Euler

 This is rather technical. Noah Smith says this equation does not work, it is the basis upon which economist model a collection of agents.   It says that the interest rates and the value of time should be correlated in a real economy.  For example, if we buy shoes every six months more or less, then their is an inventory of shoes that covers the 'more or less', enough spare shoes so that when we randomly arrive to buy a pair, there are some in stock.  If we buy our shoes with a credit card six month loan, then there must be an inventory of money to match.  The variation in both inventories will be the same when everything is balanced.

So, the inventory cost of a six month shoe supply is the six month interest rate. The economists say the theory doesn't work.
The banker needs to sample the shoe inventory often enough to set the interest rate soon enough to keep the probability of inventories going to zero small. If the banker receives the inventory level every two months, then both the shoe inventory and money inventory vary every two months, the residual error we can call it.


The figure above is also from Noah Smith, and the red dotted line is what the bankers should be setting the interest rate at, if the equation worked. When the red dotted line is high, consumption is low. But consumption increases when rates are rising. There seems to be a delay between the time interest rates are set and consumption changes. If you move the red dotted line left by five years, thing line up.

Here is nominal GDP and the one year rate. Is the banker keep up with the economy? Yes, until 1990, Greenspan waited until he updated the one year rate to match the falling growth rate.  Then again in 2001 he held it low, then in 2010 Ben never raised it.

Why did the central bank slow down its update rate? The economy became congested and the inventory levels never reverted to Guassian. The bankers were increasing looking at delayed values for nominal GDP. The congestion is government caused.

This is an under sampled economy that will oscillate on the government inventory cycle, which seems to be about five to eight years.

 Here we see what happened to government by looking at its interest expenses. The interest expense in the budget is increasing volatile. It varies about 20%, and that is about 1/3 of GDP growth, and it happens on a two and four year cycle. 

The entire economy suffers a volatility in growth, induced by this interest expense. Hence the large reserves the private sector needs.

 We see that the change in interest expense divided by the change in nominal gdp, the blue line, is growing as the debt to gdp rises, red line. The entire economy has to set aside reserves to cover the demands on GDP growth from the government debt machine.