# J. M. Keynes (Inexact Measurement, Approximation, Non- Linearity, Non-Additivity, Interdependence, Imprecision) Versus J. Tinbergen (Exact Measurement, Linearity, Additivity, Independence, Precision) on Probability in 1939–1940: There Was No Middle Ground Between Them

65 Pages Posted: 25 Mar 2019

Date Written: March 2, 2019

### Abstract

The Keynes-Tinbergen debates of 1939-40 pits two advocates of completely different, and diametrically opposed, methods of analysis.

J M Keynes was a lifelong practitioner of Inexact Measurement, approximation, nonadditive, nonlinear, indeterminate and imprecise probability, which emphasized the application of Boole’s interval-valued approach to a logical probability using upper and lower bounds or limits. The exact measurement was a special case involving problems that satisfied Keynes’s principle of Indifference (combinatorics, permutations) or frequency data that met the Lexis-Q test for stability over the long run. Probabilities for Keynes were non-(sub or super) additive, incorporated nonlinear probability preferences, and were not independent unless the data was based on the inanimate phenomenon.

J. Tinbergen was a lifelong practitioner of Exact Measurement, definite, precise, and determinate probability, which emphasized the application of the limiting frequency interpretation of probability. The exact measurement was the general case. Probabilities for Tinbergen were definite, exact, determinate, linear, additive and independent. Empirical evidence allowed one to specify a correct probability distribution of all possible outcomes before any choice needed to be made. Tinbergen’s physics background determined his approach to probability.

There was no room for compromise between Keynes’s Inexact approach to measurement and Tinbergen’s Exact approach to measurement except in areas of study where an analysis showed fairly stable behavior exhibited by decision makers that changed very slowly over time. These fields would be consumer consumption expenditure studies and business inventory studies to meet that consumer demand. Tinbergen’s concentration on Investment spending on durable capital goods in his study about the Business cycle was precisely where Keynes would argue that precision was not possible, given the constant interactions of changing expectations of future profits with difficult to judge technological advance, innovation, change, and obsolescence problems.

In August 1938, Keynes had sent Harrod his linear, first order, difference equation model that analyzed the interaction of the multiplier with the accelerator (relation) dynamically over time with respect to Harrod’s views on the relationship between full employment and the capital stock in his model of inter-temporal economic growth over time. Keynes reached the conclusion that it was impossible to identify full employment equilibriums from unemployment equilibriums, given a set of possible multiple equilibria that was being generated by the positive feedback engendered by the interplay of the multiplier-accelerator interactions. From 1939-1941, Samuelson had also reached the same conclusion using his own linear difference equation analysis. All that it was possible to conclude from the analysis was that the equilibriums, full employment or unemployment, were the dynamically stable or unstable. No type of Classical or neoclassical Benthamite or Walrasian pendulum models could be applied. Microeconomic theory, based on maximum–minimum optimization problems, could not be applied since this approach postulated the existence only of negative feedback. Samuelson essentially gave up on econometric modeling after 1945 since he realized that the econometric models were based on the existence of the Bentham-Say-Ricardo-Walras- Jevons-Fisher -Wicksell-Frisch “rocking horse(pendulum)” models that he had aptly described as being violin–sting plucking models.

An examination of Tinbergen’s 1929 dissertation (see Buitenhuis,2015, pp. 46-51) shows that, in the economics part of the dissertation, Tinbergen was doing microeconomic optimization problems similar to the type of problems done by Paul Samuelson in his 1941 dissertation and 1947 Foundations of Economic Analysis based on negative feedback, but without the macro analysis provided by Samuelson involving the positive dynamic feedback effects resulting from the interactions of the multiplier and accelerator that can’t be modeled as optimization problems at the macroeconomic level. That this was Tinbergen’s Exact approach, taken from the pendulum models in mathematical physics, is confirmed in Tinbergen (1929), Tinbergen (1938), Tinbergen (1970), Cornelisse and Van Dijk (2006), Squartini and Garlaschelli (2014), and Buitenhuis (2015). Tinbergen’s work is basically Benthamite and Walsarian pendulum model building, combined with the Benthamite assertion that the whole (Macro) can never be any more than the sum of the individual parts(micro). Therefore, a macroeconomy composed of many utility/profit maximizing consumer-producers ,who are all identical to each other and independent ,is modeled as if they were a macro ensemble of gas particles, each of which is independent and identically distributed ,where each gas particle is randomly hitting other particles and exchanging electrons, so that, in the long run, the exchanges of electrons(exchanges of different bundles of goods and services) between all of the identical particles in the macro ensemble cancels out, so that a normal (lognormal) probability distribution describes the interactions.

Tinbergen and Klein wanted to approach economics as if it were physics. Unfortunately, it is not the case that an argument of analogy holds between a particle in physics and an individual in economics. Exact, precise, linear, additive, definite, determinate probabilities are not available, in general, to provide an economic analysis except in the area of consumption and inventories. This was pointed out in great detail by Adam Smith in 1776. However, economic analysis can involve inexact, imprecise, indeterminate, nonlinear, nonadditive, indefinite quantitative analysis. Keynes and Tinbergen (Klein) came from different intellectual backgrounds. Keynes’s method is built on Boole’s approach using lower and upper probabilities. This approach runs throughout the TP. Tinbergen and Klein are using the precision of physics as their model of economic analysis.

**Keywords:** Keynes, Tinbergen, Inexact, Exact, Precise Measures, Imprecise Measures, Approximation, Upper and Lower Probabilities

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

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