Friday, August 27, 2010

Wicksellian Balance has an error

I am working with a short version of the Wicksellian Balance, taken from Delong's site:

The "Wicksellian Balance" line is what Bullard (and Benhabib et al.) call the "Fisher Relationship." I prefer to think of it in Hicksian IS or Wicksellian terms: for aggregate demand Y to be equal to potential output Y*, the market real interest rate r must be equal to the natural real interest rate re. When the market real rate r exceeds the natural real rate re, investment spending is too low for aggregate demand to match potential output and there is downward pressure on the rate of change of prices. If the market rate r is less than the natural real rate re, investment spending is too high for aggregate demand to match potential output and there is upward pressure on the rate of change of prices. Above the Wicksellian Balance line, there is downward pressure and so inflation is falling. Below the line, there is upward pressure and so inflation is rising.


Let's make a change to the model.
Instead of:
When the real rate exceeds the market rate 

I say instead:
When the curve is steeply sloped upward

With yield steeply sloped,  the market rate is signaling that retail sector must expand and producer sector contract; the distribution network should expand at the leaves and contract at the root. Another way of saying this is that the yield curve wants longer term inventories to lose variance and gain level. The process of contracting the producer side means lower transaction rates and using greater transaction sizes; that is  more economies of scale. On the retail side  the market rate wants the opposite (more retail distribution nodes), meaning reduced inventory levels and more inventory variance; which also gets   faster transaction rates and smaller transaction sizes.

So rather than have the economy walk a concentric circle toward Wicksellian balance, the economy really does a rotation in place. The key difference is that this model includes the subtle changes in transaction rates along the curve.  It is the variation in transaction rates along the curve that lets the economy walk compactly about a center point.

I doubt the Minsky model and the Wicksellian model as presented in popular blogs.
The economy generally moves to a more compact representation of distribution.    When the general economy contracts, as it has done, the distribution network is sparser, but a more compact representation of distribution to match a sudden constraint that effects all sectors.  When the economy expands from a general positive shock, as in transportation technology, then distribution becomes less sparse because transportation is not a constraint. But even in an expansion, the network is a more compact representation than before.   Each adaption is performed by expansion or contraction of the network, with subsequent changes in transaction rates and sizes.

When I say compact, I mean more accurate representation of the state of affairs, not necessarily a greater product flow. Sometimes it is more accurate to sell families three dozen eggs, once a month, rather than one dozen three times a month.

If you do not consider both transaction rates and sizes, focusing only on one, then your math leads to Debt Spirals, Negative Nominal Rates, and Widening Concentric Circles; (That is a divide by zero).

No comments: