Harrod's dynamics

[pdavidso <pdavidso@xxxxxxx>]

>----- Forwarded Message -----
>From: pdavidso <pdavidso@xxxxxxx>
>To: Daniele Besomi <dbesomi@xxxxxxx>
>Cc: pktnet <pktnet@xxxxxxxxxxxxxxxx>
>Subject: Harrod's dynamics
>
>Daniele Besomi wrote (and my responses are Capitalized):
>:
>Dear Prof. Davidson,
>
>
>I just stumbled upon an exchange you had in May in the PHT list on Harrod and
>finance: someone quoted a passage from my book on The Making of Harrod's
>Dynamics, inducing you to diagnose that if the author's interpretation of my
>passage were correct, I have misunderstood both Harrod and differential
>calculus (the relevant passages are transcribed below).
>
>
>Perhaps you may care to have my opinion as well. The passage cited was taken
>out of contest: it was part of a comparison of Harrod's Trade Cycle with his
>1939 "Essay in Dynamic Theory", and I argue that while in 1936 Harrod's
>dynamics was full of expectations etc., in 1939 he had reduced it to a
>dynamics at one point of time (you may see the full argument on the 1939
essay
>in my paper for HOPE 1995, "From The Trade Cycle to the 'Essay in Dynamic
>Theory'. The Harrod-Keynes correspondence, 1937-1938"
>(http://eco.unipv.it/~dbesomi/sec-lit/besomi/hope95.pdf) . As you correctly
>wrote, Harrod insisted that his growth rates are defined at one point of
time.
>To this, it should be added that to make the system dynamic, there should be
a
>connection between this state of the system and the next, i.e. something
>explaining the system's evolution. Such an equation is missing from Harrod's
>1939 article: there was indeed a verbal statement vaguely indicating how
>entrepreneurs react to the warranted rate differing from the actual, but no
>equation stating it. That the statement was vague is clear from (a) the fact
>that Harrod's definition of the warranted rate admits at least 6
>interpretation, as pointed out by McCord Wright in 1949 (it leaves each
>entrepreneur satisfied as well as entrepreneurs as a whole, keeps them doing
>the same thing, equates ex ante investment and saving, only concerns the part
>of investment linked to consumption, and differs from the full employment
rate
>326); (b) from the various attempts at translating Harrod's statement into an
>equation: such attempts kept interpreters busy for some 20+ years, giving
rise
>to the debate on the instability of Harrod's growth path (which wasn't a path
>at all, but an instantaneous rate) which consisted in several people trying
to
>fill in the missing equation, each producing a new one, giving the system
>different properties. (I have surveyed these developments in "Failing to Win
>Consent. Harrod's Dynamics in the Eyes of his Readers", in G. Rampa, L.
Stella
>and A. Thirlwall, eds.,  Economic Dynamics, Trade and Growth: Essays on
>Harrodian Themes  , London:  Macmillans, 1998, pp. 38-88:
>http://eco.unipv.it/~dbesomi/sec-lit/besomi/failing.pdf ).
>
>THANK YOU FOR THIS EXPLANATION. THE MANY INTERPRETATIONS YOU SUGGEST ABOVE BY
>READERS IS DUE TO THEIR MISINTERPRETING HARROD.
>HIS DYNAMICS IS ALWAYS AT A SINGLE POINT OF TIME BECAUSE HARROD (LIKE KEYNES)
>DID NOT B ELIEVE THAT ENTREPRENEURS WOULD REACT IN ANY MECHANICAL FASHION IN
>THE "NEXT" POINT OF TIME VIS-A-VIS THE CURRENT POINT OF TIME.  WHAT HE WANTED
>TO SHOW IS THAT UNLESS THE ACTUAL RATE OF GROWTH EQUALLED THE WARRANTED RATE
>OF GROWTH AT ANY MOMENT OF TIME, SO THAT ENTREPRENEURIAL EXPECTATIONS WERE
>CONSISTENT WITH EQUILIBRIUM, THE POSSIBILITY OF A STEADY GROWTH PATH OVER
TIME
>WAS VERY UNLIKELY.
>
>LIKE KEYNES, HARROD WAS WEILLING TO ENTERTAIN THE NOTION THAT ENTREPRENEURIAL
>VISIONS OF FUTURE QUASI RENTS COULD CHANGE EVEN IF AT THE CURRENT MOMENT OF
>TIME THE ACTUAL RATE OF GROWTH WAS EUAL TO THE WARRANTED RATE OF GROWTH
(WHERE
>GROWTH RAQTES WERE EXPRESSED AD PART OF THE DIFFERENTIAL CALCULUS).
>
>
>Why did Harrod confine himself to an instant (in spite of Marschak having
>warned him before publication that one equation was missing)? Because, I
>think, he didn't know how to manage the math that a coherent setting of his
>system would have implied. Harrod did NOT assume his coefficients to be
>constant, and indeed his cycle theory (of which the 1939 essay was in fact
>meant to be a development, but was radically altered under Keynes's pression:
>see the original version of the essay, and my introductory essay + editorial
>comment in HOPE 1996: http://eco.unipv.it/~dbesomi/sec-lit/besomi/hope96b.pdf
