67 The higher levels of RL are not sufficient to generate a

significant downward movement in I as the strong fiscal action and

high levels of Y are able to keep real I at a desirable level. As

with IEBl, the high levels of RL over the last four periods have no

influence on the system due to the lag structure but a significant

downward shift in I could be expected in the next planning period.

Both monetary and fiscal policy have been strongly applied to

achieve the desired targets. The requirement that both controls be allowed

to move freely has meant that G and DM have been able to bear the

burden of target achievement without excessive adjustment in all other

non-weighted state variables with the possible exception of the total

monetary base and the rates of interest. The variability in the total

function which accounts for the more subdued performance of M in

comparison with these variables. With so many income variables taking on

the role of intermediate variables, comparatively little adjustment to

complement the controls in the achievement of internal balance is

required. The behaviour of the intermediate monetary variables is

reversed however from the income variables with the requirement that they

move excessively to complement the achievement of external balance.

The optimal stochastic solution results in neither internal or

external balance being exactly achieved, which is to be expected. Fifty

monte carlo simulations reveal that the optimal paths for both Y and FR

track very close to their targets for all combinations of additive shock.

An illustrative example is given in Figure 11. The optimal path for FR

fluctuates about its target to a greater degree than real Y but the

shocks are not sufficient to move FR away from the general area of the

target as was the case in IEB1 (remember that identical shocks are used

for the illustrative examples). The additive disturbances are not

sufficient to shift real Y substantially off target with the optimal

stochastic path closely tracking its target and deterministic counterpart.

The stochastic example is so close to its target that it was not possible

to graph a sufficiently distinguishable path from the target in Figure 11.

The behaviour of the other major state variables is also similar to the

deterministic case, allowing of course for the impact of the additive

disturbances. The results clearly illustrate the self-correcting nature

of the optimal control laws in the linear/quadratic framework to additive

uncertainty. The fixed target solution is also self-correcting in relating

to past shocks as x^_ is explicitly included when we solve for the

appropriate values of the controls in each time period. It is worthwhile

it is only in a strongly-Tinbergen world with as many instruments as

targets that the dynamic fixed target approach to stabilisation will be

able to adjust to additive disturbances from period to period.

The optimal stochastic paths of the control variables provide

some interesting results. In the deterministic case strong expansionary

fiscal policy was required to achieve the desired goals. The illustrative

stochastic results (not graphed) indicate that under uncertainty this need

not be the case. The optimal G becomes closer to its target over the

final periods of the planning period than the corresponding deterministic

G. Monetary policy is once again of a stop-go nature but in the stochastic

case it is more severe, particularly in periods fifteen to twenty.

Although the direction of monetary policy has not been reversed, it is

severely contractionary in the last five periods by comparison with the

deterministic results and the target. More importantly, we have a switch

in the optimal mix of monetary and fiscal policy from a situation of an

expansionary fiscal policy in the perfect information case to a less

expansionary fiscal policy and more severe monetary policy in the imperfect

information case. The change in the mix of policy can be illustrated by

the change in the RMSD value for both control variables when we shift from

perfect information to imperfect information.

RMSD RMSD

G DM

D 167 516

S 153 807

The letters D and S refer to deterministic and stochastic solutions

respectively.

The third experiment, IEB3, consisted of attempting to achieve

was emphasised relative to fiscal policy. To achieve this policy mix a

low cost was placed on deviations of DM from its target path while high

costs were placed on G,Y and FR. G,Y and FR were weighted such that

a one percent deviation from the relevant target would have a thousand

times the cost of a similar movement in DM. The relative weights were as

follows

Y FR G DM

1000 1000 1000 1

The computer program accepts the relative weighting specifications and then

generates actual weights which will maintain the desired relativity for all

target values and all time periods. Once again we have a situation in

which the number of targets equals the number of instruments but with the

restriction that only one instrument can adjust in a completely free

manner. This situation is not completely removed from the real world as it

is not uncommon for governments to try and maintain a level of government

spending to satisfy social and political needs and then rely on monetary

policy to carry the burden of economic stabilisation.

The optimal deterministic paths for Y and FR indicate that

given a restricted application of fiscal policy and a free application of

monetary policy, the dual targets of internal and external balance cannot

be achieved simultaneously (see Figures 13 to 15). Initially, real Y is

very close to its target (the first four periods for Y have not been

graphed in Figure 13 to avoid unduly complicating the diagram) but as the

planning period progresses it begins to fall just below target with the net

result being an optimal path for Y which is very similar to the

corresponding path obtained in IEB1 where Y and G were also weighted

R e a l Y ft B il N o m i n a l F R T a r g e t _{--- I E B 3} F I G U R E 13 I E B 4

ft Bil

ieb

4

--- IEB3