Why does the yield curve slope upwards?

The question came up in the Gurkaynak and Wright paper on term structures referenced by Hamilton.

Well, my first sideline comment is that economists who do math on the term structure should first convert the structure from period space to frequency space such that the 10 year bond becomes the 1/10 transaction frequency.  In frequency space we get all the orthogonalization theorems from Fourier, Nyquist, Shannon, Parseval and Burg.  In frequency space the answer is simple, the most compact orthogonal representation of a time series is a Bell shaped curve; it holds the most variation in the smallest space.

But in economic terms the question is, why does a distribution network of real goods have the slowest transaction rates and largest transaction size at the root; and faster transaction rates and smaller transaction sizes at the branches.  It is simple to see; if the inventory cycle time of a producer is much faster than the consumer inventory cycle,  then the producer can manage inventory for the consumer and does not need a retail outlet.

Thus, as the distribution network moves from a roundabout network to a minimal spanning tree, the banker signals producers to grow inventory and signals retail outlets to shrink inventory.   So the yield curve is steep when producers need to consolidate and retail outlets need to proliferate.  The reverse never happens because mass conservation means that a retail outlet has already going bankrupt before the banker notices, there is no negative inventory; so the inverted yield curve results in immediate contraction.