>, http://eco.unipv.it/~dbesomi/sec-lit/besomi/hope96c.pdf ,
>http://eco.unipv.it/~dbesomi/sec-lit/besomi/hope96a.pdf   , respectively) was
>based on these changes: growth itself triggers a decline in the multiplier,
as
>the saved part of income is likely to increase as people become more
affluent,
>while the capital/output ratio changes with the fluctuations in the rate of
>interest. The warranted rate thus fluctuates in the curse of the cycle;
>Harrod's system was thus nonlinear, but he (nor anybody else, at the time)
did
>not know how to deal with it. He thus focused on one instant, in which
>parameters cannot change, warning that everything has to be recalculated for
>the new state towards which the first instant leads.
>
>WHAT YOU APPEAR TO BE SUGGESTING IS THAT THERE IS NO BELIEF IN HARROD THAT
THE
>CAPITAL OUTPUT RATIO AND/OR THE SAVINGS RATIO  WILL BE UNCHANGED FROM ONE
>MOMENT OF TIME TO ANOTHER.
>
>
>But as we are not told precisely where we are led the following instant, his
>system is frozen in that instant: it has no past and no future.
>
>
>
>YES BECAUSE ENTREPRENEURIAL DECISIONS ARE NOT FORZEN IN TIME --EVEN IF AT ANY
>INSTANT THEIR EXPECTATIONS ARE BEING MET!
>
>\ That is the sense of my comment. Which is not to say that the whole thing
is
>useless, or that Harrod did not know what to do with the future:
>
>
>IF THE FUTURE IS UNCERTAIN THEN ONR CAN NOT DEAL WITH THE FUTURE IN ANY
>MECHANICAL EQUAION AL "LAW OF MOTION" AS MANY ECONOMIC GROWTH THEORISTS
9E.G.,
>SOLOW, DOMAR,ETC) IMPLICITLY BELIEVE.
>
>
>With best regards, Daniele Besomi
>
>
>
>
>***************
>
>
>P.D.
>I suggest you read chapter 6 of my FINANCIAL MARKETS, MONEY AND THE REAL
>WORLD. The chapter is entitled "Planned Investment, Planned Savings,
>Liquidity and Economic Growth"
>
>
>In Chapter 7 you state that "Harrod's Growth Analysis Did not inquire into
the
>role played by financial markets and financial intermediaries in achieving
and
>maintaining any specific warranted growth." Why should financial factors be
>included in HArrod?. In 1939, Harrod stated that his analysis relates to a
>single point in time. In 1960 (Second Essay), EJ, p.279: "I regard the
>fundamental concept of dynamic economics as the rate of increase...It is the
>rate of increase that obtains at a given point of time". If as pointed out by
>Besomi, 1999, p.151: "if the temporal horizon is reduced to a single instant
>there is no room the distinction between past and future". If there is no
room
>for the distinction between past and future is there a need for financial
>markets within HArrod's own framework?.
>
>
>I had actually personally discussed this point with Roy Harrod personally in
>the 1960s. Roy's point was that the rate of growth dY/dt was a differential
>calculus concept -- and as such the rate was taken at a moment of time and
>could change from moment to moment. Harrod was, in essence, specifying the
>current (differential) rate of growth at a single point of time and NOT the
>average rate of growth over an accounting period--. The two would be the same
>only if the differential rate of growth did not change over the whole
>accounting period. [ the illustration Harrod used was that he was interested
>in the reading in miles per hour of the speedometer of a car at any moment of
>time -- and was not discussing the average speed (in miles per hour) over the
>length of a car trip.]
>
>
>Nevertheless Harrod recognized that the differential rate of flow new capital
>formation (I) required expectations about FUTURE streams of quasi-rents
>relative to the costs of producing this new capital -- Keynes's marginal
>efficiency of capital! I am sorry to say that if Besomi said what you
>attributed to him, then Besomi just misinterporeted Harrod -- and the
>differential calculus.
>--
>
>Paul Davidson
>Editor, Journal of Post Keynesian Economics
>University of Tennessee
>SMC 503
>Knoxville, Tennessee 37996-0550
>office phone #;(865)974-4221; office fax# (865)974-1686 or (865)974-4601
>home phone and fax # (865)692-0802
>email pdavidson@xxxxxxx
>http://econ.bus.utk.edu/davidsonextra/Davidson.html

Paul Davidson
Editor, Journal of Post Keynesian Economics
University of Tennessee
SMC 503
Knoxville, Tennessee 37996-0550
office phone #;(865)974-4221; office fax# (865)974-1686 or (865)974-4601
home phone and fax # (865)692-0802
email pdavidson@xxxxxxx
http://econ.bus.utk.edu/davidsonextra/Davidson.html