This one is easy. The economy grows about 3%, or .03. Call that the mean or variance if it is poisson. The .03 is also the adaptation variance, so multiply by 33 to normalize, and you get about a 5 bit two complement number which uniquely identifies, decodes, each of 30 representative transaction. This is off a little bit, I should be ontaining the second derivative, but the short end will have a compression ratio near to one so I am approximating the constrained flow tanh equation.
At maximum tanh'', the second derivative, the compression ratio is about 1/1.7, so the economy needs about 1.7*30 to encode the system, so make the total number of transactions close to 50.
How long does it take?
Look at the charts since 1972, and we bet about 50 years. That is, we sample at the seasonal adjustment rate.
Why did I get trillions of transaction before?
I likely failed to take the log, and the tanh was extremely close to one, about .999 when looking at the loan/deposit rates. The fed is a moving target, but the correct number the Fed was assuming is likely 1000 years. But that has shifted recently with the reverse repurchase, and we need to keep looking and correcting this method.
What the Fed is going
It is trying to get member banks and the reverse repurchasers to go and find business that can pay the remit tax that the fed collects for DC. So it wants loans to deposits to drop, deposits to rise up until the remits drops from 80 billion to the more reasonable 20 billion. The current remit tax drives up the transaction costs so member banks cannot make money on the 2-10 year slope of the curve.
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