target can be achieved without excessive fiscal
policy and without substantially disturbing the application of fiscal
policy to account for monetary and external factors. On the other hand
the severe stop-go monetary policy is a result not only of the
requirements of the purely external variables and the uncontrollable
exogenous variables which directly affect the external and monetary
sectors, but is also a result of the fiscal policy necessary to achieve
internal balance. This result occurs through the strong influence of the
income sector on the open and monetary sectors, an influence which is
This can be seen from the reduced form coefficients set out in Chapter
Ebur. The monetary instrument not only has to contend with trade-offs
in the non-income sectors but has to offset the influence of the income
sector as well. The model is not sophisticated enough to reveal all the
implications of a stop-go monetary policy and resulting behaviour of the
money supply and interest rates. In a more complete model the presence
of a severe monetary policy could have serious consequences for financial
and asset markets. If so, then it raises the question of whether or not
there should be a money supply or interest rate target incorporated into
the list of major policy goals of governments.
In contrast to IEB1, interest rates each higher levels in the
second experiment. The short rate is forced up by the increase in Y
relative to the first experiment and by the fact that generally there is
not a large enough increase in M to offset the influence of Y. The
result is that by the end of the planning period the long rate has risen