Probability Foundations of Economic Theory

Charles McCann

• Publisher: Taylor & Francis
• Year: 2003
• eBook ISBN: 9781134839124
• Edition: 1
• Topic: Business
• Subtopic: Business General
• Index: Business

First published in 1994. Concepts of probability are an integral component of economic theory. However there are a wide range of theories of probability and these are manifested in different approaches to economic theory itself. In this book Charles McCann, Jr provides a clear and informative survey of the area which serves to standardize terminology and so integrate probability into a discussion of the foundations of economic theory. This is illustrated by examples from Austrian, Keynesian and New Classical Economics.

NOTES

CHAPTER I: INTRODUCTION

1 Although many physicists would perhaps disagree with this assertion.

2 Emil Kauder (1957) noted that Menger, in correspondence with Walras, defined ‘exact laws’ as ‘statements about invariable sequences which are not influenced by time and place’ (Kauder, 1957, p. 416).

3 ‘Strict (exact) laws of phenomena can never be the result of the realistic school of thought in theoretical research even if this were the most perfect conceivable and its fundamental observation the most comprehensive and most critical.’ (Menger, 1883, p. 57). ‘If, therefore, exact laws are at all attainable, it is clear that these cannot be obtained from the point of view of empirical realism….’ (ibid., p. 60).

4 Some, perhaps most, may argue that Menger’s ideal laws are synthetic a priori, not analytic. However, Menger insisted they are not empirically derived but rather of the nature of mathematical truths. They are then redefinable as tautologies, and hence analytic. Barry Smith (1986) argued that Menger, writing under the influence of Aristotelianism, actually presented a theory utilizing the synthetic a priori, the outline of which does not appear explicitly in his works, but is rather dealt with in the philosophical works of Edmund Husserl. Despite Menger’s Aristotelianism, his ideal laws still seem analytic if for no other reason than their being necessary and redefinable as tautologies.

5 For Menger, the inductive method is ‘only able to increase the guarantees of the absoluteness of the laws’ but can never ‘offer absolute guarantee of it.’ (Menger, 1883, p. 57).

6 On this see the work of the philosopher Alexander Rosenberg, especially (1976).

7 The definition of classical economists used here is consistent with that given by John Maynard Keynes in the General Theory (1936), encompassing writers from Adam Smith to A.C.Pigou.

8 Mill never accepted that an objective measure of value was possible. He did, however, acknowledge that such a measure may be forthcoming for cost of production. ‘But if there existed such a commodity, we should derive this advantage from it, that whenever any other thing varied permanently in relation to it, we should know that the cause of variation was not in it, but in the other thing. It would thus be suited to serve as a measure, not indeed of the value of other things, but of their cost of production.’ (Mill, 1871, Bk.III, Ch.XV, p. 566).

9 An excellent reference on the subject of equilibrium in economic models is Robert Kuenne (1963). For the historical development of the general equilibrium concept, see E.Roy Weintraub (1985).

10 This definition is key to G.L.S.Shackle’s elucidation of a ‘scheme’ of economic theory. See esp. Shackle (1965).

11 ‘For a society then we can speak of a state of equilibrium at a point in time—but it means only that compatibility exists between the different plans which the individuals composing it have made for action in time.’ (Hayek, 1937, p. 41).

12 General equilibrium as used here refers to a more expansive concept than that of the formal axiomatic presentations of modern usage, viz., Arrow-Debreu-type models. The definition here is of classical vintage. This older definition is of particular relevance to the theories of the Austrians and Keynes.

13 The terms ‘static’ and ‘dynamic’ are not equivalent to the terms ‘stationary’ and ‘non-stationary’. A stationary system is characterized by a non-changing, equilibrium solution, while a non-stationary system is one of disequilibrium and continual change. Thus a static model is necessarily stationary, while a dynamic model need not be.

14 Self-contained models are ‘those in which a lagged interdependence of all variables could explain an unending and genuinely cyclical fluctuation.’ It is ‘a “business cycle machine” complete in itself, to which regular and therefore predictable oscillation is as natural as the tides or the seasons.’ (Shackle, 1965, p. 5). A non-self-contained model is one ‘receptive of any kind of stimulus from outside itself and responding in an appropriate and broadly reliable manner to each different kind, but not containing any perpetuum mobile of its own.’ (ibid., p. 5). This type of model ‘deliberately leaves out some of the linkages which would be needed in order to calculate the future from the past.’ (ibid., p. 98).

15 It should be noted that the partial equilibrium model may be considered as a special case of the general model, wherein the economy collapses to a single market in which is produced a single good, and the solution vector is then shifted through successive iterations along a time axis, so that time becomes incorporated explicitly into the analysis. Cobweb models of the 1920s represented early efforts to dynamize the static demand-supply analysis of classical microeconomic theory.

16 ‘Probabilistic’ does not have the same meaning as Tony Lawson’s (1988) ‘probabilistic knowledge,’ which refers to an uncertainty representable by a probability distribution. Lawson’s ‘probabilistic knowledge’ more closely corresponds to ‘stochastic’ in the present case.

