Tuesday, April 22, 2008

Decomposing Decoupling Theory

I may have to revisit this tomorrow after my weekly meeting at the trade floor, because I feel really sleepy right now. I may even bypass this later and write something else as my mind is not that coherent right now.

dW = (DW/DU) x dU + (DW/DC) x dC + 2 x DW^2/ (DU x DC) x dUdC + ( higher order impossible I think, the shape has to be "convex")

More notes added (04/24/2008): some people at work - from country C - "insisted" that D2W/DC2 is NOT NEGLIGIBLE when C relative size to the world is still rather small (5%). However, I am keeping this simple for now even if their argument has validity. Besides, they were rather silent when I told them that whatever the amount D2W/DC2 is, that amount is TIME-DEPENDENT. That means after a massive expansion of both U and C, the graph below shifted to the left at least "temporarily", making the D2W/DC2 term negligible in the SHORT RUN. That is as far as I am willing to concede. But thank you for the critique, it certainly is very valid.

if we assume:

W = U + C

then from taylor rule:

dW = dU + dC + 2 x [DW^2/ (DU x DC)] x dUdC + "HigherOrderTerm"

dW/dt = dU/dt (#1) + dC/dt (#2) + X (#3) (units shall be in US$)
[rate of change from "InteractionTerm" - to be called "X" from now]

Note again: Time to spell it out to add more clarity to the discussion
(1) dU/dt = Rate of change in USA GDP
(2) dC/dt = Rate of change in China GDP
(3) 2 x [DW^2/ (DU x DC)] x dUdC , or affectionately known as "X", the rate of change of World GDP as a reasult of USA/China trade.
HigherOrderTerm contains what I show as impossible, given the chart I posted relating W with its "Letter" components.

I 'll be back later when I have time but something tells me no matter what #2 is, #1 is gonna suck donkey d*** and #3 (X) is already negative as we speak, or less positive if you think it WAS positive before 2007. Decoupling condition is dW/dt > 0 and I really don't see how despite the ceaseless news claiming such to be a fact.

Unless d2W/dC2 that was part of the ignored terms were in fact important, but does that say the more C goods produced in sweatshops the more demand of it outside of C?

Or is it possible that a frictionless economy occur such that, like perpetual machine the C industry grows as rapidly because productivity goes to infinity and internal consumption likewise?

Or was it that I ignored half the rest of the planet?!!

W = U+C is really U + C + (E + J) + A

But A is really small ( U is $13.5T and A is like $350B).

How about E + J? Well it's actually bigger than A, but when you are concerned with changes over time isn't d(E+J)/dt = 0 or close enough - thus will drop out eventually for these "retirement communities"? [evil grin]

The only cross term that seems positive for 2008 - 2009 is that of C and A. But C is $3.5T and A is one-tenth of that, and the rate of change of the trade between the two is negligible with respect to rate of change of W.

So, the math doesn't seem to work out. I'll rest for now, but the case is still open. I want to spend sometime to get to the bottom of this even if the answer looks VERY obvious just from the #s alone.


Okay, some more notes from a couple of question this morning.

A = GDP of Arab
C = GDP of China
E = GDP of Europe
J = GDP of Japan
U = GDP of USA.
W = World GDP


illiac64 said...

Great analysis!

MTGSPY said...

Thank you my friend.

Taylor rule is the basic of basic. Try to "predict" where things will end up by expanding a known point (NOW) and add the force (slope), hessian (accelerator), and any "cross" term whenever necessary.

While the economy is open ended, after making some assumptions regarding 1) the basic curve between W and its components GDP change, and 2) googling GDP #s and their growth for U,A,C,J, etc and plugging in some #s, one can deduce the impossibility of having

dW/dt, the rate of growth of the World, to be positive given the components very likely sum to negative.

Now I must be wary of the hedge fund snipers coming my way :D