Before proceeding any further with developing the framework of this
study, it is convenient to briefly discuss some of the practical
considerations associated with implementing optimal stabilisation policies.
A discussion of this aspect is warranted in light of the attitude of many
economists working in the optimal stabilisation field. In particular,
many researchers fail to discuss the feasibility of actually using optimal
control as a tool for stabilisation. Leaving aside the traditional
criticisms of the technique on the grounds of misspecified models,
uncertainty about the structural parameters and lags, and our ability to
adequately forecast uncontrollable exogenous variables (more of this later)
I will focus on the implementation of policy.
Consider the equation relation to the optimal control to the lagged
state, u* = Fx + f . Given that some components of the lagged state t t-1 t
vector are true first order lagged variables then it is almost certain that
the type of dynamic policy response described by the feedback relationship
above will not be applicable in practice. Firstly, even if the true exact
value of x^_ ^ were known at the beginning of the current unit time period
(period t as opposed to the entire planning period), the policy decision
and transmission process of governments and the bureaucracy would prevent
the desired value of u* from being achieved in that period. The feedback
relationship implies that as data about the past state does not become
available until the end of the current time period, which of course is the
beginning of the next time period, the implementation of policy is
instantaneous! If the assumption about some components of the past state
consists of say lags greater than two or three periods (converted of
course to equivalent one period lag structures - see chapter Four) then it
with sufficient time to implement it. However, even the presence of long
lags does pose some difficulties as the new variables defined to replace
those with lags greater than one period will also play an important role
in the feedback matrix F and contribute to the formulation of u* . This
t t
will become apparent in the ensuing applied discussion in later chapters.
One possible solution to the problem would be to make the planning period
less than say the longest lag to prevent some auxiliary variables from
taking on values in the feedback matrix. Once again, the reader is
referred to future chapters where feedback matrices for the applied experi
ments are presented and where it can be seen how auxiliary variables drop
out of the feedback matrices as the planning period approaches its terminal
time. The important point to be made here is that policy planners would
need to plan some time in advance in order to ensure that their desired
policies do in fact become realised at time t. The need for forward planning
refers mainly to government spending as instruments such as tax rates and
open market operations can be carried out almost instantaneously in terms
of say a quarterly model. A further need for forward planning in relation
to government spending arises from a need to calculate the government's
budget position for the entire year. In a quarterly model this would entail
planning optimally at least four quarters in advance. The compilation
of the budget and the allocation of funds to various factors also requires
time resulting in a need for perhaps a total of six quarters advance time
before the optimal policy can be implemented. At first sight it could be
argued that all policy lags of the system (not just impact lags) could be
explicitly modelled. While this is feasible in theoretical optimal
stabilisation work, for example Preston (1975) and Turnovsky (1977a) its
extension to an applied framework is highly dubious due to the great
occur through bureaucratic, institutional and political reasons.^
The need for forward planning also necessitates using forecasts
of the state vector x , to obtain u* and thus the optimal control will not
t-1 t *
be able to adjust for additive disturbances with the result that the
implemented u^_ will be sub-optimal. Even if the shocks are extremely
small, the model may not be able to adequately forecast the future and
the policy-maker will be severely limited in his ability to take account
of uncertainty. Whether or not ignorance of future shocks and poor fore
casts will pose serious problems, especially when fine tuning is desired,
depends on the degree of sub-optimality. Even if instantaneous policy
adjustment can be carried out there still remains the problem of gaining
good information about the immediate past state. It may be necessary to
derive the optimal control before the final figures for say income,
have been formulated for a particular quarter. Initial estimates can
contain "noise" elements which may obscure the "true" value considerably.
The problem of uncertainty about the immediate past state whether generated
by a need for forward planning or by an inability to correctly observe the
state at the appropriate time could severely limit the application of
optimal techniques as a knowledge of x^ ^ is required in each time period.
As we shall see below, the computation of fixed target solutions only
relies on a single estimate of the initial condtions and hence will suffer
less from errors in the state. Nonetheless for real world applications it
would most likely be necessary to plan in advance even within the fixed
target framework. While adaptive learning techniques may be useful
when policy implementation is instantaneous, they will be extremely
limited if policy decisions need to be made well in advance of the time
they are to be implemented. In any case, the experimental use of
performance of optimal stabilisation, for example the work by Abel
(1975), Macrae (1972) and Walsh and Cruz (1976).