# On L. Klein’s Erroneous Assessments of J M Keynes’s Views on Probability, Mathematics, and Statistics: Reviewing His 1951 Review of Harrod’s the Life of John Maynard Keynes

24 Pages Posted: 15 Oct 2018

Date Written: September 22, 2018

### Abstract

Lawrence Klein was a follower of the Limiting Frequency Interpretation of probability. This concept of probability requires that probability must always be a precise, exact mathematical probability. This meant that additivity was always the case. His acceptance of Kolmogorov’s axiom of countable additivity meant that he had no idea whatsoever about the concept of interval valued probability espoused by Boole and Keynes using upper and lower probability bounds. Klein’s belief in the limiting frequency interpretation of probability meant that there can be no such things as imprecise and/or indeterminate probabilities.

This view impacts Klein’s understanding of economic statistics and Econometrics. Klein builds his approach to economic statistics and Econometrics on the application of the Multivariate Normal probability distribution a la Tinbergen in 1939-40. There is no evidence that Klein was familiar with Mandelbrot’s demonstration, starting in the late 1950’s, that the Normal Distribution is not supported by any empirical evidence or Keynes’s point that it was impossible to use a Normal Distribution to account for changes in the demand (supply) of durable, physical capital goods, due to the impact of future technological change, innovation (obsolescence), and advance that impacted the expectations of those investing in such producer goods. However, Klein’s approach could be used to analyze the consumption function and inventory changes over time since these are stable, linear functions.

Klein misunderstood Keynes’s comments about mathematical economics in the General Theory in the appendix to chapter 19 and chapter 21 of the General Theory. Keynes’s comments were a critique of Pigou’s use of Marshallian mathematics, based on ceteris paribus, partial equilibrium models that did not take into account the interdependencies and complex, complicated interactions between variables caused by the positive feedback effects emanating from, for one example, the interactions of the multiplier and accelerator.

Klein also failed to recognize that Keynes was the creator, developer and innovator of the IS-LM (LP) model, which Keynes presented as a three equation system on pp. 298-299 of the General Theory in 1936. Hicks’s and Harrod’s versions of IS-LM were just inferior versions of Keynes’s original model that left out expectations and uncertainty considerations, which Keynes had incorporated in his supporting D-Z model of chapters 20 and 21 (there is no D-Z model in chapter 3 of the GT).

**Keywords:** IS-LM, IS-LP(LM), Klein, Samuelson, Keynes, Chapter 21, Chapter 15, Keynes's Views of Math, Logical Theory of Probability

**JEL Classification:** B10, B12, B14, B16, B20, B22

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