QUERY Definition of exogenous
Posted: Tue Apr 01, 2008 6:46 am
Posted by Jean-Jacques Laublé <jean-jacques.lauble@wanadoo.fr>
Hi Bill
You write
<And perhaps my understanding of exogenous is dead wrong. I draw a
<distinction between constants that represent behavior over which
<decision makers have no control and parameters which are dimensions of
<policy or decision making over which they have control.
I have thought during the week end about what is exactly an exogenous
variable.
I found that I had not like you a clear understanding of what it was
exactly.
For instance is a variable that would represent the varying demand over a
year and formulated with the following equation exogenous?
Variable in question = base level + ( amplitude of sine wave in demand
*sin(6.283* Time/period of the sine wave)) where period of the sine wave is
12 months.
This variable represents roughly a seasonal demand with a trough and a peak
in a year. Intuitively it looks exogenous.
But somebody could argue that it depends from parameters and from the time
and even that it can be predicted and that therefore there is nothing really
exogenous in it.
The same person could argue that he would accept to name it exogenous if
there was some noise in it that would make the variable unpredictable. But
one can argue then that if there is some noise, everything in the model is
unpredictable.
Example of the equation with noise in it:
Variable in question = base level + ( (amplitude of sine wave in demand *
random (0.8,1.2)*sin(6.283* Time/period of the sine wave))
So relying on the noise to define the exogenous character of a variable does
not seem to work at least alone.
I have then a definition for an exogenous variable.
A variable that is only time dependant.
Only time dependant means that its variability comes exclusively from the
time plus some parameters and not from the behaviour of the model, and in
particular
from the state of the levels at the beginning of each period of time, like
all current variables.
The time dependency can be formulated with a function, with or without
noise, or with a rough data sequence.
Two types of exogenous data could be considered. One where the manager in
the model can predict the value in the future, and one where he cannot
predict it. This means that no decision can be taken in the model
considering future or even actual values of the variable. Decision could be
taken only considering past values.
One can imagine a model where the variable is formulated without noise and
where one supposes that the manager in the model does not know the future
value.
So the exogenous value can be considered predictable or not, depending on
the knowledge of the manager about the equation of the variable.
If the manager inside the model, knows the formulation of the variable, the
variable will become endogenous otherwise it will become exogenous.
It is necessarily exogenous if there is noise in the equation, and if the
variable is a sequence of values depending of the time (data), it will be
endogenous if the manager knows the future values and otherwise exogenous.
To resume for the people that find my description a bit lengthy.
The definition of an exogenous variable is a variable that is only time
dependant with some parameters, is independent from the behaviour of the
model and whose behaviour in the future is known or not known from the
actors taking decisions in the model.
I believe that if the manager knows the future values of the variable, one
can too eventually consider it as exogenous. Everything is a question of
definition. I
would eventually prefer to name a variable really exogenously intuitively
only if the manager does not know its future values, whatever the way it is
formulated.
In the reality, in my own problems many variables are partly endogenous and
exogenous.
Because they depend from exogenous but known factors, like the first part of
the deterministic equation, and have a noisy part unpredictable, the
difficulty being to reduce that unpredictable part to a minimum while still
formulating it precisely.
Am I right or is there something wrong in my definition?
Regards.
Jean-Jacques Laublé Eurli Allocar
Posted by Jean-Jacques Laublé <jean-jacques.lauble@wanadoo.fr>
posting date Mon, 31 Mar 2008 18:16:36 +0200
_______________________________________________
Hi Bill
You write
<And perhaps my understanding of exogenous is dead wrong. I draw a
<distinction between constants that represent behavior over which
<decision makers have no control and parameters which are dimensions of
<policy or decision making over which they have control.
I have thought during the week end about what is exactly an exogenous
variable.
I found that I had not like you a clear understanding of what it was
exactly.
For instance is a variable that would represent the varying demand over a
year and formulated with the following equation exogenous?
Variable in question = base level + ( amplitude of sine wave in demand
*sin(6.283* Time/period of the sine wave)) where period of the sine wave is
12 months.
This variable represents roughly a seasonal demand with a trough and a peak
in a year. Intuitively it looks exogenous.
But somebody could argue that it depends from parameters and from the time
and even that it can be predicted and that therefore there is nothing really
exogenous in it.
The same person could argue that he would accept to name it exogenous if
there was some noise in it that would make the variable unpredictable. But
one can argue then that if there is some noise, everything in the model is
unpredictable.
Example of the equation with noise in it:
Variable in question = base level + ( (amplitude of sine wave in demand *
random (0.8,1.2)*sin(6.283* Time/period of the sine wave))
So relying on the noise to define the exogenous character of a variable does
not seem to work at least alone.
I have then a definition for an exogenous variable.
A variable that is only time dependant.
Only time dependant means that its variability comes exclusively from the
time plus some parameters and not from the behaviour of the model, and in
particular
from the state of the levels at the beginning of each period of time, like
all current variables.
The time dependency can be formulated with a function, with or without
noise, or with a rough data sequence.
Two types of exogenous data could be considered. One where the manager in
the model can predict the value in the future, and one where he cannot
predict it. This means that no decision can be taken in the model
considering future or even actual values of the variable. Decision could be
taken only considering past values.
One can imagine a model where the variable is formulated without noise and
where one supposes that the manager in the model does not know the future
value.
So the exogenous value can be considered predictable or not, depending on
the knowledge of the manager about the equation of the variable.
If the manager inside the model, knows the formulation of the variable, the
variable will become endogenous otherwise it will become exogenous.
It is necessarily exogenous if there is noise in the equation, and if the
variable is a sequence of values depending of the time (data), it will be
endogenous if the manager knows the future values and otherwise exogenous.
To resume for the people that find my description a bit lengthy.
The definition of an exogenous variable is a variable that is only time
dependant with some parameters, is independent from the behaviour of the
model and whose behaviour in the future is known or not known from the
actors taking decisions in the model.
I believe that if the manager knows the future values of the variable, one
can too eventually consider it as exogenous. Everything is a question of
definition. I
would eventually prefer to name a variable really exogenously intuitively
only if the manager does not know its future values, whatever the way it is
formulated.
In the reality, in my own problems many variables are partly endogenous and
exogenous.
Because they depend from exogenous but known factors, like the first part of
the deterministic equation, and have a noisy part unpredictable, the
difficulty being to reduce that unpredictable part to a minimum while still
formulating it precisely.
Am I right or is there something wrong in my definition?
Regards.
Jean-Jacques Laublé Eurli Allocar
Posted by Jean-Jacques Laublé <jean-jacques.lauble@wanadoo.fr>
posting date Mon, 31 Mar 2008 18:16:36 +0200
_______________________________________________