Hi all,
congratulations. very active and intellectual list.
I just want to share my knowledge on modelling and control with you.
Since almost 2 weeks I (as a new member of the list) see that there is a
terminological inconsistency between you and me.
let me explain what I understand, giving an example on how, for
example, consumption expenditures can be modelled and controlled.
There are many factors affecting consumption expenditures. Some of
these factors are measurable (eg, income, interest rates) and some not
(tastes, habits etc).
assume that we want to explain consumption expenditures using the
equation given below.
C(t) = a + b*Y(t) + c*X(t) + d*CV(t) + e*C(t-1) + error(t)
Y(t) = GDP(t) - T(t)
where C(t) denotes consumption expenditures at time t
and Y is income (which is obtained by substracting taxes from GDP)
, X is stock exchange index, CV is real interest rate
C(t-1) is previous years consumption.
The left hand side variables C and Y are called dependent or
endogenous variables. Because they are determined in the system.
The right hand side variables which do not appear in the left hand side
(X, T, CV) are called independent or exogenous variables. Y(t-1) is
called lagged endogenous variables.
There are 2 kinds of exogenous variables.
a) non-controlled exogenous variables: in our example, it is stock
exchange index. we cannot control it. it is determined outside of the
system.
b) controlled variables: interest rates and Tax. Government can try to
change the values of these variables in order to decrease or increase
the consumption in the country.
What the economists do is
1. collect the data on those variables
2. Estimate the parameters of the model given above.
3. Test the significance of the parameters etc.
4. Simulate the model. (simulation enables us to test the validity of model,
to analyze the behavior of the model ,ie, to see where the model goes
and how endogenous variables behave by shocking the value of an
exogenous variable ,to make policy analysis and to make forecasts.)
However, by using simulation it is not an easy task to find optimal values
of T (tax) and CV (interest rate) in order to maximize Consumption (C).
simulation delivers mostly sub-optimal solutions.
That is why what is done is to use optimal control techniques. because
as is said a typical optimal control problem evolves from simulation tasks
defining some output states to be influenced by some input control.
and
one of the objective of optimal control is to minimize the fluctuation of
selected endogenous (target) variables around the appropriate desired
levels.
Objective function can include either some endogenous variables or
some endogenous AND control variables. Both are expressed in terms of
deviations of their desired values.
But control variable is not a dependent (endogenous) variable. If a
control variables is endogenized then it can not be called as CV
anymore.
However, a very important point is the role of expectations or rationality.
For example, in our example above expectations about future inflation
will certainly influence our consumption decision today. How rational is
then model and control ? and how can it influence our decision making
process.
Economics and physicology have some different arguments and
approaches, see e.g.
http://www.santafe.edu/sfi/publications/Abstracts/98-09-086abs.html
and
http://www.santafe.edu/sfi/publications/Abstracts/92-08-043abs.html
I think last past is a bit confusing.
Sorry for the length of the email.
regards.