Arne Fisher's 'Review' of J M Keynes's A Treatise on Probability: Fiasco Number Three
16 Pages Posted: 7 May 2016
Date Written: May 6, 2016
Arne Fisher attempted a cover up of an important footnote in chapter 29 of the A Treatise on Probability (1921), in which Keynes made it clear that he was not going to use the modern Method of Moments, which used a Moment Generating Function approach based on a Taylor Series expansion very similar to the Maclaurin Series, a special case of the Taylor series expansion, used by Keynes in chapter 17 of the A Treatise on Probability. Cumulants and semi-invariants, which A. Fisher claimed Keynes had no inkling of and did not understand, are simply terms used to describe particular parts of the Taylor series expansion carried out to provide the optimal estimate of a series using the Moment Generating Function technique.
A. Fisher attempted to create the illusion that Keynes had made a number of very critical comments about the mathematical capabilities of Laplace, Bernoulli, and Poisson on pp. 358-361 of the A Treatise on Probability. These are figments of Fisher’s own imagination. A. Fisher’s “review” is really about one section of one chapter, chapter 29, sections 16-18, pp. 358-361, of the A Treatise on Probability. Nowhere in these pages will a reader find any such comments.
A. Fisher, in his “review,” also sought to create the illusion that there were many mathematical errors in the A Treatise on Probability in these sections. In reality, there are no mathematical errors in these sections. Keynes simply used an older method of generating values for the Poisson distribution instead of using the most modern approach, the Method of Moments, which used the Moment Generating Function, with which Keynes was well acquainted with.
A. Fisher gambled that no one reading his “review” would go back and check to see if his comments were correct. His gambit worked for nearly 94 years.
Keywords: Cumulants, semi invariants, Taylor Series, Method of Moments, Moment Generating Function, Poisson
JEL Classification: B10, B12, B20, B22
Suggested Citation: Suggested Citation