Note to Self: The Ramsey Model Once Again

Theoretical Public Finance in the Long Run: National Saving Edition

J. Bradford DeLong (2008), "Economic Growth: From Solow to Ramsey" http://www.j-bradford-delong.net/2008_pdf/ramsey_iii.pdf

William T. Smith (2006), "A Closed Form Solution to the Ramsey Model" http://www.bepress.com/cgi/viewcontent.cgi?article=1356&context=bejm

William T. Smith (2007) "Inspecting the Mechanism Exactly: A Closed-form Solution to a Stochastic Growth Model" http://www.bepress.com/bejm/vol7/iss1/art30

Comments

[Kieran]

What an amazing chap Ramsey was. I posted this

http://crookedtimber.org/2004/05/03/conspicuous-by-his-absence/

at CT a few years ago and the comments are great, because most people just know of one or two aspects of his work, but not the whole of it.

[Matt]

I liked the Smith papers.

What I get is the social director climbs a tree and views a nice saddleback in the distance. The tribe is excited, they all climb the tree, but there is a little mound between the here and the oasis. So, there is a free trade of goods production over time, the poor willing to go with less today for more tomorrow, and visa versa. They start along with their IOUs and their production capacity.

They get to the top of the hill, suddenly we have a new configuration. Some bet lucky, and they take big Bellman steps around the bend, some goofed, and they start negotiating production agreements to take tiny Bellman steps.

But, the new information is greater than the variance in the smallest information estimator in the pack. So, Jensen's inequality kicks in and the system re-aggregates, such that the new production function is quantumly more in tune with the most innovative information, and some bits of precision were dropped off the tail end. The system gets a better estimate with different modified eigenvectors but fewer bits of precision.

This should be measurable. The trade in future goods production should be the best current estimate of the diagonal, under current production model. What is the transactions rate over time to get that.

[Matt]

Thanks Kieran and Brad for the tip on Ramsey.

It is Ramsey's Theorem on complete sub graphs within existing graphs that should lead to a formulation for finding the optimum Rank N-1 economic structure from an existing rank N, though I have just skimmed over the details.

Ramsey's theorem kicks in when the volatility exceeds the Jensen bond energy, so to speak.