From [Marc Abrams (2004.09.16.1319)]
[From Rick Marken (2004.09.16.0830)]
It's the derivative, not of GNP, but of the function relating GNP to time:
GNP = f(t). Since we don't know f() we can't find dGNP/dt analytically. So
we have to estimate it based on the data.
Rick, I wish you would think this through more clearly. How can you figure
out the derivative function f'(x), if you don't know what f(x) is?
This is _NOT_ the derivative, nor is it the _RATE OF CHANGE_. This is an
_AMOUNT_ of change and it's called a _DIFFERENCE EQUATION_. It tells you the
_difference_ in the _amount_ from one period to the next. It does _not_
specify the _RATE_, or the velocity (to use a loose term) of the gain or
loss in the accumulation. A rate determines how quickly something is
changing, not by how much.
Check out _Principles of Systems_, Jay W. Forrester, Productivity Press.
System Dynamics is based on the concept of this very notion of stocks or
levels (integrals) and rates (derivatives).
One interesting aspect is that Forrester does away with using derivatives
entirely, using algebraic equivalents and determining the levels through the
use of difference equations and simulations. A rate can be fully determined
by a level and a constant.
Forrester contends that true differentiation does not take place in the real
world and that integrals are nothing more than _averaged_ rates of change or
accumulations over a period of time
Rick, as much as you might think I'm out to bust you hump, I'm not. But how
can we have a dialogue when each of us sees the world from such different
perspectives.
The notion that aspects of our economy are 'controlled' is pretty
self-evident to me, since we as individuals are 'controlled' I would suspect
emergent behavior amongst us could be as well. But when you take something
like the GNP (Total Gross Output) of an economy, isn't that like looking at
a crowd of people and trying to attribute the purpose of each by the
observed behavior of a few (since you can't possibly observe _everyone_)
over a relatively short period of time?
How far back can you go with quarterly GNP data? Have you tried correlating
anything else to the GNP numbers over very long periods of time?
Showing the differences you did in the 5 quarters hardly gives me a good
understanding of what 'normal' fluctuations might be in the numbers and
whether the magnitude of change is important, and what kind of significance
should be attributed to the differences.
It is the formula economists use to estimate the value of the derivative
of GNP = f(t) at time t. The formula estimates economic growth (or
recession), which is the derivative of GNP = f(t) at time t. Economists
typically write this equation differently that I did. The economists'
formula is:
dGNP/dt = [GNP(t)/GNP(t-1)] -1 (1)
This is mathematically equivalent to my version, reported above:
dGNP/dt = [GNP(t)-GNP(t-1)]/GNP(t) (2)
I think it would be a good exercise for you to prove that equations (1)
and (2) are equivalent.
Rick, the question is not _equivalency_. These are _not_ _derivates_, I hope
you understand that.
This does not change your argument nor does it change the point you are
trying to make, but you need to understand you are talking, _not_ about how
fast something is changing, but about how _much_ something is changing.
When you seem to have difficulty in distinguishing between the two (Rates &
Stocks), your argument, no matter how valid, takes on credibility problems.
Can you see how that can happen?
For instance, you say above, "the formula estimates economic growth (or
recession)..." A recession does _NOT_ indicate shrinkage of the economy. It
is a _slowdown_ of growth, _not_ a _reversal_. So, during a recession the
economy is still growing but it's just at a slower rate. Economic 'growth'
can be described as a derivative _if_ you talk about the rate of change or
how quickly the debt or deficit is growing or shrinking. Both the debt and
deficit are stocks, as is the GNP. That is, they are all _accumulations_
over time of integrating processes.
When you read in the papers that "GNP grew at a rate of 3.2% last
quarter",
what is being reported is an estimate, using equation (1) or (2), of the
derivative of the function that relates GNP to time during an instant (dt)
in the middle of the last quarter (t).
What ever floats your boat Rick. I think we've just about exhausted this
subject. I have nothing more to say on the matter, but before you try and
get your 'economic' stuff published I think you might want to re-think some
of your ideas.
Marc