J.M. Keynes’s Revolution in the General Theory in Macroeconomics is Based on a Foundation of His Inexact Measurement Approach in Parts II and V of the a Treatise on Probability

Abstract

Keynes’s revolution in macroeconomic theory is based on his application in the General Theory of his Inexact measurement approach from the A Treatise on Probability. This involves the use of interval valued probability and interval valued outcomes. Keynes called this approach approximation. It entails nonadditive (sub and super) probabilities, imprecise probabilities, indefinite and indeterminate probabilities,to which Keynes added interval valued outcomes in the General Theory. Except in special cases, Keynes rejected both Exact measurement,which involved the use of precise, definite, determinate, additive, linear probabilities, which imply that the decision maker knows an exact probability distribution.

Keynes developed Boole's original logical theory of probability by developing an alternative method of solving Boole’s problems. Like Boole, Keynes’s approach involved solving systems of equations, the constraints, using linear and non linear, mathematical programming techniques. Keynes uses special aggregation assumptions in order to use and present an exact mathematical analysis in his D-Z model of chapter 20, which is the foundation for his IS-LM(LP) model of chapter 21. The D-Z model deals with expectations and uncertainty that results in a specific Y value. That Y value is an actual value that is certain, quantitative, and deterministic. Keynes then combines Y with r, the nominal, long run rate of interest, to derive the IS and LM(LP) curves on pp.298-299 of the General Theory.

The General Theory has, unfortunately, attracted two completely different types of interpreters, both of which conflict directly with Keynes’s use of inexact measurement.

The first type of interpreter essentially follows the views of Hicks(1937), Tinbergen(1940), Modigliani(1944) and Klein(1947), for example, in asserting that Keynes's approach in the General Theory was, in fact, a purely verbal, literary, prose approach, with no mathematical or statistical foundation whatsoever, that needed to be reworked in order to present it in mathematical form.

The second approach follows the Joan Robinson and G LS Shackle nihilist approach in asserting that Keynes argued that no mathematical, technical, analytic or quantitative approaches involving mathematical modeling or equations could ever be possible in macroeconomics because of the existence of what they called unknowledge or fundamental uncertainty, which meant that no decision maker has any knowledge whatsoever of anything that can occur in the future, be it the near future or the distant future, be it one day in the future, one month in the future, one year in the future, five years in the future, ten years in the future, twenty years in the future, etc. The best that could be done was to assume that decision makers could sometimes make use of a weak, ordinal probability approach. Both approaches have no support whatsoever in anything actually written by Keynes in his lifetime. The nihilistic approach of the Keynesian Fundamentalists (Moggridge, Skidelsky, Meeks, O’Donnell, Carabelli, Fitzgibbons, Runde, Davis, Winslow, etc.) is based on a gross misinterpretation of the diagram on page 39 of the A Treatise on Probability.

Once this error is corrected, it is clear that Keynes used a mathematical approach involving non linear and non additive analysis in his approach to lower and upper probabilities that Tinbergen, Modigliani, and Klein simply overlooked because they were not familiar with the concept of interval valued probability. Keynes’s Inexact approach was evolved and can be studies in the work of Hailperin (1986) and Walley (1991).There are no macroeconomists who are familiar with this work.

Keynes described his pp.298-299 model in a summary in the GT using the following words or phrases:
• One can calculate a quantitative answer
• The model is composed of three elements a), b),and c)
• It provides an analysis that is valuable in introducing order and method to the enquiry
• It is a set of simultaneous equations
• It provides a determinate answer or result.
• This result is an equilibrium

Keynes is describing his IS-LM(LP) model in the General Theory.