17 It should be noted that the terms ‘probabilistic’ and ‘stochastic’ do not reference probability types. They reflect merely two ways of representing uncertainty. Probability is a different matter entirely.

18 Although recent literature on sunspot models, to be discussed later, provides an exception.

19 This is not really a contentious point. Samuel Hollander (1973, p. 13) and Roger Backhouse (1985, p. 23) both maintained that Smith advocated a form of general equilibrium.

20 On the various uses of the term ‘tendency’ in classical economics, see Thomas Sowell (1974).

21 For Cournot, the problem with a practical application of a general equilibrium solution was in the empirical calculation: ‘But this would surpass the powers of mathematical analysis and of our practical methods of calculation, even if the values of all the constants could be assigned to them numerically.’ (Cournot, 1838, p. 127).

22 Therefore, while it is understandable that partial analysis has been and is being widely used, it is equally understandable that it has been condemned from the first by theorists of the sterner type, especially by Walras and Pareto.’ (Schumpeter, 1954, p. 991).

23 This will be more fully developed in Chapter II.

24 Statistics are useful ‘provided that careful attention be paid not only to their liability to error; but to the even greater dangers that arise from their inability to take account of some of the most important influences that bear on almost every economic issue.’ (Marshall, 1929, p. 309).

25 ‘We cannot indeed measure motives of any kind, whether high or low, as they are in themselves: we can measure only their moving force… [M]oney affords a fairly good measure of the moving force of a great part of the motives by which men’s lives are fashioned.’ (Marshall, 1920, Bk.I, Ch.IV, p. 39).

As a motivation for this contention, Marshall elaborated two fundamental assumptions of economics: (1) economics deals with measurable quantities; and (2) problems of economics ‘are found to make a fairly homogeneous group… [T]here is a fundamental unity of form underlying all the chief of them.’ (ibid., Bk.I, Ch.II, p. 27).

26 Frank H.Knight, commenting on the economic writings of the late 1920s, asserted that:

no science of economic dynamic exists…. At best it may be said that the statistical economics now being prosecuted with so much zeal in various quarters might yield data for some of these definitions…. In actual usage economic dynamics, or dynamic economics, has become merely a critical and negative term to refer to the limitations of ‘static’ analysis…. Its least vague usage is that of a son of catch-all for stressing changes in given conditions in contrast with adjustments to given conditions. In practice it suggests an insistence that there are no given conditions, which view if consistently maintained would mean that there are no predictable reactions and that science is impossible…. Economic literature includes no treatment of the relations between measured force, resistance, and movement. What it calls dynamics should be called evolutionary or historical economics.

(Knight, 1935, pp. 166–7)

27 The opinion of Sanford Grossman (1981) that the classical economists equated uncertainty with certainty is, given this interpretation, an invalid characterization.

28 Even Irving Fisher’s approach, characteristic of the ‘classical’ American school, although more mathematical than the early British presentations, was still not entirely deterministic.

29 See especially Burns and Mitchell (1947). But note the following from Mark Perlman: ‘…if Mitchell’s principal concern was to make measurements, like all sophisticated scholars he was acutely alert to the qualitative (perhaps subjective) bases in any measuring process.’ (Perlman, 1986, p. 272).

30 Cf. John R.Commons: ‘If the concept of purpose is omitted then the social scientist falls into either physics or metaphysics.’ (Commons, 1924, p. 127). See Perlman (1986) for the view that Commons is the American Institutionalist link to Austrian economic thought.

31 Milton Friedman (1955) wrote that Walras’ system was not the solution of a specific empirical problem, but rather an elegant formal statement of an idealized economic system. He further suggested that advances in input-output analysis have not been in the spirit of Walras, but rather extensions of the analysis of Cournot, whose system consisted of a detailed examination of economic interrelations founded on an empirical basis and which, as Cournot felt and Friedman concurred, was incapable of solution due to the extreme complexity and magnitude of the calculations involved. Thus, according to Friedman, Walras was concerned with form, while Cournot was more concerned with substance.

32 Including but not limited to Anna Carabelli, Bradley Bateman, Rod O’Donnell, Tony Lawson, and Jochen Runde, but excluding such Post-keynesians as Paul Davidson.

33 Note that when discussing interpretations of Keynes, the term ‘keynesian’ will be used, while when discussing Keynes’ own views, the t...

Table of contents

• COVER PAGE
• TITLE PAGE
• COPYRIGHT PAGE
• FOREWORD
• PREFACE
• ACKNOWLEDGEMENTS
• I. INTRODUCTION
• II. THEORIES OF PROBABILITY
• III. PROBABILITY AS A FUNDAMENTAL CONCEPT IN ECONOMICS
• IV. AUSTRIAN ECONOMICS
• V. KEYNESAN ECONOMICS
• VI. RATIONAL EXPECTATIONS AND THE NEW NEOCLASSICISTS
• VII. CONCLUSION
• NOTES
• BIBLIOGRAPHY