The author presents some interesting commentary on economics as a " Science ".He calls it an inexact and separate science.However,it isn't possible to accept this characterization given that economists do not follow standard scientific criteria and methods.One example will suffice.
In 1963,Benoit Mandelbrot confronted the annual Ecomometricians meeting with a summary of his empirical work on time series data in a number of commodity and financial markets.Mandelbrot reported that the probability distribution that fit the data the best was the Cauchy Distribution.The data did not come close to be being normally (log normal) distributed.Econometricians had simply been assuming since the early 1930's that the time series data was best approximated by the normal(log normal) distribution.All of their multiple regression and correlation techniques were based on the assumption of normality.No economist or econometrician had done any goodness of fit tests and/or exploratory data analysis to support their claim that the time series data was normally distributed.The reaction of the economists and econometricians to Mandelbrot in 1963 was the same as the reaction made in response to (a) J M Keynes's 1939-40 conclusion that Tinbergen's econometric research program was doomed because it would only work if the time series data was normally distributed and (b) Schumpeter's 1950 statement to the Econometricians at their annual conference that the time series data was not normally distributed;they rejected it out of hand.
In 1921,Keynes discussed the fact that a decision theory based on the mathematical theory of probability alone could only be a special case because it was based on two assumptions that were only special cases in the real world -additivity and linearity.Keynes showed in chapter 26 of the A Treatise on Probability,where he constructed his conventional coefficient of risk(nonlinear)and weight(nonlinear and nonadditive)c, that the general case was one of nonlinearity and nonadditivity.This result was identical to the result first put forth by Keynes in his second ,successful 1909 Cambridge Fellowship Thesis.The preference reversal " anomaly " is due to an attempt by economists to ignore the general case of nonlinearity and nonadditivity and continue to insist that decision theory must be based on the purely mathematical laws of addition and multiplication ,that require additivity and linearity ,in spite of the overwhelming empirical evidence that has been reported in experiments carried out by psychologists since the late 1940's.I append Keynes's technical demonstration for the interested reader.
Keynes presented a clearcut mathematical,technical analysis of ambiguity aversion using his conventional coefficient of risk and and weight( uncertainty),c,in chapter 26 of the TP. A very specific example of Keynes's nomlinear and non additive approach to probability in chapters 15,17,20,and 22 of the TP was worked out in great detail by Keynes in chapter 26 using his conventional coefficient of risk and weight ,c, on p.314 and in Footnote 2 on p.314.Edgeworth, in his 1922 article on " The Philosophy of Chance " in Mind ,was certainly correct in asking for the help of the readers of that philosophy journal in order to figure out the what and the why's involved in the application of Keynes's c coefficient.This will be provided for the reader below since it was never done in Mind or anywhere else with the exception of Brady's work.
The foundation of Neoclassical economics is merely the mathematical development of a theoretical approach first proposed by Jeremy Bentham in 1787.Bentham claimed that all individuals have the capability to calculate the odds and outcomes and act on the expected value (the probability times the outcome) in a rational way.This can be expressed by the following ,where p is the probability of success and A is the outcome:
Maximize pA.
The modern version of this is to Maximize pU(A),where p is a subjective probability that is additive,linear,precise,and exact.U(A) is a Von Neumann-Morgenstern Utility function.The goal is to
Maximize pU(A).
The modern name for Benthamite Utilitarianism in neoclassical economics is SEU theory(Subjective Expected Utility).Therefore,a microeconomic foundation based on Utility Maximization is just Benthamite Utilitarianism updated with modern mathematical techniques.Modern macro is all SEU theory.
Keynes rejected Benthamite Utilitarianism as a very special case that would only hold under the special assumptions of the subjectivist,Bayesian model-that all probabilities were additive,linear,precise,single number answers that obeyed the mathematical laws of the probabiity calculus.
Keynes specifies his conventional coefficient of risk and weight,c, model in chapter 26 of the TP on p.314 and fotnote 2 on p.314,as a counter weight to the Benthamite Utilitarian approach.
Essentially, Keynes's generalized model is given by
c=2pw/(1+q)(1+w),
where w is Keynes's weight of the evidence variable that measures the completeness of the relevant, available evidence upon which the probabilities p and q are calculated.(Benthamite Utilitarians assume that the value of w is always 1.)w is an index defined on the unit interval between 0 and 1,p is the probability of success,and q is the probability of failure.p+q sum to 1 if they are additive.This requires that w=1.Keynes's c coefficient can be rewritten as
c=p [1/(1+q)][2w/(1+w)].
Now multiply by A or U(A).One obtains
cA= p[1/(1+q)][2w/(1+w)]A.
The goal is to maximuze cA or cU(A).The weight 1/(1+q) deals with non linearity.The weight 2w/(1+w) deals with non additivity.Modern Macroeconomics amounts to nothing more than the claim that c=p or cA (cU(A)= pA (pU(A)) .
It is now straightforward to see that the neoclassical microfoundations of macroeconomics assumes that all probabilities are additive and linear.This is nothing but a special case of Keynes's generalized decision rule to maximize cA,or cU(A),as opposed to the Benthamite Utilitarian pA or neoclassical pU(A).It is now clear that Keynes had created general theories of macroeconomics,probability,and decision making between 1921 and 1936.Keynes's accomplishments,once understood,make him the only rival to Einstein for the title of the greatest scientist of the 20th century. Economists have only a very vague,hazy,cloudy understanding of Keynes 's distinction between risk and uncertainty . It is this distinction that has to be grasped first before any economist has any hope of understanding what Keynes means in the GT.
The conclusion is very straightforward. New Classical,New Keynesian,rational expectationist,and real business cycle theorists use the rule to Maximize pU(A).Keynes used the rule to maximize cU(A).This is the same type of rule used by the overwhelmingly ambiguity averse decision makers that populate the real world both in the past and today. Preference reversal is what would be expected in a world of non additivity and nonlinearity.It is only an anomaly in a world of linear and additive economists.
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