deterministic business cycles

["J. Barkley Rosser, Jr." <rosserjb@xxxxxxx>]

     OK, folks, I am about to disappear for a week,
off to Tokyo to tell the Science Council of Japan
that they should not kill whales.  However, before
doing so, I will drop a few more specific references
on this chaos stuff so that I do not look like good
old Paul Davidson just endlessly telling people
to READ MY BOOK (wonderful and definitive
as it is, nevertheless, :-)).
      So, on the Kaldor model
Original reference is
Nicholas Kaldor, 1940, "A Model of the Trade Cycle,"
Economic Journal, vol. 50, pp. 78-92.
Initial mathematization was due to
W.W. Chang and David J. Smyth, 1971, "The Existence and
Persistence of Cycles in a Nonlinear Model: Kaldor's
1940 Model Re-Examined," Review of Economic Studies,
vol. 38, pp. 37-44.
First catastrophe theory analysis appeared in
Hal R. Varian, 1979, "Catastrophe Theory and the
Business Cycle," Economic Inquiry, vol. 17, pp. 14-28.
First demonstration of possible chaotic dynamics was in
Rose-Ann Dana and P. Malgrange, 1984, "The Dynamics
of a Discrete Version of a Growth Model," in J.P. Ancot,
ed., Analyzing the Structure of Econometric Models,
Boston: Martinus Nijhoff, pp. 115-142.
First demonstration of possible non-chaotic strange
attractors and (separately) fractal basin boundaries
(don't ask if you don't know) was in
Hans-Walter Lorenz, 1992 (was wrong in my last post
on that one), "Multiple Attractors, Complex Basin Boundaries,
and Transient Motion in Deterministic Economic Systems,"
in Gustav Feichtinger, ed., Dynamic Economic Models and
Optimal Control, Amsterdam: North-Holland, pp. 411-430.
      Again, this important paper is the first to show either
of those two complex phenomena in any economic model.
       As for Goodwin, his original paper was
Richard M. Goodwin, 1951, "The Nonlinear Accelerator and
the Persistence of Business Cycles," Econometrica, vol. 19,
pp. 1-17.
       Amazingly enough, the very first demonstration of
possible chaotic dynamics in any economic model was
shown in a study of this model of Goodwin's, although the
authors did not understand the significance of what they
had discovered.  The paper is
Robert H. Strotz, J.C. McAnulty, and Joseph B. Naines, Jr.,
1953, "Goodwin's Nonlinear Theory of the Business Cycle:
An Electro-Analog Solution," Econometrica, vol. 21,
pp. 390-411.
       Needless to say other of Goodwin's work, such as his
predator-prey model of cycles, also can yield chaotic dynamics
as can some of his other models.  He got into this himself
and presented these results in his 1990 _Chaotic Economic
Dynamics_, Oxford University Press.
        Thus, Post Keynesian models lie at the very heart of the
development and application of chaos theory and complex
dynamical theory more generally in economics.  I could give
quite a few more examples and citations, but, as Uncle Paul
would say, if you want more, READ MY BOOK!   :-)
Barkley Rosser
Professor of Economics
James Madison University
http://cob.jmu.edu/rosserjb